IJERD (www.ijerd.com) International Journal of Engineering Research and Development IJERD : hard copy of journal, Call for Papers 2012, publishing of journal, journal of science and technology, research paper publishing, where to publish research paper,
This document presents a theorem that establishes the existence of a fixed point for a mapping under a general contractive condition of integral type. The mapping considered generalizes various types of contractive mappings in an integral setting. The theorem proves that if a self-mapping on a complete metric space satisfies the given integral inequality involving the distance between images of points, where the integral involves a non-negative, summable function, then the mapping has a unique fixed point. Furthermore, the sequence of repeated applications of the mapping to any starting point will converge to this fixed point. The proof involves showing the distance between successive terms in the sequence decreases according to the integral inequality.
Generalization of Tensor Factorization and ApplicationsKohei Hayashi
This document presents two tensor factorization methods: Exponential Family Tensor Factorization (ETF) and Full-Rank Tensor Completion (FTC). ETF generalizes Tucker decomposition by allowing for different noise distributions in the tensor and handles mixed discrete and continuous values. FTC completes missing tensor values without reducing dimensionality by kernelizing Tucker decomposition. The document outlines these methods and their motivations, discusses Tucker decomposition, and provides an example applying ETF to anomaly detection in time series sensor data.
On estimating the integrated co volatility usingkkislas
This document proposes a method to estimate the integrated co-volatility of two asset prices using high-frequency data that contains both microstructure noise and jumps.
It considers two cases - when the jump processes of the two assets are independent, and when they are dependent. For the independent case, it proposes an estimator that is robust to jumps. For the dependent case, it proposes a threshold estimator that combines pre-averaging to remove noise with a threshold method to reduce the effect of jumps. It proves the estimators are consistent and establishes their central limit theorems. Simulation results are also presented to illustrate the performance of the proposed methods.
This document is a section from a Calculus I course at New York University that discusses basic differentiation rules. It covers objectives like differentiating constant, sum, and difference functions. It also covers derivatives of sine and cosine. Examples are provided, like finding the derivative of the squaring function x^2, which is 2x. Notation for derivatives is explained, including Leibniz notation. The concept of the second derivative is also introduced.
This document contains the homework assignment for Dr. Ashu Sabharwal's ELEC 430 class at Rice University due on February 19, 2009. It includes 3 exercises on topics related to signaling and detection:
1. The likelihood ratio test is derived for a binary communication system with additive white Gaussian noise. Conditional probability density functions are found and used to determine the probability of error as a function of threshold.
2. Matched filters are discussed for an antipodal signaling system. The impulse response and output of the matched filter are sketched. Expressions are derived for the noise variance and probability of error.
3. Orthogonal signal properties are explored for a set of signals that are modified by subtracting
This document presents a theorem concerning fixed points in Hilbert spaces. It extends an existing theorem by introducing additional terms to the contraction mapping inequality. The extended theorem is proved by showing that the mapping T has a unique fixed point u in the closed subset C of the Hilbert space. A sequence is constructed that converges to u, proving it is the unique fixed point of T. This provides a common fixed point theorem for mappings satisfying the generalized inequality.
This document is a section from a Calculus I course at New York University that discusses basic differentiation rules. It provides objectives for understanding rules like the derivative of a constant function, the constant multiple rule, sum rule, and derivatives of sine and cosine functions. It then gives examples of finding the derivative of a squaring function using the definition, and introduces the concept of the second derivative.
11.fixed point theorem of discontinuity and weak compatibility in non complet...Alexander Decker
The document presents a theorem about fixed points for six self-maps in a non-complete non-Archimedean Menger PM-space. The theorem proves that the six maps have a unique common fixed point under certain conditions, including:
1) The maps satisfy inequality conditions involving probabilistic metric functions.
2) One of the subspaces induced by two of the maps is complete.
3) The pairs of maps are R-weakly compatible.
The proof constructs a Cauchy sequence and uses properties of probabilistic metric functions and the given conditions to show the sequence converges, establishing a common fixed point.
Fixed point theorem of discontinuity and weak compatibility in non complete n...Alexander Decker
The document presents a theorem about fixed points for six self-maps in a non-complete non-Archimedean Menger PM-space. The theorem proves that the six maps have a unique common fixed point under certain conditions, including:
1) The maps satisfy inequality conditions involving probabilistic metric functions.
2) One of the subspaces induced by two of the maps is complete.
3) The pairs of maps are R-weakly compatible.
The proof constructs a Cauchy sequence and uses properties of probabilistic metric spaces and weak compatibility to show the maps have a common fixed point.
Generalization of Tensor Factorization and ApplicationsKohei Hayashi
This document presents two tensor factorization methods: Exponential Family Tensor Factorization (ETF) and Full-Rank Tensor Completion (FTC). ETF generalizes Tucker decomposition by allowing for different noise distributions in the tensor and handles mixed discrete and continuous values. FTC completes missing tensor values without reducing dimensionality by kernelizing Tucker decomposition. The document outlines these methods and their motivations, discusses Tucker decomposition, and provides an example applying ETF to anomaly detection in time series sensor data.
On estimating the integrated co volatility usingkkislas
This document proposes a method to estimate the integrated co-volatility of two asset prices using high-frequency data that contains both microstructure noise and jumps.
It considers two cases - when the jump processes of the two assets are independent, and when they are dependent. For the independent case, it proposes an estimator that is robust to jumps. For the dependent case, it proposes a threshold estimator that combines pre-averaging to remove noise with a threshold method to reduce the effect of jumps. It proves the estimators are consistent and establishes their central limit theorems. Simulation results are also presented to illustrate the performance of the proposed methods.
This document is a section from a Calculus I course at New York University that discusses basic differentiation rules. It covers objectives like differentiating constant, sum, and difference functions. It also covers derivatives of sine and cosine. Examples are provided, like finding the derivative of the squaring function x^2, which is 2x. Notation for derivatives is explained, including Leibniz notation. The concept of the second derivative is also introduced.
This document contains the homework assignment for Dr. Ashu Sabharwal's ELEC 430 class at Rice University due on February 19, 2009. It includes 3 exercises on topics related to signaling and detection:
1. The likelihood ratio test is derived for a binary communication system with additive white Gaussian noise. Conditional probability density functions are found and used to determine the probability of error as a function of threshold.
2. Matched filters are discussed for an antipodal signaling system. The impulse response and output of the matched filter are sketched. Expressions are derived for the noise variance and probability of error.
3. Orthogonal signal properties are explored for a set of signals that are modified by subtracting
This document presents a theorem concerning fixed points in Hilbert spaces. It extends an existing theorem by introducing additional terms to the contraction mapping inequality. The extended theorem is proved by showing that the mapping T has a unique fixed point u in the closed subset C of the Hilbert space. A sequence is constructed that converges to u, proving it is the unique fixed point of T. This provides a common fixed point theorem for mappings satisfying the generalized inequality.
This document is a section from a Calculus I course at New York University that discusses basic differentiation rules. It provides objectives for understanding rules like the derivative of a constant function, the constant multiple rule, sum rule, and derivatives of sine and cosine functions. It then gives examples of finding the derivative of a squaring function using the definition, and introduces the concept of the second derivative.
11.fixed point theorem of discontinuity and weak compatibility in non complet...Alexander Decker
The document presents a theorem about fixed points for six self-maps in a non-complete non-Archimedean Menger PM-space. The theorem proves that the six maps have a unique common fixed point under certain conditions, including:
1) The maps satisfy inequality conditions involving probabilistic metric functions.
2) One of the subspaces induced by two of the maps is complete.
3) The pairs of maps are R-weakly compatible.
The proof constructs a Cauchy sequence and uses properties of probabilistic metric functions and the given conditions to show the sequence converges, establishing a common fixed point.
Fixed point theorem of discontinuity and weak compatibility in non complete n...Alexander Decker
The document presents a theorem about fixed points for six self-maps in a non-complete non-Archimedean Menger PM-space. The theorem proves that the six maps have a unique common fixed point under certain conditions, including:
1) The maps satisfy inequality conditions involving probabilistic metric functions.
2) One of the subspaces induced by two of the maps is complete.
3) The pairs of maps are R-weakly compatible.
The proof constructs a Cauchy sequence and uses properties of probabilistic metric spaces and weak compatibility to show the maps have a common fixed point.
Stuff You Must Know Cold for the AP Calculus BC Exam!A Jorge Garcia
This document provides a summary of key concepts from AP Calculus that students must know, including:
- Differentiation rules like product rule, quotient rule, and chain rule
- Integration techniques like Riemann sums, trapezoidal rule, and Simpson's rule
- Theorems related to derivatives and integrals like the Mean Value Theorem, Fundamental Theorem of Calculus, and Rolle's Theorem
- Common trigonometric derivatives and integrals
- Series approximations like Taylor series and Maclaurin series
- Calculus topics for polar coordinates, parametric equations, and vectors
This document discusses several topics related to Fourier transforms including:
1) Representing polynomials in value representation by evaluating them at roots of unity allows for faster multiplication using the Discrete Fourier Transform (DFT).
