L p uncertainty principles on Sturm–Liouville hypergroups

We use the Fourier analysis associated to a singular second-order differential operator Δ, and prove a continuous-time principle for the L ^p theory.  

Pitt’s Inequality and Logarithmic Uncertainty Principle for the Dunkl Transform on {\mathbb{R}}

We establish Pitt’s inequality and deduce Beckner’s logarithmic uncertainty principle for the Dunkl transform on \({\mathbb{R}}\) . Also, we prove Stein–Weiss inequality for the Dunkl–Bessel potentials.  

Calderón type formula in Quantum calculus

In this paper, a Calderón type reproducing formula involving finite q$q$-measures is considered in Quantum calculus.  

Magic Labelings of Type (a, b, c) of Families of Wheels

In this paper, firstly, we study magic labeling of type (1, 1, 1) for wheels and subdivided wheels. Secondly, we prove that a wheel admits a magic labeling of type (0, 1, 1). We also prove that any odd wheel admits a magic labeling of type (0, 1, 0). At the last, we find the magic labeling of type (1, 1, 0) for subdivided wheels.  

Hahn Difference Operator and Associated Jackson–N?rlund Integrals

This paper is devoted for a rigorous investigation of Hahn’s difference operator and the associated calculus. Hahn’s difference operator generalizes both the difference operator and Jackson’s q-difference operator. Unlike these two operators, the calculus associated with Hahn’s difference operator receives no attention. In particular, its right inverse has not been constructed before. We aim to establish a calculus of differences based on Hahn’s difference operator. We construct a right inverse of Hahn’s operator and study some of its properties. This inverse also generalizes both N?rlund sums and the Jackson q-integrals. We also define families of corresponding exponential and trigonometric functions which satisfy first and second order difference equations, respectively.  

A note on the regularity criteria for the Navier-Stokes equations

We consider the regularity problem for 3D Navier-Stokes equations in a bounded domain with smooth boundary. A new sufficient condition which guarantees the regularity of weak solutions on the quotient ∇p/(1+|u|^δ₁+|∇u|^δ₂) for the Navier-Stokes equations is established.  

Vertex-antimagic labelings of regular graphs

Let G = (V, E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers 1, 2, . . . , p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f (x) assigned to the vertex x together with all values f (xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1, . . . , r + 1.  

Challenges of living in the harsh environments: A mathematical modeling study

We propose and analyze a mathematical model, which mimics community dynamics of plants and animals in harsh environments. The mathematical model exploits type IV functional responses whose idiosyncrasies have been recognized only in recent years. The interaction of the middle predator with the top predator is cast into Leslie-Gower scheme. Linear and non-linear stability analyses are performed to get an idea of the stability behavior of the model food chain. It turns out that carrying capacity of the prey and the immunity parameter of the middle predator are two crucial parameters governing the model. Availability of alternative food options to the generalist predator also plays a key role in deciding the model dynamics.Simulation runs performed on this model provide insight into population dynamics of monkeys of macaque family found in northern Japan. These monkeys are social animals which reproduce sexually. The characteristic feature of the model dynamics is that the generalist predator (macaque monkeys) is able to avoid impending extinction frequently and recovers at a rate which falsify threats from exogenous external forces; extreme weather conditions, etc.  

Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space

The object of the present paper is to determine the stability of the Hyers-Ulam-Rassias type theorem concerning the Pexiderized quadratic functional equation in intuitionistic fuzzy normed spaces (IFNS).  

Uncertainty Principles for the Segal-Bargmann Transform

We recall some properties of the Segal-Bargmann transform; and we establish for this transform qualitative uncertainty principles: local uncertainty principle, Heisenberg uncertainty principle, Donoho-Stark''s uncertainty principle and Matolcsi-Sz\"ucs uncertainty principle.