16 Results Found

We study Gamma ratios evaluated at a shifted square root and finite products of their positive powers. For each ratio, we prove the complete Bernstein property and compute the representing measure explicitly. The symmetry of the Gamma parameters give...

The purpose of this note is to propose an application of the Lambert W function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular, we recognize the role of its main branch, $W_0\left(t\right)$, in a peculiar...

In the paper, the authors find a sufficient and necessary condition for the power-exponential function ${\left(1+\frac{1}{x}\right)}^{\alpha x}$ to be a Bernstein function, derive closed-form formulas for the nth derivatives of the power-exponential functions ${\left(1+\frac{1}{x}\right)}^{\alpha x}$ and ${(1}^{}$...

This paper focuses on the construction of deterministic and stochastic extensions of the Gompertz curve by means of generalized fractional derivatives induced by complete Bernstein functions. Precisely, we first introduce a class of linear stochastic...

Both the stretched exponential function and the Prony series are prominent mathematical frameworks extensively employed to characterize monotonically decaying phenomena across physics and engineering disciplines. Despite being fundamentally distinct...

Hyperbolic complete monotonicity property ($\mathrm{HCM}$) is a way to check if a distribution is a generalized gamma ($\mathrm{GGC}$), hence is infinitely divisible. In this work, we illustrate to which extent the Mittag-Leffler functions $E_{\alpha },\alpha \in (0,2]$...

A class of generalized fractional Zener-type viscoelastic models with general fractional derivatives is considered. Two integral representations are derived for the corresponding relaxation modulus. The first representation is established by applying...

The fractional order differential equation \(u'(t)=Au(t)+\gamma D_t^{\alpha} Au(t)+f(t), \ t>0\), \(u(0)=a\in X\) is studied, where \(A\) is an operator generating a strongly continuous one-parameter semigroup on a Banach space \(X\), \(D_t^{\alp...

A previous study determined criteria ensuring that a probability distribution supported in positive integers is the limiting conditional law of a subcritical Markov branching process. It is known that there is an close connection between the limiting...

We study the properties of complete parabolic constant mean curvature spacelike hypersurfaces in generalized Robertson–Walker (GRW) spacetimes $I{\times }_{\phi }{P}^n$ whose warping function $\phi$ fulfills a certain convexity criterion such that $-$...

This paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann–Liouville fractional integral and fractional Caputo deriva...

The fractional Zener constitutive law is frequently used as a model of solid-like viscoelastic behavior. In this work, a class of linear viscoelastic models of Zener type, which generalize the fractional Zener model, is studied by the use of Bernstei...

This paper extends the well-known transfinite interpolation formula, which was developed in the late 1960s by the applied mathematician William Gordon at the premises of General Motors as an extension of the pre-existing Coons interpolation formula....

This article is a survey of our recent work on the connections between Koba–Nielsen amplitudes and local zeta functions (in the sense of Gel’fand, Weil, Igusa, Sato, Bernstein, Denef, Loeser, etc.). Our research program is motivated by the fact that...

Cancerous tumor cells divide uncontrollably, which results in either tumor or harm to the immune system of the body. Due to the destructive effects of chemotherapy, optimal medications are needed. Therefore, possible treatment methods should be contr...

This article develops a unified asymptotic theory for conditional U-statistics based on delta-sequence smoothing, thereby extending, in a substantial and conceptually coherent manner, the classical kernel-based framework for localized nonlinear condi...