We describe a convenient method for distinguishing functional from nonfunctional or deleterious mutations in homologous genes. High fidelity in vitro gene recombination ("DNA shuffling") coupled with sequence analysis of a small sampling of the shuffled library exhibiting the evolved behavior allows identification of those mutations responsible for the behavior in a background of neutral and de...

the paper is concerned with robust stability criteria for takagi- sugeno (t-s) fuzzy systems with distributed delays and time delay in the leakage term. by exploiting a model transformation, the system is converted to one of the neutral delay system. global robust stability result is proposed by a new lyapunov-krasovskii functional which takes into account the range of delay and by making use o...

In this paper, we prove a theorem on local existence and uniqueness of integral solutions to a class of partial neutral functional differential equations with infinite delay. Our method of proof is based on the integrated semigroup theory and the well known Banach fixed point theorem.

Sufficient conditions for controllability of neutral functional integrodifferential systems in Banach spaces with initial condition in the phase space are established. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

and Applied Analysis 3 (A 1 ) The linear operatorW: L(J, U) → X defined by

In this paper we prove existence results for first order semilinear impulsive neutral functional differential inclusions under the mixed Lipschitz and Carathéodory conditions.

In this paper, we first present an impulsive version of Filippov’s Theorem for first-order neutral functional differential inclusions of the form, d dt [y(t)− g(t, yt)] ∈ F (t, yt), a.e. t ∈ J\{t1, . . . , tm}, y(t+k )− y(tk ) = Ik(y(tk )), k = 1, . . . , m, y(t) = φ(t), t ∈ [−r, 0], where J = [0, b], F is a set-valued map and g is a single-valued function. The functions Ik characterize the jum...

K e y w o r d s N e u t r a l functional differential equation, Analytic semigroup, Mild solution, FaedoGalerkin approximation. 1. I N T R O D U C T I O N Let H be a separable Hilbert space and 0 < T, T < ec. For 0 < t < T, Ct := C([-~-, t]; H) be the Banach space of all continuous functions from l--T, t] into H endowed with the supremum norm, Ilullt := sup I lu(s) l l , u • Ct, (1.1) -r<_s<t w...

We find sufficient conditions for the existence of positive periodic solutions of two kinds of neutral differential equations. Using Krasnoselskii’s fixed-point theorem in cones, we obtain results that extend and improve previous results. These results are useful mostly when applied to neutral equations with delay in bio-mathematics.

Neutral stochastic functional differential equations NSFDEs have recently been studied intensively. The well-known conditions imposed for the existence and uniqueness and exponential stability of the global solution are the local Lipschitz condition and the linear growth condition. Therefore, the existing results cannot be applied to many important nonlinear NSFDEs. The main aim of this paper i...