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Dilation,discrimination and Uhlmann's theorem of link products of quantum channels
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作者 雷强 操刘桁 +1 位作者 Asutosh Kumar 武俊德 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第3期201-206,共6页
We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-l... We establish the Stinespring dilation theorem of the link product of quantum channels in two different ways,discuss the discrimination of quantum channels,and show that the distinguishability can be improved by self-linking each quantum channel n times as n grows.We also find that the maximum value of Uhlmann's theorem can be achieved for diagonal channels. 展开更多
关键词 quantum channels link products Stinespring dilation theorem Uhlmann's theorem
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New Asymptotic Results on Fermat-Wiles Theorem
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作者 Kimou Kouadio Prosper Kouakou Kouassi Vincent Tanoé François 《Advances in Pure Mathematics》 2024年第6期421-441,共21页
We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Dio... We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Diophantine remainders of (a, b, c), an asymptotic approach based on Balzano Weierstrass Analysis Theorem as tools. We construct convergent infinite sequences and establish asymptotic results including the following surprising one. If z y = 1 then there exists a tight bound N such that, for all prime exponents p > N , we have xp yp zp. 展开更多
关键词 Fermat’s Last theorem Fermat-Wiles theorem Kimou’s Divisors Diophantine Quotient Diophantine Remainders Balzano Weierstrass Analysis theorem
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Diophantine equations and Fermat's last theorem for multivariate(skew-)polynomials
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作者 PAN Jie JIA Yu-ming LI Fang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期159-173,共15页
Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely... Fermat’s Last Theorem is a famous theorem in number theory which is difficult to prove.However,it is known that the version of polynomials with one variable of Fermat’s Last Theorem over C can be proved very concisely.The aim of this paper is to study the similar problems about Fermat’s Last Theorem for multivariate(skew)-polynomials with any characteristic. 展开更多
关键词 Fermat's last theorem polynomial ring skew polynomial ring
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AAK Theorem and a Design of Multidimensional BIBO Stable Filters
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作者 Bossoto Bossoto Gabriel Bissanga 《Open Journal of Discrete Mathematics》 2024年第2期9-15,共7页
Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with... Rational approximation theory occupies a significant place in signal processing and systems theory. This research paper proposes an optimal design of BIBO stable multidimensional Infinite Impulse Response filters with a realizable (rational) transfer function thanks to the Adamjan, Arov and Krein (AAK) theorem. It is well known that the one dimensional AAK results give the best approximation of a polynomial as a rational function in the Hankel semi norm. We suppose that the Hankel matrix associated to the transfer function has a finite rank. 展开更多
关键词 Multidimensional Filter DESIGN BIBO Stability Optimal AAK theorem Transfer Function Hankel Matrix
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Some convergence theorems of fuzzy concave integral on fuzzyσ-algebra
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作者 SUN Rong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期438-447,共10页
In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some ... In this paper,we consider the extension of the concave integral from classical crispσ-algebra to fuzzyσ-algebra of fuzzy sets.Firstly,the concept of fuzzy concave integral on a fuzzy set is introduced.Secondly,some important properties of such integral are discussed.Finally,various kinds of convergence theorems of a sequence of fuzzy concave integrals are proved. 展开更多
关键词 convergence theorems fuzzy concave integral fuzzyσ-algebra
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Small Modular Solutions to Fermat’s Last Theorem
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作者 Thomas Beatty 《Advances in Pure Mathematics》 2024年第10期797-805,共9页
The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infini... The proof by Andrew Wiles of Fermat’s Last Theorem in 1995 resolved the existence question for non-trivial solutions in integers x,y,zto the equation xn+yn=znfor n>2. There are none. Surprisingly, there are infinitely many solutions if the problem is recast in terms of modular arithmetic. Over a hundred years ago Issai Schur was able to show that for any n there is always a sufficiently large prime p0such that for all primes p≥p0the congruence xn+yn≡zn(modp)has a non-trivial solution. Schur’s argument wasnon-constructive, and there is no systematic method available at present to construct specific examples for small primes. We offer a simple method for constructing all possible solutions to a large class of congruences of this type. 展开更多