2) The DFT reduces the complexity of the Discrete Fourier Transform (DFT) from O(n2) to O(n log n) by formulating it recursively.
3) Converting images from the spatial to frequency domain using techniques like the Discrete Cosine Transform (DCT) allows for image compression by retaining only low frequency components with large coefficients.
This document discusses applying renewal theorems to analyze the exponential moments of local times of Markov processes. It contains three main points:
1) If γ is greater than 1/G∞(i,i), the expected exponential moment grows exponentially over time.
2) If γ equals 1/G∞(i,i), the expected exponential moment grows linearly over time if H∞(i,i) is finite, and sublinearly otherwise.
3) If γ is less than 1/G∞(i,i), the expected exponential moment converges to a constant as time increases.
The analysis simplifies and strengthens previous results by framing the problem as a renewal
Adomian decomposition method for solving higher order boundary value problemsAlexander Decker
This document presents an application of the Adomian decomposition method to solve higher order boundary value problems. The Adomian decomposition method assumes a series solution for the unknown quantity and decomposes the nonlinear operator into a series of polynomials. The document outlines how the method can be applied to solve third order singular boundary value problems and fourth order beam bending problems. It describes the key steps of the Adomian decomposition method and introduces the inverse operators used to obtain approximate solutions to the boundary value problems.
This document discusses nanotechnology and its applications to computer circuits. It begins with an overview of nanotechnology, including its history and key concepts. It then discusses various tools used in nanotechnology like electron microscopes. It provides examples of how nanotechnology can be applied to reduce the size of computer circuits. Both benefits like smaller computers and potential disadvantages are mentioned.
The document provides an overview of CMB experiments, including:
1) It describes the natural units used to measure CMB temperature and polarization maps, and how the power spectrum is derived from harmonic coefficients of the maps.
2) It shows the predicted scalar power spectrum, noting the first acoustic peak at l≈220 and subsequent Doppler peaks and troughs.
3) It discusses how instrument noise is characterized and how the likelihood function relates observed and theoretical power spectra.
4) It briefly describes how the CMB is predicted to be mildly polarized and how polarization is represented, as well as technologies used to detect CMB fluctuations like microwave horns.
This calculus cheat sheet provides definitions and formulas for:
1) Integrals including definite integrals, anti-derivatives, and the Fundamental Theorem of Calculus.
2) Common integration techniques like u-substitution and integration by parts.
3) Standard integrals of common functions like polynomials, trigonometric functions, logarithms, and exponentials.
Tensor Decomposition and its ApplicationsKeisuke OTAKI
This document discusses tensor factorizations and decompositions and their applications in data mining. It introduces tensors as multi-dimensional arrays and covers 2nd order tensors (matrices) and 3rd order tensors. It describes how tensor decompositions like the Tucker model and CANDECOMP/PARAFAC (CP) model can be used to decompose tensors into core elements to interpret data. It also discusses singular value decomposition (SVD) as a way to decompose matrices and reduce dimensions while approximating the original matrix.
The document analyzes the analytic solution of Burger's equations using the variational iteration method. It begins by introducing the variational iteration method and how it can be used to solve differential equations. It then applies the method to obtain exact solutions for the (1+1), (1+2), and (1+3) dimensional Burger equations. Lengthy iterative solutions are presented for each case. The variational iteration method is shown to provide exact solutions to these Burger equations without requiring linearization.
This document is from a Calculus I class at New York University and covers basic differentiation rules. It includes announcements about homework and a quiz. The objectives are to understand and use rules for differentiating constant functions, constants multiplied by functions, sums and differences of functions, and sine and cosine functions. Examples are provided of finding the derivatives of squaring, cubing, and square root functions using the definition of the derivative. Graphs and properties of derivatives are also discussed.
This document provides summaries of common derivatives and integrals, including:
- Basic properties and formulas for derivatives and integrals of functions like polynomials, trig functions, inverse trig functions, exponentials/logarithms, and more.
- Standard integration techniques like u-substitution, integration by parts, and trig substitutions.
- How to evaluate integrals of products and quotients of trig functions using properties like angle addition formulas and half-angle identities.
- How to use partial fractions to decompose rational functions for the purpose of integration.
So in summary, this document outlines essential derivatives and integrals for many common functions, along with standard integration strategies and techniques.
Lesson 26: The Fundamental Theorem of Calculus (slides)Matthew Leingang
The document discusses the Fundamental Theorem of Calculus, which has two parts. The first part states that if a function f is continuous on an interval, then the derivative of the integral of f is equal to f. This is proven using Riemann sums. The second part relates the integral of a function f to the integral of its derivative F'. Examples are provided to illustrate how the area under a curve relates to these concepts.
This document contains questions from a fourth semester engineering examination on design and analysis of algorithms. It asks students to:
1) Define asymptotic notations and analyze the time complexity of a sample algorithm.
2) Solve recurrence relations for different algorithms.
3) Explain how bubble sort and quicksort work, including tracing quicksort on a sample data set and deriving its worst case complexity.
4) Write the recursive algorithm for merge sort.
The document contains questions assessing students' understanding of algorithm analysis, asymptotic notations, solving recurrence relations, and sorting algorithms like bubble sort, quicksort, and merge sort.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Geodesic Method in Computer Vision and GraphicsGabriel Peyré
This document discusses geodesic methods in computer vision and graphics. It begins with an overview of topics including Riemannian data modelling, numerical computations of geodesics, geodesic image segmentation, geodesic shape representation, geodesic meshing, and inverse problems with geodesic fidelity. It then provides details on parametric surfaces, Riemannian manifolds, anisotropy and geodesics, the eikonal equation and viscosity solution, discretization methods, and numerical schemes for solving the fixed point equation.
This document presents a research paper that proves some fixed point theorems for occasionally weakly compatible maps in fuzzy metric spaces. The paper begins with an introduction discussing the importance of fixed point theory and its applications. It then provides relevant definitions for fuzzy metric spaces and concepts like weakly compatible mappings. The main results of the paper are fixed point theorems for mappings satisfying integral type contractive conditions in fuzzy metric spaces for occasionally weakly compatible maps. The proofs of these fixed point theorems generalize existing contractive conditions to establish the existence and uniqueness of a fixed point.
1) The document discusses the existence of solutions for a nonlinear fractional differential equation with an integral boundary condition. It considers equations defined on the interval [0,T] with values in the space of continuous functions C[0,T].
2) It introduces relevant definitions, lemmas, and theorems for fractional calculus and fixed point theory. It then proves that solutions exist based on the Ascoli-Arzela theorem and Schauder-Tychonoff fixed point theorem.
3) The main result provides an explicit formula for the solution in terms of integrals involving the functions defining the fractional differential equation and the boundary conditions. Existence is established by showing the solution map is a contraction.
This document summarizes key concepts in digital and analog communications:
1) It defines source coding, channel encoding/decoding, digital modulation/demodulation, and how digital communication system performance is measured in terms of error probability.
2) Thermal noise in receivers is identified as the dominant source of noise limiting performance in VHF and UHF bands.
3) Storing data on magnetic/optical disks is analogous to transmitting a signal over a radio channel, with similar signal processing used for recovery.
4) Digital processing avoids signal degradation but requires more bandwidth, while analog processing is sensitive to variations but does not lose quality over time.
5) Fourier analysis is used to derive the
Complete l fuzzy metric spaces and common fixed point theoremsAlexander Decker
This document presents definitions and theorems related to complete L-fuzzy metric spaces and common fixed point theorems. It begins with introducing concepts such as L-fuzzy sets, L-fuzzy metric spaces, and triangular norms. It then defines Cauchy sequences and completeness in L-fuzzy metric spaces. The main result is Theorem 2.2, which establishes conditions under which four self-mappings of a complete L-fuzzy metric space have a unique common fixed point. These conditions include the mappings having compatible pairs, one mapping having a closed range, and the mappings satisfying a contractive-type inequality condition. The proof of the theorem constructs appropriate sequences to show convergence.
Stuff You Must Know Cold for the AP Calculus BC Exam!A Jorge Garcia
This document provides a summary of key concepts from AP Calculus that students must know, including:
- Differentiation rules like product rule, quotient rule, and chain rule
- Integration techniques like Riemann sums, trapezoidal rule, and Simpson's rule
- Theorems related to derivatives and integrals like the Mean Value Theorem, Fundamental Theorem of Calculus, and Rolle's Theorem
- Common trigonometric derivatives and integrals
- Series approximations like Taylor series and Maclaurin series
- Calculus topics for polar coordinates, parametric equations, and vectors
This document discusses several topics related to Fourier transforms including:
1) Representing polynomials in value representation by evaluating them at roots of unity allows for faster multiplication using the Discrete Fourier Transform (DFT).
