Abstract In the present paper, we prove a global direct theorem for the modified Baskakovstancu operators in terms of Ditzian-Totik modulus of smoothness. Here, we have modified our operators by taking weight function of Beta operators and then generalizing it as stancu type generalized operators. We will also see that taking weight function of Beta operators will give better approximation. We study a global direct theorem using simultaneous approximation for ourstancu type generalized operator in 퐿푝 0,∞ . Here, first we estimate recurrence relation for moments and then develop some global direct results by making our stancu type generalized operators positive using differential and integral operators. In this paper, our effort is to give better global approximation for our stancu type generalized operator than the earlier integral modifications of Baskakov operators studied by various authors. Here, we will extend our results for the whole interval 0,∞ . In this paper, we will also make use of the fact that second modulus of smoothness introduced by Ditzian-Totik is equivalent to modified k-functional and 퐿푝푟[0,∞) is not contained in 퐿1푟[0,∞) for obtaining results. Here, Riesz-Thorin theorem and Leibnitz theorem is used extensively for doing simultaneous approximation. We have also used Fubini’s theorem for obtaining results. Key words: Stancu type generalization, simultaneous approximation, modulus of smoothness.
Backpropagation: Understanding How to Update ANNs Weights Step-by-StepAhmed Gad
This presentation explains how the backpropagation algorithm is useful in updating the artificial neural networks (ANNs) weights using two examples step by step. Readers should have a basic understanding of how ANNs work, partial derivatives, and multivariate chain rule.
This presentation won`t dive directly into the details of the algorithm but will start by training a very simple network. This is because the backpropagation algorithm is meant to be applied over a network after training. So, we should train the network before applying it to catch the benefits of backpropagation algorithm and how to use it.
On generating functions of biorthogonal polynomialseSAT Journals
Abstract In this paper, we have obtained some novel generating functions (both bilateral and mixed trilateral) involving modified bi-orthogonal polynomials 푌푛+푚훼+푛 푥;푘 , by group-theoretic method. As particular cases, we obtain the corresponding results on generalized Laguerre polynomials. Key words: AMS-2000 Classification Code :33C45,33C47, Biorthogonal polynomials, Laguerre polynomials, generating functions.
A Class of Polynomials Associated with Differential Operator and with a Gener...iosrjce
The object of this paper is to present several classes of linear and bilateral generating relations by
employing operational techniques, which reduces as a special case of (known or new) bilateral generating
relations.At last some of generating functions associated with stirling number of second kind are also discussed.
Jordan Higher (𝜎, 𝜏)-Centralizer on Prime RingIOSR Journals
Let 𝑅 be a ring and 𝜎, 𝜏 be an endomorphisms of 𝑅, in this paper we will present and study the
concepts of higher (𝜎, 𝜏)-centralizer, Jordan higher(𝜎, 𝜏)-centralizer and Jordan triple higher (𝜎, 𝜏)-
centralizer and their generalization on the ring. The main results are prove that every Jordan higher (𝜎, 𝜏)-
centralizer of prime ring 𝑅 is higher (𝜎, 𝜏)-centralizer of 𝑅 and we prove let 𝑅 be a 2-torsion free ring,𝜎 𝑎𝑛𝑑 𝜏
are commutative endomorphism then every Jordan higher (𝜎, 𝜏)-centralizer is Jordan triple higher (𝜎, 𝜏)-
centralizer.
On The Distribution of Non - Zero Zeros of Generalized Mittag – Leffler Funct...IJERA Editor
In this work, we derive some theorems involving distribution of non – zero zeros of generalized Mittag – Leffler functions of one and two variables. Mathematics Subject Classification 2010: Primary; 33E12. Secondary; 33C65, 26A33, 44A20
Backpropagation: Understanding How to Update ANNs Weights Step-by-StepAhmed Gad
This presentation explains how the backpropagation algorithm is useful in updating the artificial neural networks (ANNs) weights using two examples step by step. Readers should have a basic understanding of how ANNs work, partial derivatives, and multivariate chain rule.
This presentation won`t dive directly into the details of the algorithm but will start by training a very simple network. This is because the backpropagation algorithm is meant to be applied over a network after training. So, we should train the network before applying it to catch the benefits of backpropagation algorithm and how to use it.
On generating functions of biorthogonal polynomialseSAT Journals
Abstract In this paper, we have obtained some novel generating functions (both bilateral and mixed trilateral) involving modified bi-orthogonal polynomials 푌푛+푚훼+푛 푥;푘 , by group-theoretic method. As particular cases, we obtain the corresponding results on generalized Laguerre polynomials. Key words: AMS-2000 Classification Code :33C45,33C47, Biorthogonal polynomials, Laguerre polynomials, generating functions.
A Class of Polynomials Associated with Differential Operator and with a Gener...iosrjce
The object of this paper is to present several classes of linear and bilateral generating relations by
employing operational techniques, which reduces as a special case of (known or new) bilateral generating
relations.At last some of generating functions associated with stirling number of second kind are also discussed.
Jordan Higher (𝜎, 𝜏)-Centralizer on Prime RingIOSR Journals
Let 𝑅 be a ring and 𝜎, 𝜏 be an endomorphisms of 𝑅, in this paper we will present and study the
concepts of higher (𝜎, 𝜏)-centralizer, Jordan higher(𝜎, 𝜏)-centralizer and Jordan triple higher (𝜎, 𝜏)-
centralizer and their generalization on the ring. The main results are prove that every Jordan higher (𝜎, 𝜏)-
centralizer of prime ring 𝑅 is higher (𝜎, 𝜏)-centralizer of 𝑅 and we prove let 𝑅 be a 2-torsion free ring,𝜎 𝑎𝑛𝑑 𝜏
are commutative endomorphism then every Jordan higher (𝜎, 𝜏)-centralizer is Jordan triple higher (𝜎, 𝜏)-
centralizer.
On The Distribution of Non - Zero Zeros of Generalized Mittag – Leffler Funct...IJERA Editor
In this work, we derive some theorems involving distribution of non – zero zeros of generalized Mittag – Leffler functions of one and two variables. Mathematics Subject Classification 2010: Primary; 33E12. Secondary; 33C65, 26A33, 44A20
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, interval valued Pythagorean fuzzy bi-ideal, interval valued Pythagorean fuzzy interior ideal and homomorphism of an interval valued Pythagorean fuzzy ideal in semigroups with suitable illustration. We show that every interval valued Pythagorean fuzzy left (resp. right) ideal is an interval valued Pythagorean fuzzy bi-ideal.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
The finite difference method can be considered as a direct discretization of differential equations but in finite element methods, we generate difference equations by using approximate methods with piecewise polynomial solution. In this paper, we use the Galerkin method to obtain the approximate solution of a boundary value problem. The convergence analysis of these solution are also considered.
Exact Solutions of the Klein-Gordon Equation for the Q-Deformed Morse Potenti...ijrap
In this work, we solve the Klein-Gordon (KG) equation for the general deformed Morse potential with
equal scalar and vector potentials by using the Nikiforov-Uvarov (NU) method, which is based on the
solutions of general second-order linear differential equation with special functions. The energy
eigenvalues and corresponding normalized eigenfunctions are obtained. It is found that the eigenfunctions
can be expressed by the Laguerre polynomials. Our solutions have a good agreement with earlier study.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A System of Estimators of the Population Mean under Two-Phase Sampling in Pre...Premier Publishers
This paper deals with estimation of the population mean under two-phase sampling. Utilizing information on two-auxiliary variables, a system of estimators for estimating the finite population mean is proposed and its properties, up to the first order of approximation, are studied. As particular cases various estimators are suggested. The performance of suggested estimators is compared with some contemporary estimators of the population mean through numerical illustrations carried over the data set of some natural populations. Also, a small-scale Monte Carlo simulation is carried out for the empirical comparison.
Stability analysis for nonlinear impulsive optimal control problemsAI Publications
We consider the generic stability of optimal control problems governed by nonlinear impulsive evolution equations. Under perturbations of the right-hand side functions of the controlled system, the results of stability for the impulsive optimal control problems are proved given set-valued theory.
A machine learning method for efficient design optimization in nano-optics JCMwave
The slideshow contains a brief explanation of Gaussian process regression and Bayesian optimization. For two optimization problems, benchmarks against other local gradient-based and global heuristic optimization methods are included. They show, that Bayesian optimization can identify better designs in exceptionally short computation times.
A novel dual point clamper for low-rigidity plate milling with deformation co...eSAT Journals
Abstract
The surface profile accuracy plays a significant role in achieving the overall product’s functional performance, which is seriously impacted by the cutting forces, clamping forces, and residual stresses. Conventionally, many researches about deformation compensation focus on cutting forces and fixture layout and do not consider clamping forces. Actually, clamping forces, which would dynamically change along with the movements of cutting tools, are essential in precision machining process. In this paper, a novel dual-point clamper method with adaptive deformation compensation is proposed to improve the workpieces milling precision. Based on the Generalized Principle of Superposition Method, a mathematical model considering the deflection from both cutting forces and clamping forces has been estimated and compared with the traditional clamping scheme. Both 3D finite element model (FEM) based simulation experiments and experimental case studies are carried out, and their results show good agreement with each other. The deflection computation and prediction from numerical studies indicates the efficiency and correctness of the proposed approach.
