The aim of this paper is to introduce a decompositions namely supra bT- locally closed sets and define supra bT-locally continuous functions. This paper also discussed some of their properties.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
RW-CLOSED MAPS AND RW-OPEN MAPS IN TOPOLOGICAL SPACESEditor IJCATR
In this paper we introduce rw-closed map from a topological space X to a topological space Y as the image
of every closed set is rw-closed and also we prove that the composition of two rw-closed maps need not be rw-closed
map. We also obtain some properties of rw-closed maps.
(𝛕𝐢, 𝛕𝐣)− RGB Closed Sets in Bitopological SpacesIOSR Journals
In this paper we introduce and study the concept of a new class of closed sets called (𝜏𝑖, 𝜏𝑗)− regular generalized b- closed sets (briefly(𝜏𝑖, 𝜏𝑗)− rgb-closed) in bitopological spaces.Further we define and study new neighborhood namely (𝜏𝑖, 𝜏𝑗)− rgb- neighbourhood (briefly(𝜏𝑖, 𝜏𝑗)− rgb-nhd) and discuss some of their properties in bitopological spaces. Also, we give some characterizations and applications of it.
This document discusses probabilistic diameter and its properties. It defines probabilistic diameter (DA) as a distribution function that represents the probability that the distance between any two points in a set A is less than some value t. It presents several properties of probabilistic diameter including: (1) DA is a distribution function; (2) DA = H if A contains a single point; and (3) if A is a subset of B, then DA ≥ DB. It also defines probabilistic distance between two sets A and B as another distribution function (FAB) and establishes some of its properties.
Totally R*-Continuous and Totally R*-Irresolute Functionsinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Notions via β*-open sets in topological spacesIOSR Journals
In this paper, first we define β*-open sets and β*-interior in topological spaces.J.Antony Rex Rodrigo[3] has studied the topological properties of 𝜂 * -derived, 𝜂 * -border, 𝜂 * -frontier and 𝜂 * exterior of a set using the concept of 𝜂 * -open following M.Caldas,S.Jafari and T.Noiri[5]. By the same technique the concept of β*-derived, β*-border, β*-frontier and β*exterior of a set using the concept of β*-open sets are introduced.Some interesting results that shows the relationships between these concepts are brought about
δ ˆ – Closed Sets in Ideal Topological SpacesIOSR Journals
The document introduces the concept of δˆ-closed sets in ideal topological spaces. It defines a subset A to be δˆ-closed if the σ-closure of A is contained in every open set U containing A. Some basic properties of δˆ-closed sets are established, including that δ-closed, δ-I-closed, δg-closed, and δgˆ-closed sets are all δˆ-closed. However, the converse relationships are not always true. Examples are provided to illustrate the independence of these classes of closed sets.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
RW-CLOSED MAPS AND RW-OPEN MAPS IN TOPOLOGICAL SPACESEditor IJCATR
In this paper we introduce rw-closed map from a topological space X to a topological space Y as the image
of every closed set is rw-closed and also we prove that the composition of two rw-closed maps need not be rw-closed
map. We also obtain some properties of rw-closed maps.
(𝛕𝐢, 𝛕𝐣)− RGB Closed Sets in Bitopological SpacesIOSR Journals
In this paper we introduce and study the concept of a new class of closed sets called (𝜏𝑖, 𝜏𝑗)− regular generalized b- closed sets (briefly(𝜏𝑖, 𝜏𝑗)− rgb-closed) in bitopological spaces.Further we define and study new neighborhood namely (𝜏𝑖, 𝜏𝑗)− rgb- neighbourhood (briefly(𝜏𝑖, 𝜏𝑗)− rgb-nhd) and discuss some of their properties in bitopological spaces. Also, we give some characterizations and applications of it.
This document discusses probabilistic diameter and its properties. It defines probabilistic diameter (DA) as a distribution function that represents the probability that the distance between any two points in a set A is less than some value t. It presents several properties of probabilistic diameter including: (1) DA is a distribution function; (2) DA = H if A contains a single point; and (3) if A is a subset of B, then DA ≥ DB. It also defines probabilistic distance between two sets A and B as another distribution function (FAB) and establishes some of its properties.
Totally R*-Continuous and Totally R*-Irresolute Functionsinventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Notions via β*-open sets in topological spacesIOSR Journals
In this paper, first we define β*-open sets and β*-interior in topological spaces.J.Antony Rex Rodrigo[3] has studied the topological properties of 𝜂 * -derived, 𝜂 * -border, 𝜂 * -frontier and 𝜂 * exterior of a set using the concept of 𝜂 * -open following M.Caldas,S.Jafari and T.Noiri[5]. By the same technique the concept of β*-derived, β*-border, β*-frontier and β*exterior of a set using the concept of β*-open sets are introduced.Some interesting results that shows the relationships between these concepts are brought about
δ ˆ – Closed Sets in Ideal Topological SpacesIOSR Journals
The document introduces the concept of δˆ-closed sets in ideal topological spaces. It defines a subset A to be δˆ-closed if the σ-closure of A is contained in every open set U containing A. Some basic properties of δˆ-closed sets are established, including that δ-closed, δ-I-closed, δg-closed, and δgˆ-closed sets are all δˆ-closed. However, the converse relationships are not always true. Examples are provided to illustrate the independence of these classes of closed sets.
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
This document provides an overview and definitions related to functional analysis and Banach spaces. It discusses:
1) The definition of a Banach space as a complete normed linear space where every Cauchy sequence converges.
2) Examples of Banach spaces including l^p spaces, C(X) for compact X, C_b(X) for any topological space X, and C^k([a,b]).
3) Measure spaces and the definition of measurable functions on a measure space. It notes the closure properties of measurable functions under scalar multiplication and (sometimes) addition.
Abstract: In this paper, we define and study about a new type of generalized closed set called, g∗s-closed set.Its relationship with already defined generalized closed sets are also studied
11. gamma sag semi ti spaces in topological spacesAlexander Decker
This document introduces the concept of γ-sαg*-semi Ti spaces where i = 0, 1/2, 1, 2. It defines γ-sαg*-semi open and closed sets. Properties of γ-sαg*-semi closure and γ-sαg*-semi generalized closed sets are discussed. It is shown that every γ-sαg*-semi generalized closed set is γ-semi generalized closed. A subset A is γ-sαg*-semi generalized closed if and only if the intersection of A with the γ-sαg*-semi closure of each point in the γ-closure of A is non-empty. The γ-sαg*-semi closure of a set
This document introduces the concept of γ-sαg*-semi Ti spaces where i = 0, 1/2, 1, 2. It defines γ-sαg*-semi open and closed sets. Properties of γ-sαg*-semi closure and γ-sαg*-semi generalized closed sets are discussed. It is shown that every γ-sαg*-semi generalized closed set is γ-semi generalized closed. The paper investigates when a space is a γ-sαg*-semi Ti space by looking at when γ-sαg*-semi generalized closed sets are γ-semi closed. It concludes that for each point x in a space, the singleton {x} is either γ-
The document discusses algorithms for solving single-source shortest path problems on directed graphs. It begins by defining the problem and describing Bellman-Ford's algorithm, which can handle graphs with negative edge weights but runs in O(VE) time. It then describes how Dijkstra's algorithm improves this to O(ElogV) time using a priority queue, but requires non-negative edge weights. It also discusses how shortest paths can be found in O(V+E) time on directed acyclic graphs by relaxing edges topologically. Finally, it discusses how difference constraints can be modeled as shortest path problems on a corresponding constraint graph.
Reciprocity Law For Flat Conformal Metrics With Conical SingularitiesLukasz Obara
The document is a thesis that establishes an analogue of Weil's reciprocity law for flat conformal metrics with conical singularities on Riemann surfaces. It introduces the necessary mathematical background, including definitions of isothermal coordinates and metrics with conical singularities. The main result proves a relationship between three flat conformally equivalent metrics, each with different conical singularities.
The document discusses properties of parallelograms and provides examples of determining if a quadrilateral is a parallelogram. It defines four theorems for identifying parallelograms: if opposite sides are congruent, opposite angles are congruent, diagonals bisect each other, or one pair of opposite sides is parallel and congruent. Examples demonstrate using the slope formula to check if opposite sides are parallel and solving equations to find values where a quadrilateral satisfies parallelogram properties.
This document introduces and studies a new type of closed set called strongly τb-closed (τ*b-closed) sets. The following is summarized:
1. τ*b-closed sets are between closed sets and gsg-closed sets.
2. Properties and relationships of τ*b-closed sets are investigated, showing they are finer than τb-closed sets and contained within several other closed set classes.
3. Characterizations of τ*b-closed and τ*b-open sets are provided, such as the union of τ*b-closed sets being τ*b-closed.
In this paper we introduce a new class of sets known as
δ
ˆ
S –closed sets in ideal topological
spaces and we studied some of its basic properties and characterizations. This new class of sets lies
between –I–closed [19] sets and g–closed sets, and its unique feature is it forms topology and it is
independent of open sets.
Some forms of N-closed Maps in supra Topological spacesIOSR Journals
In this paper, we introduce the concept of N-closed maps and we obtain the basic properties and
their relationships with other forms of N-closed maps in supra topological spaces.
The document introduces the concept of generalized quasi-nonexpansive (GQN) maps. Some key results are:
1) GQN maps generalize quasi-nonexpansive maps but the fixed point set may not always be closed or convex.
2) If a subset satisfies certain conditions, it is a GQN-retract of the space.
3) Under these conditions, the class of GQN-retracts is closed under intersection and the common fixed point set of an increasing sequence of GQN maps is a GQN-retract.
The document discusses properties of rectangles. It defines a rectangle as a parallelogram with four right angles. It lists properties such as opposite sides being parallel and congruent and opposite angles being congruent. The document also presents four examples solving problems about rectangles, finding missing side lengths and determining if a quadrilateral is a rectangle based on given information.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The document is a physics examination paper containing 26 questions ranging from 2 to 5 marks each. It provides instructions for the exam, including the number and type of questions. The questions cover various topics in physics like units, motion, forces, energy, momentum, rotational motion, gravitation, and friction. Some questions ask students to derive equations, calculate numerical values, or explain concepts. The marking scheme at the end provides the expected answers and weightage for each question.
