Using the theory of orthogonal polynomials, their associated recursion relations and differential formulas we develop a new method for evaluating integrals that include orthogonal polynomials. The method is illustrated by obtaining the following integral result that involves the Bessel function and associated Laguerre polynomial: integral(infinity)(0) x(v)e(-x/2) J(v)(mu x)L-n(2v)(x)dx = 2(v)Ga...

In this paper, we  present a version of Favard's inequality for special case and then generalize it for the Sugeno integral in fuzzy measure space $(X,Sigma,mu)$, where $mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.

For electromagnetic field theories, canonical energy-momentum conservation laws can be derived from the underpinning spacetime translation symmetry according to Noether procedure. However, tensors (EMTs) are neither symmetric nor gauge-symmetric (gauge invariant). The Belinfante-Rosenfeld (BR) method is a well-known procedure symmetrize EMTs, which also renders them gauge for first-order theori...

We consider an extended QED with the addition of a dimension-five Lorentz-breaking coupling between spinor and gauge fields, involving pseudo-tensor $\kappa^{\mu\nu\lambda\rho}$. The specific form Lorentz violating considered by us have been suggested in other works, some its consequences at classical level were already studied. Here, we investigate this violation quantum level, evaluating one ...

We study the discrete spectrum of two-particle Schr\"odinger operator $\hat H_{\mu\lambda}(K),$ $K\in\mathbb{T}^2,$ associated to Bose-Hubbard Hamiltonian {\mathbb H}_{\mu\lambda}$ a system two identical bosons interacting on site and nearest-neighbor sites in dimensional lattice $\mathbb{Z}^2$ with interaction magnitudes $\mu\in\mathbb{R}$ $\lambda\in\mathbb{R},$ respectively. completely descr...

A search for $CP$ violation in charmless three-body $\Xi_b^- \to p K^- K^-$ decays is performed using $pp$ collision data recorded with the LHCb detector, corresponding to integrated luminosities of $1\,\text{fb}^{-1}$ at a centre-of-mass energy $\sqrt{s} = 7\,\text{TeV}$, $2\,\text{fb}^{-1}$ 8\,\text{TeV}$ and 13\,\text{TeV}$. good description phase-space distribution obtained an amplitude mod...

The scalar one-loop 4-point function with one massless vertex is evaluated analytically by employing the loop regularization method. According to method a characteristic scale $\mu_{s}$ introduced regularize divergent integrals. infrared parts, which take form of $\ln^{2}(\lambda^{2}/\mu^{2}_{s})$ and $\ln(\lambda^{2}/\mu^{2}_{s})$ as $\mu_{s}\rightarrow 0$ where $\lambda$ constant expressed in...

Using a surface force balance with fast video analysis, we have measured directly the attractive forces between oppositely charged solid surfaces (charge densities sigma(+), sigma(-)) across water over the entire range of interaction, in particular, at surface separations D below the Debye screening length lambda(S). At very low salt concentration we find a long-ranged attraction between the su...

BACKGROUND The current National Cholesterol Education Program lipoprotein classification system for children and adolescents is recommended for use among 2- to 19-year-olds. This classification system does not take into account gender differences or the natural fluctuations in lipoprotein concentrations that occur with growth and maturation. METHODS AND RESULTS Data from the National Health a...

A search for $CP$ violation in charmless three-body $\Xi_b^- \to p K^- K^-$ decays is performed using $pp$ collision data recorded with the LHCb detector, corresponding to integrated luminosities of $1\,\text{fb}^{-1}$ at a centre-of-mass energy $\sqrt{s} = 7\,\text{TeV}$, $2\,\text{fb}^{-1}$ 8\,\text{TeV}$ and 13\,\text{TeV}$. good description phase-space distribution obtained an amplitude mod...