2) The DFT reduces the complexity of the Discrete Fourier Transform (DFT) from O(n2) to O(n log n) by formulating it recursively.
3) Converting images from the spatial to frequency domain using techniques like the Discrete Cosine Transform (DCT) allows for image compression by retaining only low frequency components with large coefficients.
This document discusses applying renewal theorems to analyze the exponential moments of local times of Markov processes. It contains three main points:
1) If γ is greater than 1/G∞(i,i), the expected exponential moment grows exponentially over time.
2) If γ equals 1/G∞(i,i), the expected exponential moment grows linearly over time if H∞(i,i) is finite, and sublinearly otherwise.
3) If γ is less than 1/G∞(i,i), the expected exponential moment converges to a constant as time increases.
The analysis simplifies and strengthens previous results by framing the problem as a renewal
Adomian decomposition method for solving higher order boundary value problemsAlexander Decker
This document presents an application of the Adomian decomposition method to solve higher order boundary value problems. The Adomian decomposition method assumes a series solution for the unknown quantity and decomposes the nonlinear operator into a series of polynomials. The document outlines how the method can be applied to solve third order singular boundary value problems and fourth order beam bending problems. It describes the key steps of the Adomian decomposition method and introduces the inverse operators used to obtain approximate solutions to the boundary value problems.
This document discusses nanotechnology and its applications to computer circuits. It begins with an overview of nanotechnology, including its history and key concepts. It then discusses various tools used in nanotechnology like electron microscopes. It provides examples of how nanotechnology can be applied to reduce the size of computer circuits. Both benefits like smaller computers and potential disadvantages are mentioned.
The document provides an overview of CMB experiments, including:
1) It describes the natural units used to measure CMB temperature and polarization maps, and how the power spectrum is derived from harmonic coefficients of the maps.
2) It shows the predicted scalar power spectrum, noting the first acoustic peak at l≈220 and subsequent Doppler peaks and troughs.
3) It discusses how instrument noise is characterized and how the likelihood function relates observed and theoretical power spectra.
4) It briefly describes how the CMB is predicted to be mildly polarized and how polarization is represented, as well as technologies used to detect CMB fluctuations like microwave horns.
This calculus cheat sheet provides definitions and formulas for:
1) Integrals including definite integrals, anti-derivatives, and the Fundamental Theorem of Calculus.
2) Common integration techniques like u-substitution and integration by parts.
3) Standard integrals of common functions like polynomials, trigonometric functions, logarithms, and exponentials.
Tensor Decomposition and its ApplicationsKeisuke OTAKI
This document discusses tensor factorizations and decompositions and their applications in data mining. It introduces tensors as multi-dimensional arrays and covers 2nd order tensors (matrices) and 3rd order tensors. It describes how tensor decompositions like the Tucker model and CANDECOMP/PARAFAC (CP) model can be used to decompose tensors into core elements to interpret data. It also discusses singular value decomposition (SVD) as a way to decompose matrices and reduce dimensions while approximating the original matrix.
The document analyzes the analytic solution of Burger's equations using the variational iteration method. It begins by introducing the variational iteration method and how it can be used to solve differential equations. It then applies the method to obtain exact solutions for the (1+1), (1+2), and (1+3) dimensional Burger equations. Lengthy iterative solutions are presented for each case. The variational iteration method is shown to provide exact solutions to these Burger equations without requiring linearization.
This document is from a Calculus I class at New York University and covers basic differentiation rules. It includes announcements about homework and a quiz. The objectives are to understand and use rules for differentiating constant functions, constants multiplied by functions, sums and differences of functions, and sine and cosine functions. Examples are provided of finding the derivatives of squaring, cubing, and square root functions using the definition of the derivative. Graphs and properties of derivatives are also discussed.
This document provides summaries of common derivatives and integrals, including:
- Basic properties and formulas for derivatives and integrals of functions like polynomials, trig functions, inverse trig functions, exponentials/logarithms, and more.
- Standard integration techniques like u-substitution, integration by parts, and trig substitutions.
- How to evaluate integrals of products and quotients of trig functions using properties like angle addition formulas and half-angle identities.
- How to use partial fractions to decompose rational functions for the purpose of integration.
So in summary, this document outlines essential derivatives and integrals for many common functions, along with standard integration strategies and techniques.
Lesson 26: The Fundamental Theorem of Calculus (slides)Matthew Leingang
The document discusses the Fundamental Theorem of Calculus, which has two parts. The first part states that if a function f is continuous on an interval, then the derivative of the integral of f is equal to f. This is proven using Riemann sums. The second part relates the integral of a function f to the integral of its derivative F'. Examples are provided to illustrate how the area under a curve relates to these concepts.
This document contains questions from a fourth semester engineering examination on design and analysis of algorithms. It asks students to:
1) Define asymptotic notations and analyze the time complexity of a sample algorithm.
2) Solve recurrence relations for different algorithms.
3) Explain how bubble sort and quicksort work, including tracing quicksort on a sample data set and deriving its worst case complexity.
4) Write the recursive algorithm for merge sort.
The document contains questions assessing students' understanding of algorithm analysis, asymptotic notations, solving recurrence relations, and sorting algorithms like bubble sort, quicksort, and merge sort.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
Geodesic Method in Computer Vision and GraphicsGabriel Peyré
This document discusses geodesic methods in computer vision and graphics. It begins with an overview of topics including Riemannian data modelling, numerical computations of geodesics, geodesic image segmentation, geodesic shape representation, geodesic meshing, and inverse problems with geodesic fidelity. It then provides details on parametric surfaces, Riemannian manifolds, anisotropy and geodesics, the eikonal equation and viscosity solution, discretization methods, and numerical schemes for solving the fixed point equation.
Similar to IJERD (www.ijerd.com) International Journal of Engineering Research and Development IJERD : hard copy of journal, Call for Papers 2012, publishing of journal, journal of science and technology, research paper publishing, where to publish research paper,
This document presents a research paper that proves some fixed point theorems for occasionally weakly compatible maps in fuzzy metric spaces. The paper begins with an introduction discussing the importance of fixed point theory and its applications. It then provides relevant definitions for fuzzy metric spaces and concepts like weakly compatible mappings. The main results of the paper are fixed point theorems for mappings satisfying integral type contractive conditions in fuzzy metric spaces for occasionally weakly compatible maps. The proofs of these fixed point theorems generalize existing contractive conditions to establish the existence and uniqueness of a fixed point.
1) The document discusses the existence of solutions for a nonlinear fractional differential equation with an integral boundary condition. It considers equations defined on the interval [0,T] with values in the space of continuous functions C[0,T].
2) It introduces relevant definitions, lemmas, and theorems for fractional calculus and fixed point theory. It then proves that solutions exist based on the Ascoli-Arzela theorem and Schauder-Tychonoff fixed point theorem.
3) The main result provides an explicit formula for the solution in terms of integrals involving the functions defining the fractional differential equation and the boundary conditions. Existence is established by showing the solution map is a contraction.
This document summarizes key concepts in digital and analog communications:
1) It defines source coding, channel encoding/decoding, digital modulation/demodulation, and how digital communication system performance is measured in terms of error probability.
2) Thermal noise in receivers is identified as the dominant source of noise limiting performance in VHF and UHF bands.
3) Storing data on magnetic/optical disks is analogous to transmitting a signal over a radio channel, with similar signal processing used for recovery.
4) Digital processing avoids signal degradation but requires more bandwidth, while analog processing is sensitive to variations but does not lose quality over time.
5) Fourier analysis is used to derive the
Complete l fuzzy metric spaces and common fixed point theoremsAlexander Decker
This document presents definitions and theorems related to complete L-fuzzy metric spaces and common fixed point theorems. It begins with introducing concepts such as L-fuzzy sets, L-fuzzy metric spaces, and triangular norms. It then defines Cauchy sequences and completeness in L-fuzzy metric spaces. The main result is Theorem 2.2, which establishes conditions under which four self-mappings of a complete L-fuzzy metric space have a unique common fixed point. These conditions include the mappings having compatible pairs, one mapping having a closed range, and the mappings satisfying a contractive-type inequality condition. The proof of the theorem constructs appropriate sequences to show convergence.
Existence of Solutions of Fractional Neutral Integrodifferential Equations wi...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, 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.
8 fixed point theorem in complete fuzzy metric space 8 megha shrivastavaBIOLOGICAL FORUM
ABSTRACT: In this paper our works establish a new fixed point theorem for a different type of mapping in complete fuzzy metric space. Here we define a mapping by using some proved results and obtain a result on the actuality of fixed points. We inspired by the concept of Hossein Piri and Poom Kumam [15]. They introduced the fixed point theorem for generalized F-suzuki -contraction mappings in complete b-metric space. Next Robert plebaniak [16] express his idea by result “New generalized fuzzy metric space and fixed point theorem in fuzzy metric space”. This paper also induces comparing of the outcome with existing result in the literature.
