International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
NITheP WITS node Seminar by Dr Dr. Roland Cristopher F. Caballar (NITheP/UKZN)
TITLE: "One-Dimensional Homogeneous Open Quantum Walks"
ABSTRACT: In this talk, we consider a system undergoing an open quantum walk on a one-dimensional lattice. Each jump of the system between adjacent lattice points in a given direction corresponds to a jump operator, with these jump operators either commuting or not commuting. We examine the dynamics of the system undergoing this open quantum walk, in particular deriving analytically the probability distribution of the system, as well as examining numerically the behavior of the probability distribution over long time steps. The resulting distribution is shown to have multiple components, which fall under two general categories, namely normal and solitonic components. The analytic computation of the probability distribution for the system undergoing this open quantum walk allows us to determine at any instant of time the dynamical properties of the system.
Wits Node Seminar: Dr Sunandan Gangopadhyay (NITheP Stellenbosch)
TITLE: Path integral action of a particle in the noncommutative plane and the Aharonov-Bohm effect
Divergence measures are useful for comparing two probability distributions. Depending on the nature of
the problem, different divergence measures are suitable. So it is always desirable to develop a new
divergence measure.
Recently, Jain and Chhabra [6] introduced new series ( ( , ) m x P Q , ( , ) m z P Q and ( , ) m w P Q for
mÎN ) of information divergence measures, defined the properties and characterized, compared with
standard divergences and derived the new series ( ( ) * , m x P Q formÎN ) of metric spaces.
In this work, various important and interesting relations among divergences of these new series and other
well known divergence measures are obtained. Some intra relations among these new divergences are
evaluated as well and bounds of new divergence measure ( ( ) 1 x P,Q ) are obtained by using Csiszar’s
information inequalities. Numerical illustrations (Verification) regarding bounds are done as well.
NITheP UKZN Seminar: Prof. Alexander Gorokhov (Samara State University, Russi...Rene Kotze
This document discusses the application of dynamical groups and coherent states in quantum optics and molecular spectroscopy. It provides an introduction to using Lie groups and algebras to describe quantum systems and defines coherent states. Specific applications discussed include using dynamical symmetries to calculate energy levels of systems like the harmonic oscillator and hydrogen atom. Coherent states are used to derive classical equations of motion and represent open quantum systems. Examples of coherent state dynamics are shown for two-level and three-level atoms interacting with laser fields.
Prof. Vishnu Jejjala (Witwatersrand) TITLE: "The Geometry of Generations"Rene Kotze
This document summarizes Vishnu Jejjala's talk "The Geometry of Generations" given at the University of the witwatersrand on 23 September 2014. It discusses using the geometry of vacuum moduli spaces of supersymmetric gauge theories to understand phenomenological aspects of the Standard Model, such as the number of generations. It provides examples of calculating the vacuum moduli space for simple supersymmetric gauge theories and outlines a process for obtaining the moduli space from the F-term and D-term equations.
Some Dynamical Behaviours of a Two Dimensional Nonlinear MapIJMER
The document summarizes research on a two-dimensional nonlinear map known as the Nicholson Bailey model. The model describes population dynamics between hosts and parasites. The study analyzes the dynamical behaviors of the model such as steady states, stability of equilibrium points, and bifurcation points. It is observed that the model follows a period-doubling route to chaos. Numerical evaluations are used to demonstrate bifurcation diagrams and calculate the accumulation point where chaos begins. The model is modified to restrict unbounded growth in the prey population.
This document presents a theorem on generalized kC |,,,,| -summability factor. It begins with introducing some relevant concepts such as almost increasing sequences, sequences of bounded variation, and quasi- -power increasing sequences. It then states an existing theorem on kC |,,,,| summability by Tuncer. The main result of the document is a theorem that generalizes Tuncer's theorem to kC |,,,,| summability
In this paper, we study semi symmetric and pseudo symmetric conditions in S -manifolds, those are RR = 0 , RC = 0 , C R = 0 , C C = 0 , = ( , ) R R L1Q g R , = ( , ) RC L2Q g C , = ( , ) CR L3Q g R , and = ( , ) C C L4Q g C , where C is the Concircular curvature tensor and 1 2 3 4 L ,L ,L ,L are the smooth functions on M , further we discuss about Ricci soliton
NITheP WITS node Seminar by Dr Dr. Roland Cristopher F. Caballar (NITheP/UKZN)
TITLE: "One-Dimensional Homogeneous Open Quantum Walks"
ABSTRACT: In this talk, we consider a system undergoing an open quantum walk on a one-dimensional lattice. Each jump of the system between adjacent lattice points in a given direction corresponds to a jump operator, with these jump operators either commuting or not commuting. We examine the dynamics of the system undergoing this open quantum walk, in particular deriving analytically the probability distribution of the system, as well as examining numerically the behavior of the probability distribution over long time steps. The resulting distribution is shown to have multiple components, which fall under two general categories, namely normal and solitonic components. The analytic computation of the probability distribution for the system undergoing this open quantum walk allows us to determine at any instant of time the dynamical properties of the system.
Wits Node Seminar: Dr Sunandan Gangopadhyay (NITheP Stellenbosch)
TITLE: Path integral action of a particle in the noncommutative plane and the Aharonov-Bohm effect
Divergence measures are useful for comparing two probability distributions. Depending on the nature of
the problem, different divergence measures are suitable. So it is always desirable to develop a new
divergence measure.
Recently, Jain and Chhabra [6] introduced new series ( ( , ) m x P Q , ( , ) m z P Q and ( , ) m w P Q for
mÎN ) of information divergence measures, defined the properties and characterized, compared with
standard divergences and derived the new series ( ( ) * , m x P Q formÎN ) of metric spaces.
