A new three-dimensional integral containing f(x,y,z)Iv(x?) is derived where Iv(x?) the Modified Bessel Function of first kind and taken over infinite cubic space 0<x<?,0<y<?,0<z<?. The not easily evaluated for complex ranges parameters. representation in terms Hurwitz–Lerch zeta function, polylogarithm function Riemann functions are evaluated. This yields triple representation...

Null shells are a useful geometric construction to study the propagation of infinitesimally thin concentrations massless particles or impulsive waves. After recalling necessary and sufficient conditions obtained in [28] that allow for matching two spacetimes with null embedded hypersurfaces as boundaries, we will address problem across Killing horizons zero order case when symmetry generators b...

In this study, we elucidate the reaction kinetics for simultaneous hydrodeoxygenation of xylitol to 1,2-dideoxypentitol and 1,2,5-pentanetriol over a ReOx-Pd/CeO2 (2.0 weight% Re, 0.30 Pd) catalyst. The was determined be zero-order with respect xylitol. activation energy elucidated through an Arrhenius relationship as well non-Arrhenius kinetics. investigated at 150–170 °C constant H2 pressure ...

A long-standing problem in developmental biology, closely associated with pattern formation, is how continuous morphogen gradients are translated into sharp response borders that define clearcut territories in which cells express different sets of genes. To understand how gradients can generate thresholds, several mechanisms have been investigated over the years. Initially, most of these studie...

The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information, that is noisy function evaluations at any desired point. We focus on problems with high degrees of smoothness, such as logistic regression. We show that as oppo...

conclusions the present research demonstrated that the ultrasonic (us) process can be utilized as an effective and simple method for treatment of mg dye in an aqueous solution. moreover, the eeo is directly proportional to the mg concentration and power density and inversely proportional to temperature and mechanical agitation, which can be predicted by the obtained empirical kinetics model. co...

The fractal degree of adsorption on the multi-walled carbon nanotube has been investigated. The fractal-like Langmuir kinetics model has been used to obtain the fractal degree of ion adsorption on multi-walled carbon nanotube. The behavior of the fractal-like kinetics equation was compared with some famous rate equations like Langmuir, pseudo-first-order and pseudo-second-order equations. It is...

A structure theorem is proved about separable zero-dimensional spaces which are continuous images of ordered compacta and it is shown that not all spaces in this class are orderable themselves.