1) The document presents a new six point finite difference scheme for modeling nonlinear wave interaction using the coupled 1D Klein-Gordon-Zakharov system of equations.
2) The scheme is derived by discretizing the system equations with finite differences. It is shown to be equivalent to a multi-symplectic integrator.
3) Numerical simulations are presented applying the new six point scheme to solve the Klein-Gordon-Zakharov equations modeling the interaction of Langmuir waves and ion sound waves in plasma.
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.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
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.
Field Induced Josephson Junction (FIJJ) is defined as the physical system made by placement of ferromagnetic strip directly or indirectly [insulator layer in-between] on the top of superconducting strip [3, 4, 7]. The analysis conducted in extended Ginzburg-Landau, Bogoliubov-de Gennes and RCSJ [11] models essentially points that the system is in most case a weak-link Josephson junction [2] and sometimes has features of tunneling Josephson junction [1]. Generalization of Field Induced Josephson junctions leads to the case of network of robust coupled field induced Josephson junctions [4] that interact in inductive way. Also the scheme of superconducting Random Access Memory (RAM) for Rapid Single Flux [8, 9] quantum (RSFQ) computer is drawn [6, 10] using the concept of tunneling Josephson junction [1] and Field Induced Josephson junction [3, 4].
The given presentation is also available by YouTube (https://www.youtube.com/watch?v=uIqXqiwDsSM).
Literature
[1]. B.D.Josephson, Possible new effects in superconductive tunnelling, PL, Vol.1, No. 251, 1962
[2]. K.Likharev, Josephson junctions Superconducting weak links, RMP, Vol. 51, No. 101, 1979
[3]. K.Pomorski and P.Prokopow, Possible existence of field induced Josephson junctions, PSS B, Vol.249, No.9, 2012
[4]. K.Pomorski, PhD thesis: Physical description of unconventional Josephson junction, Jagiellonian University, 2015
[4]. K.Pomorski, H.Akaike, A.Fujimaki, Towards robust coupled field induced Josephson junctions, arxiv:1607.05013, 2016
[6]. K.Pomorski, H.Akaike, A.Fujimaki, Relaxation method in description of RAM memory cell in RSFQ computer, Procedings of Applied Conference 2016 (in progress)
[7]. J.Gelhausen and M.Eschrig, Theory of a weak-link superconductor-ferromagnet Josephson structure, PRB, Vol.94, 2016
[8]. K.K. Likharev, Rapid Single Flux Quantum Logic (http://pavel.physics.sunysb.edu/RSFQ/Research/WhatIs/rsfqre2m.html)
[9]. Proceedings of Applied Superconductivity Confence 2016, plenary talk by N.Yoshikawa, Low-energy high-performance computing based on superconducting technology (http://ieeecsc.org/pages/plenary-series-applied-superconductivity-conference-2016-asc-2016#Plenary7)
[10]. A.Y.Herr and Q.P.Herr, Josephson magnetic random access memory system and method, International patent nr:8 270 209 B2, 2012
[11]. J.A.Blackburn, M.Cirillo, N.Gronbech-Jensen, A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures, arXiv:1602.05316v1, 2016
Different Quantum Spectra For The Same Classical Systemvcuesta
The document discusses how the one-dimensional and two-dimensional isotropic harmonic oscillators, which correspond to a single classical system each, can have multiple quantum spectra.
Specifically, it shows that:
1) The one-dimensional oscillator admits two different quantum spectra, obtained by defining creation/annihilation operators in two different ways.
2) Similarly, the two-dimensional oscillator is shown to have four distinct quantum spectra, as the x and y directions can be quantized independently using two different operator definitions each.
3) This demonstrates that the same classical system can lead to multiple quantum descriptions and spectra, contrary to some previous works that obtained a unique spectrum for different classical formulations.
Catalan Tau Collocation for Numerical Solution of 2-Dimentional Nonlinear Par...IJERA Editor
Tau method which is an economized polynomial technique for solving ordinary and partial differential
equations with smooth solutions is modified in this paper for easy computation, accuracy and speed. The
modification is based on the systematic use of „Catalan polynomial‟ in collocation tau method and the
linearizing the nonlinear part by the use of Adomian‟s polynomial to approximate the solution of 2-dimentional
Nonlinear Partial differential equation. The method involves the direct use of Catalan Polynomial in the solution
of linearizedPartial differential Equation without first rewriting them in terms of other known functions as
commonly practiced. The linearization process was done through adopting the Adomian Polynomial technique.
