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1.
Let be a prime number and let be the group of all invertible matrices over the prime field . It is known that every irreducible -module can occur as a submodule of , the polynomial algebra with variables over . Given an irreducible -module , the purpose of this paper is to find out the first value of the degree of which occurs as a submodule of , the subset of consisting of homogeneous polynomials of degree . This generalizes Schwartz-Tri's result to the case of any prime .
2.
Michel Van den Bergh 《Proceedings of the American Mathematical Society》2000,128(2):375-381
Assume that is a surface over an algebraically closed field . Let be obtained from by blowing up a smooth point and let be the exceptional curve. Let be the category of coherent sheaves on . In this note we show how to recover from , if we know the object .
3.
Alexandre Eremenko 《Proceedings of the American Mathematical Society》2000,128(2):557-560
Bloch's Theorem is extended to -quasiregular maps , where is the standard -dimensional sphere. An example shows that Bloch's constant actually depends on for .
4.
Let be invertible bounded linear operators on a Hilbert space satisfying , and let be real numbers satisfying Furuta showed that if , then . This inequality is called the grand Furuta inequality, which interpolates the Furuta inequality
and the Ando-Hiai inequality ( ).
and the Ando-Hiai inequality ( ).
In this paper, we show the grand Furuta inequality is best possible in the following sense: that is, if , then there exist invertible matrices with which do not satisfy .
5.
Alexander Kleshchev Alexander Premet 《Proceedings of the American Mathematical Society》2000,128(3):647-655
Let be an algebraic number field and be the ring of integers of . Let be a finite group and be a finitely generated torsion free -module. We say that is a globally irreducible -module if, for every maximal ideal of , the -module is irreducible, where stands for the residue field .
Answering a question of Pham Huu Tiep, we prove that the symmetric group does not have non-trivial globally irreducible modules. More precisely we establish that if is a globally irreducible -module, then is an -module of rank with the trivial or sign action of .
6.
Elzbieta Wagner-Bojakowska Wladyslaw Wilczynski 《Proceedings of the American Mathematical Society》2000,128(2):413-418
It is well known that the sequence of real measurable functions converges in measure to some measurable function if and only if is fundamental in measure. In this note we introduce the notion of sequence fundamental in category in this manner such that the sequence of real functions having the Baire property converges in category to some function having the Baire property if and only if is fundamental in category.
7.
Byeong-Kweon Oh 《Proceedings of the American Mathematical Society》2000,128(3):683-689
Let be the minimal rank of -universal -lattices, by which we mean positive definite -lattices which represent all positive -lattices of rank . It is a well known fact that for . In this paper, we determine and find all -universal lattices of rank for .
8.
William S. Cohn 《Proceedings of the American Mathematical Society》1999,127(2):509-517
We show that a function is the derivative of a function in the Hardy space of the unit disk for if and only if where and . Here, can be chosen to be non-vanishing, , and . As an application, we characterize positive measures on the unit disk such that the operator is bounded from the tent space to , where .
9.
Let be an integer and let be a domain of . Let be an injective mapping which takes hyperspheres whose interior is contained in to hyperspheres in . Then is the restriction of a Möbius transformation.
10.
Larry Smith 《Proceedings of the American Mathematical Society》2000,128(8):2199-2201
Let be a finite group and a complex representation. Barbara Schmid has shown that the algebra of invariant polynomial functions on the vector space is generated by homogeneous polynomials of degree at most , where is the largest degree of a generator in a minimal generating set for , and is the complex regular representation of . In this note we give a new proof of this result, and at the same time extend it to fields whose characteristic is larger than , the order of the group .
11.
Philippe Caldero 《Proceedings of the American Mathematical Society》2000,128(4):943-951
Let be a complex not a root of unity and be a semi-simple Lie -algebra. Let be the quantized enveloping algebra of Drinfeld and Jimbo, be its triangular decomposition, and the associated quantum group. We describe explicitly and as a quantum Weyl field. We use for this a quantum analogue of the Taylor lemma.
12.
Marianne K. Korten 《Proceedings of the American Mathematical Society》2000,128(2):439-444
In one space dimension and for a given function (say such that in some interval), the equation can be thought of as describing the energy per unit volume in a Stefan-type problem where the latent heat of the phase change is given by . Given a solution to this equation, we prove that for a.e. , there exists where is the Radon-Nikodym derivative of the initial trace with respect to Lebesgue measure and are the parabolic ``non-tangential" approach regions. Since only is continuous, while is usually not, does not hold in general.
13.
Muneo Cho 《Proceedings of the American Mathematical Society》2000,128(8):2357-2363
Let be a doubly commuting -tuple of -hyponormal operators with unitary operators from the polar decompositions . Let and . In this paper, we will show relations between the Taylor spectrum and the Xia spectrum .
14.
Angelo Favini Gisé le Ruiz Goldstein Jerome A. Goldstein Silvia Romanelli 《Proceedings of the American Mathematical Society》2000,128(7):1981-1989
Let us consider the operator where is positive and continuous in and is equipped with the so-called generalized Wentzell boundary condition which is of the form at each boundary point, where This class of boundary conditions strictly includes Dirichlet, Neumann and Robin conditions.
Under suitable assumptions on , we prove that generates a positive -semigroup on and, hence, many previous (linear or nonlinear) results are extended substantially.
15.
Open covers and partition relations 总被引:1,自引:0,他引:1
Marion Scheepers 《Proceedings of the American Mathematical Society》1999,127(2):577-581
An open cover of a topological space is said to be an -cover if there is for each finite subset of the space a member of the cover which contains the finite set, but the space itself is not a member of the cover. We prove theorems which imply that a set of real numbers has Rothberger's property if, and only if, for each positive integer , for each -cover of , and for each function from the two-element subsets of , there is a subset of such that is constant on , and each element of belongs to infinitely many elements of (Theorem 1). A similar characterization is given of Menger's property for sets of real numbers (Theorem 6).
16.
Hsin-Ju Wang 《Proceedings of the American Mathematical Society》2000,128(4):963-973
Let be a -dimensional Cohen-Macaulay local ring with infinite residue field. Let be an -primary ideal of . In this paper, we prove that if for some minimal reduction of , then depth .
17.
In 1992, Móricz, Schipp and Wade proved the a.e. convergence of the double means of the Walsh-Fourier series () for functions in ( is the unit square). This paper aims to demonstrate the sharpness of this result. Namely, we prove that for all measurable function we have a function such as and does not converge to a.e. (in the Pringsheim sense).
18.
Marc Troyanov 《Proceedings of the American Mathematical Society》2000,128(2):541-545
We prove in this paper that the equation on a -hyperbolic manifold has a solution with -integrable gradient for any bounded measurable function with compact support.
19.
Paolo Lipparini 《Proceedings of the American Mathematical Society》2000,128(2):605-609
We prove the following: Theorem A. If is a -regular ultrafilter, then either
- (a)
- is -regular, or
- (b)
- the cofinality of the linear order is , and is -regular for all .
20.
Tomoaki Ono 《Proceedings of the American Mathematical Society》2000,128(2):353-360
Let be a tower of rings of characteristic . Suppose that is a finitely presented -module. We give necessary and sufficient conditions for the existence of -bases of over . Next, let be a polynomial ring where is a perfect field of characteristic , and let be a regular noetherian subring of containing such that . Suppose that is a free -module. Then, applying the above result to a tower of rings, we shall show that a polynomial of minimal degree in is a -basis of over .