Numerical Performance of Optimized Frolov Lattices in Tensor Product Reproducing Kernel Sobolev Spaces

Foundations of Computational Mathematics - In this paper, we deal with several aspects of the universal Frolov cubature method, which is known to achieve optimal asymptotic convergence rates in a...     

Function Values Are Enough for $$L_2$$ L 2 -Approximation

Foundations of Computational Mathematics - We study the $$L_2$$ -approximation of functions from a Hilbert space and compare the sampling numbers with the approximation numbers. The sampling number...     

Heterogeneous nanostructured catalysts in the synthesis of polyhydroquinolines (microreview)

Chemistry of Heterocyclic Compounds - This microreview focuses on the main modern synthetic approaches toward polyhydroquinolines, which represent a significant group of N-heterocycles of great...     

Effect of overlapping cellulose nanofibrils and nanoclay layers on mechanical and barrier properties of spray-coated papers

Cellulose - This work evaluates the effect of spray-coating papers using cellulose nanofibrils (CNFs) and nanoclay (NC) on the mechanical and barrier properties for application such as reinforced...     

On the First-Passage Area of a One-Dimensional Jump-Diffusion Process

For a one-dimensional jump-diffusion process X(t), starting from x?>?0, it is studied the probability distribution of the area A(x) swept out by X(t) till its first-passage time below zero. In particular, it is shown that the Laplace transform and the moments of A(x) are solutions to certain partial differential-difference equations with outer conditions. The distribution of the maximum displacement of X(t) is also studied. Finally, some explicit examples are reported, regarding diffusions with and without jumps.     

Two-sided networks for completely simple semigroups

Let S be a completely simple semigroup represented as a Rees matrix semigroup M(I,G,P) with normalized sandwich matrix P. On the congruence lattice C(S) of S we consider the relations T _i, K and T _r which identify congruences with the same left trace, kernel and right trace, respectively. These are equivalences whose classes are intervals. The upper and lower ends of these intervals induce the following operators on C(S) T_l, K, T_r, t_l, k and t_r .We construct here the semigroup generated by these operators as a homomorphic image of a semigroup given by generators and relations and demonstrate the minimality of the latter.