Keywords: Fuzzy set, Fuzzy metric space, Cauchy sequence Non- decreasing sequence, Fixed point, Mapping.
On fixed point theorems in fuzzy 2 metric spaces and fuzzy 3-metric spacesAlexander Decker
1) The document discusses fixed point theorems for mappings in fuzzy 2-metric and fuzzy 3-metric spaces.
2) It defines concepts like fuzzy metric spaces, Cauchy sequences, compatible mappings, and proves some fixed point theorems for compatible mappings.
3) The theorems show that under certain contractive conditions on the mappings, there exists a unique common fixed point for the mappings in a complete fuzzy 2-metric or fuzzy 3-metric space.
International Journal of Computational Engineering Research(IJCER)ijceronline
The document presents some fixed point theorems for expansion mappings in complete metric spaces. It begins with definitions of terms like metric spaces, complete metric spaces, Cauchy sequences, and expansion mappings. It then summarizes several existing fixed point theorems for expansion mappings established by other mathematicians. The main result proved in this document is Theorem 3.1, which establishes a new fixed point theorem for expansion mappings under certain conditions on the metric space and mapping. It shows that if the mapping satisfies the given inequality, then it has a fixed point. The proof of this theorem constructs a sequence to show that it converges to a fixed point.
A common fixed point theorem in cone metric spacesAlexander Decker
This academic article summarizes a common fixed point theorem for continuous and asymptotically regular self-mappings on complete cone metric spaces. The theorem extends previous results to cone metric spaces, which generalize metric spaces by replacing real numbers with an ordered Banach space. It proves that under certain contractive conditions, the self-mapping has a unique fixed point. The proof constructs a Cauchy sequence that converges to the fixed point.
This document provides a summary and critique of the local volatility model. It begins by briefly recalling the construction of the local volatility concept, which aims to find an implied volatility function that matches option prices. However, the document argues that the local volatility model makes an error by replacing the real stock process with an auxiliary process, as they are defined on different coordinate spaces. While the goal of eliminating discrepancies between real and implied volatility is reasonable, the implementation of the local volatility concept ignores important initial conditions. Overall, the document presents both the theoretical basis of local volatility and a critical viewpoint of its mathematical derivation.
New Contraction Mappings in Dislocated Quasi - Metric SpacesIJERA Editor
In this paper the concept of new contraction mappings has been used in proving fixed point theorems. We
establish some common fixed point theorems in complete dislocated quasi metric spaces using new contraction
mappings.
This cheat sheet summarizes techniques for solving first and second order ordinary differential equations. It provides the main methods for solving trivial, linear non-homogeneous, and separable first order differential equations, as well as finding the complementary and particular solutions for second order differential equations with constant coefficients. Students are advised to memorize and practice these problem-solving approaches.
This cheat sheet summarizes techniques for solving first and second order ordinary differential equations. It provides the main methods for solving trivial, linear non-homogeneous, and separable first order differential equations, as well as finding the complementary and particular solutions for second order differential equations with constant coefficients. Students are advised to memorize and practice these problem-solving approaches.
Fixed points of contractive and Geraghty contraction mappings under the influ...IJERA Editor
In this paper, we prove the existence of fixed points of contractive and Geraghty contraction maps in complete metric spaces under the influence of altering distances. Our results extend and generalize some of the known results.
This document summarizes a talk on Lorentz surfaces in pseudo-Riemannian space forms with horizontal reflector lifts. It introduces examples of Lorentz surfaces with zero mean curvature in these spaces. It also discusses reflector spaces and horizontal reflector lifts, and presents a rigidity theorem stating that if two isometric immersions from a Lorentz surface to a pseudo-Riemannian space form both have horizontal reflector lifts and satisfy certain curvature conditions, then the immersions must differ by an isometry of the target space.
11.some fixed point theorems in generalised dislocated metric spacesAlexander Decker
This document introduces the notion of a generalized dislocated metric space and establishes some of its topological properties. Some fixed point theorems are obtained for self-maps on these spaces that satisfy contractive conditions. Specifically:
1) A generalized dislocated metric is defined on a set that satisfies non-negativity, identity of indiscernibles, symmetry, and a generalized triangle inequality conditions.
2) A topology called the d-topology is shown to be induced by a generalized dislocated metric, and properties of this topology are established.
3) Some fixed point theorems are proved for self-maps on generalized dislocated metric spaces that satisfy contractive conditions, including analogues of Banach's contraction
Some fixed point theorems in generalised dislocated metric spacesAlexander Decker
This document presents some fixed point theorems in generalized dislocated metric spaces. It introduces the notion of a generalized dislocated metric space and establishes its topological properties. It proves an analogue of Seghal's fixed point theorem for self-maps that satisfy contractive conditions in these spaces. This allows deriving generalized dislocated analogues of fixed point theorems of Banach, Kannan, Bianchini, and Reich. The document defines generalized dislocated metrics and establishes properties like uniqueness of limits. It shows the topology induced by such a metric satisfies Kuratowski's closure axioms.
Coincidence points for mappings under generalized contractionAlexander Decker
1. The document presents a theorem that establishes conditions for the existence of coincidence points between multi-valued and single-valued mappings.
2. It generalizes previous results by Feng and Liu (2004) and Liu et al. (2005) by relaxing the contraction conditions.
3. The main theorem proves that if mappings T and f satisfy generalized contraction conditions involving α and β functions, and the space is orbitally complete, then the mappings have a coincidence point.
Similar to IJERD (www.ijerd.com) International Journal of Engineering Research and Development IJERD : hard copy of journal, Call for Papers 2012, publishing of journal, journal of science and technology, research paper publishing, where to publish research paper, (20)
A Novel Method for Prevention of Bandwidth Distributed Denial of Service AttacksIJERD Editor
Distributed Denial of Service (DDoS) Attacks became a massive threat to the Internet. Traditional
Architecture of internet is vulnerable to the attacks like DDoS. Attacker primarily acquire his army of Zombies,
then that army will be instructed by the Attacker that when to start an attack and on whom the attack should be
done. In this paper, different techniques which are used to perform DDoS Attacks, Tools that were used to
perform Attacks and Countermeasures in order to detect the attackers and eliminate the Bandwidth Distributed
Denial of Service attacks (B-DDoS) are reviewed. DDoS Attacks were done by using various Flooding
techniques which are used in DDoS attack.
The main purpose of this paper is to design an architecture which can reduce the Bandwidth
Distributed Denial of service Attack and make the victim site or server available for the normal users by
eliminating the zombie machines. Our Primary focus of this paper is to dispute how normal machines are
turning into zombies (Bots), how attack is been initiated, DDoS attack procedure and how an organization can
save their server from being a DDoS victim. In order to present this we implemented a simulated environment
with Cisco switches, Routers, Firewall, some virtual machines and some Attack tools to display a real DDoS
attack. By using Time scheduling, Resource Limiting, System log, Access Control List and some Modular
policy Framework we stopped the attack and identified the Attacker (Bot) machines
Hearing loss is one of the most common human impairments. It is estimated that by year 2015 more
than 700 million people will suffer mild deafness. Most can be helped by hearing aid devices depending on the
severity of their hearing loss. This paper describes the implementation and characterization details of a dual
channel transmitter front end (TFE) for digital hearing aid (DHA) applications that use novel micro
electromechanical- systems (MEMS) audio transducers and ultra-low power-scalable analog-to-digital
converters (ADCs), which enable a very-low form factor, energy-efficient implementation for next-generation
DHA. The contribution of the design is the implementation of the dual channel MEMS microphones and powerscalable
ADC system.
Influence of tensile behaviour of slab on the structural Behaviour of shear c...IJERD Editor
-A composite beam is composed of a steel beam and a slab connected by means of shear connectors
like studs installed on the top flange of the steel beam to form a structure behaving monolithically. This study
analyzes the effects of the tensile behavior of the slab on the structural behavior of the shear connection like slip
stiffness and maximum shear force in composite beams subjected to hogging moment. The results show that the
shear studs located in the crack-concentration zones due to large hogging moments sustain significantly smaller
shear force and slip stiffness than the other zones. Moreover, the reduction of the slip stiffness in the shear
connection appears also to be closely related to the change in the tensile strain of rebar according to the increase
of the load. Further experimental and analytical studies shall be conducted considering variables such as the
reinforcement ratio and the arrangement of shear connectors to achieve efficient design of the shear connection
in composite beams subjected to hogging moment.
