The proof of Fermat's Last Theorem

ＴＨＥＰＲＯＯＦＯＦＦＥＲＭＡＴ＇ＳＬＡＳＴＴＨＥＯＲＥＭＷｏｎｇＣｈｉａｈｏ（汪家訸）（ＲｅｃｅｉｖｅｄＡｐｒｉｌ１０,１９９５）Ａｂｓｔｒａｃｔ：（ｉ）Ｉｎｓｔｅａｄｏｆｘ￣ｎ＋ｙ￣ｎ＝ｚ￣ｎ,ｗｅｕｓｅａｓｔｈｅｇｅｎｅｒａｌｅｑｕａｔｉｏｎｏ...     

A COMMENT ON THE PROOF OF FERMAT'S LAST THEOREM

I.IntroductionItiswell-knownthatFermat'sLastTheoremll'2'31:"TheequationX" yn=Z"(l.1)hasnosolutioninpositiveintegersx,.1',:whicharealldifferentfrom0foranarbitrarynumbern>2"isahardmathematicalproblem,proposedbyFrenchmathematicianPierredeFermatinabout1637.Sincethenmorethan300yearspast,manyfamousmathematicianshavemadegreatcontributionsintheresearchesanddevelopmentsinthenumbertheoryofalgebraaswellasothermathematicalbranchestolookouttheproofoftheproblematthemoment,buttilefinalproofhasonlybeenobt…     

Nanson公式证明的诠注及一个新证明

针对现行文献对Nanson公式证明的3种不同方法, 文章分别从数学演绎与力学概念明晰化的角度对3种证明的演绎过程及其特色进行了分析, 指出了相应的优劣之处以及各自需要改进的地方. 在此基础上, 文章给出了一个改进的易于理解的证明. 文章还提出了力学问题的演绎与证明应该充分反映力学规律的论点.     

A general topological version of minimax theorem

ＡＧＥＮＥＲＡＬＴＯＰＯＬＯＧＩＣＡＬＶＥＲＳＩＯＮＯＦＭＩＮＩＭＡＸＴＨＥＯＲＥＭＺｈａｎｇＳｈｉｓｈｅｎｇ（张石生）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ,ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ,Ｃｈｅｎｇｄｕ６１００６４,Ｐ．Ｒ．Ｃｈｉｎ...     

Note on the virial theorem

Poincaré's formalism is used to develop a variant of the usual virial theorem in which the time average of the equation of motion of a certain function is expressed in terms of the generalized Poisson brackets. Recommended by Prof. Mei Fengxiang     

逐段变形效应叠加法的能量法证明及其推广

采用能量法证明了计算静定的梁、刚架和杆系位移的逐段变形效应叠加法,并讨论了对于组合变形和非线性问题的推广.     

Applications of the division theorem inH s

We prove a version of the division theorem in Sobolev spaces with an estimate of the constant ass tends to infinity. We then apply it to derive spatial decay estimates for time-periodic solutions of linear wave equations in one space dimension and to prove that the space of decaying solutions is finite-dimensional. The main point is to show that some of the arguments used to analyze embedded eigenvalues of Schrödinger operators can be extended to cases where positivity arguments are not available. This has implications for nonlinear Klein-Gordon equations. A different approach, based on the proof of the stable manifold theorem, is also worked out, under slightly different assumptions.     

A method using the reciprocal theorem to solve the bending of thin elastic semicircular plates

The bending of the thin elastic semicircular plates, because of its complicated boundary conditions, brings some difficulties for us to obtain its solution. This paper applies the reciprocal theorem to propose a general simple convenient method to obtain the transverse defiectional equations of the plates.     

A concise proof of the representation theorem for linear isotropic tensor-valued mappings of a skew argument

The title's result is proved by reduction to the corresponding representation theorem for linear isotropic vector-valued mappings of a vector argument.     