In this work, various important and interesting relations among divergences of these new series and other
well known divergence measures are obtained. Some intra relations among these new divergences are
evaluated as well and bounds of new divergence measure ( ( ) 1 x P,Q ) are obtained by using Csiszar’s
information inequalities. Numerical illustrations (Verification) regarding bounds are done as well.
NITheP UKZN Seminar: Prof. Alexander Gorokhov (Samara State University, Russi...Rene Kotze
This document discusses the application of dynamical groups and coherent states in quantum optics and molecular spectroscopy. It provides an introduction to using Lie groups and algebras to describe quantum systems and defines coherent states. Specific applications discussed include using dynamical symmetries to calculate energy levels of systems like the harmonic oscillator and hydrogen atom. Coherent states are used to derive classical equations of motion and represent open quantum systems. Examples of coherent state dynamics are shown for two-level and three-level atoms interacting with laser fields.
Prof. Vishnu Jejjala (Witwatersrand) TITLE: "The Geometry of Generations"Rene Kotze
This document summarizes Vishnu Jejjala's talk "The Geometry of Generations" given at the University of the witwatersrand on 23 September 2014. It discusses using the geometry of vacuum moduli spaces of supersymmetric gauge theories to understand phenomenological aspects of the Standard Model, such as the number of generations. It provides examples of calculating the vacuum moduli space for simple supersymmetric gauge theories and outlines a process for obtaining the moduli space from the F-term and D-term equations.
Some Dynamical Behaviours of a Two Dimensional Nonlinear MapIJMER
The document summarizes research on a two-dimensional nonlinear map known as the Nicholson Bailey model. The model describes population dynamics between hosts and parasites. The study analyzes the dynamical behaviors of the model such as steady states, stability of equilibrium points, and bifurcation points. It is observed that the model follows a period-doubling route to chaos. Numerical evaluations are used to demonstrate bifurcation diagrams and calculate the accumulation point where chaos begins. The model is modified to restrict unbounded growth in the prey population.
This document presents a theorem on generalized kC |,,,,| -summability factor. It begins with introducing some relevant concepts such as almost increasing sequences, sequences of bounded variation, and quasi- -power increasing sequences. It then states an existing theorem on kC |,,,,| summability by Tuncer. The main result of the document is a theorem that generalizes Tuncer's theorem to kC |,,,,| summability
In this paper, we study semi symmetric and pseudo symmetric conditions in S -manifolds, those are RR = 0 , RC = 0 , C R = 0 , C C = 0 , = ( , ) R R L1Q g R , = ( , ) RC L2Q g C , = ( , ) CR L3Q g R , and = ( , ) C C L4Q g C , where C is the Concircular curvature tensor and 1 2 3 4 L ,L ,L ,L are the smooth functions on M , further we discuss about Ricci soliton
Development of implicit rational runge kutta schemes for second order ordinar...Alexander Decker
This document describes the development of a one-stage implicit rational Runge-Kutta method for solving second-order ordinary differential equations. The method is derived by taking Taylor series expansions of the solution equations about the point (xn, yn, yn') and equating terms with the same powers of the step size h. This results in expressions for the parameters of the method in terms of the leading order truncation errors. The method is consistent, as the parameters satisfy constraints that ensure the method approaches the true solution in the limit as h approaches 0.
This document investigates the transitivity, primitivity, ranks, and subdegrees of the direct product of the symmetric group acting on the Cartesian product of three sets. It proves that this action is both transitive and imprimitive for all 2n ≥ 6. The rank associated with the action is a constant 3/2. The subdegrees are calculated according to their increasing magnitude. Examples are provided to illustrate the ranks and subdegrees when the sets have 2, 3, and 4 elements, respectively.
Dr. Arpan Bhattacharyya (Indian Institute Of Science, Bangalore)Rene Kotze
1. The document discusses entanglement entropy functionals for higher derivative gravity theories. It proposes new area functionals for computing entanglement entropy in higher derivative theories containing polynomials of curvature tensors.
2. These functionals are derived using the Lewkowycz-Maldacena interpretation of generalized entropy. However, attempting to derive the extremal surface equations from these functionals using bulk equations of motion leads to inconsistencies and ambiguities in some higher derivative theories like Gauss-Bonnet gravity.
3. The document suggests that the source of ambiguity lies in the limiting procedure used to extract the divergences near the conical singularity. Different limiting paths can lead to different extremal surface equations, indicating no unique prescription
Stochastic Gravity in Conformally-flat SpacetimesRene Kotze
The National Institute for Theoretical Physics, and the Mandelstam Institute for Theoretical Physics, School of Physics, would like to invite to its coming talk in the theoretical physics seminar series, entitled:
"Stochastic Gravity in Conformally-flat Spacetimes"
to be presented by Prof. Hing-Tong Cho (Tamkang University, Taiwan)
Abstract: The theory of stochastic gravity takes into account the effects of quantum field fluctuations onto the classical spacetime. The essential physics can be understood from the analogous Brownian motion model. We shall next concentrate on the case with conformally-flat spacetimes. Our main concern is to derive the so-called noise kernels. We shall also describe our on-going program to investigate the Einstein-Langevin equation in these spacetimes.
Dates: Tuesday, 17th February 2015
Venue: The Frank Nabarro lecture theatre, P216
Time: 13.20 - 14.10 - TODAY
Some Soliton Solutions of Non Linear Partial Differential Equations by Tan-Co...IOSR Journals
Tan-cot method is applied to get exact soliton solutions of non-linear partial differential equations notably generalized Benjamin-Bona-Mahony, Zakharov-Kuznetsov Benjamin-Bona-Mahony, Kadomtsov-Petviashvilli Benjamin-Bona-Mahony and Korteweg-de Vries equations, which are important evolution equations with wide variety of physical applications. Elastic behavior and soliton fusion/fission is shown graphically and discussed physically as far as possible
Rotation in 3d Space: Euler Angles, Quaternions, Marix DescriptionsSolo Hermelin
Mathematics of rotation in 3d space, a lecture that I've prepared.
