This paper is the continuation of [12]. We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. We also define the convolution of Hochschild homologies, and prove that the Hochschild class of the convolution of two coherent modules is the convolution of their Hochschild classes. We study with some details the case of symple...

In this paper we develop constructive invertibility conditions for the twisted convolution. Our approach is based on splitting the twisted convolution with rational parameters into a finite number of weighted convolutions, which can be interpreted as another twisted convolution on a finite cyclic group. In analogy with the twisted convolution of finite discrete signals, we derive an anti-homomo...

We define a topological space for the complexes of fixed dimension vector over the derived category of a finite dimensional algebra with finite global dimension. It has a local structure of affine variety under the action of the algebraic group. We consider the constructible functions which reflect the stratifications of the orbit spaces. By using the convolution rule, we obtain the geometric r...

We present an algorithm for computing the probability density function of the product of two independent random variables, along with an an implementation of the algorithm in a computer algebra system. We combine this algorithm with earlier work on transformations of random variables to create an automated algorithm for convolutions of random variables. Some examples demonstrate the algorithm’s...

In [9], a purely algebraic analogon of Katz’ middle convolution functor (see [12]) is given. It is denoted by MCλ. In this paper, we present a cohomological interpretation of MCλ and find an explicit RiemannHilbert correspondence for this functor. This leads to an algorithm for the construction of Fuchsian systems corresponding to irreducible rigid local systems under the Riemann-Hilbert corres...

In this paper, we introduce a new class of analytic functions defined by a new convolution operator La (α, β). The new class of analytic functions Σ a,t α,β (ρ; h) in U ∗ = {z : 0 < |z| < 1} is defined by means of a hypergeometric function with an integral operator associated with the Hurwitz-Lerch Zeta function and differential subordination. The authors also introduces and investigates variou...

In [6], a purely algebraic analogon of Katz’ middle convolution functor (see [10]) is given. In this paper, we find an explicit Riemann-Hilbert correspondence for this functor. This leads to a construction algorithm for differential systems which correspond to rigid local systems on the punctured affine line via the Riemann-Hilbert correspondence.

Given a horizontal monoid M in a duoidal category F , we examine the relationship between bimonoid structures on M and monoidal structures on the category F ∗M of right M -modules which lift the vertical monoidal structure of F . We obtain our result using a variant of the so-called Tannaka adjunction; that is, an adjunction inducing the equivalence which expresses Tannaka duality. The approach...

Convolutional neural networks (CNNs) are well known for producing state-of-the-art recognizers for document processing [1]. However, they can be difficult to implement and are usually slower than traditional multi-layer perceptrons (MLPs). We present three novel approaches to speeding up CNNs: a) unrolling convolution, b) using BLAS (basic linear algebra subroutines), and c) using GPUs (graphic...