In this study, linear second-order self-adjoint delta-nabla matrix systems on time scales are considered with the motivation of extending the analysis of dominant and recessive solutions from the differential and discrete cases to any arbitrary dynamic equations on time scales. These results emphasize the case when the system is non-oscillatory.

The engineering of Human-Computer Interface (HCI) is a wide-ranging and huge research field. However development models stemming from Software Engineering overlook important aspects in terms of interactive systems development. That is why an HCI-enriched model, called ∇ model (pronounced nabla model), is envisaged in this paper.

Roitman's combinatorial principle $\Delta$ is equivalent to monotone normality of the nabla product, $\nabla (\omega +1)^\omega$. If $\{ X_n : n\in \omega\}$ a family metrizable spaces and $\nabla_n X_n$ monotonically normal, then hereditarily paracompact. Hence, if holds box product $\square +1)^\omega$ Large fragments hold in $\mathsf{ZFC}$, yielding large subspaces (\omega+1)^\omega$ that ar...

In this article, we propose the definition of one parameter matrix Mittag-Leffler functions of fractional nabla calculus and present three different algorithms to construct them. Examples are provided to illustrate the applicability of suggested algorithms.

In this paper we study the concept of analyticity for complex-valued functions of a complex time scale variable, derive a time scale counterpart of the classical Cauchy–Riemann equations, introduce complex line delta and nabla integrals along time scales curves, and obtain a time scale version of the classical Cauchy integral theorem.

In this article, we consider the following two-point discrete fractional boundary value problem with constant coefficient associated Dirichlet conditions. \begin{equation*} \begin{cases} -\big{(}\nabla^{\nu}_{\rho(a)}u\big{)}(t) + \lambda u(t) = f(t, u(t)), \quad t \in \mathbb{N}^{b}_{a 2}, \\ u(a) u(b) 0, \end{cases} \end{equation*} where $1 < \nu 2$, $a,b \mathbb{R}$ $b-a\in\mathbb{N}_{3}$...

the non-commuting graph $nabla(g)$ of a non-abelian group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we 'll prove that if $g$ is a finite group with $nabla(g)congnabla(bs_{n})$, then $g cong bs_{n}$, where $bs_{n}$ is the symmetric group of degre...

The aim of this paper is to establish an extension of Minkowski’s inequality when p, s, t ∈ R−{0}, p > 0 are different such that s, t < 1, s, t = 0 and s−t p−t < 1, to isotonic linear functionals taking into account that the time scale Cauchy delta, Cauchy nabla, α-diamond, multiple Riemann, and multiple Lebesque integrals all are isotonic linear functionals. Several applications of these resul...

Although intracellular calcium ([Ca(2+)](i)) transients in cardiac cells have been well studied in the uniformly polarized cell membrane, how these transients are modified during field stimulation when the cell membrane is nonuniformly polarized has not been investigated. In this study we characterized the effects of uniform field stimuli on [Ca(2+)](i) transients in isolated guinea pig cardiac...