This presentation is at a Undergraduate in Science (Math, Physics, Engineering) level.
Please send comments and suggestions to solo.hermelin@gmail.com. Thanks!
Fore more presentations, please visit my website at
http://www.solohermelin.com/
On Some Double Integrals of H -Function of Two Variables and Their ApplicationsIJERA Editor
This paper deals with the evaluation of four integrals of H -function of two variables proposed by Singh and
Mandia [7] and their applications in deriving double half-range Fourier series for the H -function of two
variables. A multiple integral and a multiple half-range Fourier series of the H -function of two variables are
derived analogous to the double integral and double half-range Fourier series of the H -function of two
variables.
B. Dragovich: On Modified Gravity and CosmologySEENET-MTP
This document discusses modified gravity and cosmological solutions. It introduces Einstein's theory of gravity and some of its problems, including lack of renormalizability and prediction of dark energy and dark matter. It then presents a nonlocal modified gravity model to address these issues. The model yields nonsingular bouncing cosmological solutions for the scale factor in the form a(t) = a0(σeλt + τe−λt), which exist for different values of spatial curvature. These solutions depend on the cosmological constant and satisfy the equations of motion for certain conditions on the parameters of the nonlocal gravity action.
This document discusses the formulation of fractional supersymmetric theories in one dimension. It begins by presenting fractional superspace and fractional supersymmetry of order F=3, including the fractional supersymmetry transformations. It then derives the fractional supercharges and Euler-Lagrange equations for F=3. Finally, it generalizes the formulation to arbitrary fractional order F ≥ 3 by introducing fractional superspace and supersymmetry transformations of order F, as well as an action invariant under such transformations.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
Some new exact Solutions for the nonlinear schrödinger equationinventy
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.
Auto Regressive Process (1) with Change Point: Bayesian ApprochIJRESJOURNAL
Abstract : Here we consider first order autoregressive process with changing autoregressive coefficient at some point of time m. This is called change point inference problem. For Bayes estimation of m and autoregressive coefficient we used MHRW (Metropolis Hasting Random Walk) algorithm and Gibbs sampling. The effects of prior information on the Bayes estimates are also studied.
Sweeping discussions on dirac field1 update3 sqrdfoxtrot jp R
This document discusses Dirac fields and Lagrangian formulations of electron theory. It presents Lagrangians for an effective electron theory based on an SU(2)XU(1) construction. The Lagrangians include terms for the electron, neutrino interactions, and interactions with gauge bosons. Integration by parts is used to rewrite the action in terms of adjoint spinor fields. Varying the actions yields Dirac's first order equation of motion for the electron field.
Exact Solutions of the Klein-Gordon Equation for the Q-Deformed Morse Potenti...ijrap
This document presents an analysis of solving the Klein-Gordon equation for the q-deformed Morse potential using the Nikiforov-Uvarov method. The eigenfunctions and eigenvalues of the Klein-Gordon equation are obtained. It is found that the eigenfunctions can be expressed in terms of Laguerre polynomials. The energy eigenvalues and normalized eigenfunctions obtained agree with previous studies that used algebraic approaches.
The document derives equations for an over-replicated softmax model. It defines constants for the number of documents, document length, dictionary size, and hidden units. It defines the energy of the joint configuration and simplifies the energy equation by tying weights and biases. It then defines the joint probability distribution and conditional distributions over visible and hidden units. It derives the derivatives of the log-likelihood with respect to the weights. Finally, it introduces variational inference to obtain a lower bound on the log probability of a document.
The document discusses I-functions and H-functions, which generalize Fox's H-function and contain certain Feynman integrals and partition functions as special cases. It establishes new double integral relations for products involving I-functions and H-functions. Specifically, it derives double integral relations for (A) a product of an I-function and H-function, and (B) the composition of an H-function with another H-function, under certain conditions on the parameters. These relations unify and extend previous known results for various special functions.
Jurnal Study of Anisotropy Superconductor using Time-Dependent Ginzburg-Landa...Fuad Anwar
This document summarizes a study that used numerical simulations based on the time-dependent Ginzburg-Landau equation to study the properties of anisotropic superconductors. The study models an anisotropic superconductor with different effective masses for Cooper pairs along different crystal axes. It describes the theoretical formalism and numerical methods used to solve the time-dependent Ginzburg-Landau equations for an anisotropic superconductor. The results of the numerical simulations show that the anisotropic properties of superconductors can cause the critical field to be either lower or higher compared to isotropic superconductors.
The document summarizes the results of a project investigating different types of particle motion, including cyclotron motion, gradient-B drift motion, magnetic mirroring, and motion due to a magnetic dipole. Analytical solutions were derived and compared to numerical simulations for each type of motion. Key results include plots showing cyclotron and gradient-B drift motion of protons and electrons match analytical solutions, and simulations demonstrating magnetic mirroring and orbits around a dipole match theoretical expectations. Periods were estimated from simulations and calculated from equations.
On Some Integrals of Products of H -FunctionsIJMER
The object of the present paper is to evaluate an integral involving products of three H -function of different arguments which not only provides us the Laplace transform, Hankel transform ([8],p.3), Meijer’s Bessel transform ([8],p.121) and various other integral transforms of the product of two H -functions but also generalizes the result given earlier by many writers notably by Bailey ([3],
p.38), Meijer ([8],p.422) and Slater ([20], p.54(3.7.2).
This document introduces two new fractional integration operators associated with the H-function of two variables. The H-function of two variables is defined and some of its key properties are established. These operators generalize previous results given by other authors. The behavior of the H-function for small and large values of the variables is also described. When certain parameters are set to specific values, the H-function reduces to known cases.