Gold prospecting using Remote Sensing ‘A case study of Sudan’IJERD Editor
Gold has been extracted from northeast Africa for more than 5000 years, and this may be the first
place where the metal was extracted. The Arabian-Nubian Shield (ANS) is an exposure of Precambrian
crystalline rocks on the flanks of the Red Sea. The crystalline rocks are mostly Neoproterozoic in age. ANS
includes the nations of Israel, Jordan. Egypt, Saudi Arabia, Sudan, Eritrea, Ethiopia, Yemen, and Somalia.
Arabian Nubian Shield Consists of juvenile continental crest that formed between 900 550 Ma, when intra
oceanic arc welded together along ophiolite decorated arc. Primary Au mineralization probably developed in
association with the growth of intra oceanic arc and evolution of back arc. Multiple episodes of deformation
have obscured the primary metallogenic setting, but at least some of the deposits preserve evidence that they
originate as sea floor massive sulphide deposits.
The Red Sea Hills Region is a vast span of rugged, harsh and inhospitable sector of the Earth with
inimical moon-like terrain, nevertheless since ancient times it is famed to be an abode of gold and was a major
source of wealth for the Pharaohs of ancient Egypt. The Pharaohs old workings have been periodically
rediscovered through time. Recent endeavours by the Geological Research Authority of Sudan led to the
discovery of a score of occurrences with gold and massive sulphide mineralizations. In the nineties of the
previous century the Geological Research Authority of Sudan (GRAS) in cooperation with BRGM utilized
satellite data of Landsat TM using spectral ratio technique to map possible mineralized zones in the Red Sea
Hills of Sudan. The outcome of the study mapped a gossan type gold mineralization. Band ratio technique was
applied to Arbaat area and a signature of alteration zone was detected. The alteration zones are commonly
associated with mineralization. The alteration zones are commonly associated with mineralization. A filed check
confirmed the existence of stock work of gold bearing quartz in the alteration zone. Another type of gold
mineralization that was discovered using remote sensing is the gold associated with metachert in the Atmur
Desert.
Reducing Corrosion Rate by Welding DesignIJERD Editor
This document summarizes a study on reducing corrosion rates in steel through welding design. The researchers tested different welding groove designs (X, V, 1/2X, 1/2V) and preheating temperatures (400°C, 500°C, 600°C) on ferritic malleable iron samples. Testing found that X and V groove designs with 500°C and 600°C preheating had corrosion rates of 0.5-0.69% weight loss after 14 days, compared to 0.57-0.76% for 400°C preheating. Higher preheating reduced residual stresses which decreased corrosion. Residual stresses were 1.7 MPa for optimal X groove and 600°C
Router 1X3 – RTL Design and VerificationIJERD Editor
Routing is the process of moving a packet of data from source to destination and enables messages
to pass from one computer to another and eventually reach the target machine. A router is a networking device
that forwards data packets between computer networks. It is connected to two or more data lines from different
networks (as opposed to a network switch, which connects data lines from one single network). This paper,
mainly emphasizes upon the study of router device, it‟s top level architecture, and how various sub-modules of
router i.e. Register, FIFO, FSM and Synchronizer are synthesized, and simulated and finally connected to its top
module.
Active Power Exchange in Distributed Power-Flow Controller (DPFC) At Third Ha...IJERD Editor
This paper presents a component within the flexible ac-transmission system (FACTS) family, called
distributed power-flow controller (DPFC). The DPFC is derived from the unified power-flow controller (UPFC)
with an eliminated common dc link. The DPFC has the same control capabilities as the UPFC, which comprise
the adjustment of the line impedance, the transmission angle, and the bus voltage. The active power exchange
between the shunt and series converters, which is through the common dc link in the UPFC, is now through the
transmission lines at the third-harmonic frequency. DPFC multiple small-size single-phase converters which
reduces the cost of equipment, no voltage isolation between phases, increases redundancy and there by
reliability increases. The principle and analysis of the DPFC are presented in this paper and the corresponding
simulation results that are carried out on a scaled prototype are also shown.
Mitigation of Voltage Sag/Swell with Fuzzy Control Reduced Rating DVRIJERD Editor
Power quality has been an issue that is becoming increasingly pivotal in industrial electricity
consumers point of view in recent times. Modern industries employ Sensitive power electronic equipments,
control devices and non-linear loads as part of automated processes to increase energy efficiency and
productivity. Voltage disturbances are the most common power quality problem due to this the use of a large
numbers of sophisticated and sensitive electronic equipment in industrial systems is increased. This paper
discusses the design and simulation of dynamic voltage restorer for improvement of power quality and
reduce the harmonics distortion of sensitive loads. Power quality problem is occurring at non-standard
voltage, current and frequency. Electronic devices are very sensitive loads. In power system voltage sag,
swell, flicker and harmonics are some of the problem to the sensitive load. The compensation capability
of a DVR depends primarily on the maximum voltage injection ability and the amount of stored
energy available within the restorer. This device is connected in series with the distribution feeder at
medium voltage. A fuzzy logic control is used to produce the gate pulses for control circuit of DVR and the
circuit is simulated by using MATLAB/SIMULINK software.
Study on the Fused Deposition Modelling In Additive ManufacturingIJERD Editor
Additive manufacturing process, also popularly known as 3-D printing, is a process where a product
is created in a succession of layers. It is based on a novel materials incremental manufacturing philosophy.
Unlike conventional manufacturing processes where material is removed from a given work price to derive the
final shape of a product, 3-D printing develops the product from scratch thus obviating the necessity to cut away
materials. This prevents wastage of raw materials. Commonly used raw materials for the process are ABS
plastic, PLA and nylon. Recently the use of gold, bronze and wood has also been implemented. The complexity
factor of this process is 0% as in any object of any shape and size can be manufactured.
Spyware triggering system by particular string valueIJERD Editor
This computer programme can be used for good and bad purpose in hacking or in any general
purpose. We can say it is next step for hacking techniques such as keylogger and spyware. Once in this system if
user or hacker store particular string as a input after that software continually compare typing activity of user
with that stored string and if it is match then launch spyware programme.
A Blind Steganalysis on JPEG Gray Level Image Based on Statistical Features a...IJERD Editor
This paper presents a blind steganalysis technique to effectively attack the JPEG steganographic
schemes i.e. Jsteg, F5, Outguess and DWT Based. The proposed method exploits the correlations between
block-DCTcoefficients from intra-block and inter-block relation and the statistical moments of characteristic
functions of the test image is selected as features. The features are extracted from the BDCT JPEG 2-array.
Support Vector Machine with cross-validation is implemented for the classification.The proposed scheme gives
improved outcome in attacking.
Secure Image Transmission for Cloud Storage System Using Hybrid SchemeIJERD Editor
- Data over the cloud is transferred or transmitted between servers and users. Privacy of that
data is very important as it belongs to personal information. If data get hacked by the hacker, can be
used to defame a person’s social data. Sometimes delay are held during data transmission. i.e. Mobile
communication, bandwidth is low. Hence compression algorithms are proposed for fast and efficient
transmission, encryption is used for security purposes and blurring is used by providing additional
layers of security. These algorithms are hybridized for having a robust and efficient security and
transmission over cloud storage system.
Application of Buckley-Leverett Equation in Modeling the Radius of Invasion i...IJERD Editor
A thorough review of existing literature indicates that the Buckley-Leverett equation only analyzes
waterflood practices directly without any adjustments on real reservoir scenarios. By doing so, quite a number
of errors are introduced into these analyses. Also, for most waterflood scenarios, a radial investigation is more
appropriate than a simplified linear system. This study investigates the adoption of the Buckley-Leverett
equation to estimate the radius invasion of the displacing fluid during waterflooding. The model is also adopted
for a Microbial flood and a comparative analysis is conducted for both waterflooding and microbial flooding.
Results shown from the analysis doesn’t only records a success in determining the radial distance of the leading
edge of water during the flooding process, but also gives a clearer understanding of the applicability of
microbes to enhance oil production through in-situ production of bio-products like bio surfactans, biogenic
gases, bio acids etc.
Gesture Gaming on the World Wide Web Using an Ordinary Web CameraIJERD Editor
- Gesture gaming is a method by which users having a laptop/pc/x-box play games using natural or
bodily gestures. This paper presents a way of playing free flash games on the internet using an ordinary webcam
with the help of open source technologies. Emphasis in human activity recognition is given on the pose
estimation and the consistency in the pose of the player. These are estimated with the help of an ordinary web
camera having different resolutions from VGA to 20mps. Our work involved giving a 10 second documentary to
the user on how to play a particular game using gestures and what are the various kinds of gestures that can be
performed in front of the system. The initial inputs of the RGB values for the gesture component is obtained by
instructing the user to place his component in a red box in about 10 seconds after the short documentary before
the game is finished. Later the system opens the concerned game on the internet on popular flash game sites like
miniclip, games arcade, GameStop etc and loads the game clicking at various places and brings the state to a
place where the user is to perform only gestures to start playing the game. At any point of time the user can call
off the game by hitting the esc key and the program will release all of the controls and return to the desktop. It
was noted that the results obtained using an ordinary webcam matched that of the Kinect and the users could
relive the gaming experience of the free flash games on the net. Therefore effective in game advertising could
also be achieved thus resulting in a disruptive growth to the advertising firms.