The results obtained are quite comparable with the standard collocation tau methods for nonlinear partial
differential equations.
Existence of positive solutions for fractional q-difference equations involvi...IJRTEMJOURNAL
The existence of positive solutions is considered for a fractional q-difference equation with pLaplacian operator in this article. By employing the Avery-Henderson fixed point theorem, a new result is obtained
for the boundary value problems.
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.
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
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.
Field Induced Josephson Junction (FIJJ) is defined as the physical system made by placement of ferromagnetic strip directly or indirectly [insulator layer in-between] on the top of superconducting strip [3, 4, 7]. The analysis conducted in extended Ginzburg-Landau, Bogoliubov-de Gennes and RCSJ [11] models essentially points that the system is in most case a weak-link Josephson junction [2] and sometimes has features of tunneling Josephson junction [1]. Generalization of Field Induced Josephson junctions leads to the case of network of robust coupled field induced Josephson junctions [4] that interact in inductive way. Also the scheme of superconducting Random Access Memory (RAM) for Rapid Single Flux [8, 9] quantum (RSFQ) computer is drawn [6, 10] using the concept of tunneling Josephson junction [1] and Field Induced Josephson junction [3, 4].
The given presentation is also available by YouTube (https://www.youtube.com/watch?v=uIqXqiwDsSM).
Literature
[1]. B.D.Josephson, Possible new effects in superconductive tunnelling, PL, Vol.1, No. 251, 1962
[2]. K.Likharev, Josephson junctions Superconducting weak links, RMP, Vol. 51, No. 101, 1979
[3]. K.Pomorski and P.Prokopow, Possible existence of field induced Josephson junctions, PSS B, Vol.249, No.9, 2012
[4]. K.Pomorski, PhD thesis: Physical description of unconventional Josephson junction, Jagiellonian University, 2015
[4]. K.Pomorski, H.Akaike, A.Fujimaki, Towards robust coupled field induced Josephson junctions, arxiv:1607.05013, 2016
[6]. K.Pomorski, H.Akaike, A.Fujimaki, Relaxation method in description of RAM memory cell in RSFQ computer, Procedings of Applied Conference 2016 (in progress)
[7]. J.Gelhausen and M.Eschrig, Theory of a weak-link superconductor-ferromagnet Josephson structure, PRB, Vol.94, 2016
[8]. K.K. Likharev, Rapid Single Flux Quantum Logic (http://pavel.physics.sunysb.edu/RSFQ/Research/WhatIs/rsfqre2m.html)
[9]. Proceedings of Applied Superconductivity Confence 2016, plenary talk by N.Yoshikawa, Low-energy high-performance computing based on superconducting technology (http://ieeecsc.org/pages/plenary-series-applied-superconductivity-conference-2016-asc-2016#Plenary7)
[10]. A.Y.Herr and Q.P.Herr, Josephson magnetic random access memory system and method, International patent nr:8 270 209 B2, 2012
[11]. J.A.Blackburn, M.Cirillo, N.Gronbech-Jensen, A survey of classical and quantum interpretations of experiments on Josephson junctions at very low temperatures, arXiv:1602.05316v1, 2016
Different Quantum Spectra For The Same Classical Systemvcuesta
The document discusses how the one-dimensional and two-dimensional isotropic harmonic oscillators, which correspond to a single classical system each, can have multiple quantum spectra.
Specifically, it shows that:
1) The one-dimensional oscillator admits two different quantum spectra, obtained by defining creation/annihilation operators in two different ways.
2) Similarly, the two-dimensional oscillator is shown to have four distinct quantum spectra, as the x and y directions can be quantized independently using two different operator definitions each.
3) This demonstrates that the same classical system can lead to multiple quantum descriptions and spectra, contrary to some previous works that obtained a unique spectrum for different classical formulations.
