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Very Original Proofs of Two Famous Problems: “Are There Any Odd Perfect Numbers?” (Unsolved until to Date) and “Fermat’s Last Theorem: A New Proof of Theorem (Less than One and a Half Pages) and Its Generalization” 被引量:2
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作者 Demetrius Chr. Poulkas 《Advances in Pure Mathematics》 2021年第11期891-928,共38页
This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its general... This article presents very original and relatively brief or very brief proofs about of two famous problems: 1) Are there any odd perfect numbers? and 2) “Fermat’s last theorem: A new proof of theorem and its generalization”. They are achieved with elementary mathematics. This is why these proofs can be easily understood by any mathematician or anyone who knows basic mathematics. Note that, in both problems, proof by contradiction was used as a method of proof. The first of the two problems to date has not been resolved. Its proof is completely original and was not based on the work of other researchers. On the contrary, it was based on a simple observation that all natural divisors of a positive integer appear in pairs. The aim of the first work is to solve one of the unsolved, for many years, problems of the mathematics which belong to the field of number theory. I believe that if the present proof is recognized by the mathematical community, it may signal a different way of solving unsolved problems. For the second problem, it is very important the fact that it is generalized to an arbitrarily large number of variables. This generalization is essentially a new theorem in the field of the number theory. To the classical problem, two solutions are given, which are presented in the chronological order in which they were achieved. <em>Note that the second solution is very short and does not exceed one and a half pages</em>. This leads me to believe that Fermat, as a great mathematician was not lying and that he had probably solved the problem, as he stated in his historic its letter, with a correspondingly brief solution. <em>To win the bet on the question of whether Fermat was telling truth or lying, go immediately to the end of this article before the General Conclusions.</em> 展开更多
关键词 Perfect Numbers Odd Perfect Numbers Fermat’s Last theorem generalization of the Fermat’s Last theorem Prime Number Problems Millennium Problems
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A Brief New Proof to Fermat’s Last Theorem and Its Generalization
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作者 Demetrius Chr. Poulkas 《Journal of Applied Mathematics and Physics》 2020年第4期684-697,共14页
This article presents a brief and new solution to the problem known as the “Fermat’s Last Theorem”. It is achieved without the use of abstract algebra elements or elements from other fields of modern mathematics of... This article presents a brief and new solution to the problem known as the “Fermat’s Last Theorem”. It is achieved without the use of abstract algebra elements or elements from other fields of modern mathematics of the twentieth century. For this reason it can be easily understood by any mathematician or by anyone who knows basic mathematics. The important thing is that the above “theorem” is generalized. Thus, this generalization is essentially a new theorem in the field of number theory. 展开更多
关键词 BRIEF PROOF of Fermat’s LAsT theorem Unsolved Mathematical PROBLEMs Fermat’s LAsT theorem generalization of the Fermat’s LAsT theorem Prime Number PROBLEMs MILLENNIUM PROBLEMs
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A NEW CLASS OF LOCALLY CONVEX SPACES AND THE GENERALIZATION OF KALTON'S CLOSED GRAPH THEOREM
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作者 丘京辉 《Acta Mathematica Scientia》 SCIE 1985年第4期389-397,共9页
By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the clo... By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given. 展开更多
关键词 A NEW CLAss OF LOCALLY CONVEX sPACEs AND THE generalization OF KALTON’s CLOsED GRAPH theorem
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Trace Formulae of Characteristic Polynomial and Cayley-HamUton's Theorem, and Applications to Chiral Perturbation Theory and General Relativity
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作者 ZHANG Hong-Hao YAN Wen-Bin LI Xue-Song 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第4期801-808,共8页
By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, wh... By using combinatorics, we give a new proof for the recurrence relations of the characteristic polynomial coefficients, and we further obtain an explicit expression for the generic term of the coefficient sequence, which yields the trace formulae of the Cayley-Hamilton's theorem with all coefficients explicitly given. This implies a byproduct, a complete expression for the determinant of any finite-dimensional matrix in terms of the traces of its successive powers. And we discuss some of their applications to ehiral perturbation theory and general relativity. 展开更多
关键词 characteristic polynomial coefficients Cayley-Hamilton's theorem chiral perturbation theory general relativity
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POINTWISE CONVERGENCE FOR EXPANSIONS IN SPHERICAL MONOGENICS 被引量:1