In this paper, we consider the scaling invariant spaces for fractional Navier-Stokes in the
Lebesgue spaces ( ) p n L R and homogeneous Besov spaces
, ( ) s n
p q B R respectively.
The Analytical Nature of the Greens Function in the Vicinity of a Simple Poleijtsrd
It is known that the Green function of a boundary value problem is a meromorphic function of a spectral parameter. When the boundary conditions contain integro differential terms, then the meromorphism of the Greens function of such a problem can also be proved. In this case, it is possible to write out the structure of the residue at the singular points of the Greens function of the boundary value problem with integro differential perturbations. An analysis of the structure of the residue allows us to state that the corresponding functions of the original operator are sufficiently smooth functions. Surprisingly, the adjoint operator can have non smooth eigenfunctions. The degree of non smoothness of the eigenfunction of the adjoint operator to an operator with integro differential boundary conditions is clarified. It is indicated that even those conjugations to multipoint boundary value problems have non smooth eigenfunctions. Ghulam Hazrat Aimal Rasa "The Analytical Nature of the Green's Function in the Vicinity of a Simple Pole" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33696.pdf Paper Url: https://www.ijtsrd.com/mathemetics/applied-mathamatics/33696/the-analytical-nature-of-the-greens-function-in-the-vicinity-of-a-simple-pole/ghulam-hazrat-aimal-rasa
Development of implicit rational runge kutta schemes for second order ordinar...Alexander Decker
This document describes the development of a one-stage implicit rational Runge-Kutta method for solving second-order ordinary differential equations. The method is derived by taking Taylor series expansions of the solution equations about the point (xn, yn, yn') and equating terms with the same powers of the step size h. This results in expressions for the parameters of the method in terms of the leading order truncation errors. The method is consistent, as the parameters satisfy constraints that ensure the method approaches the true solution in the limit as h approaches 0.
This document investigates the transitivity, primitivity, ranks, and subdegrees of the direct product of the symmetric group acting on the Cartesian product of three sets. It proves that this action is both transitive and imprimitive for all 2n ≥ 6. The rank associated with the action is a constant 3/2. The subdegrees are calculated according to their increasing magnitude. Examples are provided to illustrate the ranks and subdegrees when the sets have 2, 3, and 4 elements, respectively.
Dr. Arpan Bhattacharyya (Indian Institute Of Science, Bangalore)Rene Kotze
1. The document discusses entanglement entropy functionals for higher derivative gravity theories. It proposes new area functionals for computing entanglement entropy in higher derivative theories containing polynomials of curvature tensors.
2. These functionals are derived using the Lewkowycz-Maldacena interpretation of generalized entropy. However, attempting to derive the extremal surface equations from these functionals using bulk equations of motion leads to inconsistencies and ambiguities in some higher derivative theories like Gauss-Bonnet gravity.
3. The document suggests that the source of ambiguity lies in the limiting procedure used to extract the divergences near the conical singularity. Different limiting paths can lead to different extremal surface equations, indicating no unique prescription
Stochastic Gravity in Conformally-flat SpacetimesRene Kotze
The National Institute for Theoretical Physics, and the Mandelstam Institute for Theoretical Physics, School of Physics, would like to invite to its coming talk in the theoretical physics seminar series, entitled:
"Stochastic Gravity in Conformally-flat Spacetimes"
to be presented by Prof. Hing-Tong Cho (Tamkang University, Taiwan)
Abstract: The theory of stochastic gravity takes into account the effects of quantum field fluctuations onto the classical spacetime. The essential physics can be understood from the analogous Brownian motion model. We shall next concentrate on the case with conformally-flat spacetimes. Our main concern is to derive the so-called noise kernels. We shall also describe our on-going program to investigate the Einstein-Langevin equation in these spacetimes.
Dates: Tuesday, 17th February 2015
Venue: The Frank Nabarro lecture theatre, P216
Time: 13.20 - 14.10 - TODAY
Some Soliton Solutions of Non Linear Partial Differential Equations by Tan-Co...IOSR Journals
Tan-cot method is applied to get exact soliton solutions of non-linear partial differential equations notably generalized Benjamin-Bona-Mahony, Zakharov-Kuznetsov Benjamin-Bona-Mahony, Kadomtsov-Petviashvilli Benjamin-Bona-Mahony and Korteweg-de Vries equations, which are important evolution equations with wide variety of physical applications. Elastic behavior and soliton fusion/fission is shown graphically and discussed physically as far as possible
Rotation in 3d Space: Euler Angles, Quaternions, Marix DescriptionsSolo Hermelin
Mathematics of rotation in 3d space, a lecture that I've prepared.
This presentation is at a Undergraduate in Science (Math, Physics, Engineering) level.
Please send comments and suggestions to solo.hermelin@gmail.com. Thanks!
Fore more presentations, please visit my website at
http://www.solohermelin.com/
On Some Double Integrals of H -Function of Two Variables and Their ApplicationsIJERA Editor
This paper deals with the evaluation of four integrals of H -function of two variables proposed by Singh and
Mandia [7] and their applications in deriving double half-range Fourier series for the H -function of two
variables. A multiple integral and a multiple half-range Fourier series of the H -function of two variables are
derived analogous to the double integral and double half-range Fourier series of the H -function of two
variables.
B. Dragovich: On Modified Gravity and CosmologySEENET-MTP
This document discusses modified gravity and cosmological solutions. It introduces Einstein's theory of gravity and some of its problems, including lack of renormalizability and prediction of dark energy and dark matter. It then presents a nonlocal modified gravity model to address these issues. The model yields nonsingular bouncing cosmological solutions for the scale factor in the form a(t) = a0(σeλt + τe−λt), which exist for different values of spatial curvature. These solutions depend on the cosmological constant and satisfy the equations of motion for certain conditions on the parameters of the nonlocal gravity action.