Hardware Analysis of Resonant Frequency Converter Using Isolated Circuits And...IJERD Editor
-LLC resonant frequency converter is basically a combo of series as well as parallel resonant ckt. For
LCC resonant converter it is associated with a disadvantage that, though it has two resonant frequencies, the
lower resonant frequency is in ZCS region[5]. For this application, we are not able to design the converter
working at this resonant frequency. LLC resonant converter existed for a very long time but because of
unknown characteristic of this converter it was used as a series resonant converter with basically a passive
(resistive) load. . Here, it was designed to operate in switching frequency higher than resonant frequency of the
series resonant tank of Lr and Cr converter acts very similar to Series Resonant Converter. The benefit of LLC
resonant converter is narrow switching frequency range with light load[6] . Basically, the control ckt plays a
very imp. role and hence 555 Timer used here provides a perfect square wave as the control ckt provides no
slew rate which makes the square wave really strong and impenetrable. The dead band circuit provides the
exclusive dead band in micro seconds so as to avoid the simultaneous firing of two pairs of IGBT’s where one
pair switches off and the other on for a slightest period of time. Hence, the isolator ckt here is associated with
each and every ckt used because it acts as a driver and an isolation to each of the IGBT is provided with one
exclusive transformer supply[3]. The IGBT’s are fired using the appropriate signal using the previous boards
and hence at last a high frequency rectifier ckt with a filtering capacitor is used to get an exact dc
waveform .The basic goal of this particular analysis is to observe the wave forms and characteristics of
converters with differently positioned passive elements in the form of tank circuits.
Simulated Analysis of Resonant Frequency Converter Using Different Tank Circu...IJERD Editor
LLC resonant frequency converter is basically a combo of series as well as parallel resonant ckt. For
LCC resonant converter it is associated with a disadvantage that, though it has two resonant frequencies, the
lower resonant frequency is in ZCS region [5]. For this application, we are not able to design the converter
working at this resonant frequency. LLC resonant converter existed for a very long time but because of
unknown characteristic of this converter it was used as a series resonant converter with basically a passive
(resistive) load. . Here, it was designed to operate in switching frequency higher than resonant frequency of the
series resonant tank of Lr and Cr converter acts very similar to Series Resonant Converter. The benefit of LLC
resonant converter is narrow switching frequency range with light load[6] . Basically, the control ckt plays a
very imp. role and hence 555 Timer used here provides a perfect square wave as the control ckt provides no
slew rate which makes the square wave really strong and impenetrable. The dead band circuit provides the
exclusive dead band in micro seconds so as to avoid the simultaneous firing of two pairs of IGBT’s where one
pair switches off and the other on for a slightest period of time. Hence, the isolator ckt here is associated with
each and every ckt used because it acts as a driver and an isolation to each of the IGBT is provided with one
exclusive transformer supply[3]. The IGBT’s are fired using the appropriate signal using the previous boards
and hence at last a high frequency rectifier ckt with a filtering capacitor is used to get an exact dc
waveform .The basic goal of this particular analysis is to observe the wave forms and characteristics of
converters with differently positioned passive elements in the form of tank circuits. The supported simulation
is done through PSIM 6.0 software tool
Amateurs Radio operator, also known as HAM communicates with other HAMs through Radio
waves. Wireless communication in which Moon is used as natural satellite is called Moon-bounce or EME
(Earth -Moon-Earth) technique. Long distance communication (DXing) using Very High Frequency (VHF)
operated amateur HAM radio was difficult. Even with the modest setup having good transceiver, power
amplifier and high gain antenna with high directivity, VHF DXing is possible. Generally 2X11 YAGI antenna
along with rotor to set horizontal and vertical angle is used. Moon tracking software gives exact location,
visibility of Moon at both the stations and other vital data to acquire real time position of moon.
“MS-Extractor: An Innovative Approach to Extract Microsatellites on „Y‟ Chrom...IJERD Editor
Simple Sequence Repeats (SSR), also known as Microsatellites, have been extensively used as
molecular markers due to their abundance and high degree of polymorphism. The nucleotide sequences of
polymorphic forms of the same gene should be 99.9% identical. So, Microsatellites extraction from the Gene is
crucial. However, Microsatellites repeat count is compared, if they differ largely, he has some disorder. The Y
chromosome likely contains 50 to 60 genes that provide instructions for making proteins. Because only males
have the Y chromosome, the genes on this chromosome tend to be involved in male sex determination and
development. Several Microsatellite Extractors exist and they fail to extract microsatellites on large data sets of
giga bytes and tera bytes in size. The proposed tool “MS-Extractor: An Innovative Approach to extract
Microsatellites on „Y‟ Chromosome” can extract both Perfect as well as Imperfect Microsatellites from large
data sets of human genome „Y‟. The proposed system uses string matching with sliding window approach to
locate Microsatellites and extracts them.
Importance of Measurements in Smart GridIJERD Editor
- The need to get reliable supply, independence from fossil fuels, and capability to provide clean
energy at a fixed and lower cost, the existing power grid structure is transforming into Smart Grid. The
development of a smart energy distribution grid is a current goal of many nations. A Smart Grid should have
new capabilities such as self-healing, high reliability, energy management, and real-time pricing. This new era
of smart future grid will lead to major changes in existing technologies at generation, transmission and
distribution levels. The incorporation of renewable energy resources and distribution generators in the existing
grid will increase the complexity, optimization problems and instability of the system. This will lead to a
paradigm shift in the instrumentation and control requirements for Smart Grids for high quality, stable and
reliable electricity supply of power. The monitoring of the grid system state and stability relies on the
availability of reliable measurement of data. In this paper the measurement areas that highlight new
measurement challenges, development of the Smart Meters and the critical parameters of electric energy to be
monitored for improving the reliability of power systems has been discussed.
Study of Macro level Properties of SCC using GGBS and Lime stone powderIJERD Editor
The document summarizes a study on the use of ground granulated blast furnace slag (GGBS) and limestone powder to replace cement in self-compacting concrete (SCC). Tests were conducted on SCC mixes with 0-50% replacement of cement with GGBS and 0-20% replacement with limestone powder. The results showed that replacing 30% of cement with GGBS and 15% with limestone powder produced SCC with the highest compressive strength of 46MPa, meeting fresh property requirements. The study concluded that this ternary blend of cement, GGBS and limestone powder can improve SCC properties while reducing costs.
Have you ever been confused by the myriad of choices offered by AWS for hosting a website or an API?
Lambda, Elastic Beanstalk, Lightsail, Amplify, S3 (and more!) can each host websites + APIs. But which one should we choose?
Which one is cheapest? Which one is fastest? Which one will scale to meet our needs?
Join me in this session as we dive into each AWS hosting service to determine which one is best for your scenario and explain why!
Best 20 SEO Techniques To Improve Website Visibility In SERPPixlogix Infotech
Boost your website's visibility with proven SEO techniques! Our latest blog dives into essential strategies to enhance your online presence, increase traffic, and rank higher on search engines. From keyword optimization to quality content creation, learn how to make your site stand out in the crowded digital landscape. Discover actionable tips and expert insights to elevate your SEO game.
Skybuffer AI: Advanced Conversational and Generative AI Solution on SAP Busin...Tatiana Kojar
Skybuffer AI, built on the robust SAP Business Technology Platform (SAP BTP), is the latest and most advanced version of our AI development, reaffirming our commitment to delivering top-tier AI solutions. Skybuffer AI harnesses all the innovative capabilities of the SAP BTP in the AI domain, from Conversational AI to cutting-edge Generative AI and Retrieval-Augmented Generation (RAG). It also helps SAP customers safeguard their investments into SAP Conversational AI and ensure a seamless, one-click transition to SAP Business AI.
With Skybuffer AI, various AI models can be integrated into a single communication channel such as Microsoft Teams. This integration empowers business users with insights drawn from SAP backend systems, enterprise documents, and the expansive knowledge of Generative AI. And the best part of it is that it is all managed through our intuitive no-code Action Server interface, requiring no extensive coding knowledge and making the advanced AI accessible to more users.
Building Production Ready Search Pipelines with Spark and MilvusZilliz
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HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
Digital Marketing Trends in 2024 | Guide for Staying AheadWask
https://www.wask.co/ebooks/digital-marketing-trends-in-2024
Feeling lost in the digital marketing whirlwind of 2024? Technology is changing, consumer habits are evolving, and staying ahead of the curve feels like a never-ending pursuit. This e-book is your compass. Dive into actionable insights to handle the complexities of modern marketing. From hyper-personalization to the power of user-generated content, learn how to build long-term relationships with your audience and unlock the secrets to success in the ever-shifting digital landscape.