关键词 Fermat’s Last theorem Modular Arithmetic CONGRUENCES Prime Numbers Primitive Roots Indices Ramsey Theory Schur’s Lemma in Ramsey Theory
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Whole Perfect Vectors and Fermat’s Last Theorem
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作者 Ramon Carbó-Dorca 《Journal of Applied Mathematics and Physics》 2024年第1期34-42,共9页
A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm de... A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures. 展开更多
关键词 Fermat’s Last theorem Whole Perfect Vectors Sine and Cosine Functions Natural and Rational Vectors Fermat Vectors
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Vanishing Theorems for p-Harmonic Forms on Submanifolds in Spheres
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作者 Nan Li 《Journal of Contemporary Educational Research》 2024年第4期48-53,共6页
In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold ... In this paper,we present some vanishing theorems for p-harmonic forms on-super stable complete submanifold M immersed in sphere Sn+m.When 2≤1≤n-2,M has a flat normal bundle.Assuming that M is a minimal submanifold andδ>1(n-1)p2/4n[p-1+(p-1)2kp],we prove a vanishing theorem for p-harmonicℓ-forms. 展开更多
关键词 p-harmonic forms Vanishing theorems SUBMANIFOLDS
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A Study on High School Mathematics Teaching Design Based on Teaching for Robust Understanding: Taking the Cosine Theorem as an Example
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作者 Zhenping Wang Tianchen Ai 《Journal of Contemporary Educational Research》 2024年第6期96-103,共8页
Teachers’teaching behavior plays a crucial role in students’development,and there are problems in the current teaching behavior of mathematics teachers such as ignoring students’cognitive needs,lack of equal opport... Teachers’teaching behavior plays a crucial role in students’development,and there are problems in the current teaching behavior of mathematics teachers such as ignoring students’cognitive needs,lack of equal opportunities for students’classroom performance as well as lack of formative evaluation of students.In order to solve the phenomenon,this paper analyzes and explains how to promote teaching based on the Teaching for Robust Understanding(TRU)evaluation framework with the goal of focusing on the development of all students,taking the teaching design of The Cosine Theorem as an example,and provides ideas and methods for first-line high school mathematics teachers. 展开更多
关键词 Mathematics education Teaching for Robust Understanding framework Instructional design Cosine theorem
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The Njiki’s Fundamental Theorem-Definition on Fractions in the Mathematical Set ℚ and by Extension in ℝ and ℂ, for the Purpose of Leading to the Construction of Some Algebraic Structures as Its Theoretical Applications and for the Practical Ones
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作者 Jean Claude Njiki 《American Journal of Computational Mathematics》 2024年第3期358-379,共22页
The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTE... The purpose of the research in the NJIKI’s fundamental THEOREM-DEFINITION on fractions in the mathematical set ℚand by extension in ℝand ℂand in order to construct some algebraic structures is about the proved EXISTENCE and the DEFINITION by NJIKI of two INNOVATIVE, IMPORTANT and TEACHABLE operations of addition or additive operations, in ℚ, marked ⊕and +α,β, and taken as VECTORIAL, TRIANGULAR, of THREE or PROPORTIONAL operations and in order to make THEM not be different from the RATIONAL ONE, +, but to bring much more and new information on fractions, and, by extension in ℝand ℂ. And the very NJIKI’s fundamental THEOREM-DEFINITION having many APPLICATIONS in the everyday life of the HUMAN BEINGS and without talking about computer sciences, henceforth being supplied with very interesting new ALGORITHMS. And as for the work done in the research, it will be waiting for its extension to be done after publication and along with the research results concerned. 展开更多
关键词 Operations of Addition Additive Operations in Laws in theorem-DEFINITION External Multiplication
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非压缩动力系统及其Perron-Frobenius算子 被引量:1
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作者 叶远灵 《华南师范大学学报(自然科学版)》 CAS 2005年第3期100-107,共8页
讨论了一维非压缩动力系统以及由其所定义的Perron-Frobenius算子.给出了所论算子具有Perron-Frobenius性质的一个充分条件.
