Abstract In this paper, we obtain the best constant and equality condition for a class of mixed-norm Hardy inequalities when weight is power function. By building solving corresponding Euler equation, look optimal One main ingredients to introduce two key auxiliary functions so that equalities are derived.

Abstract Using umbral calculus, we establish a symmetric identity for any sequence of polynomials satisfying A ′ n +1 ( x ) = + 1) with 0 constant polynomial. This allows us to obtain in simple way some known relations involving Apostol-Bernoulli polynomials, Apostol-Euler and generalized Bernoulli attached primitive Dirichlet character.

In this study, a three-dimensional CFD transient model is established for predicting species concentration distribution in the biodegradation of phenol an airlift reactor (ALR). The gas–liquid flow ALR determined by Euler–Euler method coupled with standard k-? model, and bubble size predicted population balance (PBM). A turbulent mass diffusivity developed to simulate transfer process predict d...

in this paper, free vibration of an Euler-Bernoulli beam with variable cross-section resting on elastic foundation and under axial tensile force is considered. Beam’s constant height and exponentially varying width yields variable cross-section. The problem is handled for three different boundary conditions: clamped-clamped, simply supported-simply supported and clamp-free beams. First, the equ...

Vortices (flows with closed elliptic streamlines) are exact nonlinear solutions to the compressible Euler equation. In this contribution, we use differential geometry derive transformations between Cartesian and coordinates, show that in coordinates a constant vorticity flow reduces $\dot{\mu}=0$ $\dot{\nu}={\rm const}$ along streamline $\mu_0$ matches vortex eccentricity.

The quasi-neutral limit of one-fluid Euler-Poisson systems leads to incompressible Euler equations. It was widely studied in previous works. In this paper, we deal with the a two-fluid system. This presents different feature since it compressible We justify for global smooth solutions near constant equilibrium states one space dimension. Specifically, prove existence by establishing uniform ene...

The thermodynamic Euler equation for high-energy states of large-$N$ gauge theories is derived from the dependence extensive quantities on number colors $N$. This relates energy state to temperature, entropy, degrees freedom and its chemical potential, but not volume or pressure. In context gauge/gravity duality we show that dual generalized Smarr formula black holes in presence a negative cosm...

1 Abstract This paper outlines the architecture of a systolic trigger processor for tracking detectors of the jetchamber type, operated inside a solenoidal magnetic field. It outputs the number of tracks and their radius of curvature in less than 10 μs. A detailed description of the constant data flow scheme is given which is maintained thoroughly from the read-out of the drift times up to the ...

We calculate the Euclidean actions and the entropies of lukewarm black holes, cold black holes and ultracold solutions in the Einstein-Maxwell theory with a positive cosmological constant. We find that the entropy of lukewarm black holes is sum of entropies of black hole horizon and cosmological horizon. The entropy of cold black holes is only one quarter area of cosmological horizon, and the e...

The forced vibration behaviors are examined for nonlocal strain gradient nanobeams with surface effects subjected to a moving harmonic load travelling with a constant velocity in terms of three beam models namely, the Euler-Bernoulli, Timoshenko and modified Timoshenko beam models. The modification for nonlocal strain gradient Timoshenko nanobeams is exerted to the constitutive equations by exc...