Catalan Tau Collocation for Numerical Solution of 2-Dimentional Nonlinear Par...IJERA Editor
Tau method which is an economized polynomial technique for solving ordinary and partial differential
equations with smooth solutions is modified in this paper for easy computation, accuracy and speed. The
modification is based on the systematic use of „Catalan polynomial‟ in collocation tau method and the
linearizing the nonlinear part by the use of Adomian‟s polynomial to approximate the solution of 2-dimentional
Nonlinear Partial differential equation. The method involves the direct use of Catalan Polynomial in the solution
of linearizedPartial differential Equation without first rewriting them in terms of other known functions as
commonly practiced. The linearization process was done through adopting the Adomian Polynomial technique.
The results obtained are quite comparable with the standard collocation tau methods for nonlinear partial
differential equations.
Existence of positive solutions for fractional q-difference equations involvi...IJRTEMJOURNAL
The existence of positive solutions is considered for a fractional q-difference equation with pLaplacian operator in this article. By employing the Avery-Henderson fixed point theorem, a new result is obtained
for the boundary value problems.
Stability of Iteration for Some General Operators in b-MetricKomal Goyal
This document discusses the stability of the Jungck-Mann iteration scheme for approximating fixed points of operators in b-metric spaces. It defines the Jungck-Mann iterative procedure and establishes conditions for its stability. Specifically, it proves that if two operators S and T satisfy a contractive condition in a b-metric space, and Sx converges to a coincidence point p of S and T using the Jungck-Mann scheme, then any perturbed sequence Sy will also converge to p as the perturbations go to zero. The stability result relies on deriving inequalities relating the distances between iterates.
A current perspectives of corrected operator splitting (os) for systemsAlexander Decker
This document discusses operator splitting methods for solving systems of convection-diffusion equations. It begins by introducing operator splitting, where the time evolution is split into separate steps for convection and diffusion. While efficient, operator splitting can produce significant errors near shocks.
The document then examines the nonlinear error mechanism that causes issues for operator splitting near shocks. When a shock develops in the convection step, it introduces a local linearization that neglects self-sharpening effects. This leads to splitting errors.
To address this, the document discusses corrected operator splitting, which uses the wave structure from the convection step to identify where nonlinear splitting errors occur. Terms are added to the diffusion step to compensate for
On Convergence of Jungck Type Iteration for Certain Contractive Conditionsresearchinventy
In this article we prove the strong convergence result for a pair of nonself mappings using Jungck S- iterative scheme in Convex metric spaces satisfying certain contractive condition. The results are the generalization of some existing results in the literature
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
The document discusses approximate regeneration schemes for Markov chains. It introduces the concept of regeneration blocks between visits to an atom set. For chains without an atom, the Nummelin splitting technique extends the chain to be atomic. An approximate regeneration scheme is proposed using an estimated transition density over a small set to split the chain. This allows treating blocks of data as approximately i.i.d.
Compatible discretizations in our hearts and mindsMarie E. Rognes
This document discusses a total pressure augmented formulation for simulating fluid flow in porous media, such as modeling cerebral fluid flow in the brain. The formulation introduces total pressure as a variable to overcome issues with Poisson locking in the incompressible limit. The formulation results in a coupled system of equations that describes solid displacement, total pressure, and fluid pressures. Finite element methods are developed using this formulation that achieve optimal convergence rates, including in the incompressible limit, using Taylor-Hood elements. Numerical experiments demonstrate the improved convergence rates over standard formulations.
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.
This document contains notes from a statistics course. It discusses sequences of random variables, limits, Chebyshev's theorem, the law of large numbers, and the central limit theorem. The notes provide definitions and examples of key concepts like independent and identically distributed random variables, convergence in probability, and how the sample mean approximates the population mean as the sample size increases. Students are prompted with practice problems applying the concepts.
Quantum Transitions And Its Evolution For Systems With Canonical And Noncanon...vcuesta
1. The document studies the quantum transitions and time evolution of the phase space coordinates for the one-dimensional harmonic oscillator with both canonical and noncanonical symplectic structures.
2. For the canonical case, the solutions to the classical equations of motion and the quantum transitions between energy levels are obtained. The time evolution of the transition amplitudes between states is also determined.