Ivanti’s Patch Tuesday breakdown goes beyond patching your applications and brings you the intelligence and guidance needed to prioritize where to focus your attention first. Catch early analysis on our Ivanti blog, then join industry expert Chris Goettl for the Patch Tuesday Webinar Event. There we’ll do a deep dive into each of the bulletins and give guidance on the risks associated with the newly-identified vulnerabilities.
TrustArc Webinar - 2024 Global Privacy SurveyTrustArc
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In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
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- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
GraphRAG for Life Science to increase LLM accuracyTomaz Bratanic
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Your One-Stop Shop for Python Success: Top 10 US Python Development Providersakankshawande
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Generating privacy-protected synthetic data using Secludy and MilvusZilliz
During this demo, the founders of Secludy will demonstrate how their system utilizes Milvus to store and manipulate embeddings for generating privacy-protected synthetic data. Their approach not only maintains the confidentiality of the original data but also enhances the utility and scalability of LLMs under privacy constraints. Attendees, including machine learning engineers, data scientists, and data managers, will witness first-hand how Secludy's integration with Milvus empowers organizations to harness the power of LLMs securely and efficiently.
Ocean lotus Threat actors project by John Sitima 2024 (1).pptxSitimaJohn
Ocean Lotus cyber threat actors represent a sophisticated, persistent, and politically motivated group that poses a significant risk to organizations and individuals in the Southeast Asian region. Their continuous evolution and adaptability underscore the need for robust cybersecurity measures and international cooperation to identify and mitigate the threats posed by such advanced persistent threat groups.
Ocean lotus Threat actors project by John Sitima 2024 (1).pptx
IJERD (www.ijerd.com) International Journal of Engineering Research and Development IJERD : hard copy of journal, Call for Papers 2012, publishing of journal, journal of science and technology, research paper publishing, where to publish research paper,
1. International Journal of Engineering Research and Development
e-ISSN: 2278-067X, p-ISSN: 2278-800X, www.ijerd.com
Volume 3, Issue 2 (August 2012), PP. 35-40
Fixed Point Theorems for Mappings under General Contractive
Condition of Integral Type
Shailesh T. Patel, Sunil Garg, Dr.Ramakant Bhardwaj,
The student of Singhania University
Senior Scientist,MPCST Bhopal
Truba Institute of Engineering & Information Technology,Bhopal(M.P.)
Abstract––In the present paper, we establish a fixed point theorem for a mapping and a common fixed point theorem for
a pair of mappings for rational expression. The mapping involved here generalizes various type of contractive mappings
in integral setting.
Keywords––Fixed point, Common Fixed point, complete metric space, Continuous Mapping, Compatible Mapping
I. INTRODUCTION AND PRELIMINARIES
Impact of fixed point theory in different branches of mathematics and its applications is immense.The first important result
on fixed point for contractive type mapping was the much celebrated Banach’s contraction principle by S.Banach [1] in
1922. In the general setting of complete metric space,this theorem runs as follows(see Theorem 2.1,[4] or,Theorem
1.2.2,[10]) In the present paper we will find some fixed point and common fixed point theorems for rational expression,
which will satisfy the well known results. I have developed new result in above theorem with rational expression, by using
R.Bhardwaj,Some common fixed point theorem in Metric space using integral type mappings[12].
Theorem 1.1 (Banach’s contraction principal)
Let (X,d) be a complete matric space,cє(0,1) and f:X→X be a mapping such that for each x,yєX,
d(fx,fy) ≤ c d(x,y) …………………(1.1)
then f has a unique fixed point aєX,such that for each xєX, lim f n x a.
n
after this classical result , Kannaan [5] gave a substantially new contractive mapping to prove fixed point theorem.Since then
a number of mathematicians have been working on fixed point theory dealing with mappings satisfying various type of
contractive conditions(see[3],[5],[7],[8],[9] and [11] for details).
In 2002,A.Branciari [2] analyzed the existence of fixed point for mapping f defined on a complete matric space (X,d)
satisfying a general contractive condition of integral type.
Theorem 1.2 (Branciari)
Let (X,d) be a complete matric space,cє(0,1) and f:X→X be a mapping such that for each x,yєX,
d ( fx , fy ) d ( x, y )
(t )dt c (t )dt
0 0
…………………(1.2)
Where :[0,+∞)→[0,+∞) is a Lesbesgue-integrable mapping which is summable(i.e.with finite integral) on each compact
subset of [0,+∞),nonnegative,and such that for each є>0, (t )dt ,then f has a unique fixed point aєX,such that for each
0
xєX, lim f x a.
n
n
After the paper of Branciari, a lot of research works have been carried out on generalizing contractive conditions of integral
type for different contractive mappings satisfying various known prpperties. A fine work has been done by Rhoades [6]
extending the result of Branciari by replacing the condition (1.2) by the following
[ d ( x , fy ) d ( y , fx )]
max{d ( x , y ),d ( x , fx ),d ( y , fy ), }
d ( fx , fy ) 2
(t )dt c
0
(t )dt
0
………………(1.3)
The aim of this paper is to generalize some mixed type of contractive conditions to the mapping and then a pair of mappings
satisfying a general contractive condition of integral type,which includes several known contractive mappings such as
Kannan type [5],Chatterjea type [3],Zamfirescu type [11],etc.
35
2. Fixed Point Theorems for Mappings under General Contractive Condition of Integral Type
II. MAIN RESULTS
Let f beaself mapping of a complete matric space (x,d) satisfying the following condition:
d ( fx , fy ) [ d ( x , fx ) d ( y , fy )] d ( x, y ) max{d ( x , fy ),d ( y , fx )}
(t )dt
0
(t )dt (t )dt
0 0
(t )dt
0
d ( x , fy ) d ( y , fx ) d ( x , fx )
1 d ( x , fy ).d ( y , fx ).d ( x , fx )
(t )dt
0
……………….(2.1)
For each x,yєX with non-negative reals , , , , such that 0< 2 2 3 <1,
where : R R is a Lesbesgue-integrable mapping which is summable(i.e.with finite integral) on each compact
(t )dt …………….(2.2)
subset of R ,nonnegative,and such that for each є>0,
0
Then f has a unique fixed point zєX,such that for each xєX, lim f n x z.
n
Proof: Let x0єX and, for brevity,definexn=fxn-1.For each integer n≥1,from (2.1) we get,
d ( Xn, Xn1) d ( fXn 1, fXn )
(t )dt
0
(t )dt
0
[ d ( Xn1, Xn ) d ( Xn, Xn 1)] d ( Xn1, Xn ) max{d ( Xn1, Xn1),d ( Xn, Xn )}
(t )dt
0
(t )dt
0
(t )dt
0
d ( Xn 1, Xn1) d ( Xn, Xn ) d ( Xn 1, Xn )
1 d ( Xn 1, Xn 1).d ( Xn, Xn ).d ( Xn 1, Xn )
(t )dt
0
[ d ( Xn1, Xn ) d ( Xn, Xn 1)] d ( Xn1, Xn ) d ( Xn1, Xn1)
(t )dt
0
(t )dt
0
(t )dt
0
d ( Xn1, Xn1) d ( Xn1, Xn )
(t )dt
0
d ( Xn1, Xn ) d ( Xn, Xn1)
( 2 ) (t )dt ( ) (t )dt
0 0
Which implies that
d ( Xn, Xn1) d ( Xn1, Xn )
(t )dt ( (t )dt
2
1 )
0 0
d ( Xn, Xn1) d ( Xn1, Xn)
(t )dt h (t )dt
2
And so, where h= 1
<1 …………..(2.3)
0 0
Thus by routine calculation,
d ( Xn, Xn 1) d ( X 0 , X1 )
(t )dt h (t )dt
n
0 0 ……………(2.4)
d ( Xn, Xn1)
Taking limit of (2.4) as n→∞, we get lim
n (t )dt 0
o
Which,from (2.2) implies that lim d ( Xn, Xn 1) 0 ……………(2.5)
n
36
3. Fixed Point Theorems for Mappings under General Contractive Condition of Integral Type
We now show that {Xn} is a Cauchy sequence. Suppose that it is not. Then there exists an ϵ˃0 and subsequences {m(p)} and
{n(p)} such that m(p)˂n(p)˂m(p+1) with
d(Xm(p),Xn(P))≥є, d(Xm(p),Xn(P)-1)<є ……………(2.6)
d(Xm(p)-1,Xn(P)-1)≤ d(Xm(p)-1,Xm(P))+ d(Xm(p),Xn(P)-1)
<d(Xm(p)-1,Xm(P))+є …………..(2.7)
d ( Xm ( p ) 1,, Xn ( p ) 1)
Hence lim
p (t )dt (t)dt
o o ……………(2.8)
Using (2.3),(2.6) and (2.8) we get
d ( Xm( p ),, Xn( p )) d ( Xm( p ) 1,, Xn ( p ) 1)
(t)dt
o
(t )dt h
o
(t )dt h (t )dt
o o
Which is a contradiction, since hє(0,1). Therefore {Xn} is Cauchy, hence convergent. Call the limit z.
