Te output feedback eigenvalue assignment problem for discrete-time systems is considered. Te problem is formulated frst as

an unconstrained minimization problem, where a three-term nonlinear conjugate gradient method is proposed to fnd a local

solution. In addition, a cut to the objective function is included, yielding an inequality constrained minimization problem, where a

logarithmic barrier method is proposed for fnding the local solution. Te conjugate gradient method is further extended to tackle

the eigenvalue assignment problem for the two cases of decentralized control systems and control systems with time delay. Te

performance of the methods is illustrated through various test examples.

The Holling type II harvesting term has the property that it is small for small population values, but grows monotonically with population growth, eventually saturating, at a constant value for very large populations. We consider here a population evolving according to a logistic rate, but harvested (predated) subject to a Holling type II harvesting term that varies slowly with time, possibly due to slow environmental variation. Application of a multitiming method gives us an approximation to the population at any time in two cases- survival to a slowly varying limit, and extinguishment to zero. The situation where there is a transition from survival to extinction is also analyzed, using a matched expansions approach. A uniformly valid approximate expression for the population, valid for all times is obtained. These results are shown to agree well with the results of numerical calculations.

The object of the present paper is to derive some results on differential subordination associated with a generalized derivative operator for certain normalized analytic functions in the open unit disc. The authors establish sandwich type theorems. These results extend many previously known results.

The object of the present paper is to introduce a new subclass of p-valent starlike functions with negative coefficients in the open unit disc which is defiined by a generalized derivative operator. We obtain coefficient inequalities, growth and distortion theorems and extreme points for the subclass of p-valent functions.

The aim of this paper is to introduce and study a new class of Bazilevič p-valent function of order β by using the subordination concept between this function and a generalized derivative operator. Some interesting properties are also obtained

The theory of analytic functions and more specific p-valent functions, is one of the most fascinating topics in one complex variable. There are many remarkable theorems dealing with extremal problems for a class of p-valent functions on the unit disk U. Recently, many researchers have shown great interests in the study of differential operator. The objective of this paper is to define a new generalized derivative operator of p-valent analytic functions of fractional power in the open unit disk U. This operator generalized some well-known operators studied earlier, we mention some of them in the present paper. Motivation by the generalized derivative operator; we introduce and investigate two new subclasses of starlike p-valent analytic functions of fractional power with positive coefficients and starlike p-valent analytic functions of fractional power with negative coefficients, respectively. In addition, a sufficient condition will be obtained. Some corollaries are also pointed out. Moreover, we determine the extreme points of functions belong to the class.

The aim of the article is to study a sufficient condition for the classes of starlike and convex harmonic univalent functions with respect to k- symmetric points. The necessary condition for f to be in the classes will be studied. In addition, growth bounds for functions will also be given.

In this paper, we study and introduce the majorization properties of a new class of analytic p-valent functions of complex order defined by the generalized hypergeometric function. Some known consequences of our main result will be given. Moreover, we investigate the coefficient

estimates for this class.

In the present investigation, new subclasses of analytic functions in the open unit disk which are defined using generalized derivative operator are introduced. Several interesting properties of these classes are obtained.

We provide a validation of a formal approximate solution to the problem of the evolution of a slowly varying harvested logistic population. Using a contraction mapping proof, we show that the initial value problem for the population has an exact solution lying in an appropriately small neighbourhood of this approximate solution, under quite general conditions.