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作者 费铭岗 钱涛 《Acta Mathematica Scientia》 SCIE CSCD 2009年第5期1241-1250,共10页
We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Rie... We offer a new approach to deal with the pointwise convergence of FourierLaplace series on the unit sphere of even-dimensional Euclidean spaces. By using spherical monogenics defined through the generalized Cauchy-Riemann operator, we obtain the spherical monogenic expansions of square integrable functions on the unit sphere. Based on the generalization of Fueter's theorem inducing monogenic functions from holomorphic functions in the complex plane and the classical Carleson's theorem, a pointwise convergence theorem on the new expansion is proved. The result is a generalization of Carleson's theorem to the higher dimensional Euclidean spaces. The approach is simpler than those by using special functions, which may have the advantage to induce the singular integral approach for pointwise convergence problems on the spheres. 展开更多
关键词 spherical monogenics pointwise convergence of Fourier-Laplace series generalized Cauchy-Riemann operator unit sphere generalization of fueter's theorem
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A Generalization of Caristi's Fixed Point Theorem and Its Applications 被引量:1
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作者 孙金丽 孙经先 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2006年第2期199-206,共8页
The paper generalizes the classical Caristi's fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi's fixed point ... The paper generalizes the classical Caristi's fixed point theorem. As an application. the classical Ekeland variational principle is generalized. In addition, it is proved that the generalized Caristi's fixed point theorem is equivalent to the generalized Ekeland variational principle. 展开更多
关键词 fixed point theorem Zorn's lemma general principle on ordered set variational principle.
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A Generalization of Hall-Higman's Reduction Theorem
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作者 Wang Yanming Department of Mathematics Zhongshan University Guangzhou,510275 China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1995年第1期74-80,共7页
In this paper,we generalize the Hall-Higman’s reduction theorem by dropping the restrictive hypothesis(丨G丨,丨H丨)=1 and determine the detailed structure of G.
关键词 HALL A generalization of Hall-Higman’s Reduction theorem
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A Second Main Theorem of Nevanlinna Theory for Closed Subschemes in Subgeneral Position 被引量:1
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作者 Guangsheng YU 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 2022年第4期567-584,共18页
In this paper,by using Seshadri constants for subschemes,the author establishes a second main theorem of Nevanlinna theory for holomorphic curves intersecting closed subschemes in(weak)subgeneral position.As an applic... In this paper,by using Seshadri constants for subschemes,the author establishes a second main theorem of Nevanlinna theory for holomorphic curves intersecting closed subschemes in(weak)subgeneral position.As an application of his second main theorem,he obtain a Brody hyperbolicity result for the complement of nef effective divisors.He also give the corresponding Schmidt’s subspace theorem and arithmetic hyperbolicity result in Diophantine approximation. 展开更多
关键词 second main theorem In general position Closed subscheme seshadri constant schmidt’s subspace theorem HYPERBOLICITY
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Symmetry Analysis and Conservation Laws for the Hunter-Saxton Equation 被引量:1
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作者 Mehdi Nadjafikhah Fatemeh Ahangari 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第3期335-348,共14页
In this paper, the problem of determining the most general Lie point symmetries group and conservation laws of a well known nonlinear hyperbolic PDE in mathematical physics called the Hunter-Saxton equation (HSE) is... In this paper, the problem of determining the most general Lie point symmetries group and conservation laws of a well known nonlinear hyperbolic PDE in mathematical physics called the Hunter-Saxton equation (HSE) is anaiyzed. By applying the basic Lie symmetry method for the HSE, the classical Lie point symmetry operators are obtained. Also, the algebraic structure of the Lie algebra of symmetries is discussed and an optimal system of one- dimensional subalgebras of the HSE symmetry algebra which creates the preliminary classification of group invariant solutions is constructed. Particularly, the Lie invariants as well as similarity reduced equations corresponding to in- finitesimal symmetries are obtained. Mainly, the conservation laws of the HSE are computed via three different methods including Boyer's generalization of Noether's theorem, first homotopy method and second homotopy method. 展开更多
关键词 Hunter-saxton equation (HsE) Lie symmetry method invariant solution conservation laws Boyer's generalization of Noether's theorem Homotopy operator methods
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