This document discusses the formulation of fractional supersymmetric theories in one dimension. It begins by presenting fractional superspace and fractional supersymmetry of order F=3, including the fractional supersymmetry transformations. It then derives the fractional supercharges and Euler-Lagrange equations for F=3. Finally, it generalizes the formulation to arbitrary fractional order F ≥ 3 by introducing fractional superspace and supersymmetry transformations of order F, as well as an action invariant under such transformations.
The peer-reviewed International Journal of Engineering Inventions (IJEI) is started with a mission to encourage contribution to research in Science and Technology. Encourage and motivate researchers in challenging areas of Sciences and Technology.
Some new exact Solutions for the nonlinear schrödinger equationinventy
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.
Auto Regressive Process (1) with Change Point: Bayesian ApprochIJRESJOURNAL
Abstract : Here we consider first order autoregressive process with changing autoregressive coefficient at some point of time m. This is called change point inference problem. For Bayes estimation of m and autoregressive coefficient we used MHRW (Metropolis Hasting Random Walk) algorithm and Gibbs sampling. The effects of prior information on the Bayes estimates are also studied.
Sweeping discussions on dirac field1 update3 sqrdfoxtrot jp R
This document discusses Dirac fields and Lagrangian formulations of electron theory. It presents Lagrangians for an effective electron theory based on an SU(2)XU(1) construction. The Lagrangians include terms for the electron, neutrino interactions, and interactions with gauge bosons. Integration by parts is used to rewrite the action in terms of adjoint spinor fields. Varying the actions yields Dirac's first order equation of motion for the electron field.
Exact Solutions of the Klein-Gordon Equation for the Q-Deformed Morse Potenti...ijrap
This document presents an analysis of solving the Klein-Gordon equation for the q-deformed Morse potential using the Nikiforov-Uvarov method. The eigenfunctions and eigenvalues of the Klein-Gordon equation are obtained. It is found that the eigenfunctions can be expressed in terms of Laguerre polynomials. The energy eigenvalues and normalized eigenfunctions obtained agree with previous studies that used algebraic approaches.
The document derives equations for an over-replicated softmax model. It defines constants for the number of documents, document length, dictionary size, and hidden units. It defines the energy of the joint configuration and simplifies the energy equation by tying weights and biases. It then defines the joint probability distribution and conditional distributions over visible and hidden units. It derives the derivatives of the log-likelihood with respect to the weights. Finally, it introduces variational inference to obtain a lower bound on the log probability of a document.
The document discusses I-functions and H-functions, which generalize Fox's H-function and contain certain Feynman integrals and partition functions as special cases. It establishes new double integral relations for products involving I-functions and H-functions. Specifically, it derives double integral relations for (A) a product of an I-function and H-function, and (B) the composition of an H-function with another H-function, under certain conditions on the parameters. These relations unify and extend previous known results for various special functions.
Jurnal Study of Anisotropy Superconductor using Time-Dependent Ginzburg-Landa...Fuad Anwar
This document summarizes a study that used numerical simulations based on the time-dependent Ginzburg-Landau equation to study the properties of anisotropic superconductors. The study models an anisotropic superconductor with different effective masses for Cooper pairs along different crystal axes. It describes the theoretical formalism and numerical methods used to solve the time-dependent Ginzburg-Landau equations for an anisotropic superconductor. The results of the numerical simulations show that the anisotropic properties of superconductors can cause the critical field to be either lower or higher compared to isotropic superconductors.
The document summarizes the results of a project investigating different types of particle motion, including cyclotron motion, gradient-B drift motion, magnetic mirroring, and motion due to a magnetic dipole. Analytical solutions were derived and compared to numerical simulations for each type of motion. Key results include plots showing cyclotron and gradient-B drift motion of protons and electrons match analytical solutions, and simulations demonstrating magnetic mirroring and orbits around a dipole match theoretical expectations. Periods were estimated from simulations and calculated from equations.
On Some Integrals of Products of H -FunctionsIJMER
The object of the present paper is to evaluate an integral involving products of three H -function of different arguments which not only provides us the Laplace transform, Hankel transform ([8],p.3), Meijer’s Bessel transform ([8],p.121) and various other integral transforms of the product of two H -functions but also generalizes the result given earlier by many writers notably by Bailey ([3],
p.38), Meijer ([8],p.422) and Slater ([20], p.54(3.7.2).
This document introduces two new fractional integration operators associated with the H-function of two variables. The H-function of two variables is defined and some of its key properties are established. These operators generalize previous results given by other authors. The behavior of the H-function for small and large values of the variables is also described. When certain parameters are set to specific values, the H-function reduces to known cases.
In this paper, we consider the scaling invariant spaces for fractional Navier-Stokes in the
Lebesgue spaces ( ) p n L R and homogeneous Besov spaces
, ( ) s n
p q B R respectively.
The Analytical Nature of the Greens Function in the Vicinity of a Simple Poleijtsrd
It is known that the Green function of a boundary value problem is a meromorphic function of a spectral parameter. When the boundary conditions contain integro differential terms, then the meromorphism of the Greens function of such a problem can also be proved. In this case, it is possible to write out the structure of the residue at the singular points of the Greens function of the boundary value problem with integro differential perturbations. An analysis of the structure of the residue allows us to state that the corresponding functions of the original operator are sufficiently smooth functions. Surprisingly, the adjoint operator can have non smooth eigenfunctions. The degree of non smoothness of the eigenfunction of the adjoint operator to an operator with integro differential boundary conditions is clarified. It is indicated that even those conjugations to multipoint boundary value problems have non smooth eigenfunctions. Ghulam Hazrat Aimal Rasa "The Analytical Nature of the Green's Function in the Vicinity of a Simple Pole" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-4 | Issue-6 , October 2020, URL: https://www.ijtsrd.com/papers/ijtsrd33696.pdf Paper Url: https://www.ijtsrd.com/mathemetics/applied-mathamatics/33696/the-analytical-nature-of-the-greens-function-in-the-vicinity-of-a-simple-pole/ghulam-hazrat-aimal-rasa
A coefficient inequality for the starlike univalent functions in the unit dis...Alexander Decker
This article presents two theorems regarding coefficient inequalities for starlike univalent functions with two fixed points in the unit disc. Specifically, it introduces a new class of analytic functions S*(A,B,b) with parameters A, B representing fixed points and b a non-zero complex number. Theorem 1 provides an inequality for the coefficients of functions in this class involving the parameters. Theorem 2 gives a separate coefficient inequality for functions in S*(A,B,b). The results generalize previous work on coefficient bounds for subclasses of univalent functions.
