An operator-theoretical treatment of the Maskawa–Nakajima equation in the massless abelian gluon model

The Maskawa–Nakajima equation has attracted considerable interest in elementary particle physics. From the viewpoint of operator theory, we study the Maskawa–Nakajima equation in the massless abelian gluon model. We first show that there is a nonzero solution to the Maskawa–Nakajima equation when the parameter λ   satisfies λ>2$\lambda >2$. Moreover, we show that the solution is infinitely differentiable and strictly decreasing. We thus conclude that the massless abelian gluon model generates the nonzero quark mass spontaneously and exhibits the spontaneous chiral symmetry breaking when λ>2$\lambda >2$. We next show that there is a unique solution 0 to the Maskawa–Nakajima equation when 0<λ<1$0<\lambda <1$, from which we conclude that each quark remains massless and that the model realizes the chiral symmetry when 0<λ<1$0<\lambda <1$.     

A refinement of the Hodge stratification for connected reductive groups

For connected reductive groups G over a finite extension F of and L the maximal unramified extension of F we study the sets of elements with given Hodge points . We explain the relationship to stratifications of some moduli scheme of abelian varieties defined by Goren and Oort respectively Andreatta and Goren. We show that for sufficiently large N the Newton point is constant on the sets and compute such N for certain classes of groups.     

Integral models in unramified mixed characteristic (0, 2) of hermitian orthogonal Shimura varieties of PEL type,Part II

We construct relative PEL type embeddings in mixed characteristic (0, 2) between hermitian orthogonal Shimura varieties of PEL type. We use this to prove the existence of integral canonical models in unramified mixed characteristic (0, 2) of hermitian orthogonal Shimura varieties of PEL type.     

Combinatorial structures and Lie algebras of upper triangular matrices

This work shows how to associate the Lie algebra h_n, of upper triangular matrices, with a specific combinatorial structure of dimension 2, for n∈N. The properties of this structure are analyzed and characterized. Additionally, the results obtained here are applied to obtain faithful representations of solvable Lie algebras.     

有一个指数为$p^3$的循环子群的有限$p$群

We classify up to isomorphism those finite p-groups,for odd primes p,which contain a cyclic subgroup of index p3.     

Henstock type integral in harmonic analysis on zero-dimensional groups

A Henstock type integral is defined on compact subsets of a locally compact zero-dimensional abelian group. This integral is applied to obtain an inversion formula for the multiplicative integral transform.     

Reduction of homomorphisms mod p and algebraicity

Let A be an abelian variety over a number field K. Let φ be an endomorphism of A(K) into itself which reduces modulo v for almost all finite places v of K. The question we discuss in this paper is whether φ arises from an endomorphism of the abelian variety A. We answer this question in the affirmative for many cases. The question is inspired by a work of C. Corrales and R. Schoof, and uses a recent work of Larsen. We also look at the analogue of this question for linear algebraic groups.     

Geometric aspects of frame representations of abelian groups

We consider frames arising from the action of a unitary representation of a discrete countable abelian group. We show that the range of the analysis operator can be determined by computing which characters appear in the representation. This allows one to compare the ranges of two such frames, which is useful for determining similarity and also for multiplexing schemes. Our results then partially extend to Bessel sequences arising from the action of the group. We apply the results to sampling on bandlimited functions and to wavelet and Weyl-Heisenberg frames. This yields a sufficient condition for two sampling transforms to have orthogonal ranges, and two analysis operators for wavelet and Weyl-Heisenberg frames to have orthogonal ranges. The sufficient condition is easy to compute in terms of the periodization of the Fourier transform of the frame generators.

     

不变平均和拓扑不变平均

设G为局部紧群，在一致连续函数空间U(G)上，用两种方法证明左不变平均和拓扑左不变的等价性．当G是交换群时．给出一种证明其顺从的方法．