The document provides instructions for a 3-hour physics exam for Class 11 students. It contains 30 questions ranging from 1 to 5 marks each. The questions cover a range of physics topics including fundamental forces, motion, mechanics, heat, waves, and electricity. Students are informed that calculators are not permitted and various physical constants may be used. They are advised that all questions are compulsory and instructed on the internal choices provided in some questions.
Contra * Continuous Functions in Topological SpacesIJMER
This document discusses contra α* continuous functions between topological spaces. It begins by introducing α*-open sets and various related concepts like α*-continuity. It then defines a function from one topological space to another to be contra α*-continuous if the preimage of every open set is α*-closed in the domain space. Some properties of contra α*-continuous functions are established, including that every contra-continuous function is contra α*-continuous. Examples are given to show the concepts are independent. The discussion considers the relationships between contra α*-continuity and other variations of contra-continuity.
On some locally closed sets and spaces in Ideal Topological SpacesIJMER
This document introduces and studies the concept of δˆ s-locally closed sets in ideal topological spaces. Some key points:
- A subset A is δˆ s-locally closed if A can be written as the intersection of a δˆ s-open set and a δˆ s-closed set.
- Various properties of δˆ s-locally closed sets are introduced and characterized, including relationships to other concepts like generalized locally closed sets.
- It is shown that a subset A is δˆ s-locally closed if and only if A can be written as the intersection of a δˆ s-open set and the δˆ s-closure of A.
- Theore
An Experimental Study on Strength Properties of Concrete When Cement Is Parti...IOSR Journals
This study investigated the strength properties of concrete when cement is partially replaced with two types of sugarcane bagasse ash (SBA): raw SBA (B.A.1) and SBA heated to 8500C (B.A.2). Cubes, cylinders and beams were tested after 28 days of curing. For B.A.1, maximum strengths were achieved at 5% replacement, while for B.A.2 maximum compressive strength was at 15% replacement, tensile at 20%, and flexural at 30% replacement. Results showed that concrete with B.A.2 generally had higher strengths than with B.A.1, indicating that heating SBA improves its pozzolanic
Implementation of Algorithms For Multi-Channel Digital Monitoring ReceiverIOSR Journals
Abstract: Monitoring Receivers form an important constituent of the Electronic support. In Monitoring
Receiver we can monitor, demodulate or scan the multiple channels.
In this project, the Implementation of algorithm for multi channel digital monitoring receiver. The
implementation will carry out the channelization by the way of Digital down Converters (DDCs) and Digital
Base band Demodulation. The Intermediate Frequency (IF) at 10.7 MHz will be digitalized using Analog to
Digital Converter (ADC) with sampling frequency 52.5 MHz and further converted to Base band using DDCs.
Virtually all the digital receivers perform channel access using a DDC. The Base band data will be streamed to
the appropriate demodulators. Matlab Simulink will be used to simulate the logic modules before the
implementation. This system will be prototyped on an FPGA based COTS (Commercial-off-the-shelf)
development board. Xilinx System Generator will be used for the implementation of the algorithms.
Keywords: DDC, ADC, Digital Base band demodulation, IF, Monitoring Receiver.
Efficacy Studies of Hepatoprotective Drug Isolated from Eclipta prostrata. L.IOSR Journals
In the commercial market, medicinal herbs are used as raw drugs, extracts or tinctures. Isolated
active constituents are used for applied research. Medicinal herbs are significant source of hepatoprotective
drugs, Eclipta prostrata. L. with active principle Wedelolactone is the prime focus. In the present study to derive
hepatoprotective drug, the herb E. prostrata was grown in the Periyar Maniammai College Campus, Vallam
and 1kg of the plant leaves were collected and shade dried. Dried and powdered maetria l of E. prostrata was
extracted with 80% ethanol. The active principle was isolated and identified by chromatographic technique. The
protective effect of E. prostrata on Carbon tetrachloride induced acute liver damage was also studied with male
wistar albino rats (180-230g). The protective effect was also undergone for histological studies.
Discovery of Self-Sustained 235U Fission Causing Sunlight by Padmanabha Rao E...IOSR Journals
For the first time in solar physics, this paper reports a comprehensive study how 235Uranium fission
causes Sunlight by the atomic phenomenon, Padmanabha Rao Effect against the theory of fusion. The first major
breakthrough lies in identifying as many as 153 solar lines in the Bharat Radiation range from 12.87 to 31 nm
reported by various researchers since 1960s. The Sunlight phenomenon is explained as follows. For example, the
energy equivalence 72.48 eV of the most intense 17.107 nm emission in the middle of solar spectrum is the energy
lost by β, γ, or X-ray energy of a fission product while passing through core-Coulomb space. This energy loss is the
Bharat Radiation energy that cause EUV, UV, visible, and near infrared emissions on valence excitation. From vast
data of emissions and energies of various fission products, 606.31 keV β (Eβmax) energy of 131I was chosen as the
source of 17.107 nm emission. For the first time a typical Bharat Radiation spectrum was observed when plotted
energy loss against β, γ, or X-ray energies of fission products supposedly present in solar flare and atmosphere :
113Xe, 131I, 137Cs, 95Zr, 144Cs, 134I, 140Ba, 133I, 140La, 133In etc that caused solar lines. Consistent presence of a sharp
line for four months in AIA spectral EUV band at 335A exemplifies self-sustained uranium fission from a small site
appeared in SDO/AIA image at 304A. Sun’s dark spot is explained as a large crater formed on Sun’s core surface as
a result of fission reaction that does not show any emission since fission products would be thrown away from the
site during fission. Purely the same Sun’s core material left over at the site after fission reaction devoid of fission
products and any emission seems to be the familiar dark Matter. This could be the first report on the existence of
Sun’s Dark Matter.
This document provides an overview and definitions related to functional analysis and Banach spaces. It discusses:
1) The definition of a Banach space as a complete normed linear space where every Cauchy sequence converges.
2) Examples of Banach spaces including l^p spaces, C(X) for compact X, C_b(X) for any topological space X, and C^k([a,b]).
3) Measure spaces and the definition of measurable functions on a measure space. It notes the closure properties of measurable functions under scalar multiplication and (sometimes) addition.
Abstract: In this paper, we define and study about a new type of generalized closed set called, g∗s-closed set.Its relationship with already defined generalized closed sets are also studied
11. gamma sag semi ti spaces in topological spacesAlexander Decker
This document introduces the concept of γ-sαg*-semi Ti spaces where i = 0, 1/2, 1, 2. It defines γ-sαg*-semi open and closed sets. Properties of γ-sαg*-semi closure and γ-sαg*-semi generalized closed sets are discussed. It is shown that every γ-sαg*-semi generalized closed set is γ-semi generalized closed. A subset A is γ-sαg*-semi generalized closed if and only if the intersection of A with the γ-sαg*-semi closure of each point in the γ-closure of A is non-empty. The γ-sαg*-semi closure of a set
This document introduces the concept of γ-sαg*-semi Ti spaces where i = 0, 1/2, 1, 2. It defines γ-sαg*-semi open and closed sets. Properties of γ-sαg*-semi closure and γ-sαg*-semi generalized closed sets are discussed. It is shown that every γ-sαg*-semi generalized closed set is γ-semi generalized closed. The paper investigates when a space is a γ-sαg*-semi Ti space by looking at when γ-sαg*-semi generalized closed sets are γ-semi closed. It concludes that for each point x in a space, the singleton {x} is either γ-
The document discusses algorithms for solving single-source shortest path problems on directed graphs. It begins by defining the problem and describing Bellman-Ford's algorithm, which can handle graphs with negative edge weights but runs in O(VE) time. It then describes how Dijkstra's algorithm improves this to O(ElogV) time using a priority queue, but requires non-negative edge weights. It also discusses how shortest paths can be found in O(V+E) time on directed acyclic graphs by relaxing edges topologically. Finally, it discusses how difference constraints can be modeled as shortest path problems on a corresponding constraint graph.
Reciprocity Law For Flat Conformal Metrics With Conical SingularitiesLukasz Obara
The document is a thesis that establishes an analogue of Weil's reciprocity law for flat conformal metrics with conical singularities on Riemann surfaces. It introduces the necessary mathematical background, including definitions of isothermal coordinates and metrics with conical singularities. The main result proves a relationship between three flat conformally equivalent metrics, each with different conical singularities.
The document discusses properties of parallelograms and provides examples of determining if a quadrilateral is a parallelogram. It defines four theorems for identifying parallelograms: if opposite sides are congruent, opposite angles are congruent, diagonals bisect each other, or one pair of opposite sides is parallel and congruent. Examples demonstrate using the slope formula to check if opposite sides are parallel and solving equations to find values where a quadrilateral satisfies parallelogram properties.
This document introduces and studies a new type of closed set called strongly τb-closed (τ*b-closed) sets. The following is summarized:
1. τ*b-closed sets are between closed sets and gsg-closed sets.
2. Properties and relationships of τ*b-closed sets are investigated, showing they are finer than τb-closed sets and contained within several other closed set classes.
3. Characterizations of τ*b-closed and τ*b-open sets are provided, such as the union of τ*b-closed sets being τ*b-closed.
In this paper we introduce a new class of sets known as
δ
ˆ
S –closed sets in ideal topological
spaces and we studied some of its basic properties and characterizations. This new class of sets lies
between –I–closed [19] sets and g–closed sets, and its unique feature is it forms topology and it is
independent of open sets.
Some forms of N-closed Maps in supra Topological spacesIOSR Journals
In this paper, we introduce the concept of N-closed maps and we obtain the basic properties and
their relationships with other forms of N-closed maps in supra topological spaces.