关键词 perron-frobenius算子 非压缩动力系统 Dini连续 函数迭代系统 perron-frobenius性质
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Perron-Frobenius定理的新证明 被引量:4
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作者 游兆永 永学荣 《西安交通大学学报》 EI CAS CSCD 北大核心 1992年第5期27-31,共5页
本文给出了Perron-Frobenius定理的新证明,获得了M矩阵的一个新性质,并且对非负可约矩阵A,给出了谱半径ρ(A)为单根和重根的充分必要性质。
关键词 M矩阵 谱半径 P-F定理
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具有负元素矩阵的Perron-Frobenius性质
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作者 郑艳萍 宋儒瑛 《太原科技大学学报》 2010年第3期239-242,共4页
利用算子理论方法结合矩阵分块技巧给出具有负元素矩阵及Perron-Frobenius性质的实矩阵的刻画,同时也讨论了该矩阵的性质。给出以下两个结果新的证明:(1)若A∈Rn×n,则下列性质等价。(ⅰ)A和AT具有强的Perron-Frobenius性质;(ⅱ)A... 利用算子理论方法结合矩阵分块技巧给出具有负元素矩阵及Perron-Frobenius性质的实矩阵的刻画,同时也讨论了该矩阵的性质。给出以下两个结果新的证明:(1)若A∈Rn×n,则下列性质等价。(ⅰ)A和AT具有强的Perron-Frobenius性质;(ⅱ)A是最终正的;(ⅲ)AT是最终正的。(2)若A是伪-M-矩阵,则A-1∈PFn. 展开更多
关键词 perron-frobenius性质 最终正的 伪-M-矩阵
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对称矩阵具有强Perron-Frobenius性质的条件 被引量:2
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作者 蔡占通 李耀堂 《延安大学学报(自然科学版)》 2010年第1期1-5,共5页
通过研究最终非负矩阵、最终正矩阵和不可约性之间的关系,得到若不可约对称正定矩阵A是最终非负矩阵,则A是最终正矩阵,给出对称矩阵具有强Perron-Frobenius性质的几个条件。
关键词 最终非负矩阵 最终正矩阵 不可约性 perron-frobenius性质 对称矩阵
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A nonlinear creep model for surrounding rocks of tunnels based on kinetic energy theorem 被引量:3
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作者 Wenbo Liu Hui Zhou +2 位作者 Shuguang Zhang Shuai Jiang Liu Yang 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2023年第2期363-374,共12页
The initiating condition for the accelerated creep of rocks has caused difficulty in analyzing the whole creep process.Moreover,the existing Nishihara model has evident shortcomings in describing the accelerated creep... The initiating condition for the accelerated creep of rocks has caused difficulty in analyzing the whole creep process.Moreover,the existing Nishihara model has evident shortcomings in describing the accelerated creep characteristics of the viscoplastic stage from the perspective of internal energy to analyze the mechanism of rock creep failure and determine the threshold of accelerated creep initiation.Based on the kinetic energy theorem,Perzyna viscoplastic theory,and the Nishihara model,a unified creep constitutive model that can describe the whole process of decaying creep,stable creep,and accelerated creep is established.Results reveal that the energy consumption and creep damage in the process of creep loading mainly come from the internal energy changes of geotechnical materials.The established creep model can not only describe the viscoelasticeplastic creep characteristics of rock,but also reflect the relationship between rock energy and creep deformation change.In addition,the research results provide a new method for determining the critical point of creep deformation and a new idea for studying the creep model and creep mechanical properties. 展开更多
关键词 Internal energy Kinetic energy theorem Perzyna viscoplastic theory Nishihara model Accelerated creep Initiating threshold
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Fractional Noether theorem and fractional Lagrange equation of multi-scale mechano-electrophysiological coupling model of neuron membrane 被引量:1
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作者 王鹏 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第7期409-415,共7页
Noether theorem is applied to a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics.The variable orders fractional Lagrange equation of a multiscale mechano-electrophysi... Noether theorem is applied to a variable order fractional multiscale mechano-electrophysiological model of neuron membrane dynamics.The variable orders fractional Lagrange equation of a multiscale mechano-electrophysiological model of neuron membrane dynamics is given.The variable orders fractional Noether symmetry criterion and Noether conserved quantities are given.The forms of variable orders fractional Noether conserved quantities corresponding to Noether symmetry generators solutions of the model under different conditions are discussed in detail,and it is found that the expressions of variable orders fractional Noether conserved quantities are closely dependent on the external nonconservative forces and material parameters of the neuron. 展开更多
