In this work, kinetics and thermodynamics of esterification reaction were studied. This research investigated the esterification reaction between methanol and acidified oil catalyzed by sulfonated cation exchange resin and proposed a new rate equation for consideration of kinetics of this reaction according to the Langmuir-Hinshelwood mechanism. Thermodynamics and kinetics parameters were calcu...

In this work, kinetics and thermodynamics of esterification reaction were studied. This research investigated the esterification reaction between methanol and acidified oil catalyzed by sulfonated cation exchange resin and proposed a new rate equation for consideration of kinetics of this reaction according to the Langmuir-Hinshelwood mechanism. Thermodynamics and kinetics parameters were calcu...

in this paper‎, ‎we prove a multiplicity result for some biharmonic elliptic equation of kirchhoff type and involving nonlinearities with critical exponential growth at infinity‎. ‎using some variational arguments and exploiting the symmetries of the problem‎, ‎we establish a multiplicity result giving two nontrivial solutions‎.

We present an exponential time integrator for the incompressible Navier-Stokes equation based on the exponential block Krylov (EBK) method [2]. The exact solution of the semi-discrete system, given by a discretization of the Navier--Stokes equation in the spatial dimensions, involves the matrix exponential function. So-called exponential integrators are usually directly based on the formal expr...

In this paper, a definition of the fundamental operator for the linear autonomous functional differential equation with infinite delay in a Banach space is given, and some sufficient and necessary conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisfy some suitable hypotheses are obtained. Moreover, we discuss the relation between the exponentia...

In this paper we study k-noncrossing RNA structures with minimum arc-length 4 and at most k − 1 mutually crossing bonds. Let T k (n) denote the number of knoncrossing RNA structures with arc-length ≥ 4 over n vertices. We prove (a) a functional equation for the generating function ∑ n≥0 T [4] k (n)z n and (b) derive for k ≤ 9 the asymptotic formula T k (n) ∼ ck n +(k−1)/2) γ k . Furthermore we ...

In this paper we study k-noncrossing RNA structures with minimum arc-length 4 and at most k − 1 mutually crossing bonds. Let T [4] k (n) denote the number of k-noncrossing RNA structures with arc-length ≥ 4 over n vertices. We prove (a) a functional equation for the generating function P n≥0 T [4] k (n)z n and (b) derive for k ≤ 9 the asymptotic formula T [4] k (n) ∼ c k n −((k−1) 2 +(k−1)/2) γ...