The document introduces the concept of generalized quasi-nonexpansive (GQN) maps. Some key results are:
1) GQN maps generalize quasi-nonexpansive maps but the fixed point set may not always be closed or convex.
2) If a subset satisfies certain conditions, it is a GQN-retract of the space.
3) Under these conditions, the class of GQN-retracts is closed under intersection and the common fixed point set of an increasing sequence of GQN maps is a GQN-retract.
The document discusses properties of rectangles. It defines a rectangle as a parallelogram with four right angles. It lists properties such as opposite sides being parallel and congruent and opposite angles being congruent. The document also presents four examples solving problems about rectangles, finding missing side lengths and determining if a quadrilateral is a rectangle based on given information.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The document is a physics examination paper containing 26 questions ranging from 2 to 5 marks each. It provides instructions for the exam, including the number and type of questions. The questions cover various topics in physics like units, motion, forces, energy, momentum, rotational motion, gravitation, and friction. Some questions ask students to derive equations, calculate numerical values, or explain concepts. The marking scheme at the end provides the expected answers and weightage for each question.
The document provides instructions for a 3-hour physics exam for Class 11 students. It contains 30 questions ranging from 1 to 5 marks each. The questions cover a range of physics topics including fundamental forces, motion, mechanics, heat, waves, and electricity. Students are informed that calculators are not permitted and various physical constants may be used. They are advised that all questions are compulsory and instructed on the internal choices provided in some questions.
Contra * Continuous Functions in Topological SpacesIJMER
This document discusses contra α* continuous functions between topological spaces. It begins by introducing α*-open sets and various related concepts like α*-continuity. It then defines a function from one topological space to another to be contra α*-continuous if the preimage of every open set is α*-closed in the domain space. Some properties of contra α*-continuous functions are established, including that every contra-continuous function is contra α*-continuous. Examples are given to show the concepts are independent. The discussion considers the relationships between contra α*-continuity and other variations of contra-continuity.
On some locally closed sets and spaces in Ideal Topological SpacesIJMER
This document introduces and studies the concept of δˆ s-locally closed sets in ideal topological spaces. Some key points:
- A subset A is δˆ s-locally closed if A can be written as the intersection of a δˆ s-open set and a δˆ s-closed set.
- Various properties of δˆ s-locally closed sets are introduced and characterized, including relationships to other concepts like generalized locally closed sets.
- It is shown that a subset A is δˆ s-locally closed if and only if A can be written as the intersection of a δˆ s-open set and the δˆ s-closure of A.
- Theore
An Experimental Study on Strength Properties of Concrete When Cement Is Parti...IOSR Journals
This study investigated the strength properties of concrete when cement is partially replaced with two types of sugarcane bagasse ash (SBA): raw SBA (B.A.1) and SBA heated to 8500C (B.A.2). Cubes, cylinders and beams were tested after 28 days of curing. For B.A.1, maximum strengths were achieved at 5% replacement, while for B.A.2 maximum compressive strength was at 15% replacement, tensile at 20%, and flexural at 30% replacement. Results showed that concrete with B.A.2 generally had higher strengths than with B.A.1, indicating that heating SBA improves its pozzolanic
Implementation of Algorithms For Multi-Channel Digital Monitoring ReceiverIOSR Journals
Abstract: Monitoring Receivers form an important constituent of the Electronic support. In Monitoring
Receiver we can monitor, demodulate or scan the multiple channels.
In this project, the Implementation of algorithm for multi channel digital monitoring receiver. The
implementation will carry out the channelization by the way of Digital down Converters (DDCs) and Digital
Base band Demodulation. The Intermediate Frequency (IF) at 10.7 MHz will be digitalized using Analog to
Digital Converter (ADC) with sampling frequency 52.5 MHz and further converted to Base band using DDCs.
Virtually all the digital receivers perform channel access using a DDC. The Base band data will be streamed to
the appropriate demodulators. Matlab Simulink will be used to simulate the logic modules before the
implementation. This system will be prototyped on an FPGA based COTS (Commercial-off-the-shelf)
development board. Xilinx System Generator will be used for the implementation of the algorithms.
Keywords: DDC, ADC, Digital Base band demodulation, IF, Monitoring Receiver.
Efficacy Studies of Hepatoprotective Drug Isolated from Eclipta prostrata. L.IOSR Journals
In the commercial market, medicinal herbs are used as raw drugs, extracts or tinctures. Isolated
active constituents are used for applied research. Medicinal herbs are significant source of hepatoprotective
drugs, Eclipta prostrata. L. with active principle Wedelolactone is the prime focus. In the present study to derive
hepatoprotective drug, the herb E. prostrata was grown in the Periyar Maniammai College Campus, Vallam
and 1kg of the plant leaves were collected and shade dried. Dried and powdered maetria l of E. prostrata was
extracted with 80% ethanol. The active principle was isolated and identified by chromatographic technique. The
protective effect of E. prostrata on Carbon tetrachloride induced acute liver damage was also studied with male
wistar albino rats (180-230g). The protective effect was also undergone for histological studies.
Discovery of Self-Sustained 235U Fission Causing Sunlight by Padmanabha Rao E...IOSR Journals
For the first time in solar physics, this paper reports a comprehensive study how 235Uranium fission
causes Sunlight by the atomic phenomenon, Padmanabha Rao Effect against the theory of fusion. The first major
breakthrough lies in identifying as many as 153 solar lines in the Bharat Radiation range from 12.87 to 31 nm
reported by various researchers since 1960s. The Sunlight phenomenon is explained as follows. For example, the
energy equivalence 72.48 eV of the most intense 17.107 nm emission in the middle of solar spectrum is the energy
lost by β, γ, or X-ray energy of a fission product while passing through core-Coulomb space. This energy loss is the
Bharat Radiation energy that cause EUV, UV, visible, and near infrared emissions on valence excitation. From vast
data of emissions and energies of various fission products, 606.31 keV β (Eβmax) energy of 131I was chosen as the
source of 17.107 nm emission. For the first time a typical Bharat Radiation spectrum was observed when plotted
energy loss against β, γ, or X-ray energies of fission products supposedly present in solar flare and atmosphere :
113Xe, 131I, 137Cs, 95Zr, 144Cs, 134I, 140Ba, 133I, 140La, 133In etc that caused solar lines. Consistent presence of a sharp
line for four months in AIA spectral EUV band at 335A exemplifies self-sustained uranium fission from a small site
appeared in SDO/AIA image at 304A. Sun’s dark spot is explained as a large crater formed on Sun’s core surface as
a result of fission reaction that does not show any emission since fission products would be thrown away from the
site during fission. Purely the same Sun’s core material left over at the site after fission reaction devoid of fission
products and any emission seems to be the familiar dark Matter. This could be the first report on the existence of
Sun’s Dark Matter.
Low Power FPGA Based Elliptical Curve CryptographyIOSR Journals
Abstract: Cryptography is the study of techniques for ensuring the secrecy and authentication of the information. The development of public-key cryptography is the greatest and perhaps the only true revolution in the entire history of cryptography. Elliptic Curve Cryptography is one of the public-key cryptosystem showing up in standardization efforts, including the IEEE P1363 Standard. The principal attraction of elliptic curve cryptography compared to RSA is that it offers equal security for a smaller key-size, thereby reducing the processing overhead. As a Public-Key Cryptosystem, ECC has many advantages such as fast speed, high security and short key. It is suitable for the hardware of implementation, so ECC has been more and more focused in recent years. The hardware implementation of ECC on FPGA uses the arithmetic unit that has small area, small storage unit and fast speed, and it is an extremely suitable system which has limited computation ability and storage space.[1][2] The modular arithmetic division operations are carried out using conditional successive subtractions, thereby reducing the area. The system is implemented on Vertex-Pro XCV1000 FPGA. Index Terms – VHDL, FSM, FPGA, Elliptic Curve Cryptography.
Sensitivity Analysis of Process Parameters for Polyurethane Based Panel Air F...IOSR Journals
This document summarizes research conducted on the sensitivity of process parameters for polyurethane-based panel air filters. Experiments varied parameters like nucleation, mixing speed, mold temperature, mixing ratio, and analyzed their effects on density, hardness, and rise time. Increasing nucleation and mold temperature decreased density and hardness. Higher mixing speeds had little effect with nucleation but decreased density without. Density decreased and hardness was stable at standard mixing ratios but varied above and below. The goal is to define optimized parameter settings to minimize defects for high productivity and yield.
Analytical Determination of Antihestamine drugs Pure and its pharmaceutical P...IOSR Journals
A quick and convenient method has been developed for the micro estimation of antihistamine drugs. 1-5 mg of sample is allowed to react with 10 ml of 0.02 M, N-bromosaccharin solution. Unconsumed reagent can be accurately titrated with 5 ml of 15% KI and 0.02N sodium thiosulphate solution using starch as indica-tor. SD and CV was calculated for reproducible and accurate result. The accuracy of the method is within + 1 % and possible course of reaction was suggested on the basis of stoichiometry as well as find reaction product.
Effective Leadership-Employee Retention-Work Life Balance: A Cyclical ContinuumIOSR Journals
This document summarizes a study on the relationship between effective leadership, employee work-life balance, and employee retention. It discusses how leadership styles can help balance employees' work and personal lives, leading to improved employee retention. The study presents different leadership theories and styles, and analyzes how they may impact work-life balance and retention. Specifically, it suggests that participative leadership approaches that balance task and employee orientation can foster understanding and job satisfaction, while autocratic styles focused solely on tasks may increase productivity but not retention. The document concludes that synchronized leadership considering employees' capabilities can help identify and retain talented staff.
