在模情况时二面体群$D_{2p}$作用下的transfer理想

In this paper, we determine the structures of the transfer ideal and its radical ideal for the ring of polynomials F p[x, y] under the action of dihedral group D2 p in the modular case. We mainly use Transfer variety, p order elements, and Hilbert’s Nullstellensatz Theorem.     

Factoriality for the reductive Zassenhaus variety and quantum enveloping algebra

Let U(g)$U(\mathfrak{g})$ be the enveloping algebra of a finite dimensional reductive Lie algebra g$\mathfrak{g}$ over an algebraically closed field of prime characteristic. Let _U?,P(s:)$U_{?,P}(\mathfrak{s}:)$ be the simply connected quantum enveloping algebra at the root of unity ?  , of a complex semi-simple finite dimensional Lie algebra s:$\mathfrak{s}:$. We show, by similar proofs, that the centers of both are factorial. While the first result was established by R. Tange [32] (by different methods), the second one confirms a conjecture in [4]. We also provide a general criterion for the factoriality of the centers of enveloping algebras in prime characteristic.     

The effect of variety seeking behaviour on optimal product positioning

In this paper we develop a stochastic (first order Markovian) consumer choice model that represents variety seeking behaviour and we investigate the practical implications of this model for optimal product positioning relative to a zero order model that does not incorporate variety seeking. We show that the optimal positioning implications of a variety seeking process is indeed different than those of a (no-variety-seeking) zero order process. Based on intuition, one might expect increased variety seeking to imply that firms should increase the distance between their products in an attribute space. In fact, we show that this effect does occur for relatively low share brands. But just the opposite effect holds for relatively high share brands. That is, variety seeking behaviour generates a desire to more differentiation among low share brands, and a desire for less differentiation among high share brands.     

The Intersection of Opposed Big Cells in The Real Flag Variety of Type G2

We compute the Euler characteristics of the individual connectedcomponents of the intersection of two opposed big cells in thereal flag variety of type G₂, verifying a conjecture of Rietsch[6]. 2000 Mathematical Subject Classification: primary 14M15; secondary20G20.     

On systems of binomials in the ideal of a toric variety

Let be a toric set in the affine space . Given a set of binomials in the toric ideal of , we give a criterion for deciding the equality rad( ) = . This criterion extends to arbitrary dimension, and to arbitrary fields, an earlier result which concerned only monomial curves over an algebraically closed field of characteristic zero.

     

Differential operators on a polarized abelian variety

Let be an ample line bundle over a complex abelian variety . We show that the space of all global sections over of and are both of dimension one. Using this it is shown that the moduli space of rank one holomorphic connections on a compact Riemann surface does not admit any nonconstant algebraic function. On the other hand, is biholomorphic to the moduli space of characters of , which is an affine variety. So is algebraically distinct from the character variety if is of genus at least one.

     

A Class of Strongly Decomposable Abelian Groups

Let G be a completely decomposable torsion-free Abelian group and G= G_i, where G _i is a rank 1 group. If there exists a strongly constructive numbering of G such that (G,) has a recursively enumerable sequence of elements g _i G _i , then G is called a strongly decomposable group. Let pi, i, be some sequence of primes whose denominators are degrees of a number p _i and let . A characteristic of the group A is the set of all pairs ‹ p,k› of numbers such that for some numbers i ₁,...,i _k . We bring in the concept of a quasihyperhyperimmune set, and specify a necessary and sufficient condition on the characteristic of A subject to which the group in question is strongly decomposable. Also, it is proved that every hyperhyperimmune set is quasihyperhyperimmune, the converse being not true.     

Transfer Operators and State Spaces for Discrete Multidimensional Linear Systems

This paper treats multidimensional discrete input-output systems from the constructive point of view. We adapt and improve recursive algorithms, derived earlier by E. Zerz and the second author from standard Gröbner basis algorithms, for the solution of the canonical Cauchy problem for linear systems of partial difference equations with constant coefficients on the lattices N = ^r1 × ^r2. These recursive algorithms, in turn, furnish four other solution methods for the initial value problem, namely by transfer operators, by canonical Kalman global state equations, by parametrizations of controllable systems and, for systems with proper transfer matrix and left bounded input signals, by convolution with the transfer matrix. In the 2D-case N = ² the last method was studied by S. Zampieri. Minimally embedded systems are studied and give rise to especially simple Kalman equations. The latter also imply a useful characterization of the characteristic or polar variety of the system by eigenvalue spectra. For N = ^r we define reachability of a system and prove that controllability implies reachability, but not conversely. Moreover we solve, in full generality, the modelling problem which was introduced and partially solved by F. Pauer and S. Zampieri. Various algorithms have been implemented by the first author in axiom, and examples are demonstrated by means of computer generated pictures. Related work on state space representations has been done by the Padovian and Groningian system theory schools.     

A Judging Method for Normal Family

ＡＪｕｄｇｉｎｇＭｅｔｈｏｄｆｏｒＮｏｒｍａｌＦａｍｉｌｙ￥ＺｈｕＺｈｅｎｘｉｎｇ（Ｄｅｐｔ．ｏｆＳｙｓｔｅｍＳｃｉｅｎｃｅａｎｄＭａｔｈ．，ＺｈｅｎｇｚｈｏｕＵｎｉｖｅｒｓｉｔｙ，Ｚｈｅｎｇｚｈｏｕ，４５００５２）Ａｂｓｔｒａｃｔ：Ｉｎ１９６４，Ｈ...