Keywords: Compensation; Deformation; Fixture; Milling
Economy and forecast for 2020 3 key trends in the futureeSAT Journals
Abstract The article deals with 3 key trends in the future and their general implications including 3D, RFID, Business Intelligence and new managerial positions. 3D by 2020 could replace conventional mass-production. The basic trends in the RFID aplications will be: RFID Wearables,RFID On Merchandise, Host Card Emulation (HCE) Payment Solutions,Printed RFID Technology, RFID chip tracking everyone everywhere in the near future. Business intelligence will be transformed to the general intelligence.The contribution covers the the following topics: selected Aspects of economy and social Aspects of Information Systems, complex technological and human Issues in today’s globalized and interconnected World and presents new results in the diffused way. Key words: 3 Key trends, 3D, RFID, Business Intelligence, Computer Feudal Monarchy, New Managerial Positions JEL Classification: A10, A11, A19, E27, E69
Modeling of the damped oscillations of the viscous beams structures with swiv...eSAT Journals
Abstract
Mechanic studies realized on the two dimensional beams structures with swivel joints show that in statics, the vertical displacement is
continuous, but the rotation is discontinuous at the node where there is a swivel joint. Moreover, in dynamics, many authors do not
usually take into account the friction effect, modeling of these structures. We propose in this paper, a modeling of the beams structures
with swivel joints which integrates viscosity effects in dynamics. Hence this work we will present the formulation of motion equations
of such structures and the modal analysis method which is used to solve these equations.
Keywords: Beams, Swivel joint, Viscosity, Vibration, Modal Method.
Upgradation of low cost roughness measuring equipment and development of perf...eSAT Journals
Abstract
Today road and transport authorities around the world collectively spend large sums of money each year enhancing and maintaining their road networks. Road users in the majority of countries around the world continue to desire better and smoother roads, despite pressure on road authorities to further reduce expenditure. This pressure is brought about, because funding for road infrastructure is only one of the many priorities competing for Government funds. Pavements cannot be managed to the degree desired by decision makers, unless detailed accurate information and analysis supports the system. Road roughness data is considered one of the most important aspects of road condition information used in practice in pavement management systems.
At present in the market, we have various roughness measuring equipments starting from costliest equipment such as ARAN laser (which uses laser beam to measure the roughness) to moderately costly Bump integrator (which uses the bump counts made by the probe wheel), to cheaper equipment such as MERLIN (which uses the slope value of the wheel to calculate the roughness). In the present research work, an attempt is made to develop low cost roughness measuring equipment and to check its reliability and repeatability to minimize the calibration error. It is calibrated using Bump integrator.
Keywords: roughness, low cost equipment, calibration error
Research issues and priorities in the field of agriculture sector and dairy s...eSAT Journals
Abstract Indian Agriculture is an economic symbiosis of crop production and animal rearing. In India 70 percent population and their livelihood is depending upon the agriculture. Same scenario is applicable for Tripura as well as the same North East India. Agriculture is an important sector in the economy of the North East Region (NER), with its share in state domestic product (SDP) ranging from 19 percent to 37 percent in different states. In Tripura the total population of 70% population and their livelihood is dependents on the agriculture. The paper contributes to the effectual research is very necessary and their implacability to continued development process in agriculture at Tripura. On the other aspects is animal, husbandry which is really substitute occupation for agriculture. one is dependent on another. Animal Husbandry is a state subject and the State Governments are primarily responsible for the growth of the sector. The Department of Animal Husbandry, Dairying & Fisheries has, however, been operating 30 Central Livestock Organizations and allied Institutions for production and distribution of superior germ plasms to the State Governments for cross breeding and genetic upgradation of the stocks. Besides, the Department has been implementing 11 Central Sector and Centrally Sponsored Schemes for the development of requisite infrastructure and supplementing the efforts of the State Governments for achieving the accelerated growth of animal husbandry sector. The study mainly focuses the issues of problems ,present status of animal husbandry and agriculture sector in Tripura. Keyword: Animal Husbandry, crossbreed Cattle, Research Priorities, Sri (System Rice intensification) etc.
Analytical Solution Of Schrödinger Equation With Mie–Type Potential Using Fac...ijrap
we have obtained the analytical solution of Schrödinger wave equation with Mie – type potential
using factorization method. We have also obtained energy eigenvalues of our potential and the
corresponding wave function using an ansatz and then compare the result to standard Laguerre’s
differential equation. Under special cases our potential model reduces two well known potentials such as
Coulomb and the Kratzer Feus potentials.
In this paper, we define the new notion of interval-valued Pythagorean fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of interval valued Pythagorean fuzzy sub-semigroup, interval valued Pythagorean fuzzy left (resp. right) ideal, interval valued Pythagorean fuzzy bi-ideal, interval valued Pythagorean fuzzy interior ideal and homomorphism of an interval valued Pythagorean fuzzy ideal in semigroups with suitable illustration. We show that every interval valued Pythagorean fuzzy left (resp. right) ideal is an interval valued Pythagorean fuzzy bi-ideal.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
The finite difference method can be considered as a direct discretization of differential equations but in finite element methods, we generate difference equations by using approximate methods with piecewise polynomial solution. In this paper, we use the Galerkin method to obtain the approximate solution of a boundary value problem. The convergence analysis of these solution are also considered.
Exact Solutions of the Klein-Gordon Equation for the Q-Deformed Morse Potenti...ijrap
In this work, we solve the Klein-Gordon (KG) equation for the general deformed Morse potential with
equal scalar and vector potentials by using the Nikiforov-Uvarov (NU) method, which is based on the
solutions of general second-order linear differential equation with special functions. The energy
eigenvalues and corresponding normalized eigenfunctions are obtained. It is found that the eigenfunctions
can be expressed by the Laguerre polynomials. Our solutions have a good agreement with earlier study.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
A System of Estimators of the Population Mean under Two-Phase Sampling in Pre...Premier Publishers
This paper deals with estimation of the population mean under two-phase sampling. Utilizing information on two-auxiliary variables, a system of estimators for estimating the finite population mean is proposed and its properties, up to the first order of approximation, are studied. As particular cases various estimators are suggested. The performance of suggested estimators is compared with some contemporary estimators of the population mean through numerical illustrations carried over the data set of some natural populations. Also, a small-scale Monte Carlo simulation is carried out for the empirical comparison.
Stability analysis for nonlinear impulsive optimal control problemsAI Publications
We consider the generic stability of optimal control problems governed by nonlinear impulsive evolution equations. Under perturbations of the right-hand side functions of the controlled system, the results of stability for the impulsive optimal control problems are proved given set-valued theory.
A machine learning method for efficient design optimization in nano-optics JCMwave
The slideshow contains a brief explanation of Gaussian process regression and Bayesian optimization. For two optimization problems, benchmarks against other local gradient-based and global heuristic optimization methods are included. They show, that Bayesian optimization can identify better designs in exceptionally short computation times.
A novel dual point clamper for low-rigidity plate milling with deformation co...eSAT Journals
Abstract
The surface profile accuracy plays a significant role in achieving the overall product’s functional performance, which is seriously impacted by the cutting forces, clamping forces, and residual stresses. Conventionally, many researches about deformation compensation focus on cutting forces and fixture layout and do not consider clamping forces. Actually, clamping forces, which would dynamically change along with the movements of cutting tools, are essential in precision machining process. In this paper, a novel dual-point clamper method with adaptive deformation compensation is proposed to improve the workpieces milling precision. Based on the Generalized Principle of Superposition Method, a mathematical model considering the deflection from both cutting forces and clamping forces has been estimated and compared with the traditional clamping scheme. Both 3D finite element model (FEM) based simulation experiments and experimental case studies are carried out, and their results show good agreement with each other. The deflection computation and prediction from numerical studies indicates the efficiency and correctness of the proposed approach.
Keywords: Compensation; Deformation; Fixture; Milling
Economy and forecast for 2020 3 key trends in the futureeSAT Journals
Abstract The article deals with 3 key trends in the future and their general implications including 3D, RFID, Business Intelligence and new managerial positions. 3D by 2020 could replace conventional mass-production. The basic trends in the RFID aplications will be: RFID Wearables,RFID On Merchandise, Host Card Emulation (HCE) Payment Solutions,Printed RFID Technology, RFID chip tracking everyone everywhere in the near future. Business intelligence will be transformed to the general intelligence.The contribution covers the the following topics: selected Aspects of economy and social Aspects of Information Systems, complex technological and human Issues in today’s globalized and interconnected World and presents new results in the diffused way. Key words: 3 Key trends, 3D, RFID, Business Intelligence, Computer Feudal Monarchy, New Managerial Positions JEL Classification: A10, A11, A19, E27, E69
Modeling of the damped oscillations of the viscous beams structures with swiv...eSAT Journals
Abstract
Mechanic studies realized on the two dimensional beams structures with swivel joints show that in statics, the vertical displacement is
continuous, but the rotation is discontinuous at the node where there is a swivel joint. Moreover, in dynamics, many authors do not
usually take into account the friction effect, modeling of these structures. We propose in this paper, a modeling of the beams structures
with swivel joints which integrates viscosity effects in dynamics. Hence this work we will present the formulation of motion equations
of such structures and the modal analysis method which is used to solve these equations.
