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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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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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基于S-R和分解定理的二维几何非线性问题的虚单元法求解
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作者 江巍 尹豪 +3 位作者 吴剑 汤艳春 李坤鹏 郑宏 《工程力学》 EI CSCD 北大核心 2024年第8期23-35,共13页
应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝... 应变-旋转(Strain-Rotation,S-R)和分解定理为分析几何非线性问题提供了合理可靠的理论基础,但用有限元求解时会遇到大变形发生后的网格畸变问题。近年提出的虚单元法(Virtual element method,VEM)适用于一般的多边形网格,因此,该文尝试使用一阶虚单元求解基于S-R和分解定理的二维几何非线性问题,以克服网格畸变的影响。基于重新定义的多项式位移空间基函数,推演获得一阶虚单元分析线弹性力学问题时允许位移空间向多项式位移空间的投影表达式;按照虚单元法双线性格式的计算规则,分析处理基于更新拖带坐标法和势能率原理的增量变分方程;进而建立离散系统方程及其矩阵表达形式,并编制MATLAB求解程序;采用常规多边形网格和畸变网格,应用该文算法分析均布荷载下的悬臂梁和均匀内压下的厚壁圆筒变形。结果与已有文献和ANSYS软件的对比表明:该文算法在两种网格中均可有效执行且具备足够数值精度。总体该文算法为基于S-R和分解定理的二维几何非线性问题求解提供了一种鲁棒方法。 展开更多
关键词 s-R和分解定理 虚单元法 几何非线性 网格畸变 多边形网格
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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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Improve regression-based models for prediction of internal-bond strength of particleboard using Buckingham's pi-theorem 被引量:1
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作者 Akbar Rostampour Haftkhani Mohammad Arabi 《Journal of Forestry Research》 SCIE CAS CSCD 2013年第4期735-740,共6页
Internal bond (IB) strength is one of the most important me- chanical properties that indicate particleboard quality. The aim of this study was to find a simple regression model that considers the most important par... Internal bond (IB) strength is one of the most important me- chanical properties that indicate particleboard quality. The aim of this study was to find a simple regression model that considers the most important parameters that can influence on IB strength. In this study, IB strength was predicted by three kinds of equations (linear, quadratic, and exponential) that were based on the percentage of adhesive (8%, 9.5%, and 11%), particle size (+5, -5 +8, -8 12, and -12 mesh), and density (0.65, 0.7, and 0.75 g/cm3). Our analysis of the results (using SHAZAM 9 software) showed that the exponential function best fitted the experi- mental data and predicted the IB strength with 18~,/0 error. In order de- crease the error percentage, the Buckingham Pi theorem was used to build regression models for predicting IB strength based on particle size, 展开更多
关键词 buckinghams Pi theorem intemal bond strength particle-board screw withdrawal resistance.
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基于TDLAS的天然气泄漏范围重构方法
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作者 曹理想 文耀华 +2 位作者 张伯君 周泽华 业成 《激光与红外》 CAS CSCD 北大核心 2024年第9期1387-1391,共5页
可调谐半导体激光光谱(TDLAS)技术因其灵出色的灵敏度、精度和抗干扰性的特性,现已被广泛应用于场站天然气泄漏的监测工作。为克服单台TDLAS激光遥测仪无法获得泄漏气体扩散影响范围的局限性,本文提出了一种基于多台TDLAS遥测仪协同的... 可调谐半导体激光光谱(TDLAS)技术因其灵出色的灵敏度、精度和抗干扰性的特性,现已被广泛应用于场站天然气泄漏的监测工作。为克服单台TDLAS激光遥测仪无法获得泄漏气体扩散影响范围的局限性,本文提出了一种基于多台TDLAS遥测仪协同的智能监测方法,通过在不同斜平面内对泄漏气团进行扫查,依据Brianchon定理获得不同斜平面内气体泄漏的外轮廓方程,重构天然气的三维空间泄漏影响区域,实时开展监测与预警。 展开更多
关键词 天然气 TDLAs 泄漏监测 Brianchon定理
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Products of Odd Numbers or Prime Number Can Generate the Three Members’ Families of Fermat Last Theorem and the Theorem Is Valid for Summation of Squares of More Than Two Natural Numbers
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作者 Susmita Pramanik Deepak Kumar Das Panchanan Pramanik 《Advances in Pure Mathematics》 2023年第10期635-641,共7页
Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number great... Fermat’s last theorem, had the statement that there are no natural numbers A, B, and C such that A<sup>n</sup> + B<sup>n</sup> = C<sup>n</sup>, in which n is a natural number greater than 2. We have shown that any product of two odd numbers can generate Fermat or Pythagoras triple (A, B, C) following n = 2 and also it is applicable A<sup>2</sup> + B<sup>2</sup> + C<sup>2</sup> + D<sup>2</sup> + so on =A<sub>n</sub><sup>2 </sup>where all are natural numbers. 展开更多
关键词 Fermat Last theorem Generation of Fermat’s Numbers Extension of Fermat’s Expression Fermat’s Expression from Products of Odd Numbers
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N次幂下S-凸函数和其性质研究
