Related papers: Linear independence measures for values of certain…

We consider nonlinear, or "event-dependent", sampling, i.e. such that the sampling instances {tk} depend on the function being sampled. The use of such sampling in the construction of Lebesgue's integral sums is noted and discussed as…

We derive completeness criteria for sequences of functions of the form $% f(x\lambda_{n})$, where $\lambda_{n}$ is the $nth$ zero of a suitably chosen entire function. Using these criteria, we construct systems of nonorthogonal…

We present a general theory for studying the difference analogues of special functions of hypergeometric type on the linear-type lattices, i.e., the solutions of the second order linear difference equation of hypergeometric type on a…

In this article, we establish a new linear independence criterion for the values of certain {\it Lauricella hypergeometric series} $F_D$ with rational parameters, in both the complex and $p$-adic settings, over an algebraic number field.…

We give criteria for graded ideals to have the property that all their powers are componentwise linear. Typical examples to which our criteria can be applied include the vertex cover ideals of certain finite graphs.

We prove several power series identities involving the refined generating function of interval orders, as well as the refined generating function of the self-dual interval orders. These identities may be expressed as $\sum_{n\ge…

We show that classical processes corresponding to operators what satisfy a q-commutative relation have linear regressions and quadratic conditional variances. From this we deduce that Bell's inequality for their covariances can be extended…

Let $\mathfrak g$ be a complex semisimple Lie algebra. We define what it means for a finite dimensional representation of $\mathfrak g$ to be rectangular and completely classify faithful rectangular representations. As an application, we…

Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…

Certain types of bilinearly defined sets in $\mathbb{R}^n$ exhibit a higher degree of linearity than what is apparent by inspection.

We conjecture recurrence relations satisfied by the degrees of some linearizable lattice equations. This helps to prove linear growth of these equations. We then use these recurrences to search for lattice equations that have linear growth…

Linear models are foundational tools in statistics and ubiquitous across the applied sciences. However, conventional statistical inference -- such as $t$-tests and $F$-tests -- are only valid at fixed sample sizes, making them unsuitable…

We investigate finite sections of Gabor frames and study the asymptotic behavior of their lower Riesz bound. From a numerical point of view, these sets of time-frequency shifts are linearly dependent, whereas from a rigorous analytic point…

We present a systematic study of integrals over [0,1] where the integrand is of the form Q(x) log log 1/x. Here Q is a rational function.

Let $f$ be an $E$-function (in Siegel's sense) not of the form $e^{\beta z}$, $\beta \in \overline{\mathbb{Q}}$, and let $\log$ denote any fixed determination of the complex logarithm. We first prove that there exists a finite set $S(f)$…

We consider the category of linear relations over an arbitrary commutative ring, and identify it as a subcategory of the category of Kronecker representations. We observe that this subcategory forms a definable, faithful and hereditary…

In this paper, we consider procedures for testing hypotheses on the dimension of the linear span generated by a growing number of $p\times p$ covariance matrices from independent $q$ populations. Under a proper limiting scheme where all the…

We establish $L^p\times L^q$ to $L^r$ estimates for some paraproducts, which arise in the study of the bilinear Hilbert transform along curves.

In this note, we review the latest qualitative results, referring to the Li\'enard Equation, in the framework of non-conformable, generalized and fractional differential operators.

We define what it means for a joint probability distribution to be compatible with a set of independent causal mechanisms, at a qualitative level -- or, more precisely, with a directed hypergraph ${\mathcal{A}}$, which is the qualitative…