From (2.1) we get
d ( fz , Xn1) [ d ( z , fz ) d ( Xn, Xn1)] d ( z , Xn) max{d ( z , Xn1),d ( Xn, fz )}
(t )dt
o
(t )dt
0
(t )dt
0
(t )dt
0
d ( z , Xn1) d ( Xn, fz ) d ( z , fz )
1 d ( z , Xn1).d ( Xn, fz ).d ( z , fz )
(t )dt
0
Taking limit as n→∞, we get
d ( fz , z ) d ( z , fz )
(t )dt
o
( 2 ) (t )dt
0
As
d ( fz , z )
2 2 3 <1, (t )dt 0
o
Which, from (2.2), implies that d(fz,z)=0 or fz=z.
Next suppose that w (≠ z) be another fixed point of f. Then from (2.1) we have
d ( z , w) d ( fz , fw )
(t )dt
o
(t )dt
o
d ( z , w) [ d ( z , fz ) d ( w, fw )] d ( z , w) max{d ( z , fw ),d ( w, fz )}
(t )dt
o
(t )dt (t )dt
0 0
(t )dt
0
d ( z , fw ) d ( w, fz ) d ( z , fz )
1 d ( z , fw ).d ( w, fz ).d ( z , fz )
(t )dt
0
d ( z , w)
( 2 ) (t )dt
0
Since,
d ( z , w)
2 <1 this implies that, , (t )dt 0
o
Which from (2.2), implies that d(z,w)=0 or, z=w and so the fixed point is unique.
37
4. Fixed Point Theorems for Mappings under General Contractive Condition of Integral Type
Remark. On setting (t ) 1 over R+, the contractive condition of integral type transforms into a general contractive
condition not involving integrals.
Remark. From condition (2.1) of integraltype,several contractive mappings of integral type can be obtained.
1. 0 є(0, 1 ) gives Kannanof integral type.
2 and
2. 0 and (0, 1 ) gives Chatterjea [3] map of integral type.
2
Theorem 2.3. Let f and g be self mappings of a complete metric space (X,d) satisfying the following condition:
d ( fx , gy ) [ d ( x , fx ) d ( y , gy )] d ( x, y ) max{d ( x , gy ),d ( y , fx )}
(t )dt
o
(t )dt
0
(t )dt
0
(t )dt
0
d ( x , gy ) d ( y , fx ) d ( x , fx )
1 d ( x , gy ).d ( y , fx ).d ( x , fx )
(t )dt
0 ………………(2.9)
For each x,yєX with nonnegative reals , , , such that 2 2 3 <1, where :
R R is a Lesbesgue-integrable mapping which is summable(i.e.with finite integral) on each compact subset of R
,nonnegative,and such that for each є>0, (t )dt …………….(2.10)
0
Then f and g have a unique common fixed point zєX.
Proof. Let x0єX and, for brevity,define x2n+1=fx2n and x2n+2=gx2n+1. For each integer n≥0, from (2.9) we get,
d ( X 2 n 1, X 2 n 2 ) d ( fX 2 n , gX 2 n 1)
(t )dt
0
(t )dt
0
[ d ( X 2 n , X 2 n 1) d ( X 2 n 1, X 2 n 2 )] d ( X 2 n , X 2 n 1) max{d ( X 2 n , X 2 n 2 ),d ( X 2 n 1, X 2 n 1)}
(t )dt
0
(t )dt
0
(t )dt
0
d ( X 2 n , X 2 n 2 ) d ( X 2 n 1, X 2 n 1) d ( X 2 n , X 2 n 1)
1 d ( X 2 n , X 2 n 2 ).d ( X 2 n 1, X 2 n 1).d ( X 2 n , X 2 n 1)
(t )dt
0
d ( X 2 n , X 2 n 1) d ( X 2 n 1, X 2 n 2 )
( 2 ) (t )dt ( )
0
(t )dt
0
Which implies that
d ( X 2 n 1, X 2 n 2 ) d ( X 2 n , X 2 n 1)
(t )dt ( (t )dt
2
1 )
0 0
d ( X 2 n 1, X 2 n 2 ) d ( X 2 n , X 2 n 1)
(t )dt h (t )dt where
2
And so, h= 1
<1 ………….(2.11)
0 0
d ( X 2 n , X 2 n 1) d ( X 2 n 1, X 2 n )
Similarly (t )dt h (t )dt
0 0 ………….(2.12)
Thus in general, for all n=1,2,……………
d ( Xn, Xn1) d ( Xn1, Xn)
(t )dt h (t )dt
0 0 ………….(2.13)
38
5. Fixed Point Theorems for Mappings under General Contractive Condition of Integral Type
Thus by routine calculation, we have
d ( Xn, Xn 1) d ( X 0 , X1 )
(t )dt h (t )dt
n
0 0
d ( Xn, Xn1)
Taking limit as n→∞, we get lim
n (t )dt 0
o
Which,from (2.10) implies that lim d ( Xn, Xn 1) 0 ……………(2.14)
n
We now show that {Xn} is a Cauchy sequence. Suppose that it is not. Then there exists an є>0 and subsequences {2m(p)}
and {2n(p)} such that p<2m(p)<2n(p) with
d(X2m(p),X2n(P))≥є, d(X2m(p),X2n(P)-2)<є ……………(2.15)
Now
d(X2m(p),X2n(P))≤ d(X2m(p),X2n(P)-2)+ d(X2n(p)-2,X2n(P)-1)+ d(X2n(p)-1,X2n(P))
<є+d(X2n(p)-2,X2n(P)-1)+ d(X2n(p)-1,X2n(P)) ……………(2.16)
…………..(2.7)
d ( X 2 m ( p ), X 2 n ( p ))
Hence lim
p (t )dt (t)dt
o o ……………(2.17)
Then by (2.13) we get
d ( X 2 m ( p ),, X 2 n ( p )) d ( X 2 m ( p ) 1,, X 2 n ( p ) 1)
(t )dt h
o
(t )dt
o
d ( X 2 m ( p ) 1,, X 2 m ( p )) d ( X 2 m ( p ),, X 2 n ( p )) d ( X 2 n ( p ) 1, X 2 n ( p ))
h[ (t )dt
o
(t )dt
o
(t )dt ]
o
Taking limit as p→∞ we get
(t )dt h (t )dt
0 0
Which is a contradiction, since hє(0,1). Therefore {Xn} is Cauchy, hence convergent. Call the limit z.
From (2.9) we get
d ( fz , X 2 n 2 ) d ( fz , gX 2 n 1)
(t )dt
o
(t )dt
0
[ d ( z , fz ) d ( X 2 n 1, X 2 n 2 )] d ( z , X 2 n 1) max{d ( z , X 2 n 2 ),d ( X 2 n 1, fz )}
(t )dt
0
(t )dt
0
(t )dt
0
d ( z , X 2 n 2 ) d ( X 2 n 1, fz ) d ( z , fz )
1 d ( z , X 2 n 2 ).d ( X 2 n 1, fz ).d ( z , fz )
(t )dt
0
Taking limit as n→∞, we get
d ( fz , z ) d ( z , fz )
(t )dt
o
( 2 ) (t )dt
0
As
d ( fz , z )
2 2 3 <1, (t )dt 0
o
39
6. Fixed Point Theorems for Mappings under General Contractive Condition of Integral Type
Which, from (2.10), implies that d(fz,z)=0 or fz=z. Similarly it can be shown that gz=z. So f and g have a common fixed
point zєX. We now show that z is the unique common fixed point of f and g.Ifnot,then let
w (≠ z) be another fixed point of f and g. Then from (2.9) we have
d ( z , w) d ( fz , gw )
(t )dt (t )dt
o o
d ( z , w) [ d ( z , fz ) d ( w, gw)] d ( z , w) max{d ( z , gw),d ( w, fz )}
(t )dt
o
(t )dt (t )dt
0 0
(t )dt
0
d ( z , gw ) d ( w, fz ) d ( z , fz )
1 d ( z , gw ).d ( w, fz ).d ( z , fz )
(t )dt
0
d ( z , w)
( 2 ) (t )dt
0
Since,
d ( z , w)
2 <1 this implies that, , (t )dt 0
o
Which from (2.10), implies that d(z,w)=0 or, z=w and so the fixed point is unique.
ACKNOWLEDGMENTS
The authors would like to thank the referee for his comments that helped us improve this article.
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