关键词 Hamilton’s principle Noether theorem fractional derivative multiscale electromechanical coupling neuron membrane
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DISTORTION THEOREMS FOR CLASSES OF g-PARAMETRIC STARLIKE MAPPINGS OF REAL ORDER IN C^(n)
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作者 刘红炎 涂振汉 熊良鹏 《Acta Mathematica Scientia》 SCIE CSCD 2023年第4期1491-1502,共12页
In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the d... In this paper,we define the class S_(g)^(BX)of g-parametric starlike mappings of real order γ on the unit ball BX in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the distortion theorem of the Fr´echet-derivative type of S_(g)^(BX)with a weak restrictive condition,we further obtain the distortion results of the Jacobi-determinant type and the Fr´echet-derivative type for the corresponding classes(compared with S_(g)^(BX))defined on the unit polydisc(resp.unit ball with the arbitrary norm)in the space of n-dimensional complex variables,n≥2.Our results extend the classic distortion theorem of holomorphic functions from the case in one-dimensional complex space to the case in the higher dimensional complex space.The main theorems also generalize and improve some recent works. 展开更多
关键词 Banach space distortion theorem of Jacobi-determinant type distortion theorems of the Frechet-derivative type g-parametric starlike mappings
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REAL PALEY-WIENER THEOREMS FOR THE SPACE-TIME FOURIER TRANSFORM
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作者 Youssef EL HAOUI Mohra ZAYED 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1105-1115,共11页
This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourie... This paper presents an extension of certain forms of the real Paley-Wiener theorems to the Minkowski space-time algebra. Our emphasis is dedicated to determining the space-time valued functions whose space-time Fourier transforms(SFT) have compact support using the partial derivatives operator and the Dirac operator of higher order. 展开更多
关键词 Paley-Wiener theorem Minkowski algebra space-time algebra space-time Fourier transform
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A fixed point theorem for Proinov mappings with a contractive iterate
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作者 Erdal Karapnar Andreea Fulga 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2023年第3期403-412,共10页
In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the compl... In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces.We consider examples to illustrate the validity of the obtained result. 展开更多
关键词 contractive iterate at a point Proinov mappings fixed point theorems
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GLOBAL RIGIDITY THEOREMS FOR SUBMANIFOLDS WITH PARALLEL MEAN CURVATURE
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作者 潘鹏飞 许洪伟 赵恩涛 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期169-183,共15页
In this paper,we mainly study the global rigidity theorem of Riemannian submanifolds in space forms.Let Mn(n≥3)be a complete minimal submanifold in the unit sphere Sn+p(1).Forλ∈[0,n2−1/p),there is an explicit posit... In this paper,we mainly study the global rigidity theorem of Riemannian submanifolds in space forms.Let Mn(n≥3)be a complete minimal submanifold in the unit sphere Sn+p(1).Forλ∈[0,n2−1/p),there is an explicit positive constant C(n,p,λ),depending only on n,p,λ,such that,if∫MSn/2dM<∞,∫M(S−λ)n/2+dM<C(n,p,λ),then Mn is a totally geodetic sphere,where S denotes the square of the second fundamental form of the submanifold and∫+=max{0,f}.Similar conclusions can be obtained for a complete submanifold with parallel mean curvature in the Euclidean space Rn+p. 展开更多
关键词 Euclidean space the unit sphere submanifolds with parallel mean curvature global rigidity theorem
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