Keywords: Beams, Swivel joint, Viscosity, Vibration, Modal Method.
Upgradation of low cost roughness measuring equipment and development of perf...eSAT Journals
Abstract
Today road and transport authorities around the world collectively spend large sums of money each year enhancing and maintaining their road networks. Road users in the majority of countries around the world continue to desire better and smoother roads, despite pressure on road authorities to further reduce expenditure. This pressure is brought about, because funding for road infrastructure is only one of the many priorities competing for Government funds. Pavements cannot be managed to the degree desired by decision makers, unless detailed accurate information and analysis supports the system. Road roughness data is considered one of the most important aspects of road condition information used in practice in pavement management systems.
At present in the market, we have various roughness measuring equipments starting from costliest equipment such as ARAN laser (which uses laser beam to measure the roughness) to moderately costly Bump integrator (which uses the bump counts made by the probe wheel), to cheaper equipment such as MERLIN (which uses the slope value of the wheel to calculate the roughness). In the present research work, an attempt is made to develop low cost roughness measuring equipment and to check its reliability and repeatability to minimize the calibration error. It is calibrated using Bump integrator.
Keywords: roughness, low cost equipment, calibration error
Research issues and priorities in the field of agriculture sector and dairy s...eSAT Journals
Abstract Indian Agriculture is an economic symbiosis of crop production and animal rearing. In India 70 percent population and their livelihood is depending upon the agriculture. Same scenario is applicable for Tripura as well as the same North East India. Agriculture is an important sector in the economy of the North East Region (NER), with its share in state domestic product (SDP) ranging from 19 percent to 37 percent in different states. In Tripura the total population of 70% population and their livelihood is dependents on the agriculture. The paper contributes to the effectual research is very necessary and their implacability to continued development process in agriculture at Tripura. On the other aspects is animal, husbandry which is really substitute occupation for agriculture. one is dependent on another. Animal Husbandry is a state subject and the State Governments are primarily responsible for the growth of the sector. The Department of Animal Husbandry, Dairying & Fisheries has, however, been operating 30 Central Livestock Organizations and allied Institutions for production and distribution of superior germ plasms to the State Governments for cross breeding and genetic upgradation of the stocks. Besides, the Department has been implementing 11 Central Sector and Centrally Sponsored Schemes for the development of requisite infrastructure and supplementing the efforts of the State Governments for achieving the accelerated growth of animal husbandry sector. The study mainly focuses the issues of problems ,present status of animal husbandry and agriculture sector in Tripura. Keyword: Animal Husbandry, crossbreed Cattle, Research Priorities, Sri (System Rice intensification) etc.
Study on properties of concrete with different levels of replacement of cemen...eSAT Journals
Abstract Concrete is a widely used construction material which contains four major ingredients such as coarse aggregate, fine aggregate, cement and water. The consumption of concrete is increasing every year with the number of developmental activities in infrastructure sector. The production of cement involves high energy consumption. Hence, there is a need to reduce the consumption of cement in concrete by using other alternate materials which posses cementitious properties. Fly ash is one such material which can be used as a replacement to cement in concrete. The present study aims in observing the variation of strength of different grades of concrete with different levels of fly ash replacement. The objective of the study is to re-establish the findings of earlier research done in the area of fly ash concrete. The grades of concrete selected for the study are M20, M35 and M50. The fly ash replacements considered for the study are 0%, 20%, 35% and 50% of cement by weight. The results of this study indicates that for M20 and M35 grades of concrete, there is increase in strength with 35% cement replacement by fly ash. For M50 grade of concrete, there is decrease in strength for all replacement levels selected for the study. Keywords: Concrete, Cementitious material, Fly ash.
Object recognition from image using grid based color moments feature extracti...eSAT Journals
Abstract Image processing is a mechanism to convert an image into digital form and perform various operations on it, in order to get an enhanced image or to extract some useful information from it. In Image processing system, it treats images as two dimensional signals while applying number of image processing methods to them. This leads to an increasing number of generated digital images. Therefore it is required automatic systems to recognize the objects from the images. These systems may collect the number of features of a image and specification of image and consequently the different features of an object will identify the object from the image. Image processing is among rapidly growing technologies today, with its applications in various aspects of a business. Image Processing forms core research area within engineering and computer science disciplines too. Its most common and effective method is retrieve the textual features from various methods. But most of the methods do not yield the more accurate features form the image. So there is a requirement of an effective and efficient method for features extraction from the image. Moreover, images are rich in content, so some approaches are proposed based on various features derived directly from the content of the image: these are the grid-based-color-moments (GBCM) approaches. They allow users to search the desired object from image by specifying visual features (e.g., colour, texture and shape). Once the features have been defined and extracted, the retrieval becomes a task of measuring similarity between image features. In this paper, we have proposed a number of existing methods for GBCM applications. Keywords- object, grid-based-color-moments (gbcm), features, feature extraction, textual features, Image Processing, Digital form, Object Identification
Mitigation of harmonics using thyristor based 12 pulse voltage source pwm rec...eSAT Journals
Abstract Three-phase thyristor rectifiers have been used in industries for obtaining a variable dc voltage, but they have a problem of including large lower-order harmonics in the input currents. For high-power applications, a 12-pulse configuration is useful for reducing the harmonics, but it still includes the (12m ± 1) th (m: integer) harmonics. In order to further reduce the harmonics, this paper proposes to supply a ramp wave voltage at the input of a 12-pulse phase-controlled rectifier. Theoretical investigation to reduce harmonics is presented, and a strategy to control the regulated voltage and unity power factor at input side based on 12 pulse modulation technique. This paper discuss the impact of using 3-phase and 12-pulse rectifier circuit commonly found in unity power factor at input ac mains and regulate output voltage. The 12-pulse topology is known to be more expensive, but produce the least input current harmonics. However, the latter statement is completely true under balanced line conditions. In practice, the lines are inherently unbalanced. Hence, the question of whether the 12-pulse rectifier will indeed perform better in terms of the harmonics injected to the line is still under on-going discussions. This presents the modelling and simulation of both rectifier topologies to compare their input current and regulated output voltage harmonics. The rectifiers are modelled using the MATLAB/SIMULINK simulation model and several common cases conditions will be simulated to compare their harmonic levels. Keywords: Pulse Width Modulation (PWM), unity Power factor (UPF).
Abstract
This paper proposes a survey on the classification techniques of lung nodules. We have the different classifications about the nodules in the lungs. It contains the different methods of classification, segmentation and detection techniques. Malignant cell presented in the lungs named , nodules are classified for the treatment processes. Thresholding and Robust segmentation techniques are used in the segmentation process and the feature set is used for classification. Low Dose CT(Computed Tomography) images are applied. This survey has the information about the efficient techniques which are all used for the nodule classification. In these days lung cancer is the dangerous dead disease in the world, So we need to have the knowledge of that cancer. In starting stages the micro nodules are then formed into a cancer cell. Among the cancer affected population about 20% of the people are dead due to lung cancer. If nodules are found in a starting stage, we can be extend the lifetime of the patient. The main process of this paper involves with the nodule classification and segmentation process of the lung nodules. Here we taken the different procedures involved with nodule detections. CT is the most appropriate imaging technique to obtain anatomical information about lung nodules and the surrounding structures. Here we taken the Low Dose CT(LDCT) images for operations. This paper has the various approaches of the nodule classification. In this survey different techniques are presented which are used for detection and classification of the nodules in the lungs. By differentiating the nodules from the anatomical parts of the lungs, the nodules are identified.
Keywords: PLSA, Robust Segmentation and Partitioning.
Abstract The evolution in the technology of automobiles has reached its peak. One of the most innovative features is the invention of driver less car or an autonomous car. An autonomous car controls the motion, sensor activation and action automatically without any human intervention. Such vehicles ensure high degree of safety, comfort and ease of driving. The project aims at designing a system to be used in such autonomous cars. The project is to develop an automatic headlight beam intensity switcher. Such a system will sense the beam status of opposing vehicle and switch the beam intensity of headlight. A sensor based mechanism is utilized to develop the system. The beam intensity switcher plays a very important role while driving. During night time, when two vehicles approach each other in opposite direction the high intensity headlight creates an effect called “Troxler effect”. This effect creates a temporary blindness for some seconds thus resulting in unfortunate accidents. Thus, the high beam of both the vehicles must be switched to low so as to have a comfortable driving. The use of such a device in cars can prevent accidents at night time due to driver inattentiveness and provides an ease of driving. We have used the Arduino UNO board as our micro-controller and application specific sensors. In our project we have designed a device which is a combination of software and hardware coding. The sensor used is a light intensity sensor named BH1750 which has a wide range of sensing capacity. The light sensor takes the “lux ” reading of the headlight rays from the opposing vehicle and checks for a threshold value assigned in the coding. Based on the threshold value the beam switches from high to low state and vice-versa when both the vehicles pass by each other. The same process takes place in opposite vehicle too. This device can be implanted on the front part of the car at an appropriate position and angle. Keywords: automatic, low cost, accurate, headlight beam intensity switcher, Troxler effect, sensor based mechanism and lux readings.