Dust Interception Capacity And Alteration Of Various Biometric And Biochemica...IOSR Journals
The dust accumulation capacity of Ficus carica L. was evaluated from eight different sites in and around Multan. The impact of dust accumulation was observed via various biometric attributes (leaf area, leaf fresh and dry weights) and biochemical attributes (chlorophyll contents, carotenoids & ascorbic acid) from leaves of F. carica. The maximum dust accumulation was occurred in the plants growing at Road sides while, the minimum dust was found on plants growing at Bahauddin Zakariya University. Dust accumulation has caused a significant effect on almost all foliage and biochemical attributes of F. carica. A positive correlation was found between dust accumulation and biometric attributes in F. carica. Biochemical responses had shown an inconsistency as chlorophylls (a, b & total), carotenoids decreased and ascorbic acid contents increased with an increase in dust accumulation. A negative correlation was found between dust deposition and chlorophyll contents. Whereas, accumulation of ascorbic acid was associated with a decline in pigment contents
The influence of Rolling process on the porosity and wear behavior of Spray-f...IOSR Journals
Spray forming, also called spray casting or spray deposition, is the inert gas atomization of a liquid metal stream into variously sized droplets. These droplets are interrupted by a substrate which collects and solidifies the droplets into coherent, near fully dense perform. The present work concerns with this techniques. This technology was applied to produce Al-6%Si-20%Pb alloys. The spray droplets were deposited over a copper substrate to achieve a disc shape perform. After spray deposition samples were rolled at room temperature on two high rolling mills and total porosity and wear characteristic of spray deposits were studies. The total porosity decreases with the increase in the percentage of reduction in thickness of the samples. Thickness of the samples in both middle and peripheral region. Wear testing of spray formed and rolled Al-Si-Pb alloy were investigated on a pin on disc type wear machine. Wear rate behavior with applied load and increase in percentage of reduction in thickness of samples was observed. Wear rate increased with increasing the load and decreased with increase in percentage of reduction in thickness of the sample.
Uranium Concentrations measurement for Ground Water and Soil Samples in Al-Na...IOSR Journals
In this work, Uranium concentrations in groundwater and soil samples from some areas of Al-Najaf city, Iraq were measured solid state nuclear track detector (CR-39) detector technique. The uranium concentration in groundwater samples was found to vary from (1.617782869±0.04342) μgl−1 to (5.079235843±0.137827) μgl−1, while in soil samples vary from (0.093558±0.000938) ppm to (0.184325±0.017511) ppm.
This study showed that levels of uranium concentration in groundwater and soil of study area of were compared with safe limit values recommended by WHO and UNSCEAR below the safe limit
This document proposes a modified Newton's method for solving nonlinear equations that uses harmonic mean. It begins by reviewing Newton's method and some existing variants that use arithmetic mean or other integration rules to modify Newton's method and achieve cubic convergence without using second derivatives. It then presents the new Harmonic-Simpson-Newton method, which replaces the arithmetic mean in an existing Simpson Newton's method with harmonic mean. The method is proven to have cubic convergence. Numerical examples are provided to compare the efficiency of the new method to other cubic convergent methods.
The document describes a method for de-noising electrocardiogram (ECG) signals using empirical mode decomposition (EMD) combined with higher order statistics (HOS). EMD is used to decompose ECG signals into intrinsic mode functions (IMFs). Then, HOS measures including kurtosis and bispectrum are applied to the IMFs to identify and remove Gaussian noise components. The algorithm is tested on ECG signals with different levels of signal-to-noise ratio, and signal improvement is measured using SNR improvement and percent root mean square difference. Results show the method effectively de-noises ECG signals.
Asif’s Equation of Charge Variation and Special RelativityIOSR Journals
The theory of special relativity plays an important role in the modern theory of classical electromagnetism. Considering deeply the effect of Special relativity in Electromagnetism, when a charge particle moves with high speed as comparable to the speed of light in vacuum tube or in space under influence of electromagnetic field, its mass varies under Lorentz transformation [1].The question arises that does its charge vary under Lorentz transformation? In this paper, Asif's equation of charge variation demonstrates the variation of electric charge under Lorentz transformation. The more sophisticated view of electromagnetism expressed by electromagnetic fields in moving inertial frame can be achieved by considering some relativistic effect including charge as well. One can easily achieve the mass-energy relation from Asif’s equation of charge variation as proved in this paper.
Electrophoretic Patterns of Esterases in Eri silkworm Samia Cynthia riciniIOSR Journals
The present study was carried out to investigate the patterns of esterase isozymes extracted from the silk gland, haemolymph and mid gut of Eri silkworm (Samia Cynthia ricini). The qualitative analysis of esterases was carried out by 7.5% of native Polyacrylamide Gel Electrophoresis (PAGE). The inhibitor sensitivity of the enzymes towards paraxon, eserine and pCMB was used to classify the individual zones of esterases. Three zones of esterases were observed in different tissues of Eri silkworm. Silk gland esterases were classified as CHsp (Cholinesterase like enzymes) esterases. The haemolymph and mid gut esterases were classified into Esdp (Enzyme inhibited by paraxon and pCMB).
The Historical Lack of Capital Accumulation in Iran's Agricultural PartIOSR Journals
The increasing amount of income due to the discovery of oil in Iran has caused a gap between the production and need of agricultural products, causing the increase in the import of agricultural products in Iran's economy. The existing gap caused a drastic increase in the prices, and since the growth of agricultural products needed Infrastructure investment, it has been tried to control the increase in the prices with an increase in the import rate. So capital accumulation has not been done to the required rate and the production in agriculture has not increased to the expected rate. The share of workers in the agricultural sector of Iran has faced a decrease since 1980. This is while in the international level, agriculture for the growth of economy, decrease of poverty, food security, and the stability of environment is of high importance. A general investment can reduce risks in the agriculture and increase efficiency in private sectors, so the motives of farmers for investment will be increased.
The need for a rapid, famous method for hair removal has led to the development of various laser for
hair removal. These include ruby, alexandrite, diode, and Nd:YAG lasers. This research discusses the basic
principles of laser hair removal, examines theoretically the properties of specific laser systems, and focuses on
patient selection and treatment protocols for the various systems designed to ensure safe and effective treatment.
Analysis Of Lpg Cylinder Using Composite MaterialsIOSR Journals
This paper aims is innovation of alternative materials of Liquid petroleum gas (LPG). So, the finite
element analysis of Liquefied Petroleum Gas (LPG) cylinders made of Steel and Fiber Reinforced Plastic (FRP)
composites has been carried out. Finite element analysis of composite cylinder subjected to internal pressure is
performed. Layered shell element of a versatile FE analysis package ANSYS (version 11.0) has been used to
model the shell with FRP composites.
A number of cases are considered to study the stresses and deformations due to pressure loading inside the
cylinder. First, the results of stresses and deformation for steel cylinders are compared with the analytical
solution available in literature in order to validate the model and the software. The weight savings are also
presented for steel, Glass Fiber Reinforced Plastic (GFRP) composites LPG cylinders. Variations of stresses
and deformations throughout the cylinder made of steel and GFRP are studied.
Post Endodontic Restoration: Are You Serious?IOSR Journals
After root canal obturation of sound posterior teeth, dentists are always in hurry of giving full
crown. They are not serious in giving proper post endodontic restoration which results in fracture of tooth or
restoration, if patient delays the full crown treatment. The inherent causes of failures are rarely evaluated.
Thus, it was the purpose of this study to analyze the opinion of practicing dentist and after 24 months of clinical
observation to present a logical approach to this subject as the final success of endodontic treatment is depend
on the proper and timely coronal restoration.
Quark Model Three Body Calculations for the Hypertriton Bound StateIOSR Journals
Hyperspherical three body calculations are performed to study and review the various properties of
the hypertriton bound state nucleus
3H in the quark model using -N potentials. In these calculations we study
the different effects of the -N potentials on the hypertriton bound states as well as the separation energy B. A
combination of realistic two body N-N potentials with various - N potentials are considered. Complete
symmetric and mixed symmetric wave functions are introduced. using the renormalized Numerov method. The
agreement between the calculated
3H binding energies and the available experimental data basically depends
on the type of the -N interactions used in the calculations. It was found that the -N potentials are the most
effective part in the hypertriton binding energy as well as the separation energy B where the -N potentials is
very effective to bound or unbound the
3H hyper nucleus
Pacs numbers: 21.30. + y, 21.10.+dr,27.20.+n
International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Some properties of gi closed sets in topological space.docxAlexander Decker
This document introduces generalized *i-closed (g*i-closed) sets in topological spaces and studies some of their properties. It defines what a g*i-closed set is and shows that every closed, i-closed, semi-closed, g-closed, gs-closed, and δg-closed set is also a g*i-closed set. However, the converses of these statements are not always true. Examples are provided to illustrate this. The relationships between g*i-closed sets and other generalized closed sets are also examined.
This document discusses generalized closed sets in topological spaces. It begins by introducing several types of generalized closed sets that have been defined in previous literature, such as g-closed sets, sg-closed sets, gs-closed sets, etc. It then defines a new type of generalized closed set called a g*s-closed set, which is a subset A such that the semi-closure of A is contained in every g-open set containing A. Examples are provided to illustrate g*s-closed sets. Properties of g*s-closed sets are discussed, such as every semi-closed set being g*s-closed, but the converse is not true. The relationship between g*s-closed sets and other
This document introduces the concept of γ-sαg*-semi open sets in topological spaces and some of their properties. It begins by discussing previous related concepts like γ-open sets, γ-closure, and γ-semi open sets. It then defines what a γ-sαg*-semi open set is and establishes some basic properties. The main part of the document introduces and defines the concepts of γ-sαg*-semi Ti spaces for i=0, 1/2, 1, 2. It establishes properties of γ-sαg*-semi g-closed sets and proves several theorems about γ-sαg*-semi closure operators and their relationships to other concepts. The document contributes to the mathematical
On Fuzzy - Semi Open Sets and Fuzzy - Semi Closed Sets in Fuzzy Topologic...IOSR Journals
Abstract: The aim of this paper is to introduce the concept of fuzzy - semi open and fuzzy - semi closed sets of a fuzzy topological space. Some characterizations are discussed, examples are given and properties are established. Also, we define fuzzy - semi interior and fuzzy - semi closure operators. And we introduce fuzzy
- t-set, -SO extremely disconnected space analyse the relations between them.
MSC 2010: 54A40, 03E72.
