On the Shintani Zeta Function for the Space of Pairs of Binary Hermitian Forms

In this paper we determine the principal part of the adjusted zeta function for the space of pairs of binary Hermitian forms.     

Fixed Point Theorems for Non-convex Valued Multifunctions

The purpose of this paper is to establish fixed point theorems for non-convex valued multifunctions which generalize known results in the literature. We also derive coincidence theorems in the non-compact setting.AMS Subject Classification (2000): 47H, 54H     

b-Functions of Prehomogeneous Vector Spaces of Dynkin–Kostant Type for Exceptional Groups

The purpose of this paper is to determine the b-functions of all the prehomogeneous vector spaces associated to nilpotent orbits in the Dynkin–Kostant theory for all the complex simple algebraic groups of exceptional type. Our method to calculate b-functions is based on the structure theorem for b-functions of several variables and the functional equations for them.     

Separation theorems and minimax theorems for fuzzy sets

In this paper, we prove some theorems on fuzzy sets. We first show that, in order to demonstrate that the equality of shadows ofA andB implies the equality ofA andB, it is necessary to assume thatA andB are closed and thatS _H (A)=S _H (B) for any closed hyperplane hyperplaneH. We also obtain a separation theorem for two convex fuzzy sets in a Hilbert space. Finally, we investigate results relating to minimax theorems for fuzzy sets. We obtain a necessary and sufficient condition for compactness.The authors wish to express their sincere thanks to Professor Hisaharu Umegaki for his invaluable suggestions and advice.     

Embedding of function spaces of variable order of differentiation in function spaces of variable order of integration

The paper deals with embeddings of function spaces of variable order of differentiation in function spaces of variable order of integration. Here the function spaces of variable order of differentiation are defined by means of pseudodifferential operators.     

Orlicz-Sobolev Algebras

The Orlicz-Sobolev spaces that are multiplicative Banach algebras are characterized.      

Traces of functions of generalized Sobolev classes

Considering the Sobolev type function classes on a metric space equipped with a Borel measure we address the question of compactness of embeddings of the space of traces into Lebesgue spaces on the sets of less “dimension.” Also, we obtain compactness conditions for embeddings of the traces of the classical Sobolev spaces W _p ¹ on the “zero” cusp with a Hölder singularity at the vertex.     

Nonconical optimality conditions: Some additional results

The purpose of the present note is to provide a somewhat more flexible statement of the sufficiency conditions in Section 4 of Ref. 1 and to give explicit statements of the fundamental necessity and sufficiency results, which were only implicitly presented there. The additional flexibility is obtained by considering local, rather than global, pseudoconcavity requirements.     

Hom-Orthogonal Partial Tilting Modules for Dynkin Quivers

We count the number of isomorphism classes of hom-orthogonal partial tilting modules over path algebras of Dynkin quiver of type 𝔸 _n , 𝔻 _n , 𝔼 _n . This number is independent on the choice of an orientation of the arrows, and the number for 𝔸 _n or 𝔻 _n -type can be expressed as a special value of a hypergeometric function. As a consequence of our theorem, we obtain a minimum value of the number of basic relative invariants of corresponding regular prehomogeneous vector spaces.     

实值函数与某些覆盖性质

In the paper [properties defined with semi-continuous functions and some related spaces',Houston J.Math.,2015,41(3):1097–1106] properties(U L)~(wl)_m,(U L)~K_m and(U L)_m were defined and it was shown that spaces having these properties coincide with countably paracompact spaces,countably mesocompact spaces and countably metacompact spaces,respectively.In this paper,we continue with the study on the relationship between properties defined with real-valued functions and some covering properties.Some characterizations of countably compact spaces and pseudo-compact spaces in terms of real-valued functions are obtained.     

Nonlinear Leray–Schauder Alternatives for Decomposable Operators in Dunford–Pettis Spaces and Application to Nonlinear Eigenvalue Problems

We present some new variants of Leray–Schauder type fixed point theorems and eigenvalue results for decomposable single-valued nonlinear weakly compact operators in Dunford-Pettis spaces.     

Zeta functions of prehomogeneous vector spaces with coefficients related to periods of automorphic forms

The theory of zeta functions associated with prehomogeneous vector spaces (p.v. for short) provides us a unified approach to functional equations of a large class of zeta functions. However the general theory does not include zeta functions related to automorphic forms such as the HeckeL-functions and the standardL-functions of automorphic forms on GL(n), even though they can naturally be considered to be associated with p.v.’s. Our aim is to generalize the theory to zeta functions whose coefficients involve periods of automorphic forms, which include the zeta functions mentioned above. In this paper, we generalize the theory to p.v.’s with symmetric structure ofK _ε-type and prove the functional equation of zeta functions attached to automorphic forms with generic infinitesimal character. In another paper, we have studied the case where automorphic forms are given by matrix coefficients of irreducible unitary representations of compact groups. Dedicated to the memory of Professor K G Ramanathan