Limnological studies related to physico chemical characteristics of shri shar...eSAT Journals
Abstract The present study deals with the seasonal limnological investigation related to physico-chemical characteristics of water of the Shri Sharanabasaveshwara Lake, Karnataka State. Besides temperature and meteorological data, 11 limnological parameters were tested following standard methods at 5 sampling sites/stations of the lake. The physico-chemical parameters (pH, DO, BOD, HCO3, TDS, Chloride, Nitrate, TH, Ca, Mg and SO4 etc.) showed distinct variation in the lake sites. Keywords: Limnology, Physico-chemical parameters, Shri Sharanabasaweshwara Lake
Test case prioritization using hyperlink ranking eSAT Journals
Abstract Era of cloud computing where majority of the application is becoming web based enterprise computing. User prefer online web application for easy of use and business continuity [1]. Software companies have come up in huge numbers for developing web based enterprise application. Testing is an integral part of any software company which requires more effort. Enterprise applications are complex and navigation is largely based on hyperlink connecting the web pages. Testing phase mostly associated with time constrain to accomplish the task associated in this phase. Main activity of testing phase is execution of test case to test the application. Exhaustive testing is not possible and release a software system without testing the entire application is risk [2]. This paper demonstrates how graph theory can be used to prioritize the test case execution. Keywords: Testing, Graph theory application
Structural sizing and shape optimisation of a load celleSAT Journals
Abstract This paper presents a structural application of a sizing and shape based on a reliability-related multi-factor optimisation. The application to a load cell design confirmed that this method is highly effective and efficient in terms of sizing and shape optimisation. A simple model of the S-type load cell is modelled in finite element analysis software and the systematic optimisation method is applied. Structural responses and geometrical sensitivities are analysed by a FE method, and reliability performance is calculated by a reliability loading-case index (RLI). The evaluation indices of performances and loading cases are formulated, and an overall performance index is presented to quantitatively evaluate a design. Index Terms: Multifactor optimisation, Finite element analysis, Load cell
Maximizing network capacity and reliable transmission in mimo cooperative net...eSAT Journals
Abstract Network capacity is an important factor to measure the performance of a network. Cooperative networking is a phenomenon which helps network to have significant gains in terms of transmission reliability and network capacity. Cooperating networking has been applied to multi-hop ad hoc networks. However, the existing works have two limitations. They support only single antenna model and three node relay scheme. The reason behind this limitation due to lack of complete understands of optimal power allocation structure Multiple Input and Multiple Output (MIMO) cooperative networks. Recently Liu et al. studied structural properties with respect to MIMO cooperative networks in presence of node power constraints. Each power allocation at source follows corresponding MIMO structure so as to ensure optimal power allocation. They establish relationship between cooperative relay and pure relay to quantify performance gain. In this paper we did experiments on this concept. Our simulations reveal that the proposed system for cooperative network is able to achieve both transmission reliability and network capacity. Keywords –Cooperative networking, MIMO, optimal power allocation, transmission reliability
Experimental investigation of performance and combustion characteristics on a...eSAT Journals
Abstract In this study, for the first time, a nanoceramic Al2O3 was used as a coating material in the low heat rejection engine concept. Experiments were conducted on single cylinder, four stroke, water cooled, and direct injection diesel engine. First, the engine was tested at different load conditions without coating. Then, combustion chamber surfaces cylinder head, cylinder liner, valves, and piston crown face were coated with nanoceramic material of Al2O3 using plasma spray method. Comparative evaluation on performance and combustion characteristics using diesel, multi-blend biodiesel and its blends was studied in the ceramic coated and uncoated engines under the same running conditions. An increase in engine power, brake thermal efficiency and a decrease in specific fuel consumption were observed in the ceramic coated engine compared to that of normal engine. Keywords: Multi-blend biodiesel, low heat rejection engine
Control analysis of a high frequency resonant inverter for induction cooking ...eSAT Journals
Abstract
Stability of three possible close-loop control of a series resonant inverter is studied for induction cooking application. Ultimately,
a single close-loop control technique is proposed in this work which can ensure both the power control as well as a satisfactory
zero voltage switching (ZVS) in a finite control range near the operating point. A phase shift controlled series resonant inverter is
used as a power supply for an induction cooking system. Its linearized model is developed for small signal analysis and a PID
controller is designed for the proposed close-loop control and its performances are judged under various operating conditions
using MATLAB/Simulink® platform.
Keywords: ZVS, linearization, bode plot, step response, PID control.
Voltage collapse mitigation by reactive power compensation at the load sideeSAT Journals
Abstract Power system stability may be defined as the property of a power system that enables it to remain in a state of operating equilibrium under normal operating conditions and to regain an acceptable state of equilibrium after being subjected to a disturbance. A general and formal definition is given below. The IEEE/CIGRE Joint Task Force has proposed the following definition-“Power system stability is the ability of an electric power system, for a given initial operating condition, to regain a state of operating equilibrium after being subjected to a physical disturbance, with most system variables bounded, so that practically the entire system remains intact.” The challenge faced in the modern power system is the collapse of voltages at heavy loads at the load buses of a power system. The voltage collapse will in turn will effect the stability of the power system. In this paper a novel way of mitigating the voltage collapse by supplying the reactive power at load buses is discussed and encouraging simulation results are obtained. The method employed is as fallows. Simulation is done without SVC and STATCOM at load buses. On comparison of the results at the load buses it is seen that with SVC and STATCOM at the load buses voltage collapse is mitigated in spite of heavily loading the system. Keywords: Voltage Collapse, Reactive Power Management, Load Bus, Power System Stability.
Determination of period of vibration of buildings with open stilt floor and s...eSAT Journals
Abstract To estimate the natural period of vibration, codes consign the empirical formula that solely relies on height of the structure. Present dissertation is carried out considering aspects such as building material, type of structure and structural dimensions. The foremost objective of the present systematic study has led to a simplified period-height equation for use in the seismic evaluation of reinforced concrete structures, taking due significance of the existence of stilt floors and shear walls. Current study also highlights the criteria that affects the period of vibration. The period of vibration which has been procured in this study represents the time period of first mode of vibration. This article comprises the seismic response of structures on different types of soil. The parameters considered for the given study are three different types of soil i.e., soft soil, medium soil and hard rock for high seismic zone and different building irregularities as per IS: 1893-2002 for 10, 15, 20 storey buildings. The analytical models for the modulus study are modeled through ETABS.V.9.2. Various parametric studies are carried out to determine the fundamental time period of the structures. These ameliorate formulas to determine the fundamental time period are developed using nonlinear regression analysis through ORIGIN pro software. The generalized equation finally obtained can be used in general form to calculate the time period of structures with open stilt floor and shear walls irrespective of soil types, seismic zone or building height. Keywords- Time period, open stilt floor, Shear walls, Irregularities in buildings, nonlinear regression
Mx/G(a,b)/1 With Modified Vacation, Variant Arrival Rate With Restricted Admi...IJRES Journal
In this paper, a bulk arrival general bulk service queuing system with modified M-vacation policy, variant arrival rate under a restricted admissibility policy of arriving batches and close down time is considered. During the server is in non- vacation, the arrivals are admitted with probability with ' α ' whereas, with probability 'β' they are admitted when the server is in vacation. The server starts the service only if at least ‘a’ customers are waiting in the queue, and renders the service according to the general bulk service rule with minimum of ‘a’ customers and maximum of ‘b’ customers. At the completion of service, if the number of waiting customers in the queue is less than ‘𝑎’ then the server performs closedown work , then the server will avail of multiple vacations till the queue length reaches a consecutively avail of M number of vacations, After completing the Mth vacation, if the queue length is still less than a then the server remains idle till it reaches a. The server starts the service only if the queue length b ≥ a. It is considered that the variant arrival rate dependent on the state of the server.
The aim of this paper is to study the existence and approximation of periodic solutions for non-linear systems of integral equations, by using the numerical-analytic method which were introduced by Samoilenko[ 10, 11]. The study of such nonlinear integral equations is more general and leads us to improve and extend the results of Butris [2].
Least Square Plane and Leastsquare Quadric Surface Approximation by Using Mod...IOSRJM
Now a days Surface fitting is applied all engineering and medical fields. Kamron Saniee ,2007 find a simple expression for multivariate LaGrange’s Interpolation. We derive a least square plane and least square quadric surface Approximation from a given N+1 tabular points when the function is unique. We used least square method technique. We can apply this method in surface fitting also.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Generalized Laplace - Mellin Integral TransformationIJERA Editor
The main propose of this paper is to generalized Laplace-Mellin Integral Transformation in between the positive regions of real axis. We have derived some new properties and theorems .And give selected tables for Laplace-Mellin Integral Transformation.
