Related papers: Normality through partial sharing of sets with dif…
In this paper we investigate the question of normality for special monomial ideals in a polynomial ring over a field. We first include some expository sections that give the basics on the integral closure of a ideal, the Rees algebra on an…
We extend the fundamental normality test due to Carath\'eodory in the sense of shared functions.
Image normalization is a building block in medical image analysis. Conventional approaches are customarily utilized on a per-dataset basis. This strategy, however, prevents the current normalization algorithms from fully exploiting the…
We give a construction of a family of (weighted) graphs that are pairwise cospectral with respect to the normalized Laplacian matrix, or equivalently probability transition matrix. This construction can be used to form pairs of cospectral…
We discuss in detail a well known method for obtaining the frequencies of the normal modes of coupled harmonic oscillators that is based on the simultaneous diagonalization of two symmetric matrices. We apply it to some simple illustrative…
It is known that families of graphs with a semialgebraic edge relation of bounded complexity satisfy much stronger regularity properties than arbitrary graphs, and that they can be decomposed into very homogeneous semialgebraic pieces up to…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
We study a relationship between rational proper maps of balls in different dimensions and strongly plurisubharmonic exhaustion functions of the unit ball induced by such maps. Putting the unique critical point of this exhaustion function at…
Let K be a complete algebraically closed p-adic field of characteristic zero. Let f, g be two transcendental meromorphic functions in the whole field K or meromorphic functions in an open disk that are not quotients of bounded analytic…
Partial methods play an important role in formal methods and beyond. Recently such methods were developed for parity games, where polynomial-time partial solvers decide the winners of a subset of nodes. We investigate here how effective…
The aim of this paper is to prove that every polynomial function that maps the natural integers to the positive integers is the growth function of some D0L-system.
The functional calculus for normal elements in $C^*$-algebras is an important tool of analysis. We consider polynomials $p(a,a^*)$ for elements $a$ with small self-commutator norm $\|[a,a^*]\| \le \delta$ and show that many properties of…
A symmetric function of $N$ variables can be given in terms of symmetric polynomials of these variables. We determine those symmetric polynomials in which the dual differential operators take the neatest form when expressed in terms of our…
We prove a version of Montel's theorem for analytic functions over a non-archimedean complete valued field. We propose a definition of normal family in this context, and give applications of our results to the dynamics of non-archimedean…
We study a new kind of symmetric polynomials P_n(x_1,...,x_m) of degree n in m real variables, which have arisen in the theory of numerical semigroups. We establish their basic properties and find their representation through the power sums…
We determine all pairs $(f,g)$ of meromorphic functions that share four pairs of values $(a_\nu,b_\nu)$, $1\le\nu\le 4$, and a fifth pair $(a_5,b_5)$ under some mild additional condition.
In this paper, as an application of Zalcman's lemma in $\mathbb{C}^n$, we give a sufficient condition for normality of holomorphic functions of several complex variables, which generalizes previous known one-dimensional criterion of A.J.…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
Let D be a domain, n, k be positive integers and n >= K+3. Let F be a family of functions meromorphic in D. If each f in F satisfies (f^n)^(k) not equal to 1 for z in D, then F is normal family. This result was proved by Schwick. In this…