3. An analogous analysis is performed for the noncanonical case, where modified commutation relations and modified expressions for the creation/annihilation operators are obtained. The quantum transitions and their time evolution are determined.
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.
The document describes an algorithm for simulating stochastic lineshapes using a multidimensional array approach. It involves:
1. Generating a 6D array to represent the Liouville matrix and casting it into a 2D array.
2. Inverting the 2D array and casting it back to 6D.
3. Using indexing methods to reference elements between the 2D and 6D arrays and perform summations to calculate lineshapes.
Examples are provided of NMR lineshapes simulated for a spin-1/2 nucleus with different jump rates of a fluctuating magnetic field along the x, y, and z axes.
Stability criterion of periodic oscillations in a (7)Alexander Decker
This document introduces the concept of nano continuous functions between nano topological spaces. It defines nano continuous functions as those whose inverse image of every nano-open set is nano-open. Several characterizations of nano continuous functions are provided in terms of nano closed sets, nano closure, and nano interior. Nano continuous functions are shown to preserve nano closed sets under inverse image and nano closure under inverse image composition. The concept of a basis for a nano topology is used to provide another characterization of nano continuous functions in terms of the inverse image of basis elements.
The document summarizes several results on metric embeddings. It begins by defining metric embeddings and distortion. It then states three theorems:
1) There is a randomized polynomial-time algorithm that embeds any metric space into a tree metric with expected distortion O(log n).
2) Any n-point 2-metric can be embedded into R^O(log n) with distortion 1+ε.
3) There is an algorithm that embeds any metric space into l_1 with distortion O(log k) such that it preserves distances between k given terminal pairs up to a factor of O(log k).
The document then discusses properties and algorithms for embeddings into l_1, l
- The thesis studies numerical methods for stochastic partial differential equations (SPDEs) subject to generalized Levy noise.
- It develops both deterministic methods using the Fokker-Planck equation and probabilistic methods like polynomial chaos.
- Key contributions include developing adaptive multi-element polynomial chaos for discrete measures, comparing approaches to construct orthogonal polynomials over discrete measures, and improving efficiency and accuracy through adaptive integration meshes and sparse grids.
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.
A new approach to constants of the motion and the helmholtz conditionsAlexander Decker
1) The document discusses a new approach to determining constants of motion based on Helmholtz conditions for the existence of a Lagrangian.
2) It shows that constants of motion determined by this new approach vanish when the symmetry group is related to an actual invariance of the Lagrangian, as in this case the classical Noether invariants can be used.
3) The key equations of the approach are presented, including an equation (9) that provides an expression for constants of motion associated with any symmetry of a dynamical system with a Lagrangian.
Existence of Solutions of Fractional Neutral Integrodifferential Equations wi...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
An Introduction to HSIC for Independence TestingYuchi Matsuoka
This document introduces Hilbert-Schmidt Independence Criterion (HSIC) for testing independence between random variables. HSIC embeds probability distributions into reproducing kernel Hilbert spaces and computes the distance between joint and product distributions using the Maximum Mean Discrepancy. It presents HSIC as a completely nonparametric measure of dependence that is applicable to high dimensional data. The document outlines how to compute HSIC from samples and discusses its relationship to U-statistics, providing an independence test using HSIC with permutations.
Epidemic processes on switching networksNaoki Masuda
Presentation slides for the following two papers:
- Leo Speidel, Konstantin Klemm, Víctor M. Eguíluz, Naoki Masuda.
New Journal of Physics, 18, 073013 (2016).
- Tomokatsu Onaga, James P. Gleeson, Naoki Masuda.
Physical Review Letters, 119, 108301 (2017).
Wow! Signal Decoded as Foundations of Theory of EverythingXequeMateShannon
The document decodes the "Wow! Signal" as containing information about the foundations of a Theory of Everything. It presents three ways the signal can be divided and analyzed:
1) The first two numbers in the signal (6 and 14) indicate its true length and that the second part verifies the first.
2) Dividing the main part into two groups of three elements yields equal sums, justifying this division.
3) The numbers correspond to degrees of freedom of stable and meta-stable manifolds described in Scale Symmetric Theory, which underlie different levels of nature.
This paper provides alternative optimal expressions for determining matrices of a class of double-delay autonomous linear differential systems. The paper extends previous work by resolving ambiguities in permutations and analyzing computational complexity and cardinalities of determining matrices. Key results include theorems and corollaries that provide expressions for determining matrices ( )kQ jh in terms of sums of permutation products involving system matrices A, A1, A2. The expressions are proven to be consistent with previous work and fill gaps in the prior literature.
Solvability of Fractionl q -Difference Equations of Order 2 3 Involving ...journal ijrtem
This document summarizes a research paper that studies the existence of solutions for nonlinear fractional q-difference equations involving the p-Laplacian operator with boundary conditions where α is between 3/2 and 2. The paper represents the solution of the boundary value problem as an integral equation and proves, under certain conditions, that the nonlinear fractional boundary value problem has a unique solution using the Banach contraction mapping principle. It also provides relevant definitions and preliminary results from fractional q-calculus that are used in the analysis.
Stability of Iteration for Some General Operators in b-MetricKomal Goyal
This document discusses the stability of the Jungck-Mann iteration scheme for approximating fixed points of operators in b-metric spaces. It defines the Jungck-Mann iterative procedure and establishes conditions for its stability. Specifically, it proves that if two operators S and T satisfy a contractive condition in a b-metric space, and Sx converges to a coincidence point p of S and T using the Jungck-Mann scheme, then any perturbed sequence Sy will also converge to p as the perturbations go to zero. The stability result relies on deriving inequalities relating the distances between iterates.
A current perspectives of corrected operator splitting (os) for systemsAlexander Decker
This document discusses operator splitting methods for solving systems of convection-diffusion equations. It begins by introducing operator splitting, where the time evolution is split into separate steps for convection and diffusion. While efficient, operator splitting can produce significant errors near shocks.
The document then examines the nonlinear error mechanism that causes issues for operator splitting near shocks. When a shock develops in the convection step, it introduces a local linearization that neglects self-sharpening effects. This leads to splitting errors.
To address this, the document discusses corrected operator splitting, which uses the wave structure from the convection step to identify where nonlinear splitting errors occur. Terms are added to the diffusion step to compensate for
On Convergence of Jungck Type Iteration for Certain Contractive Conditionsresearchinventy
In this article we prove the strong convergence result for a pair of nonself mappings using Jungck S- iterative scheme in Convex metric spaces satisfying certain contractive condition. The results are the generalization of some existing results in the literature
Research Inventy : International Journal of Engineering and Scienceresearchinventy
Research Inventy : International Journal of Engineering and Science is published by the group of young academic and industrial researchers with 12 Issues per year. It is an online as well as print version open access journal that provides rapid publication (monthly) of articles in all areas of the subject such as: civil, mechanical, chemical, electronic and computer engineering as well as production and information technology. The Journal welcomes the submission of manuscripts that meet the general criteria of significance and scientific excellence. Papers will be published by rapid process within 20 days after acceptance and peer review process takes only 7 days. All articles published in Research Inventy will be peer-reviewed.
The document discusses approximate regeneration schemes for Markov chains. It introduces the concept of regeneration blocks between visits to an atom set. For chains without an atom, the Nummelin splitting technique extends the chain to be atomic. An approximate regeneration scheme is proposed using an estimated transition density over a small set to split the chain. This allows treating blocks of data as approximately i.i.d.
Compatible discretizations in our hearts and mindsMarie E. Rognes
This document discusses a total pressure augmented formulation for simulating fluid flow in porous media, such as modeling cerebral fluid flow in the brain. The formulation introduces total pressure as a variable to overcome issues with Poisson locking in the incompressible limit. The formulation results in a coupled system of equations that describes solid displacement, total pressure, and fluid pressures. Finite element methods are developed using this formulation that achieve optimal convergence rates, including in the incompressible limit, using Taylor-Hood elements. Numerical experiments demonstrate the improved convergence rates over standard formulations.
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.
This document contains notes from a statistics course. It discusses sequences of random variables, limits, Chebyshev's theorem, the law of large numbers, and the central limit theorem. The notes provide definitions and examples of key concepts like independent and identically distributed random variables, convergence in probability, and how the sample mean approximates the population mean as the sample size increases. Students are prompted with practice problems applying the concepts.
