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.  

Dunkl Multiplier Operators on a Class of Reproducing Kernel Hilbert Spaces

We study some class of Dunkl multiplier operators; and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark''s uncertainty principle. For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.  

Inversion Formula for the Dunkl-Wigner Transform and Compactness Property for the Dunkl-Weyl Transforms

We define and study the Fourier-Wigner transform associated with the Dunkl operators, and we prove for this transform an inversion formula. Next, we introduce and study the Weyl transforms $W_{\sigma}$ associated with the Dunkl operators, where $\sigma$ is a symbol in the Schwartz space $\mathcal{S}(\mathbb{R}^d\times\mathbb{R}^d)$. An integral relation between the precedent Weyl and Wigner transforms is given. At last, we give criteria in terms of $\sigma$ for boundedness and compactness of the transform $W_{\sigma}$.  

ON CLASSES OF REGULAR GRAPHS WITH CONSTANT METRIC DIMENSION

In this paper,we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks Jn,a class of cubic convex polytopes considering the open problem raised in [M.Imran et al.,families of plane graphs with constant metric dimension,Utilitas Math.,in press] and finally Harary graphs H 5,n by partially answering to an open problem proposed in [I.Javaid et al.,Families of regular graphs with constant metric dimension,Utilitas Math.,2012,88:43-57].We prove that these classes of regular graphs have constant metric dimension.