Related papers: Luzin-type properties and the difference quotient …
In this work we discuss a formal way of dealing with properties of contextual systems. Our approach is to assume that properties describing the same physical quantity, but belonging to different measurement contexts, are indistinguishable…
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coeficients in $\K$. We compute the semigroup Poincar\'e…
Recently, a new definition for quantum $f$-divergences was introduced based on an integral representation. These divergences have shown remarkable properties, for example when investigating contraction coefficients under noisy channels. At…
We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…
It is a well-known fact that Riemann Hypothesis will follows if the function identically equal to -1 can be arbitrarily approximated in the norm $\norma{.}$ of $L^{2}([0,1],dx)$ by functions of the form $f(x)=\sum_{k=1}^{n}a_{k}…
The f-invariant is a higher version of the e-invariant that takes values in the divided congruences between modular forms; in the situation of a cartesian product of two framed manifolds, the f-invariant can actually be computed from the…
The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of…
We propose a new concept of generalized differentiation of set-valued maps that captures the first order information. This concept encompasses the standard notions of Frechet differentiability, strict differentiability, calmness and…
We introduce more general concepts of Riemann-Liouville fractional integral and derivative on time scales, of a function with respect to another function. Sufficient conditions for existence and uniqueness of solution to an initial value…
In this paper we introduce the notion of a weak uniform Diophantine exponent of a real number and obtain the complete description of the spectrum of its values.
Let $D\in\mathbb{N}$, $q\in[2,\infty)$ and $(\mathbb{R}^D,|\cdot|,dx)$ be the Euclidean space equipped with the $D$-dimensional Lebesgue measure. In this article, the authors establish the Fefferman-Stein decomposition of Triebel-Lizorkin…
In this paper we study the integrals of fractional parts of given functions, and develop some new tools to understand the behaviour of prime differences. We demonstrate how simply some seemingly difficult conjectures related to prime…
We introduce a natural definition for sums of the form \[ \sum_{\nu=1}^x f(\nu) \] when the number of terms x is a rather arbitrary real or even complex number. The resulting theory includes the known interpolation of the factorial by the…
We attach a ring of sequences to each number from a certain class of extremal real numbers, and we study the properties of this ring both from an analytic point of view by exhibiting elements with specific behaviors, and also from an…
There is a mismatch between the standard theoretical analyses of statistical machine learning and how learning is used in practice. The foundational assumption supporting the theory is that we can represent features and models using…
We introduce a new real valued invariant for finitely presented groups called residual deficiency. Its main property is the following. Let G be a finitely presented group. If the residual deficiency of G is greater than one, then G has a…
We describe those unipotent representations of a finite group of Lie type which are defined over the rational numbers.
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…
Ultrafunctions are a particular class of functions defined on a Non Archimedean field E. They have been introduced and studied in some previous works. In this paper we develop the notion of fine ultrafunctions which improves the older…
We prove a uniform estimate of the number of points for difference algebraic varieties in finite difference fields in the spirit of Lang-Weil. More precisely, we give uniform lower and upper bounds for the number of rational points of a…