A graphical approach to computing Selmer groups of congruent number curves

Let E _n:y ²=x ³−n ² x denote the family of congruent number elliptic curves. Feng and Xiong (2004) equate the nontriviality of the Selmer groups associated with E _n to the presence of certain types of partitions of graphs associated with the prime factorization of n. In this paper, we extend the ideas of Feng and Xiong in order to compute the Selmer groups of E _n. 2000 Mathematics Subject Classification Primary—11G05; Secondary—14H52, 14H25, 05C90     

Some conformally flat spin manifolds, Dirac operators and automorphic forms

In this paper we study Clifford and harmonic analysis on some examples of conformal flat manifolds that have a spinor structure, or more generally, at least a pin structure. The examples treated here are manifolds that can be parametrized by U/Γ where U is a subdomain of either Sn or Rn and Γ is a Kleinian group acting discontinuously on U. The examples studied here include RPn and the Hopf manifolds S¹×Sn−1. Also some hyperbolic manifolds will be treated. Special kinds of Clifford-analytic automorphic forms associated to the different choices of Γ are used to construct explicit Cauchy kernels, Cauchy integral formulas, Green's kernels and formulas together with Hardy spaces and Plemelj projection operators for Lp spaces of hypersurfaces lying in these manifolds.     

Recognition of the Finite Simple Groups F 4(2m) by Spectrum

The spectrum of a finite group is the set of its element orders. A finite group G is said to be recognizable by spectrum, if every finite group with the same spectrum as G is isomorphic to G. The purpose of the paper is to prove that for every natural m the finite simple Chevalley group F ₄(2 ^m ) is recognizable by spectrum.     

Computations of critical groups and applications to asymptotically linear wave equation and beam equation

In this paper, by using the Morse index theory for strongly indefinite functionals developed in [Nonlinear Anal. TMA, in press], we compute precisely the critical groups at the origin and at infinity, respectively. The abstract theorems are used to study the existence (multiplicity) of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero.     

The Hopf Property for Subgroups of Hyperbolic Groups

A group is said to be Hopfian if every surjective endomorphism of the group is injective. We show that finitely generated subgroups of torsion-free hyperbolic groups are Hopfian. Our proof generalizes a theorem of Sela (Topology 35 (2) 1999, 301–321).     

Group classification of unsteady boundary layer equations of a class of non-Newtonian fluids

Two dimensional unsteady boundary layer equations of a general model of non-Newtonian fluids were investigated in this study. In this model, the shear stress is taken as an arbitrary function of the velocity gradient. Group classification of the equations with respect to shear stress is done using two different approaches: (1) classical theory (2) equivalence transformations. Both approaches yield identical results. It is found that the principle Lie Algebra extends only for cases of Newtonian and Power-Law flows.     

Reflection quotients in Riemannian geometry. A geometric converse to Chevalley's theorem

Chevalley's theorem and its converse, the Sheppard-Todd theorem, assert that finite reflection groups are distinguished by the fact that the ring of invariant polynomials is freely generated. We show that, in the Euclidean case, a weaker condition suffices to characterize finite reflection groups, namely, that a freely-generated polynomial subring is closed with respect to the gradient product.

     

用横波推导简谐波的能量

本文提出用横波推导简谐波能量的方法，并就此进行了具体时推导。     

Primary abelian <Emphasis Type="Italic">n</Emphasis>-Σ-groups

We prove the following theorem: Any abelian p-group is an n-Σ-group which is a strong ω-elongation of a totally projective group by a p ^ω+n -projective group precisely when it is totally projective. In particular, each p-torsion p ^ω+n -projective n-Σ-group is a direct sum of countable p-groups of length not exceeding ω + n and vice versa. These two claims generalize our recent results in [6] and [7]. Published in Lietuvos Matematikos Rinkinys, Vol. 47, No. 2, pp. 155–162, April–June, 2007.     

Rn上的非初等变换群及其极限集

该文对高维非初等Mò'bius变换群进行了研究,得到了一些重要性质,给出了几个关于离散准则和代数收敛性的定理.