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作者 刘明术 方宏彬 《池州学院学报》 2024年第3期6-9,共4页
以凸函数、S-凸函数、平方凸函数、平方S-凸函数的定义和性质为研究基础,根据从平方凸函数到平方S-凸函数的演变推进过程,采用了凸函数概念的代数不等式形式,给出了N次幂下S-凸函数的概念,并对其判别定理和性质进行了讨论,定义并证明了... 以凸函数、S-凸函数、平方凸函数、平方S-凸函数的定义和性质为研究基础,根据从平方凸函数到平方S-凸函数的演变推进过程,采用了凸函数概念的代数不等式形式,给出了N次幂下S-凸函数的概念,并对其判别定理和性质进行了讨论,定义并证明了N次幂下S-凸函数的Jensen型不等式。研究表明,N次幂下S-凸函数包含了凸函数、平方凸函数、平方S-凸函数的性质,是凸函数的一种广义凸函数的推广,开辟了全新的推广途径。 展开更多
关键词 JENsEN不等式 s-凸函数 平方凸函数 平方s-凸函数 判别定理
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On Fermat Last Theorem: The New Efficient Expression of a Hypothetical Solution as a Function of Its Fermat Divisors
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作者 Prosper Kouadio Kimou 《American Journal of Computational Mathematics》 2023年第1期82-90,共9页
Denote by a non-trivial primitive solution of Fermat’s equation (p prime).We introduce, for the first time, what we call Fermat principal divisors of the triple defined as follows. , and . We show that it is possible... Denote by a non-trivial primitive solution of Fermat’s equation (p prime).We introduce, for the first time, what we call Fermat principal divisors of the triple defined as follows. , and . We show that it is possible to express a,b and c as function of the Fermat principal divisors. Denote by the set of possible non-trivial solutions of the Diophantine equation . And, let<sub></sub><sub></sub> (p prime). We prove that, in the first case of Fermat’s theorem, one has . In the second case of Fermat’s theorem, we show that , ,. Furthermore, we have implemented a python program to calculate the Fermat divisors of Pythagoreans triples. The results of this program, confirm the model used. We now have an effective tool to directly process Diophantine equations and that of Fermat. . 展开更多
关键词 Fermat’s Last theorem Fermat Divisors Barlow’s Relations Greatest Common Divisor
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A Proof of Brouwer’s Fixed Point Theorem Using Sperner’s Lemma
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作者 Cassie Lu 《数学计算(中英文版)》 2023年第2期1-6,共6页
This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the correspo... This article offers a simple but rigorous proof of Brouwer’s fixed point theorem using Sperner’s Lemma.The general method I have used so far in the proof is mainly to convert the n-dimensional shapes to the corresponding case under the Sperner’s Labeling and apply the Sperner’s Lemma to solve the question. 展开更多
关键词 Brouwer’s Fixed Point theorem sperner’s Lemma PROOF
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Gravitation, Density Upper Limit and Quantization of Space
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作者 Doron Kwiat 《Journal of High Energy Physics, Gravitation and Cosmology》 CAS 2024年第2期534-545,共12页
The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified,... The singularity at distance r → 0 at the center of a spherically symmetric non-rotating, uncharged mass of radius R, is considered here. Under inverse square law force, the Schwarzschild metric, needs to be modified, to include Newton’s Shell Theorem (NST). By including NST for r, both Schwarzschild singularity at r = 2GM/c2 and at r → 0 singularities are removed from the metric. Near R → 0, the question of maximal density is considered based on Schwarzschild’s modified metric, and compared to the quantum limit of maximal mass density put by Planck’s quantum-based universal units. It is asserted, that General relativity, when combined with Planck’s universal units, inevitably leads to quantization of gravity. 展开更多
关键词 GRAVITATION shell theorem sINGULARITY schwarzschild Radius CGH Physics: Planck’s scale
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具有饱和恢复率的SEIR时滞模型的行波解
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作者 卫珍妮 《西北师范大学学报(自然科学版)》 2024年第1期20-29,共10页
研究一类具有饱和恢复率的SEIR时滞模型的行波解.首先,考虑一类二维系统初值问题的适定性;然后,通过构造一对有界的向量值上、下解得到一个闭凸集;最后,利用Schauder不动点定理证明:当基本再生数R^(0)>1,波速c>c^(*)时模型存在非... 研究一类具有饱和恢复率的SEIR时滞模型的行波解.首先,考虑一类二维系统初值问题的适定性;然后,通过构造一对有界的向量值上、下解得到一个闭凸集;最后,利用Schauder不动点定理证明:当基本再生数R^(0)>1,波速c>c^(*)时模型存在非平凡行波解. 展开更多
关键词 sEIR模型 饱和恢复率 时滞 行波解 sCHAUDER不动点定理
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数论中的Wilson定理通过群论中的Cauchy定理的证明
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作者 张海诚 《高等数学研究》 2024年第5期93-93,F0003,共2页
本文利用近世代数课程中有限群的Cauchy定理证明数论课程里的Wilson定理.