Analysis of variance of global experiments with repeated measurements with pr...IJMCERJournal
ABSTRACT: The global experiments in the presence of repeated measurements are represented in the case
of three overlapping factors and the third factor is represented by experimental units (Subjects). Repeated
measurements or treatments are taken for experimental units and these treatments are treated as a fourth factor.
This type of experiment has been analyzed by the parameterized methods represented by the F test. If the
conditions for variance analysis are available for repeated measurement experiments, and if the conditions are
not met, we use the non-parametric methods of converting to the ranks.
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International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
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International Journal of Mathematics and Statistics Invention (IJMSI)inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
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International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
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International Journal of Mathematics and Statistics Invention (IJMSI)
1. International Journal of Mathematics and Statistics Invention (IJMSI)
E-ISSN: 2321 – 4767 || P-ISSN: 2321 - 4759
www.ijmsi.org || Volume 2 || Issue 1 || February - 2014 || PP-21-27
Some Integral Properties of Aleph Function, General Class of
Polynomials Associated With Feynman Integrals
1,
Yashmeen Khan, and 2, Pallavi Sharma
1,
2,
Department of Mathematics, Government College, Kota, Rajasthan
Department of Mathematics, Kautilya Institute of Technology and Engineering, Jaipur, Rajasthan
ABSTRACT: The aim of the present paper is to discuss certain integral properties of Aleph function and
general class of polynomials. The exact partition of a Gaussian model in statistical mechanics and several other
functions as its particular cases. During the course of finding, we establish certain new double integral
relations pertaining to a product involving a general class of polynomials and the Aleph function.
KEY WORDS AND PHRASES: Feynman integrals, Aleph function, General Class of Polynomials, Hermite
Polynomials, Laguerre Polynomials.
I.
INTRODUCTION
The conventional formulation may fail pertaining to the domain of quantum cosmology but Feynman
path integrals apply interesting by Feynman path integrals are reformulation of quantum mechanics on more
fundamental than the conventional formulation in term of operator. Feynman integral are useful in the study and
development of simple and multiple variable hypergeometric series which in turn are useful in statistics
mechanics.
The Aleph ()-functions, introduced by Südland et al.[9], however the notation and complete definition
is presented here in the following manner in terms of the Mellin-Barnes type integrals
z]
1
2
m, n
y r
i i
L
z]
m, n
x , y r
i i i
s) z
x y r
i i i
z
m, n
For all z 0 where
(s)
(a A
a A
j
j 1, n i
ji
ji n 1, x r
i
(b B
b B
j
j 1, m i
ji
ji m 1, y r
i
…(1)
ds
1 and
m
n
m, n
x y r
i i i
s)
b
j1
x
r
i 1
1 a
j1
i
a
j n 1
the integration path L L
j
y
i
j
B s)
i
ji
R
A
ji
A s
j
…(2)
i
s
j
1 b
j m 1
ji
B
ji
s
extends from i to i and is such that the poles, assumed
to be simple, of 1 a A s), j = 1,…,n do not coincide with the pole of b B s), j= 1,…,m the
j
j
j
j
parameter xi, yi are non-negative integers satisfying:
0 n x 1 m y
i
i
The parameters A B A
j
j
ji
B
ji
i
0 for i 1,..., r
0 and a b a
j
j
ji
b
ji
C. The empty product in (2) is interpreted
as unity. The existence conditions for the defining integral (1) are given below
0 arg (z) |
2
1 r
www.ijmsi.org
…(3)
21 | P a g e
2. Some Integral Properties Of Aleph Function, General Class Of…
0 arg (z) |
and R { 1 0
2
…(4)
where
n
B
j
m
A
j
j1
j1
x
y
A
j n 1
j
B
x
y
b a b a
j
j
j
j
j1
j1
j n 1
j m 1
For detailed account of the Aleph ()-function see (9) and (10).
The general class of polynomial introduced by Srivastava (9)
m
n
n)
[n/m]
S
m
p]
n
mk
B
k!
k0
n, k
p
k
j
j m 1
…(5)
1
x y 1 r
2
…(6)
n 0,1,2,...
Main Results:
We shall establish the following results:
(A)
1
1
0 0
n/m]
1 p
q
1 pq
n)
mk
B
k!
k0
.
i 1
y
i 1
m
1 pq
S
(1 p)(1 q) n
r
i
1 p
m, n
wq
x y r
i i i
1 pq
1 q
w dp dq
1 pq
k
k w
n, k
m, n 1
x
1 q
1 pq
1 ;1), (a j A j 1, n i a ji A ji n 1, x i r
b B
b B
1 k 1
j j 1, m i ji ji m 1, y i r i
w
…(2.1)
provided that
T
Re[ b 0 arg w |
j
j
2
m is an arbitrary positive integer and the coefficient B
n, k 0) are arbitrary constant, real or complex.
n, k
Proof. We have
m
S
n
1 p
wq
1 pq
m, n
x
i
y r
i i
m
2
L
b
j1
x
r
i 1
i
(-n)
mk
B
k !
