含分布时滞的时滞微分系统多步龙格-库塔方法的时滞相关稳定性

本文研究了一类含分布时滞的时滞微分系统的多步龙格-库塔方法的稳定性.基于辐角原理，本文给出了多步龙格-库塔方法弱时滞相关稳定性的充分条件，并通过数值算例验证了理论结果的有效性.     

On nonexistence of Kneser solutions of third-order neutral delay differential equations

The aim of this paper is to complement existing oscillation results for third-order neutral delay differential equations by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Combining newly obtained results with existing ones, we attain oscillation of all solutions of the studied equations.     

On the Differential Polynomial of a Graph

We introduce the differential polynomial of a graph. The differential polynomial of a graph G of order n is the polynomial B(G; x) :=∑?(G)k=-nB_k(G) x~(n+k), where B_k(G) denotes the number of vertex subsets of G with differential equal to k. We state some properties of B(G;x) and its coefficients.In particular, we compute the differential polynomial for complete, empty, path, cycle, wheel and double star graphs. We also establish some relationships between B(G; x) and the differential polynomials of graphs which result by removing, adding, and subdividing an edge from G.     

Well‐posedness of fractional integro‐differential equations in vector‐valued functional spaces

We study the well‐posedness of the fractional differential equations with infinite delay on Lebesgue–Bochner spaces and Besov spaces , where A and B are closed linear operators on a Banach space X satisfying ,  and . Under suitable assumptions on the kernels a and b, we completely characterize the well‐posedness of in the above vector‐valued function spaces on by using known operator‐valued Fourier multiplier theorems. We also give concrete examples where our abstract results may be applied.     

Electrochemical Characterization and Voltammetric Determination of Benzoyl Derivatives of Phenobarbital Using Glassy Carbon Electrode

The electrochemical behavior of a number of benzoyl barbiturates was studied using a glassy carbon electrode (GCE). The kinetics of the electrode process is determined, the contribution of physical adsorption to the electrochemical process is estimated, and the mechanism of the possible electrochemical reaction is proposed. It is shown that the electrochemical reduction potentials of benzoyl phenobarbital derivatives are determined by the LUMO energies, calculated by the B3LYP 6‐311+G method. It is established that the process is quasi‐reversible, complicated by adverse reactions. The influence of halogen type and its position in the benzoyl residue of the studied substances on the analytical signal is established. The effective values of the dissociation constants of various forms of benzoyl derivatives were calculated using the example of halonal, for which the values 3.16 ? 10^?8 and 6.31 ? 10^?12, respectively, were found.     

Implicit–explicit schemes for nonlinear nonlocal equations with a gradient flow structure in one space dimension

Nonlinear convection–diffusion equations with nonlocal flux and possibly degenerate diffusion arise in various contexts including interacting gases, porous media flows, and collective behavior in biology. Their numerical solution by an explicit finite difference method is costly due to the necessity of discretizing a local spatial convolution for each evaluation of the convective numerical flux, and due to the disadvantageous Courant–Friedrichs–Lewy (CFL) condition incurred by the diffusion term. Based on explicit schemes for such models devised in the study of Carrillo et al. a second‐order implicit–explicit Runge–Kutta (IMEX‐RK) method can be formulated. This method avoids the restrictive time step limitation of explicit schemes since the diffusion term is handled implicitly, but entails the necessity to solve nonlinear algebraic systems in every time step. It is proven that this method is well defined. Numerical experiments illustrate that for fine discretizations it is more efficient in terms of reduction of error versus central processing unit time than the original explicit method. One of the test cases is given by a strongly degenerate parabolic, nonlocal equation modeling aggregation in study of Betancourt et al. This model can be transformed to a local partial differential equation that can be solved numerically easily to generate a reference solution for the IMEX‐RK method, but is limited to one space dimension.     

Closed‐form approximations for spread options in Lévy markets

We provide new closed‐form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, ie, when log‐returns are modeled as Brownian motions (Black‐Scholes model), variance gamma processes (VG model), or normal inverse Gaussian processes (NIG model). For the specific case of exchange options (spread options with zero strike), we generalize the well‐known Margrabe formula (1978) that is valid in a Black‐Scholes model to the VG model under a homogeneity assumption.