where x ∈ Ŝk is minimal such that ν = λ.x satisfies νi < νi+1 for i = 1, 2 . . . k− 1 and νi− νk ≥ 1− k−n, and μ = λ.x y. This conjecture is proved by Kazhdan-Lusztig [KL] and Kashiwara-Tanisaki [KT]. The proof relies on an equivalence between the category of finite-dimensional Uǫ(slk)-modules and a category of negative-level representations of the affine algebra ŝlk which are integrable with r...

The standard OpenMath is an enabling technology for creating an integrated computer environment in which software packages for computer algebra and for proof checking can be combined. Here we demonstrate how OpenMath can be employed for generating interactive mathematical documents containing primality proofs. Our case study takes place within a browser; once a prime number is specified, a docu...

Let M be a compact manifold and D a Dirac type differential operator on M . Let A be a C∗-algebra. Given a bundle W (with connection) of A-modules over M , the operator D can be twisted with this bundle. One can then use a trace on A to define numerical indices of this twisted operator. We prove an explicit formula for these indices. Our result does complement the Mishchenko–Fomenko index theor...

The processes involved in past tense verb generation have been central to models of inflectional morphology. However, the empirical support for such models has often been based on studies of accuracy in past tense verb formation on a relatively small set of items. We present the first large-scale study of past tense inflection (the Past Tense Inflection Project, or PTIP) that affords response t...

We present recent results about Capelli polynomials with involution or graded and their asymptotics. In the associative case, asymptotic equality between codimensions of $T$-ideal generated by polynomial rank $k^2+1$ matrix algebra $M_k(F)$ was proved. This result extended to superalgebras. Recently, similar have been determined authors in case algebras superalgebras involution.

In class, we’ve been talking about the integers, which we’ve denoted Z. We started off talking about equality in Z, but then moved on to talking about congruences, which is a weaker notion. This handout explains how “congruence modulo n” is something called an equivalence relation, and we can use it to construct a set Z/nZ that’s a “quotient” of Z. The key point is that a congruence modulo n in...

R. E. Thayer (1989) proposed 2 types of activation: energetic arousal (awake-tired) and tense arousal (tense-calm). This view has been challenged by claims that energetic arousal and tense arousal are mixtures of valence and a single activation dimension. The authors present a direct test of this hypothesis by computing the correlation between the residuals of energetic arousal and tense arousa...

In this thesis, we consider bi-intuitionistic logic and tense logic, as well as the combined bi-intuitionistic tense logic. Each of these logics contains a pair of dual connectives, for example, Rauszer’s bi-intuitionistic logic [100] contains intuitionistic implication and dual intuitionistic exclusion. The interaction between these dual connectives makes it non-trivial to develop a cut-free s...