On a generalized taylor theorem: A rational proof of the validity of the homotopy analysis method

IntroductionIn 1 7thcenturyIsaacNewton[1]gavesuchabinomialexpressionforfractionalandnegativeexponents(1 +t) α,i.e.,(1 +t) α =1 + +∞k=1α(α-1 ) (α-2 )… (α -k+ 1 )k !tk　　 (α≠ 0 ,1 ,2 ,… ) ,(1 )whoseconvergenceradiusisone.Furthermore ,theclassicalTaylorseries (seeRef.[2 ] )limm→+∞ mk=0f(k) (z0 )k !(z-z0 ) k (2 )ofacomplexfunctionf(z)atz=z0 isvalidmostlyinarestrictedconvergenceregion｜z-z0 ｜相似文献   

A generalization of Browder's fixed point theorem with applications

１ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＩｎ１９６８,Ｂｒｏｗｄｅｒ［１］ｐｒｏｖｅｄｔｈｅｆｏｌｌｏｗｉｎｇｔｈｅｏｒｅｍ．Ｔｈｅｏｒｅｍ１１（Ｂｒｏｗｄｅｒ［１］）　ＬｅｔＥｂｅａＨａｕｓｄｏｒｆｆｔｏｐｏｌｏｇｉｃａｌｌｉｎｅａｒｓｐａｃｅ,ＸａｃｏｍｐａｃｔｃｏｎｖｅｘｓｕｂｓｅｔｏｆＥａｎｄＦ：Ｘ→２Ｘａｍａｐｐｉｎｇｓａｔｉｓｆｙｉｎｇｔｈｅｆｏｌｌｏｗｉｎｇｃｏｎｄｉｔｉｏｎｓ：ⅰ）Ｆｏｒａｎｙｘ∈Ｘ,Ｆ（ｘ）ｉｓｎｏｎｅｍｐｔｙａｎｄｃｏｎｖｅｘ;ⅱ）Ｆｏｒａ…     

Use of the reciprocity theorem for axially symmetric transient problems

Summary A fundamental solution, to be used in reciprocal theorem for the solutions of axially symmetric transient problem of elastodynamics, is presented. A cylindrical cavity problem has been solved to check the formulation. The strong singularity of the resulting integral equation for this problem has been reduced to the weak form. The new formulation provides the initial velocity on the surface for a transient loading. Some differences have been introduced for the use of generalized functions.     

Lattice Boltzmann simulations of high-order statistics in isotropic turbulent flows

The lattice Boltzmann method (LBM) is coupled with the multiple-relaxation-time (MRT) collision model and the three-dimensional 19-discrete-velocity (D3Q19) model to resolve intermittent behaviors on small scales in isotropic turbulent flows. The high-order scaling exponents of the velocity structure functions, the probability distribution functions of Lagrangian accelerations, and the local energy dissipation rates are investigated. The self-similarity of the space-time velocity structure functions is explored using the extended self-similarity (ESS) method, which was originally developed for velocity spatial structure functions. The scaling exponents of spatial structure functions at up to ten orders are consistent with the experimental measurements and theoretical results, implying that the LBM can accurately resolve the intermittent behaviors. This validation provides a solid basis for using the LBM to study more complex processes that are sensitive to small scales in turbulent flows, such as the relative dispersion of pollutants and mesoscale structures of preferential concentration of heavy particles suspended in turbulent flows.     

Vertex solution theorem for the upper and lower bounds on the dynamic response of structures with uncertain-but-bounded parameters

The aim of this paper is to evaluate the effects of uncertain-but-bounded parameters on the dynamic response of structures. By combining the interval mathematics and the finite element analysis, the mass matrix, damping matrix, stiffness matrix and the external loads are represented as interval matrices and vector. With the help of the optimization theory, we present the vertex solution theorem for determining both the exact upper bounds or maximum values and the exact lower bounds or minimum values of the dynamic response of structures, in which these parameters reach their extreme values on the boundary of the interval mass, damping, stiffness matrices and the interval extemal loads vector. Three examples are used to illustrate the computational aspects of the presented vertex solution theorem.     

STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY

The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.