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We study the factorization of quasi generalized quark distributions with twist-2 generalized parton distributions. We use an approach which is different than that used in literature. Using the approach we derive the factorization relations…

We introduce the concept of isolated factorizations of an element of a commutative monoid and study its properties. We give several bounds for the number of isolated factorizations of simplicial affine semigroups and numerical semigroups.…

We investigate the asymptotic behaviour of solutions of a class of nonlocal Fokker--Planck equations defined by nonsingular, heavy-tailed convolution kernels and characterised by a scaling parameter $\e\in(0,1]$ and a fractional index…

We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…

We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…

This paper aims to investigate the asymptotic error distribution of several numerical methods for stochastic partial differential equations (SPDEs) with multiplicative noise. Firstly, we give the limit distribution of the normalized error…

We provide a rigorous basis for factorization for a large class of non-leptonic two-body $B$-meson decays in the heavy-quark limit. The factorization formula incorporates elements of the naive factorization approach and the hard-scattering…

Asymptotic expansions with explicit upper bounds for remainders are given for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces. The corresponding algorithms are based on a special technique of…

Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…

Randomly sampling an acyclic orientation on the complete bipartite graph $K_{n,k}$ with parts of size $n$ and $k$, we investigate the length of the longest path. We provide a probability generating function for the distribution of the…

Global fits to moments of kinematic distributions measured in inclusive semileptonic $B\rightarrow X_c l \nu_l$ enable the determination of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cb}|$ together with non-perturbative matrix…

We establish asymptotic expansions for factorial moments of following distributions: number of cycles in a random permutation, number of inversions in a random permutation, and number of comparisons used by the randomized quick sort…

We study matrix coefficients of the unitary (and also the completely bounded) representations of SL(2;R) and its universal covering group. We describe the asymptotic distribution of column vectors in terms of Whittaker functions, exhibiting…

We investigate fast diffusions on finite directed graphs. We prove results in a way dual to presented in Bobrowski, A. Ann. Henri Poincar\'e (2012) 13(6): 1501-1510 and Bobrowski, A., Morawska, K. DCDS-B (2012), 17(7): 2313-2327, and obtain…

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the limiting probability distribution and the…

We obtain characterizations of asymptotic properties of Schwartz distribution by using Gabor frames. Our characterizations are indeed Tauberian theorems for shift asymptotics (S-asymptotics) in terms of short-time Fourier transforms with…

We derive the dominant asymptotic form and the order of the correction terms of the finite-perimeter partition function of self-avoiding polygons on the square lattice, which are weighted according to their area A as q^A, in the inflated…

We consider the set ${\mathscr S}_Q$ of Farey fractions $d/b$ of order $Q$ with the property that there exists a matrix $\left( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \right) \in \operatorname{SL}(2,{\mathbb Z})$ of trace at…

In this paper, we study the asymptotic behavior of supremum distribution of some classes of iterated stochastic processes $\{X(Y(t)) : t \in [0, \infty)\}$, where $\{X(t) : t \in \mathbb{R} \}$ is a centered Gaussian process and $\{Y(t): t…

In a recent paper (Tran et al., Ann.Phys.311(2004)204), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We…