Related papers: Linear forms of a given Diophantine type and latti…
The goal of this paper is to generalize the main results of [KM] and subsequent papers on metric Diophantine approximation with dependent quantities to the set-up of systems of linear forms. In particular, we establish `joint strong…
A closed-form expression for the amplitudes of source waves in 2D discrete lattice with local and linear (waveguides) defects is derived. The numerical implementation of this analytic expression is demonstrated by several examples.
In this paper, we prove several generalizations and applications of a fixed point theorem. This theorem is used to prove the existence and uniqueness of solutions of the linear sparse matrix problem considered.
A linear system of difference equations and a nonlinear perturbation are considered. We propose sufficient conditions to ensure that the homeomorphism of topological equivalence between them is actually a $C^1$ diffeomorphism. These…
In recent years the investigation of hadron structure using lattice techniques has attracted growing attention. In this talk we give an overview on recent work with a focus on results for nucleon spectrum and structure from the QCDSF…
We give a necessary and sufficient condition for a system of linear inhomogeneous fractional differential equations to have at least one bounded solution. We also obtain an explicit description for the set of all bounded (or decay)…
We study multiplicative Diophantine approximation property of vectors and compute Diophantine exponents of hyperplanes via dynamics.
We show how lattice paths and the reflection principle can be used to give easy proofs of unimodality results. In particular, we give a "one-line" combinatorial proof of the unimodality of the binomial coefficients. Other examples include…
Recently, a new fractional derivative called the conformable fractional derivative is given on based basic limit definition derivative in [4]. Then, the fractional versions of chain rules, exponential functions, Gronwalls inequality,…
In this paper, we use the perspective of linear series, and in particular results following from the degeneration tools of limit linear series, to give a number of new results on existence and non-existence of branched covers of the…
Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.
In this note we introduce a new technique to answer an issue posed in [7] concerning geometric properties of the set of non-surjective linear operators. We also extend and improve a related result from the same paper.
We study connections between linear equations over various semigroups and recursively enumerable sets of positive integers. We give variants of the universal Diophantine representation of recursively enumerable sets of positive integers…
This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…
We establish a Liouville type theorem for some conformally invariant fully nonlinear equations
In this paper the metric theory of Diophantine approximation associated with the small linear forms is investigated. Khintchine-Groshev theorems are established along with Hausdorff measure generalization without the monotonic assumption on…
In this paper we study counting functions representing the number of solutions of systems of linear inequalities which arise in the theory of Diophantine approximation. We develop a method that allows us to explain the random-like behavior…
By applying Schmidt's lattice method, we prove results on simultaneous Diophantine approximation modulo 1 for systems of polynomials in a single prime variable provided that certain local conditions are met.
Some recent advances in the theoretical description of the Nucleon electromagnetic form factors, both in the space- and time-like regions, will be briefly illustrated. In particular, both the present stage of the lattice calculations and…