k0
n, k
1 p
wq
1 pq
k
n
1
[n/m]
1 q
w dp dq
1 pq
j
B s
j
y
i
j n 1
1 a
j1
a
ji
A
ji
s
j
A s
j
i
1 b
j m 1
ji
B
ji
s
1 q
w
1 pq
s
ds
…(2.2)
Multiplying both sides of (2.2) by
1 p
1 q
1 pq
w
and integrating with respect to p and q between 0 and 1 for both
1 pq
1 pq (1 p)(1 q)
the variable and we get the result
www.ijmsi.org
22 | P a g e
3. Some Integral Properties Of Aleph Function, General Class Of…
(B)
0
1
f( w
0
n/m]
n)
mk
B
k!
k0
.
i 1
y
i 1
n
m, n
x y r
i i i
w] d dw
k
1 ;1), (a j A j 1, n i a ji A ji n 1, x i r
b B
b B
1 k 1
j j 1, m i ji ji m 1, y i r i
m, n 1
x
S
k 1
f(
0
n, k
m
1
w
r
i
d
…(2.3)
provided that
Re( b 0 m is an arbitrary positive integer and coefficients B
j
i
n, k
n, k 0) are arbitrary
constants, real or complex.
Proof. We have
m
S
n
n)
[n/m]
m, n
w)
x y r
i i i
mk
B
k!
k0
m
n
1
2
b B s)
j
j1
L
x
r
k
n, k
i 1
j
j1
y
a
j n 1
A
ji
Multiplying both side (2.4) by f( w
1
s
1 a A s (w)
i
i
j
1 b
j m 1
1
w
…(2.4)
ds
i
s)
ji
j
B s)
ji
ji
and integrating with respect to and w between 0 and
for both side the variable and get the result (2.3).
1
n/m]
1
0 0
(C)
w 1 w
n)
1
1
w
m
S
1
mk
B
k!
k0
1
n, k
k
f( 1
n
m, n
w(1
k 1
x y r
i i i
1 w d dw
d
0
1 ;1), (a j A j 1, n i a ji A ji n 1, x i r
…(2.5)
1
x
y
r b B
b B
1 k 1
i 1 i 1 i
j
j 1, m
i
ji
ji m 1, y r i
i
provided that Re() >0, Re() >0, m is an arbitrary positive integer and coefficient Bn,k (n,k ≥ 0) are arbitrary
constant, real or complex.
Proof. We have
m, n 1
m
S
n
w 1
n/m]
m, n
x y r
i i i
1 w
n)
2
L
b B s)
j
j1
x
r
i 1
i
n, k
k
w
1
k
n
B
k!
k0
m
1
mk
j
j
q
i
j n 1
1 a A s)
j1
a
ji
A
ji
s)
j
1 w
s
ds
…(2.6)
i
1 b
j m 1
www.ijmsi.org
ji
B s)
ji
23 | P a g e
4. Some Integral Properties Of Aleph Function, General Class Of…
Multiplying both side of (2.6) by w 1
1
1 w
1
w
and integrating with respect to and w
between 0 and 1 for both the variable and get the result.
1
0 0
(D)
n/m]
q(1 p)
(1 pq)
1
n)
mk
.
i 1
y
1
q(1 p) m, n
wq(1 p)
x y r
dp dq
i i i
(1 pq)
1 pq
m
S
1 p)
n
k z 1
n, k
1 k 1 ), (a j A j 1, n i a ji A ji n 1, x i r
b B
b B
1 k 1
j j 1, m i ji ji m 1, y i r i
m, n
x
1 q
1 pq
k z 1
B
k!
k0
i 1
r
i
T
provided that Re( b 0 arg w |
j
i
w
…(2.7)
m is an arbitrary integer and the coefficient B n,k
2
(n,k ≥ 0) are arbitrary constant, real or complex.
Proof. We have
m
S
n
q(1 p) m, n
wq(1 p)
x y r
i i i 1 pq)
1 pq
n/m]
2
L
b B s)
j
j1
x
r
i 1
i
B
n, k
q(1 p)
1 pq
k
n
mk
k!
k0
m
1
n)
j
j
y
i
1 a A s)
j1
a
j n 1
ji
A
ji
i
s)
j
1 b
j m 1
ji
B s)
wq(1 p)
1 pq)
s
ds
ji
…(2.8)
q(1 p)
1 q
1
and integrating with respect to p and q
Multiplying both side by
1 pq
1 pq 1 p)
between 0 and 1for both the variable and get the result (2.7).
3. Particular Cases
By applying our result given in (2.1), (2.3), (2.5), (2.7) to the case of Hermite polynomial (8) and (11)
and by setting
1
n
n
2 p
In which case m = 2, Bn,k = (1)k.
2
S p] p
1
(A)
1
0 0
.
n/2
H
1 p
1 q
q
1 pq 1 pq
m, n
x y r
i i i
1 p
qw
(1 p)(1 q) 1 pq
1 q
w dp dq H
1 pq
1 pq)
n
2
n/2
1
1 p
wq
1 pq
www.ijmsi.org
24 | P a g e
5. Some Integral Properties Of Aleph Function, General Class Of…
n/2]
n)
2k
1
k
k
w
k
k!
k0
m, n 1
x 1 y 1 r
i
i
i
1 1 a A
a A
j
j 1, n i
ji
ji n 1, x r
i
. w
(b B
b B
1 k 1
j
j 1, m
i
ji
ji m 1, y r i
i
valid under the same conditions as obtained from (A).
(B)
0
n)
.
1
k
1 n/2
i 1
y
i 1
f(
0
m, n 1
x
2k
k!
k0
p 1
f( w w
0
n/2]
r
i
H
n
1 m, n
x y r w dw d
i i i
2 n
k 1
d k
1 1 a A
a A
j
j 1, n
i
ji
ji n 1, x r
i
(b B
b B
1 k 1
j
j 1, m
i
ji
ji m 1, y r i
i
valid under the same conditions as required for (B).
