We prove that the space of intertwining operators associated with certain admissible modules over vertex operator algebras is isomorphic to a quotient vector conformal blocks on three-pointed rational curve defined by same data. This provides new proof and alternative version Frenkel Zhu's fusion rules theorem in terms dimension bimodules algebra, without assumption rationality.

A novel and simple combination of inductive logic programming with kernel methods is presented. The kFOIL algorithm integrates the well-known inductive logic programming system FOIL with kernel methods. The feature space is constructed by leveraging FOIL search for a set of relevant clauses. The search is driven by the performance obtained by a support vector machine based on the resulting kern...

‎This paper extends the scope of algebraic computation based on a non standard $times$ to ‎the more basic case of a non standard $+$‎, ‎where standard means associative ‎and commutative‎. ‎Two physically meaningful examples of a non standard $+$ are ‎provided by the observation of motion in Special Relativity‎, ‎from either ‎outside (3D) or inside (2D or more)‎, ‎We revisit the ``gyro''-theory ...

We discuss some challenging open problems in the geometric control theory and sub-Riemannian geometry. It is getting harder to prove theorems and easier to force other people to prove them when you are sixty. Some colleagues asked me to describe interesting open problems in geometric control and sub-Riemannian geometry. Here I list few really challenging problems; some of them are open for a lo...

Abstract For a connected reductive group G over finite field, we study automorphic vector bundles on the stack of -zips. In particular, give formula in general case for space global sections an bundle terms Brylinski-Kostant filtration. Moreover, equivalence categories between category -zips and admissible modules with actions 0-dimensional algebraic subgroup Levi monodromy operators.

this paper deals with three-dimensional evaluation of the slopes on the basis of limit analysis. an upper-bound technique of limit analysis is used in this paper to determine either the bearing capacity of a shallow foundation near a slope or the safety factor of the slope. the theorems of limit analysis (upper and lower bound) provide a powerful tool for solving problems in which limit loads n...

We investigate a vector-valued version of the classical continuous wavelet transform. Special attention is given to the case when the analyzing vector consists of the first elements of the basis of admissible functions, namely the functions whose Fourier transform is a Laguerre function. In this case, the resulting spaces are, up to a multiplier isomorphism, poly-Bergman spaces. To demonstrate ...

Abstract. We provide a proof of global existence of solutions to quasilinear wave equations satisfying the null condition in certain exterior domains. In particular, our proof does not require estimation of the fundamental solution for the free wave equation. We instead rely upon a class of Keel-Smith-Sogge estimates for the perturbed wave equation. Using this, a notable simplification is made ...

Dynamical systems with a network structure can display anomalous bifurcations as a generic phenomenon. As an explanation for this it has been noted that homogeneous networks can be realized as quotient networks of so-called fundamental networks. The class of admissible vector fields for these fundamental networks is equal to the class of equivariant vector fields of the regular representation o...