In general topology many strong and weak forms of open and closed sets have been defined
and studied. Govindappa Navalagi introduced the concept of semi α-open sets which is a weaker form of
α-open sets. Semi*α-open set is defined analogously by replacing the closure operator by the
generalized closure operator due to Dunham in the definition of semi α-open sets. In this paper we
introduce a new class of sets, namely semi*α-closed sets, as the complement of semi*α-open sets. We
find characterizations of semi*α-closed sets. We also define the semi*α-closure of a subset. Further we
investigate fundamental properties of the semi*α-closure. We define the semi*α-derived set of a subset
and study its properties.
This document summarizes a research paper that introduces new concepts related to characterizing kernel sets in fuzzy topological spaces. Specifically, it defines kernelled fuzzy points, boundary kernelled fuzzy points, and derived kernelled fuzzy points of a subset. Using these notions, the paper presents a new definition of the kernel set of a fuzzy topological space as the union of the set itself and the set of all boundary kernelled fuzzy points. It also introduces the concept of a fuzzy topological kr-space and uses these concepts to characterize weak separation axioms between TF0 and TF1 spaces.
This document summarizes research on generalized β-closure spaces and β-connectedness. It defines key concepts such as β-closure functions, β-separated sets, and β-connectedness. Several important results are proven, including: (1) A set is β-connected if its subsets satisfy the Hausdorff-Lennes condition; (2) If a function between neighborhood spaces is β-continuous, the preimage of a β-connected set is β-connected; (3) The β-closure of a β-connected set is β-connected. The document establishes relationships between β-closure, β-separation, and β-connectedness in generalized closure spaces.
International Refereed Journal of Engineering and Science (IRJES) is a peer reviewed online journal for professionals and researchers in the field of computer science. The main aim is to resolve emerging and outstanding problems revealed by recent social and technological change. IJRES provides the platform for the researchers to present and evaluate their work from both theoretical and technical aspects and to share their views.
This document summarizes a research paper that studied the class of β-normal spaces. β-normal spaces generalize p-normal and s-normal spaces. The paper investigates the relationships between these classes of spaces and properties of β-normal spaces. It also studies various forms of generalized β-closed functions and their properties. Key results shown include that a space is β-normal if and only if it satisfies two equivalent properties and that if a function is β-closed and continuous and the domain space is normal, then the range space is β-normal. Diagrams of implications between the different classes of spaces and types of functions are also presented.
This document summarizes a research paper that studied the class of β-normal spaces. β-normal spaces generalize p-normal and s-normal spaces. The paper investigates the relationships between these classes of spaces and properties of β-normal spaces. It also studies various forms of generalized β-closed functions and their properties. Key results shown are that the implications in normality hold for β-normal, p-normal, and s-normal spaces, and properties characterizing β-normal spaces. The paper defines concepts like β-closed sets and β-neighborhoods that are used to study β-normality and generalized β-closed functions.
The aim of this paper is to study the class of β-normal spaces. The relationships among s-normal spaces, pnormal spaces and β-normal spaces are investigated. Moreover, we study the forms of generalized β-closed
functions. We obtain characterizations of β-normal spaces, properties of the forms of generalized β-closed
functions and preservation theorems.
The aim of this paper is to study the class of β-normal spaces. The relationships among s-normal spaces, pnormal spaces and β-normal spaces are investigated. Moreover, we study the forms of generalized β-closed
functions. We obtain characterizations of β-normal spaces, properties of the forms of generalized β-closed
functions and preservation theorems.
This document introduces and studies the concept of ˆ-closed sets in topological spaces. Some key points:
1. ˆ-closed sets are defined as sets whose δ-closure is contained in any semi-open set containing the set.
2. It is shown that ˆ-closed sets lie between δ-closed sets and various other classes like δg-closed and ω-closed sets.
3. Several characterizations of ˆ-closed sets are provided in terms of properties of the difference between the δ-closure of the set and the set itself.
4. The concept of the ˆ-kernel of a set is introduced, defined as the intersection of all ˆ-
Congruence Lattices of Isoform LatticesIOSR Journals
This document discusses isoform lattices and congruence lattices. It begins by defining isoform congruences and isoform lattices. Every finite distributive lattice D can be represented as the congruence lattice of a finite isoform lattice. A new lattice construction called N(A,B,θ) is introduced, where A is a finite bounded lattice, B is a finite lattice with a discrete transitive congruence θ, and N(A,B,θ) is their pruned direct product. It is proved that N(A,B,θ) is a lattice. The document then discusses the congruences of N(A,B,θ) and proves the main theorem that
The determination of this paper is to introduce two new spaces , namely 𝑆𝑔
∗
-compact and 𝑆𝑔
∗
-
connected spaces. Additionally some properties of these spaces are investigated.
Mathematics Subject Classification: 54A05
On Zα-Open Sets and Decompositions of ContinuityIJERA Editor
In this paper, we introduce and study the notion of Zα-open sets and some properties of this class of sets are investigated. Also, we introduce the class of A *L-sets via Zα-open sets. Further, by using these sets, a new decompositions of continuous functions are presented. (2000) AMS Subject Classifications: 54D10; 54C05; 54C08.
The document provides an overview of key concepts in set theory, relations, and graph theory that are important foundations for computer science. It defines what a set is, and methods for describing sets. It discusses operations on sets like unions, intersections, complements and differences. It presents results on the number of elements in sets and provides examples to illustrate set concepts. Graph theory concepts like graphs, subgraphs, trees and their applications in computer science are also introduced. The document aims to build awareness of these fundamental mathematical concepts used extensively in computer languages and their utility.
This document summarizes key concepts related to cluster points (also called limit or accumulation points) of a set in a topological space. It defines a cluster point as a point x such that every neighborhood of x contains at least one other point from the set. The derived set of a set A is the set of all cluster points of A. It is proven that the closure of A is equal to the union of A and its derived set. Additionally, if a point has a neighborhood containing only finitely many points from the set, it cannot be a cluster point, and if it is a cluster point every neighborhood must contain infinitely many points from the set.
Similar to bT-Locally Closed Sets and bT-Locally Continuous Functions In Supra Topological Spaces. (20)
This document provides a technical review of secure banking using RSA and AES encryption methodologies. It discusses how RSA and AES are commonly used encryption standards for secure data transmission between ATMs and bank servers. The document first provides background on ATM security measures and risks of attacks. It then reviews related work analyzing encryption techniques. The document proposes using a one-time password in addition to a PIN for ATM authentication. It concludes that implementing encryption standards like RSA and AES can make transactions more secure and build trust in online banking.
This document analyzes the performance of various modulation schemes for achieving energy efficient communication over fading channels in wireless sensor networks. It finds that for long transmission distances, low-order modulations like BPSK are optimal due to their lower SNR requirements. However, as transmission distance decreases, higher-order modulations like 16-QAM and 64-QAM become more optimal since they can transmit more bits per symbol, outweighing their higher SNR needs. Simulations show lifetime extensions up to 550% are possible in short-range networks by using higher-order modulations instead of just BPSK. The optimal modulation depends on transmission distance and balancing the energy used by electronic components versus power amplifiers.
This document provides a review of mobility management techniques in vehicular ad hoc networks (VANETs). It discusses three modes of communication in VANETs: vehicle-to-infrastructure (V2I), vehicle-to-vehicle (V2V), and hybrid vehicle (HV) communication. For each communication mode, different mobility management schemes are required due to their unique characteristics. The document also discusses mobility management challenges in VANETs and outlines some open research issues in improving mobility management for seamless communication in these dynamic networks.
This document provides a review of different techniques for segmenting brain MRI images to detect tumors. It compares the K-means and Fuzzy C-means clustering algorithms. K-means is an exclusive clustering algorithm that groups data points into distinct clusters, while Fuzzy C-means is an overlapping clustering algorithm that allows data points to belong to multiple clusters. The document finds that Fuzzy C-means requires more time for brain tumor detection compared to other methods like hierarchical clustering or K-means. It also reviews related work applying these clustering algorithms to segment brain MRI images.
1) The document simulates and compares the performance of AODV and DSDV routing protocols in a mobile ad hoc network under three conditions: when users are fixed, when users move towards the base station, and when users move away from the base station.
2) The results show that both protocols have higher packet delivery and lower packet loss when users are either fixed or moving towards the base station, since signal strength is better in those scenarios. Performance degrades when users move away from the base station due to weaker signals.
3) AODV generally has better performance than DSDV, with higher throughput and packet delivery rates observed across the different user mobility conditions.
This document describes the design and implementation of 4-bit QPSK and 256-bit QAM modulation techniques using MATLAB. It compares the two techniques based on SNR, BER, and efficiency. The key steps of implementing each technique in MATLAB are outlined, including generating random bits, modulation, adding noise, and measuring BER. Simulation results show scatter plots and eye diagrams of the modulated signals. A table compares the results, showing that 256-bit QAM provides better performance than 4-bit QPSK. The document concludes that QAM modulation is more effective for digital transmission systems.
The document proposes a hybrid technique using Anisotropic Scale Invariant Feature Transform (A-SIFT) and Robust Ensemble Support Vector Machine (RESVM) to accurately identify faces in images. A-SIFT improves upon traditional SIFT by applying anisotropic scaling to extract richer directional keypoints. Keypoints are processed with RESVM and hypothesis testing to increase accuracy above 95% by repeatedly reprocessing images until the threshold is met. The technique was tested on similar and different facial images and achieved better results than SIFT in retrieval time and reduced keypoints.
This document studies the effects of dielectric superstrate thickness on microstrip patch antenna parameters. Three types of probes-fed patch antennas (rectangular, circular, and square) were designed to operate at 2.4 GHz using Arlondiclad 880 substrate. The antennas were tested with and without an Arlondiclad 880 superstrate of varying thicknesses. It was found that adding a superstrate slightly degraded performance by lowering the resonant frequency and increasing return loss and VSWR, while decreasing bandwidth and gain. Specifically, increasing the superstrate thickness or dielectric constant resulted in greater changes to the antenna parameters.