关键词 数论 WILsON定理 群论 CAUCHY定理
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层次化的K.Fan’s Theorem
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作者 朱凤梅 李令强 孟广武 《聊城大学学报(自然科学版)》 2010年第2期1-3,89,共4页
在L-拓扑空间中,对任意LF集,我们利用层次化的K.Fan’s Theorem定义了一种层次连通并研究了其基本性质.
关键词 L-拓扑空间 层次连通 K.Fan’s theorem
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VECTORIAL EKELAND'S VARIATIONAL PRINCIPLE WITH A W-DISTANCE AND ITS EQUIVALENT THEOREMS 被引量:8
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作者 丘京辉 李博 贺飞 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2221-2236,共16页
By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variatio... By using the properties of w-distances and Gerstewitz's functions, we first give a vectorial Takahashi's nonconvex minimization theorem with a w-distance. From this, we deduce a general vectorial Ekeland's variational principle, where the objective function is from a complete metric space into a pre-ordered topological vector space and the perturbation contains a w-distance and a non-decreasing function of the objective function value. From the general vectorial variational principle, we deduce a vectorial Caristfs fixed point theorem with a w-distance. Finally we show that the above three theorems are equivalent to each other. The related known results are generalized and improved. In particular, some conditions in the theorems of [Y. Araya, Ekeland's variational principle and its equivalent theorems in vector optimization, J. Math. Anal. Appl. 346(2008), 9-16] are weakened or even completely relieved. 展开更多
关键词 Takahashi's minimization theorem Ekeland's variational principle Caristi'sfixed point theorem Gerstewitz's function w-distance
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Noether's theorems of a fractional Birkhoffian system within Riemann-Liouville derivatives 被引量:17
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作者 周燕 张毅 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第12期281-288,共8页
The Noether symmetry and the conserved quantity of a fractional Birkhoffian system are studied within the Riemann–Liouville fractional derivatives. Firstly, the fractional Birkhoff's equations and the corresponding ... The Noether symmetry and the conserved quantity of a fractional Birkhoffian system are studied within the Riemann–Liouville fractional derivatives. Firstly, the fractional Birkhoff's equations and the corresponding transversality conditions are given. Secondly, from special to general forms, Noether's theorems of a standard Birhoffian system are given, which provide an approach and theoretical basis for the further research on the Noether symmetry of the fractional Birkhoffian system. Thirdly, the invariances of the fractional Pfaffian action under a special one-parameter group of infinitesimal transformations without transforming the time and a general one-parameter group of infinitesimal transformations with transforming the time are studied, respectively, and the corresponding Noether's theorems are established. Finally, an example is given to illustrate the application of the results. 展开更多
关键词 fractional Birkhoffian system Noether's theorem fractional conserved quantity Riemann–Liouville fractional derivative
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SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES 被引量:3
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作者 Fridoun MORADLOU Peyman SALIMI Pasquale VETRO 《Acta Mathematica Scientia》 SCIE CSCD 2013年第4期1049-1058,共10页
In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive ... In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 (1962), 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces. 展开更多
关键词 G-metric spaces G-cone metric spaces fixed point Edelstein's theorem suzuki's theorem
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Mei’s symmetry theorem for time scales nonshifted mechanical systems 被引量:7
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作者 Yi Zhang 《Theoretical & Applied Mechanics Letters》 CSCD 2021年第5期246-251,共6页
We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities.Firstly,the dynamic equations of time scales nonshifted holonomic systems a... We focus on Mei symmetry for time scales nonshifted mechanical systems within Lagrangian framework and its resulting new conserved quantities.Firstly,the dynamic equations of time scales nonshifted holonomic systems and time scales nonshifted nonholonomic systems are derived from the generalized Hamilton’s principle.Secondly,the definitions of Mei symmetry on time scales are given and its criterions are deduced.Finally,Mei’s symmetry theorems for time scales nonshifted holonomic conservative systems,time scales nonshifted holonomic nonconservative systems and time scales nonshifted nonholonomic systems are established and proved,and new conserved quantities of above systems are obtained.Results are illustrated with two examples. 展开更多
关键词 Mei’s symmetry theorem Nonholonomic system Nonconservative system Time scales Nonshifted calculus of variation
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ON THE CONDITIONAL VERSION OFKOLMOGOROV'S THREE-SERIES THEOREM 被引量:1
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作者 刘国欣 《Acta Mathematica Scientia》 SCIE CSCD 1999年第3期300-306,共7页
This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the con... This paper studies the conditional version of Kolmogorov’s three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained. 展开更多
关键词 Three-series theorem dependent r.v. ’s predictable local absolute CONTINUITY MARTINGALE
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