ethyl benzene used increasingly each year is the raw material of producing styrene monomer. this substanceis produced from benzene alkylation with ethylene or ethanol, depending on the availability and cost of rawmaterials. in this study benzene alkylation in the presence of ethanol in a catalytic fixed bed reactor inthree states of isotherm, adiabatic and non-isotherm-non-adiabatic is mathemat...

Ethyl benzene used increasingly each year is the raw material of producing styrene monomer. This substanceis produced from benzene alkylation with ethylene or ethanol, depending on the availability and cost of rawmaterials. In this study benzene alkylation in the presence of ethanol in a catalytic fixed bed reactor inthree states of isotherm, adiabatic and non-isotherm-non-adiabatic is mathemat...

We describe general-relativistically a spherically symmetric stationary fluid accretion onto a black hole. Relativistic effects enhance mass accretion, in comparison to the Bondi model predictions, in the case when backreaction is neglected. That enhancement depends on the adiabatic index and the asymptotic gas temperature and it can magnify accretion by one order in the ultrarelativistic regim...

A stability result for the compressible Navier-Stokes system with transport equation for entropy s is shown. The proof comes as an outcome of the isentropic case and additional properties of the effective viscous flux. We deal with the pressure term in the form ρ γ e s with adiabatic index γ > 3/2; therefore the crucial renormalization method is restricted.

In this paper we study a Hamiltonian system with a spatially asymmetric potential. We are interested in the effects on the dynamics when the potential becomes symmetric slowly in time. We focus on a highly simplified non-trivial model problem (a metaphor) to be able to pursue explicit calculations as far as possible. Using the techniques of averaging and adiabatic invariants, we are able to stu...

We extend the notion of basic classes (for the Donaldson invariants) to 4-manifolds with b > 1 which are (potentially) not of simple type or satisfy b1 > 0. We also give a structure theorem for the Donaldson invariants of 4-manifolds with b > 1, b1 > 0 and of strong simple type.

We present a theoretical formalism for determining the structure of molecular clouds and the precollapse conditions in star–forming regions. The model consists of a pressure-bounded, self-gravitating sphere of an ideal gas that is supported by several distinct pressures. Since each pressure component is assumed to obey a polytropic law Pi(r) ∝ ρ γpi , we refer to these models as multi–pressure ...

Given two maps f1, f2 : M −→ N between manifolds of the indicated arbitrary dimensions, when can they be deformed away from one another? More generally: what is the minimum number MCC(f1, f2) of pathcomponents of the coincidence space of maps f ′ 1 , f ′ 2 where f ′ i is homotopic to fi, i = 1, 2 ? Approaching this question via normal bordism theory we define a lower bound N(f1, f2) which gener...