Properties of Lp (K)-Solutions of Linear Nonhomogeneous Impulsive Differential Equations with Unbounded Linear Operator

Sufficient conditions for the existence of Lp(k)-solutions of linear nonhomogeneous impulsive differential equations with unbounded linear operator are found. An example of the theory of the linear nonhomogeneous partial impulsive differential equations of parabolic type is given.

Impulsive Partial Hyperbolic Functional Differential Equations of Fractional Order with State-Dependent Delay

MSC 2010: 26A33, 34A37, 34K37, 34K40, 35R11

Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations

Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.

Application of Lyapunov's Direct Method to the Existence of Integral Manifolds of Impulsive Differential Equations

The present paper investigates the existence of integral manifolds for impulsive differential equations with variable perturbations. By means of piecewise continuous functions which are generalizations of the classical Lyapunov’s functions, sufficient conditions for the existence of integral manifolds of such equations are found.

Practical Stability and Vector-Lyapunov Functions for Impulsive Differential Equations with "Supremum"

Stability of nonlinear impulsive differential equations with "supremum" is studied. A special type of stability, combining two different measures and a dot product on a cone, is defined. Perturbing cone-valued piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

Differential Games of Mixed Type with Control and Stopping Times

We study a zero sum differential game of mixed type where each player uses both control and stopping times. Under certain conditions we show that the value function for this problem exists and is the unique viscosity solution of the corresponding variational inequalities. We also show the existence of saddle point equilibrium for a special case of differential game.

A generic polynomial solution for the differential equation of hypergeometric type and six sequences of orthogonal polynomials related to it

In this work, we present a generic formula for the polynomial solution families of the well-known differential equation of hypergeometric type s(x)y"n(x) + t(x)y'n(x) - lnyn(x) = 0 and show that all the three classical orthogonal polynomial families as well as three finite orthogonal polynomial families, extracted from this equation, can be identified as special cases of this derived polynomial sequence. Some general properties of this sequence are also given.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Oscillation criteria for differential equations of second order

In this article, we give sufficient condition in the form of integral inequalities to establish the oscillatory nature of non linear homogeneous differential equations of the form where r, q, p, f and g are given data. We do this by separating the two cases f is monotonous and non monotonous.

Numerical procedure for second order non-linear ordinary differential equations and application to heat transfer problem

In this paper, we have first given a numerical procedure for the solution of second order non-linear ordinary differential equations of the type y″ = f (x;y, y′) with given initial conditions. The method is based on geometrical interpretation of the equation, which suggests a simple geometrical construction of the integral curve. We then translate this geometrical method to the numerical procedure adaptable to desk calculators and digital computers. We have studied the efficacy of this method with the help of an illustrative example with known exact solution. We have also compared it with Runge-Kutta method. We have then applied this method to a physical problem, namely, the study of the temperature distribution in a semi-infinite solid homogeneous medium for temperature-dependent conductivity coefficient.

Existence of Value in Stochastic Differential Games of Mixed Type

In this article, we address stochastic differential games of mixed type with both control and stopping times. Under standard assumptions, we show that the value of the game can be characterized as the unique viscosity solution of corresponding Hamilton-Jacobi-Isaacs (HJI) variational inequalities.

Differential recognition of the type I interferon receptor by interferons tau and alpha is responsible for their disparate cytotoxicities.

Interferon tau (IFN tau), originally identified as a pregnancy recognition hormone, is a type I interferon that is related to the various IFN alpha species (IFN alpha s). Ovine IFN tau has antiviral activity similar to that of human IFN alpha A on the Madin-Darby bovine kidney (MDBK) cell line and is equally effective in inhibiting cell proliferation. In this study, IFN tau was found to differ from IFN alpha A in that is was > 30-fold less toxic to MDBK cells at high concentrations. Excess IFN tau did not block the cytotoxicity of IFN alpha A on MDBK cells, suggesting that these two type I IFNs recognize the type I IFN receptor differently on these cells. In direct binding studies, 125I-IFN tau had a Kd of 3.90 x 10(-10) M for receptor on MDBK cells, whereas that of 125I-IFN alpha A was 4.45 x 10(-11) M. Consistent with the higher binding affinity, IFN alpha A was severalfold more effective than IFN tau in competitive binding against 125I-IFN tau to receptor on MDBK cells. Paradoxically, the two IFNs had similar specific antiviral activities on MDBK cells. However, maximal IFN antiviral activity required only fractional occupancy of receptors, whereas toxicity was associated with maximal receptor occupancy. Hence, IFN alpha A, with the higher binding affinity, was more toxic than IFN tau. The IFNs were similar in inducing the specific phosphorylation of the type I receptor-associated tyrosine kinase Tyk2, and the transcription factors Stat1 alpha and Stat2, suggesting that phosphorylation of these signal transduction proteins is not involved in the cellular toxicity associated with type I IFNs. Experiments using synthetic peptides suggest that differences in the interaction at the N terminal of IFN tau and IFN alpha with the type I receptor complex contribute significantly to differences in high-affinity equilibrium binding of these molecules. It is postulated that such a differential recognition of the receptor is responsible for the similar antiviral but different cytotoxic effects of these IFNs. Moreover, these data imply that receptors are "spare'' with respect to certain biological properties, and we speculate that IFNs may induce a concentration-dependent selective association of receptor subunits.

Regular singular points of a system of homogeneous linear differential equations of the first order.

"From Proceedings of the American Academy of Arts and Sciences, v.38, no. 9, Oct. 1902."

Implicit stochastic Runge-Kutta methods for stochastic differential equations

In this paper we construct implicit stochastic Runge-Kutta (SRK) methods for solving stochastic differential equations of Stratonovich type. Instead of using the increment of a Wiener process, modified random variables are used. We give convergence conditions of the SRK methods with these modified random variables. In particular, the truncated random variable is used. We present a two-stage stiffly accurate diagonal implicit SRK (SADISRK2) method with strong order 1.0 which has better numerical behaviour than extant methods. We also construct a five-stage diagonal implicit SRK method and a six-stage stiffly accurate diagonal implicit SRK method with strong order 1.5. The mean-square and asymptotic stability properties of the trapezoidal method and the SADISRK2 method are analysed and compared with an explicit method and a semi-implicit method. Numerical results are reported for confirming convergence properties and for comparing the numerical behaviour of these methods.