Time Delay and Mean Square Stochastic Differential Equations in Impetuous Sta...ijtsrd
This paper specially exhibits about the time delay and mean square stochastic differential equations in impetuous stabilization is analyzed. By projecting a delay differential inequality and using the stochastic analysis technique, a few present stage for mean square exponential stabilization are survived. It is express that an unstable stochastic delay system can be achieved some stability by impetuous. This example is also argued to derived the efficiency of the obtained results. G. Pramila | S. Ramadevi"Time Delay and Mean Square Stochastic Differential Equations in Impetuous Stabilization" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-3 , April 2018, URL: http://www.ijtsrd.com/papers/ijtsrd11062.pdf http://www.ijtsrd.com/humanities-and-the-arts/other/11062/time-delay-and-mean-square-stochastic-differential-equations-in-impetuous-stabilization/g-pramila
A Non Local Boundary Value Problem with Integral Boundary ConditionIJMERJOURNAL
ABSTRACT: In this article a three point boundary value problem associated with a second order differential equation with integral type boundary conditions is proposed. Then its solution is developed with the help of the Green’s function associated with the homogeneous equation. Using this idea and Iteration method is proposed to solve the corresponding linear problem.
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
We give an elementary exposition of a method to obtain the infinitesimal point symmetries of Lagrangians.Besides, we exhibit the Lanczos approach to Noether’s theorem to construct the first integral associated with each symmetry.
MSC 2010:49S05, 58E30, 70H25, 70H33
In this paper, we introduced the modified differential transform which is a modified version of a two-dimensional differential transform method. First, the properties of the modified differential transform method (MDTM) are presented. After this, by using the idea modified differential transform method we will find an analytical-numerical solution of linear partial integro-differential equations (PIDE) with convolution kernel which occur naturally in various fields of science and engineering. In some cases, the exact solution may be achieved. The efficiency and reliability of this method are illustrated by some examples.
Further Results On The Basis Of Cauchy’s Proper Bound for the Zeros of Entire...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
International Journal of Modern Engineering Research (IJMER) covers all the fields of engineering and science: Electrical Engineering, Mechanical Engineering, Civil Engineering, Chemical Engineering, Computer Engineering, Agricultural Engineering, Aerospace Engineering, Thermodynamics, Structural Engineering, Control Engineering, Robotics, Mechatronics, Fluid Mechanics, Nanotechnology, Simulators, Web-based Learning, Remote Laboratories, Engineering Design Methods, Education Research, Students' Satisfaction and Motivation, Global Projects, and Assessment…. And many more.
Some Common Fixed Point Results for Expansive Mappings in a Cone Metric SpaceIOSR Journals
The purpose of this work is to extend and generalize some common fixed point theorems for Expansive type mappings in complete cone metric spaces. We are attempting to generalize the several well- known recent results. Mathematical subject classification; 54H25, 47H10
Mechanical properties of hybrid fiber reinforced concrete for pavementseSAT Journals
Abstract
The effect of addition of mono fibers and hybrid fibers on the mechanical properties of concrete mixture is studied in the present
investigation. Steel fibers of 1% and polypropylene fibers 0.036% were added individually to the concrete mixture as mono fibers and
then they were added together to form a hybrid fiber reinforced concrete. Mechanical properties such as compressive, split tensile and
flexural strength were determined. The results show that hybrid fibers improve the compressive strength marginally as compared to
mono fibers. Whereas, hybridization improves split tensile strength and flexural strength noticeably.
Keywords:-Hybridization, mono fibers, steel fiber, polypropylene fiber, Improvement in mechanical properties.
Material management in construction – a case studyeSAT Journals
Abstract
The objective of the present study is to understand about all the problems occurring in the company because of improper application
of material management. In construction project operation, often there is a project cost variance in terms of the material, equipments,
manpower, subcontractor, overhead cost, and general condition. Material is the main component in construction projects. Therefore,
if the material management is not properly managed it will create a project cost variance. Project cost can be controlled by taking
corrective actions towards the cost variance. Therefore a methodology is used to diagnose and evaluate the procurement process
involved in material management and launch a continuous improvement was developed and applied. A thorough study was carried
out along with study of cases, surveys and interviews to professionals involved in this area. As a result, a methodology for diagnosis
and improvement was proposed and tested in selected projects. The results obtained show that the main problem of procurement is
related to schedule delays and lack of specified quality for the project. To prevent this situation it is often necessary to dedicate
important resources like money, personnel, time, etc. To monitor and control the process. A great potential for improvement was
detected if state of the art technologies such as, electronic mail, electronic data interchange (EDI), and analysis were applied to the
procurement process. These helped to eliminate the root causes for many types of problems that were detected.
Managing drought short term strategies in semi arid regions a case studyeSAT Journals
Abstract
Drought management needs multidisciplinary action. Interdisciplinary efforts among the experts in various fields of the droughts
prone areas are helpful to achieve tangible and permanent solution for this recurring problem. The Gulbarga district having the total
area around 16, 240 sq.km, and accounts 8.45 per cent of the Karnataka state area. The district has been situated with latitude 17º 19'
60" North and longitude of 76 º 49' 60" east. The district is situated entirely on the Deccan plateau positioned at a height of 300 to
750 m above MSL. Sub-tropical, semi-arid type is one among the drought prone districts of Karnataka State. The drought
management is very important for a district like Gulbarga. In this paper various short term strategies are discussed to mitigate the
drought condition in the district.
Keywords: Drought, South-West monsoon, Semi-Arid, Rainfall, Strategies etc.
Life cycle cost analysis of overlay for an urban road in bangaloreeSAT Journals
Abstract
Pavements are subjected to severe condition of stresses and weathering effects from the day they are constructed and opened to traffic
mainly due to its fatigue behavior and environmental effects. Therefore, pavement rehabilitation is one of the most important
components of entire road systems. This paper highlights the design of concrete pavement with added mono fibers like polypropylene,
steel and hybrid fibres for a widened portion of existing concrete pavement and various overlay alternatives for an existing
bituminous pavement in an urban road in Bangalore. Along with this, Life cycle cost analyses at these sections are done by Net
Present Value (NPV) method to identify the most feasible option. The results show that though the initial cost of construction of
concrete overlay is high, over a period of time it prove to be better than the bituminous overlay considering the whole life cycle cost.
The economic analysis also indicates that, out of the three fibre options, hybrid reinforced concrete would be economical without
compromising the performance of the pavement.
Keywords: - Fatigue, Life cycle cost analysis, Net Present Value method, Overlay, Rehabilitation
Laboratory studies of dense bituminous mixes ii with reclaimed asphalt materialseSAT Journals
Abstract
The issue of growing demand on our nation’s roadways over that past couple of decades, decreasing budgetary funds, and the need to
provide a safe, efficient, and cost effective roadway system has led to a dramatic increase in the need to rehabilitate our existing
pavements and the issue of building sustainable road infrastructure in India. With these emergency of the mentioned needs and this
are today’s burning issue and has become the purpose of the study.
In the present study, the samples of existing bituminous layer materials were collected from NH-48(Devahalli to Hassan) site.The
mixtures were designed by Marshall Method as per Asphalt institute (MS-II) at 20% and 30% Reclaimed Asphalt Pavement (RAP).
RAP material was blended with virgin aggregate such that all specimens tested for the, Dense Bituminous Macadam-II (DBM-II)
gradation as per Ministry of Roads, Transport, and Highways (MoRT&H) and cost analysis were carried out to know the economics.
Laboratory results and analysis showed the use of recycled materials showed significant variability in Marshall Stability, and the
variability increased with the increase in RAP content. The saving can be realized from utilization of recycled materials as per the
methodology, the reduction in the total cost is 19%, 30%, comparing with the virgin mixes.
Keywords: Reclaimed Asphalt Pavement, Marshall Stability, MS-II, Dense Bituminous Macadam-II
Laboratory investigation of expansive soil stabilized with natural inorganic ...eSAT Journals
Abstract
Soil stabilization has proven to be one of the oldest techniques to improve the soil properties. Literature review conducted revealed
that uses of natural inorganic stabilizers are found to be one of the best options for soil stabilization. In this regard an attempt has
been made to evaluate the influence of RBI-81 stabilizer on properties of black cotton soil through laboratory investigations. Black
cotton soil with varying percentages of RBI-81 viz., 0, 0.5, 1, 1.5, 2, and 2.5 percent were studied for moisture density relationships
and strength behaviour of soils. Also the effect of curing period was evaluated as literature review clearly emphasized the strength
gain of soils stabilized with RBI-81 over a period of time. The results obtained shows that the unconfined compressive strength of
specimens treated with RBI-81 increased approximately by 250% for a curing period of 28 days as compared to virgin soil. Further
the CBR value improved approximately by 400%. The studies indicated an increasing trend for soil strength behaviour with
increasing percentage of RBI-81 suggesting its potential applications in soil stabilization.
