Related papers: Taylor Domination, Difference Equations, and Bauti…
Many hard combinatorial problems can be modeled by a system of polynomial equations. N. Alon coined the term polynomial method to describe the use of nonlinear polynomials when solving combinatorial problems. We continue the exploration of…
We study the Borel map, which maps infinitely differentiable functions on an interval to the jets of their Taylor coefficients at a given point in the interval. Our main results include a complete description of the image of the Borel map…
Let $\mathcal{V}_p(\lambda)$ be the collection of all functions $f$ defined in the unit disc $\ID$ having a simple pole at $z=p$ where $0<p<1$ and analytic in $\ID\setminus\{p\}$ with $f(0)=0=f'(0)-1$ and satisfying the differential…
We give a survey of results on zero distribution and factorization of analytic functions in the unit disc in classes defined by the growth of $\log|f(re^{i\theta})|$ in the uniform and integral metrics. We restrict ourself by the case of…
A density function for an algebraic invariant is a measurable function on $\mathbb{R}$ which measures the invariant on an $\mathbb{R}$-scale. This function carries a lot more information related to the invariant without seeking extra data.…
We consider analytic functions of the Riemann zeta type, for which, if $s$ is a zero, so is $1-s$. We use infinite product representations of these functions, assuming their zeros to be of first order. We use exponential factors to…
We consider the dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a…
For a fixed positive integer $\;k,\;$ limit laws of linearly normalized $\;k$-th upper order statistics are well known. In this article, a comprehensive study of tail behaviours of limit laws of normalized $k$-th upper order statistics…
The test ideal $\tau(R)$ of a ring $R$ of prime characteristic is an important object in the theory of tight closure. In this paper, we study a generalization of the test ideal, which is the ideal $\tau(\a^t)$ associated to a given ideal…
The Taylor expansion of thermodynamic observables at a finite baryon chemical potential $\mu_B$ is an oft-used method to circumvent the well-known sign problem of Lattice QCD. Owing to the associated difficulty and limitations of precision…
Consider the operator $E$ on arithmetic functions such that $Ef$ is the multiplicative arithmetic function defined by $(Ef)(p^a) = f(a)$ for every prime power $p^a$. We investigate the behaviour of $E^m\tau_k$, where $\tau_k$ is a…
Let L be the Leavitt path algebra of an arbitrary directed graph E over a field K. This survey article describes how this highly non-commutative ring L shares a number of the characterizing properties of a Dedekind domain or a Pr\"ufer…
In this paper we obtain some statements concerning ideals of polynomials and apply these results in a number of different situations. Among other results, we present new characterizations of $\mathcal{L}_{\infty}$-spaces, Coincidence…
Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…
A detailed Dirac's canonical analysis for a topological four dimensional $BF$-like theory with a compact dimension is developed. By performing the compactification process we find out the relevant symmetries of the theory, namely, the full…
In the paper paradoxes underlying thermodynamics and a quantum mechanics are discussed. Their solution is given from the point of view of influence of the exterior observer (surrounding medium) destroying correlations of system, or…
Let $f(x)$, $x\in\mathbb R^2$, be a piecewise smooth function with a jump discontinuity across a smooth surface $\mathcal S$. Let $f_{\Lambda\epsilon}$ denote the Lambda tomography (LT) reconstruction of $f$ from its discrete Radon data…
The manuscript reviews Dirichlet Series of important multiplicative arithmetic functions. The aim is to represent these as products and ratios of Riemann zeta-functions, or, if that concise format is not found, to provide the leading…
Given a measure $\mu$ of polynomial growth, we refine a deep result by David and Mattila to construct an atomic martingale filtration of $\mathrm{supp}(\mu)$ which provides the right framework for a dyadic form of nondoubling harmonic…
Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \| f(z) \|=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty…