It is well-known that the associated analytic space of an affine variety defined over complex number field is Stein but the converse is not true, that is, an algebraic Stein variety is not necessarily affine. In this talk, we will give sufficient and necessary conditions for an algebraic Stein variety to be affine. One of our results is that a quasi-projective variety Y defined over complex num...

The Boolean expression of an analogical proportion, i.e., a statement of the form “a is to b as c is to d”, expresses that “a differs from b as c differs from d, and vice-versa. This is the basis of an analogical inference principle, which is shown to be a particular instance of the analogical “jump”: from P (s), P (t), and Q(s), deduceQ(t). Roughly speaking, an analogical proportion sounds lik...

Recognizing objects that have undergone certain viewing transformations is an important problem in the field of computer vision. Most current research has focused almost exclusively on single aspects of the problem, concentrating on a few geometric transformations and distortions. Probably, the most important one is the affine transformation which may be considered as an approximation to perspe...

We derive the N-point one-loop correlation functions for the currents of an arbitrary affine Kac-Moody algebra. The one-loop amplitudes, which are elliptic functions defined on the torus Riemann surface, are specified by group invariant tensors and certain constant taudependent functions. We compute the elliptic functions via a generating function, and explicitly construct the invariant tensor ...

In contemporary convex geometry, the rapidly developing Lp-Brunn Minkowski theory is a modern analogue of the classical Brunn Minkowski theory. A cornerstone of this theory is the Lp-affine surface area for convex bodies. Here, we introduce a functional form of this concept, for log concave and s-concave functions. We show that the new functional form is a generalization of the original Lp-affi...

‎highest weight modules of the double affine lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎singular vectors of verma modules are‎ ‎determined using a similar condition with horizontal affine lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

We give a type free formula for the expansion of k-Schur functions indexed by fundamental coweights within the affine nilCoxeter algebra. Explicit combinatorics are developed in affine type C.

Classification of Non-linear Boolean functions is a long-standing problem in the area of theoreticalcomputer science. In this paper, effort has been made to achieve a systematic classification of all n-variableBoolean functions, where only one affine Boolean function belongs to each class. Two different methods areproposed to achieve this classification. The first method is a recurs...

In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities new affine invariant entropy obtain on functional surface area lower upper bounds Kullback-Leibler divergence in terms area. The lead to L_p-affine areas convex bodies.

‎Let $R$ be a ring‎ ‎with the Jacobson radical $J(R)$ and let $picolon Rto R/J(R)$ be‎ the canonical map‎. ‎Then $pi$ induces an order preserving group homomorphism‎ ‎$K_0picolon K_0(R)to K_0(R/J(R))$ and an‎ ‎affine continuous map $S(K_0pi)$ between the state space $St(R/J(R))$ and the‎ ‎state space $St(R).$‎ ‎In this paper‎, ‎we consider the natural affine map $S(K_0pi).$ We give a condition ...