Influence of reinforcement on the behavior of hollow concrete block masonry p...eSAT Journals
Abstract
Reinforced masonry was developed to exploit the strength potential of masonry and to solve its lack of tensile strength. Experimental
and analytical studies have been carried out to investigate the effect of reinforcement on the behavior of hollow concrete block
masonry prisms under compression and to predict ultimate failure compressive strength. In the numerical program, three dimensional
non-linear finite elements (FE) model based on the micro-modeling approach is developed for both unreinforced and reinforced
masonry prisms using ANSYS (14.5). The proposed FE model uses multi-linear stress-strain relationships to model the non-linear
behavior of hollow concrete block, mortar, and grout. Willam-Warnke’s five parameter failure theory has been adopted to model the
failure of masonry materials. The comparison of the numerical and experimental results indicates that the FE models can successfully
capture the highly nonlinear behavior of the physical specimens and accurately predict their strength and failure mechanisms.
Keywords: Structural masonry, Hollow concrete block prism, grout, Compression failure, Finite element method,
Numerical modeling.
Influence of compaction energy on soil stabilized with chemical stabilizereSAT Journals
Abstract
Increase in traffic along with heavier magnitude of wheel loads cause rapid deterioration in pavements. There is a need to improve
density, strength of soil subgrade and other pavement layers. In this study an attempt is made to improve the properties of locally
available loamy soil using twin approaches viz., i) increasing the compaction of soil and ii) treating the soil with chemical stabilizer.
Laboratory studies are carried out on both untreated and treated soil samples compacted by different compaction efforts. Studies
show that increase in compaction effort results in increase in density of soil. However in soil treated with chemical stabilizer, rate of
increase in density is not significant. The soil treated with chemical stabilizer exhibits improvement in both strength and performance
properties.
Keywords: compaction, density, subgradestabilization, resilient modulus
Geographical information system (gis) for water resources managementeSAT Journals
Abstract
Water resources projects are inherited with overlapping and at times conflicting objectives. These projects are often of varied sizes
ranging from major projects with command areas of millions of hectares to very small projects implemented at the local level. Thus,
in all these projects there is seldom proper coordination which is essential for ensuring collective sustainability.
Integrated watershed development and management is the accepted answer but in turn requires a comprehensive framework that can
enable planning process involving all the stakeholders at different levels and scales is compulsory. Such a unified hydrological
framework is essential to evaluate the cause and effect of all the proposed actions within the drainage basins.
The present paper describes a hydrological framework developed in the form of a Hydrologic Information System (HIS) which is
intended to meet the specific information needs of the various line departments of a typical State connected with water related aspects.
The HIS consist of a hydrologic information database coupled with tools for collating primary and secondary data and tools for
analyzing and visualizing the data and information. The HIS also incorporates hydrological model base for indirect assessment of
various entities of water balance in space and time. The framework would be maintained and updated to reflect fully the most
accurate ground truth data and the infrastructure requirements for planning and management.
Keywords: Hydrological Information System (HIS); WebGIS; Data Model; Web Mapping Services
Forest type mapping of bidar forest division, karnataka using geoinformatics ...eSAT Journals
Abstract
The study demonstrate the potentiality of satellite remote sensing technique for the generation of baseline information on forest types
including tree plantation details in Bidar forest division, Karnataka covering an area of 5814.60Sq.Kms. The Total Area of Bidar
forest division is 5814Sq.Kms analysis of the satellite data in the study area reveals that about 84% of the total area is Covered by
crop land, 1.778% of the area is covered by dry deciduous forest, 1.38 % of mixed plantation, which is very threatening to the
environmental stability of the forest, future plantation site has been mapped. With the use of latest Geo-informatics technology proper
and exact condition of the trees can be observed and necessary precautions can be taken for future plantation works in an appropriate
manner
Keywords:-RS, GIS, GPS, Forest Type, Tree Plantation
Factors influencing compressive strength of geopolymer concreteeSAT Journals
Abstract
To study effects of several factors on the properties of fly ash based geopolymer concrete on the compressive strength and also the
cost comparison with the normal concrete. The test variables were molarities of sodium hydroxide(NaOH) 8M,14M and 16M, ratio of
NaOH to sodium silicate (Na2SiO3) 1, 1.5, 2 and 2.5, alkaline liquid to fly ash ratio 0.35 and 0.40 and replacement of water in
Na2SiO3 solution by 10%, 20% and 30% were used in the present study. The test results indicated that the highest compressive
strength 54 MPa was observed for 16M of NaOH, ratio of NaOH to Na2SiO3 2.5 and alkaline liquid to fly ash ratio of 0.35. Lowest
compressive strength of 27 MPa was observed for 8M of NaOH, ratio of NaOH to Na2SiO3 is 1 and alkaline liquid to fly ash ratio of
0.40. Alkaline liquid to fly ash ratio of 0.35, water replacement of 10% and 30% for 8 and 16 molarity of NaOH and has resulted in
compressive strength of 36 MPa and 20 MPa respectively. Superplasticiser dosage of 2 % by weight of fly ash has given higher
strength in all cases.
Keywords: compressive strength, alkaline liquid, fly ash
Experimental investigation on circular hollow steel columns in filled with li...eSAT Journals
Abstract
Composite Circular hollow Steel tubes with and without GFRP infill for three different grades of Light weight concrete are tested for
ultimate load capacity and axial shortening , under Cyclic loading. Steel tubes are compared for different lengths, cross sections and
thickness. Specimens were tested separately after adopting Taguchi’s L9 (Latin Squares) Orthogonal array in order to save the initial
experimental cost on number of specimens and experimental duration. Analysis was carried out using ANN (Artificial Neural
Network) technique with the assistance of Mini Tab- a statistical soft tool. Comparison for predicted, experimental & ANN output is
obtained from linear regression plots. From this research study, it can be concluded that *Cross sectional area of steel tube has most
significant effect on ultimate load carrying capacity, *as length of steel tube increased- load carrying capacity decreased & *ANN
modeling predicted acceptable results. Thus ANN tool can be utilized for predicting ultimate load carrying capacity for composite
columns.
Keywords: Light weight concrete, GFRP, Artificial Neural Network, Linear Regression, Back propagation, orthogonal
Array, Latin Squares
Experimental behavior of circular hsscfrc filled steel tubular columns under ...eSAT Journals
Abstract
This paper presents an outlook on experimental behavior and a comparison with predicted formula on the behaviour of circular
concentrically loaded self-consolidating fibre reinforced concrete filled steel tube columns (HSSCFRC). Forty-five specimens were
tested. The main parameters varied in the tests are: (1) percentage of fiber (2) tube diameter or width to wall thickness ratio (D/t
from 15 to 25) (3) L/d ratio from 2.97 to 7.04 the results from these predictions were compared with the experimental data. The
experimental results) were also validated in this study.
Keywords: Self-compacting concrete; Concrete-filled steel tube; axial load behavior; Ultimate capacity.
Evaluation of punching shear in flat slabseSAT Journals
Abstract
Flat-slab construction has been widely used in construction today because of many advantages that it offers. The basic philosophy in
the design of flat slab is to consider only gravity forces; this method ignores the effect of punching shear due to unbalanced moments
at the slab column junction which is critical. An attempt has been made to generate generalized design sheets which accounts both
punching shear due to gravity loads and unbalanced moments for cases (a) interior column; (b) edge column (bending perpendicular
to shorter edge); (c) edge column (bending parallel to shorter edge); (d) corner column. These design sheets are prepared as per
codal provisions of IS 456-2000. These design sheets will be helpful in calculating the shear reinforcement to be provided at the
critical section which is ignored in many design offices. Apart from its usefulness in evaluating punching shear and the necessary
shear reinforcement, the design sheets developed will enable the designer to fix the depth of flat slab during the initial phase of the
design.
Keywords: Flat slabs, punching shear, unbalanced moment.
Evaluation of performance of intake tower dam for recent earthquake in indiaeSAT Journals
Abstract
Intake towers are typically tall, hollow, reinforced concrete structures and form entrance to reservoir outlet works. A parametric
study on dynamic behavior of circular cylindrical towers can be carried out to study the effect of depth of submergence, wall thickness
and slenderness ratio, and also effect on tower considering dynamic analysis for time history function of different soil condition and
by Goyal and Chopra accounting interaction effects of added hydrodynamic mass of surrounding and inside water in intake tower of
dam
Key words: Hydrodynamic mass, Depth of submergence, Reservoir, Time history analysis,
Evaluation of operational efficiency of urban road network using travel time ...eSAT Journals
Abstract
Efficiency of the road network system is analyzed by travel time reliability measures. The study overlooks on an important measure of
travel time reliability and prioritizing Tiruchirappalli road network. Traffic volume and travel time were collected using license plate
matching method. Travel time measures were estimated from average travel time and 95th travel time. Effect of non-motorized vehicle
on efficiency of road system was evaluated. Relation between buffer time index and traffic volume was created. Travel time model has
been developed and travel time measure was validated. Then service quality of road sections in network were graded based on
travel time reliability measures.