This document describes a wireless environment monitoring system that utilizes soil energy as a sustainable power source for wireless sensors. The system uses a microbial fuel cell to generate electricity from the microbial activity in soil. Two microbial fuel cells were created using different soil types and various additives to produce different current and voltage outputs. An electronic circuit was designed on a printed circuit board with components like a microcontroller and ZigBee transceiver. Sensors for temperature and humidity were connected to the circuit to monitor the environment wirelessly. The system provides a low-cost way to power remote sensors without needing battery replacement and avoids the high costs of wiring a power source.
1) The document proposes a model for a frequency tunable inverted-F antenna that uses ferrite material.
2) The resonant frequency of the antenna can be significantly shifted from 2.41GHz to 3.15GHz, a 31% shift, by increasing the static magnetic field placed on the ferrite material.
3) Altering the permeability of the ferrite allows tuning of the antenna's resonant frequency without changing the physical dimensions, providing flexibility to operate over a wide frequency range.
This document summarizes a research paper that presents a speech enhancement method using stationary wavelet transform. The method first classifies speech into voiced, unvoiced, and silence regions based on short-time energy. It then applies different thresholding techniques to the wavelet coefficients of each region - modified hard thresholding for voiced speech, semi-soft thresholding for unvoiced speech, and setting coefficients to zero for silence. Experimental results using speech from the TIMIT database corrupted with white Gaussian noise at various SNR levels show improved performance over other popular denoising methods.
This document reviews the design of an energy-optimized wireless sensor node that encrypts data for transmission. It discusses how sensing schemes that group nodes into clusters and transmit aggregated data can reduce energy consumption compared to individual node transmissions. The proposed node design calculates the minimum transmission power needed based on received signal strength and uses a periodic sleep/wake cycle to optimize energy when not sensing or transmitting. It aims to encrypt data at both the node and network level to further optimize energy usage for wireless communication.
This document discusses group consumption modes. It analyzes factors that impact group consumption, including external environmental factors like technological developments enabling new forms of online and offline interactions, as well as internal motivational factors at both the group and individual level. The document then proposes that group consumption modes can be divided into four types based on two dimensions: vertical (group relationship intensity) and horizontal (consumption action period). These four types are instrument-oriented, information-oriented, enjoyment-oriented, and relationship-oriented consumption modes. Finally, the document notes that consumption modes are dynamic and can evolve over time.
The document summarizes a study of different microstrip patch antenna configurations with slotted ground planes. Three antenna designs were proposed and their performance evaluated through simulation: a conventional square patch, an elliptical patch, and a star-shaped patch. All antennas were mounted on an FR4 substrate. The effects of adding different slot patterns to the ground plane on resonance frequency, bandwidth, gain and efficiency were analyzed parametrically. Key findings were that reshaping the patch and adding slots increased bandwidth and shifted resonance frequency. The elliptical and star patches in particular performed better than the conventional design. Three antenna configurations were selected for fabrication and measurement based on the simulations: a conventional patch with a slot under the patch, an elliptical patch with slots
1) The document describes a study conducted to improve call drop rates in a GSM network through RF optimization.
2) Drive testing was performed before and after optimization using TEMS software to record network parameters like RxLevel, RxQuality, and events.
3) Analysis found call drops were occurring due to issues like handover failures between sectors, interference from adjacent channels, and overshooting due to antenna tilt.
4) Corrective actions taken included defining neighbors between sectors, adjusting frequencies to reduce interference, and lowering the mechanical tilt of an antenna.
5) Post-optimization drive testing showed improvements in RxLevel, RxQuality, and a reduction in dropped calls.
This document describes the design of an intelligent autonomous wheeled robot that uses RF transmission for communication. The robot has two modes - automatic mode where it can make its own decisions, and user control mode where a user can control it remotely. It is designed using a microcontroller and can perform tasks like object recognition using computer vision and color detection in MATLAB, as well as wall painting using pneumatic systems. The robot's movement is controlled by DC motors and it uses sensors like ultrasonic sensors and gas sensors to navigate autonomously. RF transmission allows communication between the robot and a remote control unit. The overall aim is to develop a low-cost robotic system for industrial applications like material handling.
This document reviews cryptography techniques to secure the Ad-hoc On-Demand Distance Vector (AODV) routing protocol in mobile ad-hoc networks. It discusses various types of attacks on AODV like impersonation, denial of service, eavesdropping, black hole attacks, wormhole attacks, and Sybil attacks. It then proposes using the RC6 cryptography algorithm to secure AODV by encrypting data packets and detecting and removing malicious nodes launching black hole attacks. Simulation results show that after applying RC6, the packet delivery ratio and throughput of AODV increase while delay decreases, improving the security and performance of the network under attack.
The document describes a proposed modification to the conventional Booth multiplier that aims to increase its speed by applying concepts from Vedic mathematics. Specifically, it utilizes the Urdhva Tiryakbhyam formula to generate all partial products concurrently rather than sequentially. The proposed 8x8 bit multiplier was coded in VHDL, simulated, and found to have a path delay 44.35% lower than a conventional Booth multiplier, demonstrating its potential for higher speed.
This document discusses image deblurring techniques. It begins by introducing image restoration and focusing on image deblurring. It then discusses challenges with image deblurring being an ill-posed problem. It reviews existing approaches to screen image deconvolution including estimating point spread functions and iteratively estimating blur kernels and sharp images. The document also discusses handling spatially variant blur and summarizes the relationship between the proposed method and previous work for different blur types. It proposes using color filters in the aperture to exploit parallax cues for segmentation and blur estimation. Finally, it proposes moving the image sensor circularly during exposure to prevent high frequency attenuation from motion blur.
This document describes modeling an adaptive controller for an aircraft roll control system using PID, fuzzy-PID, and genetic algorithm. It begins by introducing the aircraft roll control system and motivation for developing an adaptive controller to minimize errors from noisy analog sensor signals. It then provides the mathematical model of aircraft roll dynamics and describes modeling the real-time flight control system in MATLAB/Simulink. The document evaluates PID, fuzzy-PID, and PID-GA (genetic algorithm) controllers for aircraft roll control and finds that the PID-GA controller delivers the best performance.
ESPP presentation to EU Waste Water Network, 4th June 2024 “EU policies driving nutrient removal and recycling
and the revised UWWTD (Urban Waste Water Treatment Directive)”
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...Sérgio Sacani
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
The debris of the ‘last major merger’ is dynamically youngSérgio Sacani
The Milky Way’s (MW) inner stellar halo contains an [Fe/H]-rich component with highly eccentric orbits, often referred to as the
‘last major merger.’ Hypotheses for the origin of this component include Gaia-Sausage/Enceladus (GSE), where the progenitor
collided with the MW proto-disc 8–11 Gyr ago, and the Virgo Radial Merger (VRM), where the progenitor collided with the
MW disc within the last 3 Gyr. These two scenarios make different predictions about observable structure in local phase space,
because the morphology of debris depends on how long it has had to phase mix. The recently identified phase-space folds in Gaia
DR3 have positive caustic velocities, making them fundamentally different than the phase-mixed chevrons found in simulations
at late times. Roughly 20 per cent of the stars in the prograde local stellar halo are associated with the observed caustics. Based
on a simple phase-mixing model, the observed number of caustics are consistent with a merger that occurred 1–2 Gyr ago.
We also compare the observed phase-space distribution to FIRE-2 Latte simulations of GSE-like mergers, using a quantitative
measurement of phase mixing (2D causticality). The observed local phase-space distribution best matches the simulated data
1–2 Gyr after collision, and certainly not later than 3 Gyr. This is further evidence that the progenitor of the ‘last major merger’
did not collide with the MW proto-disc at early times, as is thought for the GSE, but instead collided with the MW disc within
the last few Gyr, consistent with the body of work surrounding the VRM.
Current Ms word generated power point presentation covers major details about the micronuclei test. It's significance and assays to conduct it. It is used to detect the micronuclei formation inside the cells of nearly every multicellular organism. It's formation takes place during chromosomal sepration at metaphase.
ESR spectroscopy in liquid food and beverages.pptxPRIYANKA PATEL
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Phenomics assisted breeding in crop improvementIshaGoswami9
As the population is increasing and will reach about 9 billion upto 2050. Also due to climate change, it is difficult to meet the food requirement of such a large population. Facing the challenges presented by resource shortages, climate
change, and increasing global population, crop yield and quality need to be improved in a sustainable way over the coming decades. Genetic improvement by breeding is the best way to increase crop productivity. With the rapid progression of functional
genomics, an increasing number of crop genomes have been sequenced and dozens of genes influencing key agronomic traits have been identified. However, current genome sequence information has not been adequately exploited for understanding
the complex characteristics of multiple gene, owing to a lack of crop phenotypic data. Efficient, automatic, and accurate technologies and platforms that can capture phenotypic data that can
be linked to genomics information for crop improvement at all growth stages have become as important as genotyping. Thus,
high-throughput phenotyping has become the major bottleneck restricting crop breeding. Plant phenomics has been defined as the high-throughput, accurate acquisition and analysis of multi-dimensional phenotypes
during crop growing stages at the organism level, including the cell, tissue, organ, individual plant, plot, and field levels. With the rapid development of novel sensors, imaging technology,
and analysis methods, numerous infrastructure platforms have been developed for phenotyping.
ANAMOLOUS SECONDARY GROWTH IN DICOT ROOTS.pptxRASHMI M G
Abnormal or anomalous secondary growth in plants. It defines secondary growth as an increase in plant girth due to vascular cambium or cork cambium. Anomalous secondary growth does not follow the normal pattern of a single vascular cambium producing xylem internally and phloem externally.
BREEDING METHODS FOR DISEASE RESISTANCE.pptxRASHMI M G
Plant breeding for disease resistance is a strategy to reduce crop losses caused by disease. Plants have an innate immune system that allows them to recognize pathogens and provide resistance. However, breeding for long-lasting resistance often involves combining multiple resistance genes
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
Nucleic Acid-its structural and functional complexity.
bT-Locally Closed Sets and bT-Locally Continuous Functions In Supra Topological Spaces.