1
(C)
1
w 1
0 0
. H
n/2]
n)
n
.
1
w
n/2
1
2k
k
1 k
m, n 1
x
1 w
1
n/2
m, n
1
x , y r 1 w dw d
i i i
2 w 1
k!
k0
1
i 1
y
i 1
r
i
1
k 1
0
1 1 a j A j 1, n i a ji A ji n 1, x i r
b B
b B
1 k 1
j j 1, m i ji ji n 1, y i r i
1
valid under the same condition as required for (C).
(D)
1
1
0 0
q(1 p)
1 pq
H
n/2]
n)
2k
n
2
1 q
1 pq
1
q(1 p)
1 pq
k
1 1
k!
k0
1
1 n 2
1 p)
m, n
x y r
i i i
q
x
i 1
y
1 pq)
wq(1 p)
1 pq
m, n 1
i 1
r
i
n/2
n/2
dp dq
1 k 1 a j A j 1, n i a ji A ji n 1, x i r
w
(b B
b B
1 k 1
j j 1, m i ji ji m 1, y i r i
valid under the same conditions as obtained from (D).
For
the
B
n r
1
n r 1)
n, k
Laguerre
polynomials
([8]and
[11])
setting
'
r
n
n
S x) L x) in
which
case
the result (A), (B),(C) and D reduced to the following formulae
k
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25 | P a g e
6. Some Integral Properties Of Aleph Function, General Class Of…
(1)
1
1 p
1 q
q
1 pq 1 pq
1
0 0
n/2]
n)
n r
1
n r 1)
k
k!
k0
r 1 p
m, n
1 q
1 pq)
L
wq
w dp dq
n
x y r
i i i 1 pq
(1 p)(1 q)
1 pq
k
w
k
k
1 1 a A
a A
j
j 1, n
i
ji
ji n 1, x r
i
(b
m, n 1
.
x 1 y 1 r
i
i
i
j
B
b B
1 k 1
j 1, m
i
ji
ji m 1, y r i
i
w
valid under the same conditions as required for (A).
(2)
0
0
n)
n
1
f( w w
k
k!
k0
.
r
m, n
n
1
x y r
i i i
L
n r
1
n r 1)
f(
0
k
w] dw d
k 1
k
1 1 a A
a A
j
j 1, n i
ji
ji n 1, x r
i
(b
m, n 1
x 1 y 1 r
i
i
i
j
B
b B
1 k 1
j 1, m i
ji
ji m 1, y r i
i
valid under the same condition as required for (B).
1
(3)
1
w 1
0
0
n)
n
.
i 1
y
1
w
r
L
n
w 1
1
k
k'
0
f 1
1 1 a A
a A
j
j 1, n i
ji
ji n 1, x r
i
m, n 1
x
1 w
n r
1
n r 1)
k
k!
k0
1
i 1
r
i
m, n
x , y r
i i i
1 w dw d
k 1
b B
b B
1 k 1
j j 1, m i ji ji n 1, y i r i
valid under the same condition as required for (C).
(4)
1
q(1 p)
1 pq
1
0 0
L
n
n
q(1 p)
(1 pq
n)
k
k!
k0
.
r
1 q
1 pq
i 1
y
1
1 p)
m, n
x y r
i i i
n r
1
n r 1)
wq(1 p)
1 pq
dp dq
1
k'
1 k 1 a A
a A
j
j 1, n
i
ji
ji n 1, x r
i
m, n 1
x
i 1
r
i
(b
j
B
b B
1 k 1
j 1, m
i
ji
ji m 1, y r i
i
w
valid under the same condition as obtained for (D).
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26 | P a g e
7. Some Integral Properties Of Aleph Function, General Class Of…
II.
CONCLUSION
The results obtained here are basic in nature and are likely to find useful applications in the study of
simple and multiple variable hypergeometric series which in turn are useful in statistical mechanics, electrical
networks and probability theory. These integrals reformulation of quantum mechanics are more fundamental
than the conventional formulation in terms of operators.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
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Grosche, C. and Steiner, F., Hand book of Feynman path integrals, Springer tracts in modern physics, Vol.145, Springer-Verlag,
Berlin Heidelberg, New York (1998).
Mathai.A.M. and Saxena,R.K., The H-function with applications in Statistics and other disciplines, Wiley Eastern, New Delhi,
1978.
Saxena, Ram K and Pogany, Tiber K., On fractional integration formula for Aleph functions, Vol. 218(3), 2011 Applied Math.
Comput. Ilsevier.
Saxena, R.K. and Kumar, R., A basic analogue of generalized H-function, Matematiche (Catania) 50 (1995), 263-271.
Saxena, R.K., Mathai, A.M. and Haubold, H.J., Unified fractional kinetic equation and a diffusion equation, Astrophys. Space Sci.
290 (2004), 299-310.
Srivastava, H.M., Indian J. Math. 14(1972), 1-6.
Srivastava, H.M. and N.P. Singh, The integration of certain products of the multivariable H-function with a general class of
polynomials. Rend. Circ. Mat. Palermo, 2(32), 157-187 (1983).
Südland,N., Bauman,B. and Nonnenmacher,T.F., Open problem; who know about the Aleph ()-functions? Fract. Calc. Appl. Anal.
1(4) (1998); 401-402.
Südland,B., Baumann,B. and Nonnenmacher,T.F., Fractional driftless, Fokker-Planck equation with power law diffusion
coefficients. In V.G. Gangha, E.W. Mayr, W.G. Varozhtsov, editors, Computer Algebra in Scientific Computing (CASC Konstanz
2001), Springer, Berlin (2001); 513-525.
Szego, C., Orthogonal Polynomial, Amer. Math. Soc. Colloq. Publ. 23 fourth edition, Amer. Math. Soc. Providence, Rhode Island,
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