Related papers: On functions with a unique identification minor

This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…

Characterizations of the star, minus and diamond orders of operators are given in various contexts and the relationship between these orders is made more transparent. Moreover, we introduce a new partial order of operators which provides a…

Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness for a large class of subordinate killed Brownian motions in bounded C1,1 domains, C1,1 domains with…

We provide an explicit characterization of the properties of primitive recursive functions that are decidable or semi-decidable, given a primitive recursive index for the function. The result is much more general as it applies to any c.e.…

Functions with uniform sublevel sets can represent orders, preference relations or other binary relations and thus turn out to be a tool for scalarization that can be used in multicriteria optimization, decision theory, mathematical…

The present article is devoted to certain examples of functions whose argument represented in terms of Cantor series.

Consider a class of functions of one real variable with the following uniqueness property: if a function f(x) from the class vanishes on a set of positive measure, then f is the zero function. In many instances, we would like to have a…

We consider the set of Baire 1 functions endowed with the pointwise partial ordering and investigate the structure of the linearly ordered subsets.

We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…

In this paper we consider class of continuous functions, called quasiaharmonic functions, admitting best approximations by harmonic polynomials. In this class we prove a uniqueness theorem by analogy with the analytic functions.

We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences…

We give short proofs of conjectural identities due to Gordon and McIntosh involving two 10th order mock theta functions.

We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…

In this paper, a new formula for {\pi}^(2)(N) is formulated, it is a function that counts the number of semi-primes not exceeding a given number N. A semi-prime is a natural number that is the product of precisely two prime numbers, the two…

It is shown that quasi all continuous functions on the unit circle have the property that, for many small subsets E of the circle, the partial sums of their Fourier series considered as functions restricted to E exhibit certain universality…

Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…

We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…

The z-zeros of the modified Bessel function of the third kind K_{nu}(z), also known as modified Hankel function or Macdonald function, are considered for arbitrary complex values of the order nu. Approximate expressions for the zeros,…

We employ computer algebra algorithms to prove a collection of identities involving Bessel functions with half-integer orders and other special functions. These identities appear in the famous Handbook of Mathematical Functions, as well as…

We establish the existence and uniqueness of rational conformal maps of minimal degree $n+1$ for opening up $n$ arcs. In earlier results, the degree was exponential in $n$. We also discuss two related problems. (a) We establish existence of…