1. IOSR Journal of Mathematics (IOSR-JM)
e-ISSN: 2278-5728,p-ISSN: 2319-765X, Volume 6, Issue 4 (May. - Jun. 2013), PP 18-22
www.iosrjournals.org
www.iosrjournals.org 18 | Page
bT-Locally Closed Sets and bT-Locally Continuous Functions In
Supra Topological Spaces.
K.Krishnaveni And M.Vigneshwaran
Department of Mathematics Kongunadu Arts and Science College Coimbatore,Tamil Nadu, India.
Abstract: The aim of this paper is to introduce a decompositions namely supra bT- locally closed sets and
define supra bT-locally continuous functions. This paper also discussed some of their properties.
Keyword S-BTLC set, S-BTL- continuous,S-BTL- irresolute.
I. Introduction
In 1983 Mashhour et al [8] introduced Supra topological spaces and studied S- continuous maps
and S*
- continuous maps. In 2011,Bharathi.S[3] introduced and investigated several properties of
generalization of locally b- closed sets. In 1997, Arokiarani .I[2] introduced and investigated some properties
of regular generalized locally closed sets and RGL-continuous functions. In this paper, we define a new set
called supra bT- locally closed and also define supra bT- locally continuous functions and investigated some of
the basic properties for this class of functions.
II. Preliminaries
Definition 2.1[8,10] A subfamily of µ of X is said to be a supra topology on X, if
(i) X, µ
(ii) if Ai µ for all i J then Ai µ.
The pair (X,µ) is called supra topological space. The elements of µ are called supra open sets in
(X,µ) and complement of a supra open set is called a supra closed set.
Definition 2.2[10] (i) The supra closure of a set A is denoted by clµ(A) and is
defined as clµ (A) = ∩{B : B is a supra closed set and A B}.
(ii) The supra interior of a set A is denoted by intµ(A) and defined as
intµ(A) = {B :B is a supra open set and A B}.
Definition 2.3[8] Let (X,τ ) be a topological spaces and µ be a supra topology on X. We call µ a
supra topology associated with τ if τ µ.
Definition 2.4[10] Let (X,µ) be a supra topological space. A set A is called a supra b-open set if A
clµ (intµ(A)) intµ(clµ(A)). The complement of a supra b-open set is called a supra b-closed set.
Definition 2.5[7] A subset A of a supra topological space (X,µ) is called bTµ -closed set if bclµ(A) U
whenever A U and U is Tµ - open in (X,µ).
Definition 2.6[9] Let A and B be subsets of X. Then A and B are said to be supra
separated, if Acl
(B) = Bcl
(A) = .
Definition 2.7[5] Let (X,)(Y,) be two topological spaces and . A function f:
(X,)(Y,) is called supra continuous, if the inverse image of each open set of Y is a supra
open set in X.
Definition 2.8[6] Let (X,)(Y,) be two topological spaces and and be supra
topologies associated with and respectively. A function f: (X,)(Y,) is called supra
irresolute, if f-1
(A) is supra open set of X for every supra open set A in Y.
Notations
S-BTLC*
denotes supra bT*
- locally closed set and S-BTLC**
denotes supra bT**
– locally
closed set.
2. Bt-Locally Closed Sets And Bt-Locally Continuous Functions In Supra Topological Spaces.
www.iosrjournals.org 19 | Page
III. SUPRA bT-LOCALLY CLOSED SETS
Definition 3.1
Let (X,µ) be a supra topological space. A subset A of (X,µ) is called supra bT – locally closed set, if
A = U∩V , where U is supra bT – open in (X,µ) and V is supra bT – closed in (X,µ). The collection of all
supra bT- locally closed set S of X will be denoted by S-BTLC(X).
Remark 3.2
Every supra bT-closed set (resp. supra bT- open set) is S-BTLC.
Definition 3.3
For a subset A of supra topological space (X,µ), A S-BTLC*
(X,µ), if there exist a supra bT- open
set U and a supra closed set V of (X,µ), respectively such that A = U∩V.
Remark 3.4
Every supra bT-closed set (resp. supra bT-open set) is S-BTLC*
.
Definition 3.5
For a subset A of supra topological space (X,µ), A S-BTLC**
(X,µ), if there exist a supra open set
U and a supra bT - closed set V of (X,µ), respectively such that A = U∩V.
Remark 3.6
Every supra bT-closed set (resp. supra bT-open set) is S-BTLC**
.
Theorem 3.7 Let A be a subset of (X,µ) . If A S-BTLC*
(X,µ) (or) S-BTLC**
(X,µ) then A is S-BTLC
(X,µ).
Proof Given A S-BTLC*
(X,µ) (or) S-BTLC**
(X,µ),by definition A= U∩V, where U is supra bT- open
set and V is supra closed set (or) U is supra open set and V is supra bT – closed set. By theorem 3.2 [7] every
supra closed set is supra bT – closed set , therefore V is supra bT – closed set (or) every supra open set is supra
bT – closed set, therefore U is supra bT- open set. Then A is S-BTLC (X,µ).
Example 3.8
Let X= {a,b,c} and µ = {X,φ,{a},{b},{a,b}}.In this (X,µ), S-BTLC*
(X,µ) and S-BTLC**
(X,µ) are
the proper subset of S-BTLC (X,µ), because S-BTLC (X,µ) = P(X).
Theorem 3.9 Let A be a subset of (X,µ) . If A S-LC (X,µ) then A is S-BTLC (X,µ).
Proof Given A S-LC,by definition A = U∩V, where U is supra open set and V is supra closed set. Since
every supra open set is supra bT – open set and every supra closed set is supra bT – closed set. Then A S-
BTLC (X,µ)
The converse of the above theorem is not true from the following example.
Example 3.10
Let X= {a,b,c} and µ = {X,φ,{a}}. S-LC(X,µ) = {X,φ,{a},{b,c}} and S-BTLC(X,µ) = P(X).
Theorem 3.11 For a subset A of (X,µ), the following are equivalent:
(i) A S-BTLC**
(X,µ)
(ii) A = U∩bclµ
(A), for some supra open set U
(iii) bclµ
(A) –A is supra bT- closed
(iv) A[X-bclµ
(A)] is supra bT– open
Proof (i)(ii): Given A S-BTLC**
(X,µ), then there exist a supra open subset U and a supra bT- closed
subset V such that A = U ∩V. Since AU and Abclµ
(A), then AU∩bclµ
(A).
Conversely, we have bclµ
(A) V and hence A = U∩VU∩bclµ
(A). Therefore A = U∩bclµ
(A).
(ii)(i): Let A = U∩bclµ
(A), for some supra open set U. Clearly, bcl
(A) is supra bT- closed and hence A =
U∩bclµ
(A)S-BTLC**
(X,).
(ii) (iii): Let A = U∩bclµ
(A), for some supra open set U. Then A S-BTLC**
(X,µ). This implies U is supra
open and bclµ
(A) is supra bT – closed. Therefore bclµ
(A) –A is supra bT- closed.
(iii) (ii): Let U= X-[ bclµ
(A) –A].By (iii) U is supra bT- open in X. We know that every supra open is
supra bT- open , therefore U is supra open in X. Then A = U∩bclµ
(A) holds.
(iii) (iv): Let Q = bclµ
(A) –A be supra bT – closed. Then X-Q = X-[ bclµ
(A) –A] = A[X-bclµ
(A)].
Since X-Q is supra bT – open, A[X-bclµ
(A)] is supra bT – open.
(iv) (iii): Let U = A[X-bclµ
(A)]. Since X-U is supra bT – closed and X-U = bclµ
(A) –A is supra bT –
closed.
Definition 3.12
Let A be subset of (X,). Then
(i) The supra bT-closure of a set A is denoted by bT-cl
(A), define as bT-cl
(A)={B:B is supra bT-
closed and AB}.
3. Bt-Locally Closed Sets And Bt-Locally Continuous Functions In Supra Topological Spaces.
www.iosrjournals.org 20 | Page
(ii) The supra bT-interior of a set A is denoted by bT-int
(A), define as bT-int
(A)={B:B is supra bT-
open and BA}.
Theorem 3.13 For a subset A of (X,µ), the following are equivalent:
(i) A S-BTLC (X,µ)
(ii) A = U∩bT-clµ
(A), for some supra bT - open set U
(iii) bT-clµ
(A) –A is supra bT- closed
(iv) A[X–bT-clµ
(A)] is supra bT- open
Proof (i)(ii): Given A S-BTLC (X,µ), then there exist a supra bT - open subset U and a supra bT-
closed subset V such that A = U ∩V. Since AU and AbT-clµ
(A), then AU∩bT-clµ
(A).
Conversely, we have bT-clµ
(A) V and hence A = U∩VU∩bT-clµ
(A). Therefore A = U∩bT-clµ
(A).
(ii)(i): Let A = U∩bT-clµ
(A), for some supra bT - open set U. Clearly, bT-cl
(A) is supra bT- closed and
hence A = U∩bT-clµ
(A)S-BTLC (X,).
(ii) (iii): Let A = U∩bT-clµ
(A), for some supra bT - open set U. Then A S-BTLC (X,µ). This implies U is
supra bT - open and bT-clµ
(A) is supra bT – closed. Therefore bT-clµ
(A) –A is supra bT- closed.
(iii) (ii): Let U= X– [ bT-clµ
(A) –A].By (iii) U is supra bT- open in X. Then A = U∩bT-clµ
(A) holds.
(iii) (iv): Let Q = bT-clµ
(A) –A be supra bT – closed. Then X–Q = X– [ bT-clµ
(A) –A] = A[X–bT-
clµ
(A)]. Since X-Q is supra bT – open, A[X–bT-clµ
(A)] is supra bT -open.
(iv) (iii): Let U = A[X– bT-clµ
(A)]. Since X–U is supra bT – closed and X–U = bT-clµ
(A) –A is
supra bT – closed.