Keywords: Buffer Time Index (BTI); Average Travel Time (ATT); Travel Time Reliability (TTR); Buffer Time (BT).
Estimation of surface runoff in nallur amanikere watershed using scs cn methodeSAT Journals
Abstract
The development of watershed aims at productive utilization of all the available natural resources in the entire area extending from
ridge line to stream outlet. The per capita availability of land for cultivation has been decreasing over the years. Therefore, water and
the related land resources must be developed, utilized and managed in an integrated and comprehensive manner. Remote sensing and
GIS techniques are being increasingly used for planning, management and development of natural resources. The study area, Nallur
Amanikere watershed geographically lies between 110 38’ and 110 52’ N latitude and 760 30’ and 760 50’ E longitude with an area of
415.68 Sq. km. The thematic layers such as land use/land cover and soil maps were derived from remotely sensed data and overlayed
through ArcGIS software to assign the curve number on polygon wise. The daily rainfall data of six rain gauge stations in and around
the watershed (2001-2011) was used to estimate the daily runoff from the watershed using Soil Conservation Service - Curve Number
(SCS-CN) method. The runoff estimated from the SCS-CN model was then used to know the variation of runoff potential with different
land use/land cover and with different soil conditions.
Keywords: Watershed, Nallur watershed, Surface runoff, Rainfall-Runoff, SCS-CN, Remote Sensing, GIS.
Estimation of morphometric parameters and runoff using rs & gis techniqueseSAT Journals
Abstract
Land and water are the two vital natural resources, the optimal management of these resources with minimum adverse environmental
impact are essential not only for sustainable development but also for human survival. Satellite remote sensing with geographic
information system has a pragmatic approach to map and generate spatial input layers of predicting response behavior and yield of
watershed. Hence, in the present study an attempt has been made to understand the hydrological process of the catchment at the
watershed level by drawing the inferences from moprhometric analysis and runoff. The study area chosen for the present study is
Yagachi catchment situated in Chickamaglur and Hassan district lies geographically at a longitude 75⁰52’08.77”E and
13⁰10’50.77”N latitude. It covers an area of 559.493 Sq.km. Morphometric analysis is carried out to estimate morphometric
parameters at Micro-watershed to understand the hydrological response of the catchment at the Micro-watershed level. Daily runoff
is estimated using USDA SCS curve number model for a period of 10 years from 2001 to 2010. The rainfall runoff relationship of the
study shows there is a positive correlation.
Keywords: morphometric analysis, runoff, remote sensing and GIS, SCS - method
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Effect of variation of plastic hinge length on the results of non linear anal...eSAT Journals
Abstract The nonlinear Static procedure also well known as pushover analysis is method where in monotonically increasing loads are applied to the structure till the structure is unable to resist any further load. It is a popular tool for seismic performance evaluation of existing and new structures. In literature lot of research has been carried out on conventional pushover analysis and after knowing deficiency efforts have been made to improve it. But actual test results to verify the analytically obtained pushover results are rarely available. It has been found that some amount of variation is always expected to exist in seismic demand prediction of pushover analysis. Initial study is carried out by considering user defined hinge properties and default hinge length. Attempt is being made to assess the variation of pushover analysis results by considering user defined hinge properties and various hinge length formulations available in literature and results compared with experimentally obtained results based on test carried out on a G+2 storied RCC framed structure. For the present study two geometric models viz bare frame and rigid frame model is considered and it is found that the results of pushover analysis are very sensitive to geometric model and hinge length adopted. Keywords: Pushover analysis, Base shear, Displacement, hinge length, moment curvature analysis
Effect of use of recycled materials on indirect tensile strength of asphalt c...eSAT Journals
Abstract
Depletion of natural resources and aggregate quarries for the road construction is a serious problem to procure materials. Hence
recycling or reuse of material is beneficial. On emphasizing development in sustainable construction in the present era, recycling of
asphalt pavements is one of the effective and proven rehabilitation processes. For the laboratory investigations reclaimed asphalt
pavement (RAP) from NH-4 and crumb rubber modified binder (CRMB-55) was used. Foundry waste was used as a replacement to
conventional filler. Laboratory tests were conducted on asphalt concrete mixes with 30, 40, 50, and 60 percent replacement with RAP.
These test results were compared with conventional mixes and asphalt concrete mixes with complete binder extracted RAP
aggregates. Mix design was carried out by Marshall Method. The Marshall Tests indicated highest stability values for asphalt
concrete (AC) mixes with 60% RAP. The optimum binder content (OBC) decreased with increased in RAP in AC mixes. The Indirect
Tensile Strength (ITS) for AC mixes with RAP also was found to be higher when compared to conventional AC mixes at 300C.
Keywords: Reclaimed asphalt pavement, Foundry waste, Recycling, Marshall Stability, Indirect tensile strength.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Some approximation properties of modified baskakov stancu operators
1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 08 | August-2015, Available @ http://www.ijret.org 91
SOME APPROXIMATION PROPERTIES OF MODIFIED BASKAKOV
STANCU OPERATORS
Anshul Srivastava1
1
Assistant professor, Department of Applied Science and Humanities, Northern India Engineering
College,Indraprastha University, New Delhi, India.
Abstract
In the present paper, we prove a global direct theorem for the modified Baskakovstancu operators in terms of Ditzian-Totik
modulus of smoothness. Here, we have modified our operators by taking weight function of Beta operators and then generalizing
it as stancu type generalized operators. We will also see that taking weight function of Beta operators will give better
approximation. We study a global direct theorem using simultaneous approximation for ourstancu type generalized operator in
𝐿 𝑝 0, ∞ . Here, first we estimate recurrence relation for moments and then develop some global direct results by making our
stancu type generalized operators positive using differential and integral operators. In this paper, our effort is to give better
global approximation for our stancu type generalized operator than the earlier integral modifications of Baskakov operators
studied by various authors. Here, we will extend our results for the whole interval 0, ∞ . In this paper, we will also make use of
the fact that second modulus of smoothness introduced by Ditzian-Totik is equivalent to modified k-functional and 𝐿 𝑝
𝑟
[0, ∞) is not
contained in 𝐿1
𝑟
[0, ∞) for obtaining results. Here, Riesz-Thorin theorem and Leibnitz theorem is used extensively for doing
simultaneous approximation. We have also used Fubini’s theorem for obtaining results.
Key words: Stancu type generalization, simultaneous approximation, modulus of smoothness.
---------------------------------------------------------------------***---------------------------------------------------------------------
1. INTRODUCTION
Several authors have defined and studied different
modifications of Baskakov operators. V.Gupta [1] modified
Baskakov operators by taking weight function of Beta
operators on 𝐿1[0, ∞) as,
𝐺 𝑛 𝑓, 𝑥 = 𝑘 𝑛,𝑚 𝑥 𝑏 𝑛,𝑚
∞
0
∞
𝑚=0 𝑡 𝑓 𝑡 𝑑𝑡∀ 𝑥 ∈ [0, ∞)
(1.1)
where𝑘 𝑛,𝑚 𝑥 = 𝑛+𝑚−1
𝑚
𝑥 𝑘
1+𝑥 𝑛+𝑘
and𝑏 𝑛,𝑚 𝑡 =
𝑡 𝑚
1+𝑡 𝑛+𝑚 +1 𝐵 𝑚+1,𝑛
Here, 𝐵 𝑚 + 1, 𝑛 =
𝑚! 𝑛−1 !
𝑛+𝑚 !
is Beta function .
In the present paper, we will study global direct theorem in
simultaneous approximation for Stancu type generalization
[2] of above modifiedBaskakov operators defined as,
𝐺 𝑛
𝛼,𝛽
𝑓, 𝑥 = 𝑘 𝑛,𝑚 𝑥∞
𝑚=0 𝑏 𝑛,𝑚 𝑡 𝑓
𝑛𝑡 +𝛼
𝑛+𝛽
∞
0
𝑑𝑡
(1.2)
Here, for 𝛼 = 0 , 𝛽 = 0 the above operator reduces to (1.1).
Ditzian-Totik [3] defined second order modulus of
smoothness as,
𝜔 𝜑 𝑥
2
𝑓, 𝑡 𝑝 =
𝑠𝑢𝑝
0 ≤ ≤ 𝑡
∆ 𝜑 𝑥
2
𝑓 𝑥
𝑝
(1.3)
where 𝜑 𝑥 =
1
𝑥 1+𝑥 −1 2
and ∆
2
𝑓 𝑥 =
𝑓 𝑥 − − 2𝑓 𝑥 + 𝑓 𝑥 + , 𝑖𝑓 𝑥 − , 𝑥 + ⊂ [0, ∞)
0 𝑜𝑡𝑒𝑟𝑤𝑖𝑠𝑒 .
(1.4)
It may be noted that,
𝐿 𝑝
𝑟
[0, ∞) ⊄ 𝐿1
𝑟
[0, ∞)
where 𝐿1
𝑟
[0, ∞) denotes the class of functions 𝑔 and is
defined as,
𝐿1
𝑟
[0, ∞) ≔
𝑔: 𝑔 𝑟
∈ 𝐿1 0, ∞ , ∀ 𝛼 ∈ 0, ∞ 𝑎𝑛𝑑 𝑔 𝑟
𝑡 ≤
𝐷
1+𝑡 −𝑑
(1.5)
Here, 𝐷 and 𝑑 are constants depending on 𝑔.
Throughout the paper we denote by 𝐶 the positive constants
not necessarily the same at each occurrence.
2. SOME DEFINITIONS AND RESULTS.
Definition 2.1
For every 𝑛 ∈ 𝑁 and 𝑛 > 𝑟 + 1 , we have ,
a) 𝐾 𝑛,𝑚
∞
𝑚=0 𝑥 = 1.
b) 𝑏 𝑛,𝑚 𝑡 𝑑𝑡 = 1.
∞
0
2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 04 Issue: 08 | August-2015, Available @ http://www.ijret.org 92
c) 𝑚𝑘 𝑛,𝑚 𝑥 = 𝑛𝑘 𝑛+1,𝑚−1 𝑥 .
d) 𝑡𝑏 𝑛−𝑟,𝑚+𝑟
∞
0
𝑡 𝑑𝑡 =
𝑚 + 𝑟 + 1 𝑛 − 𝑟 − 1 .
Lemma 2.2.[1] Let𝑞, 𝑟 ∈ 𝑁0, we define, 𝑞th moment as,
𝑇 𝑟,𝑛,𝑞
𝛼,𝛽
𝑥 = 𝑘 𝑛+𝑟 ,𝑚 𝑥 𝑏 𝑛−𝑟 ,𝑚+𝑟 𝑡
∞
0
∞
𝑚=0
𝑛𝑡 +𝛼
𝑛+𝛽
− 𝑥
𝑞
𝑑𝑡
(2.1)
Here, for each 𝑥 ∈ [0, ∞) and 𝛼 = 0 , 𝛽 = 0,
𝑇 𝑟,𝑛,𝑞 𝑥 = 𝑂 𝑛− 𝑞+1 2
(2.2)
where 𝛾 denotes integral part of 𝛾.
Also for 𝛼 = 0, 𝛽 = 0, we have [6] [7],
𝑇 𝑟,𝑛,2𝑞 𝑥 = 𝑞 𝑖,𝑞,𝑛 𝑥𝑠
𝑖=0 𝜑2
𝑥 𝑛 𝑞−𝑖 1
𝑛2𝑖 (2.3)
𝑇𝑟,𝑛,2𝑞+1 𝑥 =
1 + 2𝑥 𝑢 𝑖,𝑞,𝑛 𝑥 𝜑2
𝑥 𝑛 𝑞−𝑖𝑞
𝑖=0
1
𝑛 2𝑖+1 (2.4)
Here, 𝑞 𝑖,𝑞,𝑛 𝑥 and 𝑢 𝑖,𝑞,𝑛 𝑥 are polynomials in 𝑥 of fixed
degree with coefficients that are bounded uniformly for all
𝑛.
Proof.The proof of above lemma easily follows along the
lines of [4], [5].
Lemma 2.3.If 𝑓 ∈ 𝐿 𝑝
𝑟
0, ∞ ∪ 𝐿1
𝑟
0, ∞ , 1 ≤ 𝑝 ≤ ∞, 𝑛 >
𝑟
1+𝑠 −1and 𝑥 ∈ 0, ∞ , then,
𝐺 𝑛
𝛼,𝛽
𝑓 𝑟
, 𝑥
= 𝜇 𝑛,𝑟 𝑘 𝑛+𝑟,𝑚
∞
𝑚=0
𝑥 𝑏 𝑛−𝑟,𝑚+𝑟 𝑡 𝑓 𝑟
𝑛𝑡 + 𝛼
𝑛 + 𝛽
𝑑𝑡
∞
0
(2.5)
Where,
𝜇 𝑛,𝑟 = 𝑛 + 𝑟 − 1 ! 𝑛 − 𝑟 − 1 ! 𝑛 − 1 !
−2
= 𝑛 + 𝑙 𝑛 − 𝑙 + 1 −1
𝑟−1
𝑙=0
Proof.Using Leibnitz theorem, we have ,
𝐺 𝑛
𝛼,𝛽
𝑓 𝑟
, 𝑥 =
𝑟
𝑖
𝑛 + 𝑚 + 𝑟 − 𝑖 − 1 !
𝑛 − 1 ! 𝑚 − 𝑖 !
∞
𝑚=𝑖
𝑟
𝑖=0
×
−1 𝑟−𝑖
𝑥 𝑚−𝑖
1 + 𝑥 𝑛+𝑚+𝑟−𝑖
× 𝑏 𝑛,𝑚
∞
0
𝑡 𝑓
𝑛𝑡 + 𝛼
𝑛 + 𝛽
𝑑𝑡
=
𝑛 + 𝑟 − 1 !
𝑛 − 1 !
𝑘 𝑛+𝑟,𝑚 𝑥
∞
𝑚=0
× −1 𝑟−𝑖
𝑟
𝑖
𝑟
𝑖=0
∞
0
𝑏 𝑛,𝑚+𝑖 𝑡 𝑓
𝑛𝑡 + 𝛼
𝑛 + 𝛽
𝑑𝑡.
Using again Leibnitz theorem, we have,
𝑏 𝑛−𝑟,𝑚+𝑟
𝑟
𝑡 =
𝑛 − 1 ! 𝑛 − 𝑟 − 1 ! −1
−1 𝑟𝑟
𝑖=0
𝑟
𝑖
𝑏 𝑛,𝑚+𝑖 𝑡 .
Hence,
𝐺 𝑛
𝛼,𝛽
𝑓 𝑟
, 𝑥
= 𝜇 𝑛,𝑟 𝑘 𝑛+𝑟,𝑚 𝑥 −1 𝑟 𝑏 𝑛−𝑟,𝑚+𝑟
𝑟
𝑡 𝑓
𝑛𝑡 + 𝛼
𝑛 + 𝛽
𝑑𝑡
∞
0
∞
𝑚=0
.
On integrating 𝑟 times by parts, we get the required result.
Here, we see that,operators defined by (2.5)are not positive.
To make the operators positive, we introduce the operator,
𝐺 𝑛,𝑟
𝛼,𝛽
𝑓 ≡ 𝐷 𝑟
𝐺 𝑛
𝛼,𝛽
𝐼 𝑟
𝑓, 𝑓 ∈ 𝐿 𝑝[0, ∞) ∪ 𝐿1[0, ∞),
where 𝐷 and 𝐼 are differential and integral operators
respectievely.
Therefore we define the operators by,
𝐺 𝑛,𝑟
𝛼,𝛽
𝑓, 𝑥 =
𝜇 𝑛,𝑟 𝑘 𝑛+𝑟,𝑚 𝑥∞
𝑚=0 𝑏 𝑛−𝑟,𝑚+𝑟 𝑓
𝑛𝑡 +𝛼
𝑛+𝛽
𝑑𝑡
∞
0
,
𝑓 ∈ 𝐿 𝑝 0, ∞ ∪ 𝐿1 0, ∞ , 𝑛 > 𝑟 1 + 𝑚 ,
The operators 𝐺 𝑛,𝑟
𝛼,𝛽
are positive and the estimation
𝐺 𝑛
𝛼,𝛽
𝑓 𝑟
− 𝑓 𝑟
𝑝
, 𝑓 ∈ 𝐿 𝑝
𝑟
0, ∞ is equivalent to
𝐺 𝑛,𝑟
𝛼,𝛽
𝑓 − 𝑓
𝑝
, 𝑓 ∈ 𝐿 𝑝 [0, ∞).
We can also very easily prove that for 𝑛 > 𝑟 + 1 ,
𝐺 𝑛,𝑟
𝛼,𝛽
𝑓
1
≤ 𝐶 𝑓 1, for 𝑓 ∈ 𝐿1[0, ∞)and
𝐺 𝑛,𝑟
𝛼,𝛽
𝑓 ≤ 𝐶 𝑓 ∞, for 𝑓 ∈ 𝐿∞[0, ∞).
Using Riesz-Thorin theorem , we get,
𝐺 𝑛,𝑟
𝛼,𝛽
𝑓
𝑝
≤ 𝐶 𝑓 𝑝, for 1≤ 𝑝 ≤ ∞, 𝑛 > 𝑟 + 1 .
Corollary 2.4.For every 𝑞 ∈ 𝑁0, 𝑛 > 𝑟 + 2𝑞 + 1 and
𝑥 ∈ 0, ∞ , we have,
𝐺 𝑛,𝑟
𝛼,𝛽 𝑛𝑡 +𝛼
𝑛+𝛽
− 𝑥
2𝑞
, 𝑥 ≤
𝐶
𝑛 𝑞 𝜑2
𝑥 +
1
𝑛
𝑞
and