Quantum Transitions And Its Evolution For Systems With Canonical And Noncanon...vcuesta
1. The document studies the quantum transitions and time evolution of the phase space coordinates for the one-dimensional harmonic oscillator with both canonical and noncanonical symplectic structures.
2. For the canonical case, the solutions to the classical equations of motion and the quantum transitions between energy levels are obtained. The time evolution of the transition amplitudes between states is also determined.
3. An analogous analysis is performed for the noncanonical case, where modified commutation relations and modified expressions for the creation/annihilation operators are obtained. The quantum transitions and their time evolution are determined.
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.
The document describes an algorithm for simulating stochastic lineshapes using a multidimensional array approach. It involves:
1. Generating a 6D array to represent the Liouville matrix and casting it into a 2D array.
2. Inverting the 2D array and casting it back to 6D.
3. Using indexing methods to reference elements between the 2D and 6D arrays and perform summations to calculate lineshapes.
Examples are provided of NMR lineshapes simulated for a spin-1/2 nucleus with different jump rates of a fluctuating magnetic field along the x, y, and z axes.
Stability criterion of periodic oscillations in a (7)Alexander Decker
This document introduces the concept of nano continuous functions between nano topological spaces. It defines nano continuous functions as those whose inverse image of every nano-open set is nano-open. Several characterizations of nano continuous functions are provided in terms of nano closed sets, nano closure, and nano interior. Nano continuous functions are shown to preserve nano closed sets under inverse image and nano closure under inverse image composition. The concept of a basis for a nano topology is used to provide another characterization of nano continuous functions in terms of the inverse image of basis elements.
The document summarizes several results on metric embeddings. It begins by defining metric embeddings and distortion. It then states three theorems:
1) There is a randomized polynomial-time algorithm that embeds any metric space into a tree metric with expected distortion O(log n).
2) Any n-point 2-metric can be embedded into R^O(log n) with distortion 1+ε.
3) There is an algorithm that embeds any metric space into l_1 with distortion O(log k) such that it preserves distances between k given terminal pairs up to a factor of O(log k).
The document then discusses properties and algorithms for embeddings into l_1, l
- The thesis studies numerical methods for stochastic partial differential equations (SPDEs) subject to generalized Levy noise.
- It develops both deterministic methods using the Fokker-Planck equation and probabilistic methods like polynomial chaos.
- Key contributions include developing adaptive multi-element polynomial chaos for discrete measures, comparing approaches to construct orthogonal polynomials over discrete measures, and improving efficiency and accuracy through adaptive integration meshes and sparse grids.
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.
A new approach to constants of the motion and the helmholtz conditionsAlexander Decker
1) The document discusses a new approach to determining constants of motion based on Helmholtz conditions for the existence of a Lagrangian.
2) It shows that constants of motion determined by this new approach vanish when the symmetry group is related to an actual invariance of the Lagrangian, as in this case the classical Noether invariants can be used.
3) The key equations of the approach are presented, including an equation (9) that provides an expression for constants of motion associated with any symmetry of a dynamical system with a Lagrangian.
Existence of Solutions of Fractional Neutral Integrodifferential Equations wi...inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
An Introduction to HSIC for Independence TestingYuchi Matsuoka
This document introduces Hilbert-Schmidt Independence Criterion (HSIC) for testing independence between random variables. HSIC embeds probability distributions into reproducing kernel Hilbert spaces and computes the distance between joint and product distributions using the Maximum Mean Discrepancy. It presents HSIC as a completely nonparametric measure of dependence that is applicable to high dimensional data. The document outlines how to compute HSIC from samples and discusses its relationship to U-statistics, providing an independence test using HSIC with permutations.
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A new six point finite difference scheme for nonlinear waves interaction model
1. Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.3, 2013
A New Six Point Finite Difference Scheme for
Nonlinear Waves Interaction Model
Dr. Arun Kumar*
Department of Mathematics, Government College, Kota (Raj.), India,
Dr. R. D. Pankaj
Department of Mathematics, J.N.V. University, Jodhpur (Raj.), India
Dr. Jyoti Sachdeva
Department of Mathematics, M.V.N. University, Palwal (Haryana), India
Abstract: In the paper, the coupled 1D Klein-Gordon-Zakharov system (KGZ-equations in
short) is considered as the model equation for wave-wave interaction in ionic media. A finite
difference scheme is derived for the model equations. A new six point scheme, which is
equivalent to the multi-symplectic integrator, is derived. The numerical simulation is also
presented for the model equations.