Theorem 3.14 For a subset A of (X,µ), the following are equivalent:
(i) A S-BTLC*
(X,µ)
(ii) A = U∩clµ
(A), for some supra bT - open set U
(iii) bclµ
(A) –A is supra bT- closed
(iv) A[X–bclµ
(A)] is supra bT- open
Proof (i)(ii): Given A S-BTLC*
(X,µ), then there exist a supra bT - open subset U and a supra
closed subset V such that A = U ∩V. Since AU and Aclµ
(A), then AU∩clµ
(A).
Conversely, we have clµ
(A) V and hence A = U∩VU∩clµ
(A). Therefore A = U∩clµ
(A).
(ii)(i): Let A = U∩clµ
(A), for some supra bT - open set U. Clearly,cl
(A) is supra closed and hence A =
U∩clµ
(A)S-BTLC*
(X,).
(ii) (iii): Let A = U∩clµ
(A), for some supra bT - open set U. Then A S-BTLC*
(X,µ). This implies U is
supra bT - open and clµ
(A) is supra closed. Therefore clµ
(A) –A is supra closed. We know that every supra
closed is supra bT- closed, therefore bcl
(A) –A is supra bT - closed.
(iii) (ii): Let U= X– [ bclµ
(A) –A].By (iii) U is supra bT- open in X. Then A = U∩clµ
(A) holds.
(iii) (iv): Let Q =bclµ
(A) –A be supra bT -closed. Then X–Q = X– [ bclµ
(A) –A] = A[X– bclµ
(A)].
Since X– Q is supra bT - open, A[X–bclµ
(A)] is supra bT - open.
(iv) (iii): Let U = A[X–bclµ
(A)]. Since X–U is supra bT -closed and X–U = bclµ
(A) –A is supra bT -
closed.
Theorem 3.15 For a subset A of (X,), if AS-BTLC**
(X,), then there exist an supra open set G such
that A = GbT-cl
(A).
Proof Let AS-BTLC**
(X,). Then A = GVAG. Then AbT-cl
(A). Therefore, AGbT-cl
(A).
Also, we have bT-cl
(A)V. This implies A=GVGbT-cl
(A)AGbT-cl
(A).Thus A = GbT-cl
(A).
Theorem 3.16 For a subset A of (X,), if AS-BTLC**
(X,), then there exist an supra open set G such
that A = Gbcl
(A).
Proof Let AS-BTLC**
(X,). Then A = GV, where G is supra open set and V is supra bT-closed set. Then
A = GV AG. Obviously, Abcl
(A).
Therefore, AGbcl
(A). ----------------------(1)
Also, we have bcl
(A)V. This implies A=GVGbcl
(A)AGbcl
(A).------------(2)
From (1) and (2), we get A = Gbcl
(A).
Theorem 3.17 Let A be a subset of (X,). If A S-BTLC**
(X,), then bT-cl
(A) –A is supra bT- closed and
A[X–bT-cl
(A)] is supra bT - open.
Proof Given A S-BTLC**
(X,). Then there exist a supra open subset U and a supra bT- closed subset V
such that A = UV. This implies bT-cl
(A) is supra bT- closed. Therefore, bT-cl
(A) –A is supra bT- closed.
Also, [X– [ bT-cl
(A) –A]] = A[X–bT-cl
(A)] . Therefore A[X–bT-cl
(A)] is supra bT - open.
Remark 3.18 The converse of the above theorem need not be true as seen from the following example.
Example 3.19 Let X={a,b,c,d} and = (X,,{a},{b},{a,b}}.Then
{X,,{a},{b},{c},{d},{a,c},{a,d},{b,c},{b,d},{c,d},{a,c,d},{b,c,d}} is the set of all supra bT-closed set in X
4. Bt-Locally Closed Sets And Bt-Locally Continuous Functions In Supra Topological Spaces.
www.iosrjournals.org 21 | Page
and S-BTLC**
(X,) =P(X) – {{a,b,c},{a,b,d}}.If A = {a,b,c}, then bT-cl
(A) –A = {d} is supra bT- closed and
A[X-bT-cl
(A)] = A is supra bT – open but A∉ S-BTLC**
(X,).
Theorem 3.20 If A S-BTLC*
(X,) and B is supra open, then AB S-BTLC*
(X,).
Proof Suppose A S-BTLC*
(X,), then there exist a supra bT- open set U and supra closed set V such that
A = UV. So AB = UVB = (UB)V, where UB is supra bT- open. Therefore, AB S-
BTLC*
(X,).
Theorem 3.21 If A S-BTLC(X,) and B is supra open, then AB S-BTLC(X,).
Proof Suppose A S-BTLC(X,), then there exist a supra bT- open set U and supra bT - closed set V such
that A = UV. So AB = UVB = (UB)V, where UB is supra bT- open. Therefore, AB S-
BTLC(X,).
Theorem 3.22 If A S-BTLC**
(X,) and B is supra closed, then AB S-BTLC**
(X,).
Proof Suppose A S-BTLC**
(X,), then there exist a supra open set U and supra bT- closed set V such
that A = UV. So AB = UVB = U(BV), where BV is supra bT- closed. Hence, AB S-
BTLC**
(X,).
IV. SUPRA bT- LOCALLY CONTINUOUS FUNCTIONS
In this section, we define a new type of functions called supra bT- locally continuous functions (S-
BTL -continuous functions),supra bT – locally irresolute functions(S-BTL-irresolute) and study some of their
properties.
Definition 4.1
Let (X,) and (Y,) be two topological spaces and . A function f: (X,)(Y,) is called S-BTL-
continuous (resp., S-BTL*
- continuous, and S-BTL**
- continuous), if 𝑓−1
(A) S-BTLC(X,),(resp., 𝑓−1
(A)
S-BTLC*
(X,), and 𝑓−1
(A) S-BTLC**
(X,)) for each A.
Definition 4.2
Let (X,) and (Y,) be two topological spaces and and be a supra topologies associated with and
respectively.A function f: (X,)(Y,) is said to be S-BTL-irresolute(resp., S-BTL*
- irresolute, resp., S-
BTL**
-irresolute) if 𝑓−1
(A) S-BTLC(X,),(resp., 𝑓−1
(A) S-BTLC*
(X,), resp., 𝑓−1
(A) S-
BTLC**
(X,)) for each AS-BTLC(Y,)(resp., AS-BTLC*
(Y,), resp., AS-BTLC**
(Y,)).
Theorem 4.3 Let (X,) and (Y,) be two topological spaces and be a supra topology associated with .
Let f: (X,)(Y,) be a function. If f is S-BTL*
- continuous (or) S-BTL**- continuous, then it is S-BTL-
continuous.
Proof Let f: (X,)(Y,) be a function. If f is S-BTL*
- continuous (or) S-BTL**- continuous, by definition
𝑓−1
(A) S-BTLC*
(X,), and 𝑓−1
(A) S-BTLC**
(X,) for each A. By theorem 3.7 , 𝑓−1
(A) S-
BTLC(X,). Then it is S-BTL- continuous.
Theorem 4.4 Let (X,) and (Y,) be two topological spaces and and be a supra topologies associated
with and respectively. Let f: (X,)(Y,) be a function . If f is S-BTL-irresolute(resp., S-BTL*
- irresolute,
and S-BTL**
-irresolute) , then it is S-BTL- continuous( resp., S-BTL*
- continuous, and S-BTL**
- continuous).
Proof Let f: (X,)(Y,) be a function . Let A is supra closed of Y. By theorem 3.2[7] every supra closed
set is supra bT-closed set, therefore A is supra bT – closed set. Since f is S-BTL-irresolute(resp., S-BTL*
-
irresolute, and S-BTL**
-irresolute), 𝑓−1
(A) is S-BTL-closed. Therefore f is S-BTL-continuous ( resp., S-BTL*
-
continuous, and S-BTL**
- continuous).
Theorem 4.5 If g:XY is S-BTL- continuous and h: YZ is supra continuous, then hog: XZ is S-BTL-
continuous.
Proof Let g:XY is S-BTL- continuous and h: YZ is supra continuous. By definition, g-1
(V)S-
BTLC(X),VY and h-1
(W)Y, WZ. Let WZ, then (hog)-1
(W) = (g-1
h-1
)(W) = g-1
(h-1
(W)) =g-1
(V), for
VY. This implies, (hog)-1
(W) = g-1
(V)S-BTLC(X),WZ. Hence hog is S-BTL- continuous.
Theorem 4.6 If g:XY is S-BTL-irresolute and h: YZ is S-BTL-continuous, then hog : XZ is S-
BTL- continuous.
Proof Let g:XY is S-BTL-irresolute and h: YZ is S-BTL-continuous. By definition, g-1
(V)S-
BTLC(X), for VS-BTLC(Y) and h-1
(W)S-BTLC(Y), for WZ. Let WZ, then (hog)-1
(W) = (g-1
h-1
)(W) = g-
1
(h-1
(W)) =g-1
(V), for VS-BTLC(Y). This implies, (hog)-1
(W) = g-1
(V)S-BTLC(X),WZ. Hence hog is S-
BTL- continuous.
Theorem 4.7 If g:XY and h: YZ are S-BTL- irresolute, then hog : XZ is S-BTL- irresolute.
5. Bt-Locally Closed Sets And Bt-Locally Continuous Functions In Supra Topological Spaces.
www.iosrjournals.org 22 | Page
Proof By the hypothesis and the definition, we have g-1
(V) S-BTLC(X) , for V S-BTLC(Y)
and and h-1
(W)S-BTLC(Y), for WS-BTLC(Z).Let WS-BTLC(Z), then (hog)-1
(W) = (g-1
h-1
)(W) = g-1
(h-
1
(W)) =g-1
(V), for VS-BTLC(Y). Therefore, (hog)-1
(W) = g-1
(V)S-BTLC(X),WS-BTLC(Z). Thus, hog is
S-BTL- irresolute.
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