Related papers: Second main theorems with weighted counting functi…
We establish two-point distortion theorems for sense-preserving planar harmonic mappings $f=h+\overline{g}$ which satisfies the univalence criteria in the unit disc such that, Becker's and Nehari`s harmonic version. In addition, we find the…
The main purpose of this work is to extend the properties of multivalued transformations to the integral type transformations and to obtain the existence of fixed points under F-contraction. In addition, the results of this study were…
This is the second of two coupled papers estimating the mean values of multiplicative functions, of unknown support, on arithmetic progressions with large differences. Applications are made to the study of primes in arithmetic progression…
We supplement the result of the first part of the work with estimates of the integrals of the difference of subharmonic functions in measure with some deterioration of the absolute constants, but these estimates have the form of a…
We present a generalization of Warning's Second Theorem to polynomial systems over a finite local principal ring with suitably restricted input and output variables. This generalizes a recent result with Forrow and Schmitt (and gives a new…
We prove some analogues of the central point theorem and Tverberg's theorem, where instead of points, we consider hyperplanes or affine flats of given dimension.
In this article we introduce generalized projective spaces (Definitions $[2.1, 2.5]$) and prove three main theorems in two different contexts. In the first context we prove, in main Theorem $A$, the surjectivity of the Chinese remainder…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
The escalating parameter counts in modern deep learning models pose a fundamental challenge to efficient training and resolution of overfitting. We address this by introducing the \emph{Mapping Networks} which replace the high dimensional…
In this paper, an Askey-Wilson version of the Wronskian-Casorati determinant $\mathcal{W}(f_{0}, \dots, f_{n})(x)$ for meromorphic functions $f_{0}, \dots, f_{n}$ is introduced to establish an Askey-Wilson version of the general form of the…
In this paper, we prove a monotonicity formula and some Bernstein type results for translating solitons of hypersurfaces in $\re^{n+1}$, giving some conditions under which a trantranslating soliton is a hyperplane. We also show a gap…
In a previous work by the authors the one dimensional (doubling) renormalization operator was extended to the case of quasi-periodically forced one dimensional maps. The theory was used to explain different self-similarity and universality…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
The essential elements in the construction of the couplings of vector multiplets to supergravity using the conformal approach are repeated. This approach leads automatically to the basic quantities on which the symplectic transformations,…
We consider the problem of computing the distance-dependent two-point function of general planar maps and hypermaps, i.e. the problem of counting such maps with two marked points at a prescribed distance. The maps considered here may have…
In this document I develop a weight function theory of positive order basis function interpolants and smoothers. **In Chapter 1 the basis functions and data spaces are defined directly using weight functions. The data spaces are used to…
We establish a connection between linear codes and hyperplane arrangements using the Thomas decomposition of polynomial systems and the resulting counting polynomial. This yields both a generalization and a refinement of the weight…
In this paper we find the second generalized Hamming weight of some evaluation codes arising from a projective torus, and it allows to compute the second generalized Hamming weight of the codes parameterized by the edges of any complete…
Arrangement theory plays an essential role in the study of the unfolding model used in many fields. This paper describes how arrangement theory can be usefully employed in solving the problems of counting (i) the number of admissible…
We consider directed weighted graphs and define various families of path counting functions. Our main results are explicit formulas for the main term of the asymptotic growth rate of these counting functions, under some irrationality…