Keywords: Coupled 1D Klein-Gordon-Zakharov system; Energy conservation; Six-point
scheme
1. Introduction
Nonlinear evolution equations have a major role in various scientific fields, such as fluid
mechanics, plasma physics, optical fibres, solid state physics, chemical physics, and
geochemistry. Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and
convection are very important in nonlinear wave equations. In recent years, solving nonlinear
evolution equations has become a valuable task in many scientific areas including applied
mathematics as well as the physical sciences and engineering. For this purpose, some accurate
methods have been presented, such as Inverse scattering transform method[1], Bä cklund
transformation method[2], Jacobi elliptic function method[3], F-expansion method[4],
Hirota’s bilinear method[5], the extended hyperbolic functions method[6, 7], Homotopy
perturbation method[8], Bifurcation method [9–11] and so on.
Wave-wave interaction is an important problem for both physical and mathematical reasons.
Physically, the wave-wave interaction or the wave collisions are common phenomena in
science and engineering for both solitary and non-solitary waves. Mathematically solitary
wave collision is a major branch of nonlinear wave interaction in ionic media.
We consider as the model equation the following Klein-Gordon-Zakharov (KGZ) equations
Ett Exx E nE 0,
(1)
ntt nxx E xx 0
2
This system is describe [12, 13] the interaction of a Langmuir wave and an ion sound wave in
plasma. More precisely, E is the fast scale component of the electric field, where η denotes
the deviation of ion density, in the paper, we discretize the system with finite difference
schemes to show the multi-symplectic structure of CNLKGZ system.
53
2. Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.3, 2013
2. A difference scheme for CNLKGZ system
We consider the following generalized CNLKGZ system
Ett Exx E nE 0,
ntt nxx E xx 0
2
Where E p x, t iq x, y , x, t i x, y (2)
We
pxx ptt p 1 q qxx qtt p q 1 have
tt xx p xx q xx 0
2 2
tt xx 0
(3)
Introducing the canonical momenta
px a, qx b, pt c, qt d , x e, x f , t g , t h, u p 2 , v q 2
x x
The above system can be written in the following form
Kz t Lz x z S z (4)
with independent variable (t, x) R and state variable z R , d ≥ 2. Here K, L R are two
2 d dxd
skew-symmetric matrices and S : Rd →R is a scalar-valued smooth function. z is the
standard gradient in Rd. For S(z) and z S(z) , the system is multi-symplectic in the sense that
K is a skew-symmetric matrix representative of the t direction and L is a skew-symmetric
matrix representative of the x direction. S represents a Hamiltonian function [14, 15, 16]. The
equation (4) is multi-symplectic in nature with the state variables
z p, q, a, b, c, d , , , e, f , g , h, u, v, p 2 , q 2 T
R16
So the z S z kp, kq, a, b, c, d , , , e, f , g , h, u, v, p , q
2
2 T
kp p 1 q ; kq p q 1
We get
ax ct p 1 q bx dt p q 1
px a qx b, pt c, qt d
gt ex u x vx 0 ht f x 0
x e, x f , t g , t h,
u p2 , v q2
x x
and the pair of skew symmetric matrix K and L are
54
4. Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.3, 2013
pln12 pln1 2 n 1 2
1
cn 1 2
t (9)
n 1
ql 1 2 qln1 2 n 1 2
d n 1 2
t (10)
g ln12 g ln1 2 eln1 2 eln1 2 uln1 2 uln1 2 vln1 2 vln1 2
1 1 0
1 1
t x x x (11)
hln12 hln1 2 f l n 1 1 2 f l n 1 2
1
0
t x
(12)
ln1 2 ln 1 2
1
eln1122
x (13)
ln 1 2 ln 1 2 n
1
f l 1 1 2
x
2
(14)
ln 12 ln 1 2
1
g ln 122
1
t
(15)
ln 12 ln 1 2
1
hln 122
1
t
(16)
p 2
x
n 1 2
l 1
p2 x
n 1 2
l
uln 122
1
x
(17)
q 2 n 1 2
x l 1
q2 x l
n 1 2
vln 122
1
x
(18)
ˆ ˆ ˆ ˆ
ln122 , q qln122 , p pln122 , ln122
1 1 1 1
Eliminate a, and c from (5), using (7), (9) so we can get
2 pln21 2 2 pln1 2 pln1 2 2 pn1 2 2 pn1 2 pn1 2
n 3 2 n1 2 n1 2
1
x 2 t 2
n 1
2
n1
2
n 1 2
pn3 2 1 n3 2 q n3 2 n3 2 pn1 2 1 n1 2 q n1 2 n1 2
n1 2 n 1 2 n 1 2 n 1 2 n 1 2
(19)
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5. Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.3, 2013
Eliminate b, and d from (6), using (8), (10) so we can get
2qln21 2 2qln1 2 qln1 2 2qn1 2 2qn1 2 qn1 2
n 3 2 n1 2 n1 2
1
x 2 t 2
n1
2
n1
2
n1 2
qn3 2 1 n3 2 p n3 2 n3 2 qn1 2 1 n1 2 p n1 2 n1 2
n 1 2 n1 2 n1 2 n1 2 n1 2
(20)
Eliminate g, e, u, and v from (11), using (13), (15), (17), (18) so we can get
nn13 22 2 nn11 22 nn11 22 ln21 2 2ln11 2 ln1 2
t 2 x 2
p2
n 1 2
n 1 2
x l 2 2 p x l 1 p x l
2 2
n 1 2
n 1 2 n 1 2
q 2 x l 2 2 q 2 x l 1 q 2
n1 2
x l
0
x 2 x 2
(21)
Eliminate h, and f from (12), using (14), (16) so we can get
nn13 22 2 nn11 22 nn11 22 ln21 2 2ln1 2 ln 1 2
0
1
t 2 x 2
(22)
Multiply (20) with i. and adding Eq. (19) then we can get
2 Eln21 2 2 Eln1 2 Eln 1 2
1 2E n 3 2
n 1 2
2 Enn11 22 Enn11 22
x t
2 2
Enn 3 2 1 nn 3 2 Enn11 22 1 nn11 22
1 2 1 2
(23)
Multiply (22) with i. And adding Eq. (21) then we can get
n 1 2 n 1 2 n 1 2
nn13 22 2nn11 22 nn11 22 n1 2 2 n1 2 n1 2 E x
2
2 E2 E2
l 2 l 1
l 2
0
l x l 1 x l
(24)
t
2
x
2
x
2
3. Numerical simulation
In this section, we present the numerical result of the Coupled Klein-Gordon-Zakharov
system using the multi-symplectic integrator. Now we consider the CNLKGZ system
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6. Mathematical Theory and Modeling www.iiste.org
ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.3, 2013
Ett Exx E nE 0,
ntt nxx E xx 0
2
with the initial value
1
u ( x, o ) 2r1 sec h(r1 x D0 )etV0 x / 4
2 (25)
1
v ( x, o ) 2r1 sec h(r2 x D0 )e tV0 x / 4
2
We take the time step ∆ t = 0.02 and a space step ∆x = 0.02, -0.3 ≤ x ≤ 0.3, D0 = 25, r1 = r2 =
1 and V0=1. In Fig. 1, the computation is done for 0 ≤ t ≤ 2.
(a)
(b)
Fig. 1. Simulation results of the interaction of the two waves
4. Conclusion: In this paper, the multi-symplectic formulation for the coupled Klein-
Gordon-Zakharov system is presented. Numerical simulations are also reported. We
observe that the multi-symplectic scheme well simulates the evolution of the solitons. It
has advantage for the long time computing accuracy and preserving the energy
conservation property.
References
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Philadelphia: SIAM.
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ISSN 2224-5804 (Paper) ISSN 2225-0522 (Online)
Vol.3, No.3, 2013
[2] Miura, R. M. (1996). Bäcklund transformation. New York: Springer-Verlag.
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