In the article, the noted Darboux’s formula of functions with single variable is generalized to that of functions of two independent variables with integral remainder, some important special cases of Darboux’s formula of functions with two variables are obtained, and some estimates of the integral remainders and Darboux’s expansion of the function ln(x + y) are given. These results generalize A...

In this paper a gainscheduling scheme of a proportional integral (GSPI) controller is proposed for a synchronous generator. In presented scheme, both proportional and integral gains are allowed to vary within a predetermined range. In order to validate the effectiveness of GSPI controller, simulation studies for a single-machine infinite bus power system are used .The results verify improved pe...

Power systems are subjected to small–signal oscillations that can be caused by sudden change in the value of large loads. To avoid the dangers of these oscillations, the Power System Stabilizers (PSSs) are used. When the PSSs can not be effective enough, installation of the Thyristor–based compensators to increase the oscillations damping is a suitable method. In this paper, a Static Synchronou...

In this paper we study boundary integral formulations of the interior and exterior Dirichlet problem for the bi{Laplacian in a plane domain with a piecewise smooth boundary having corner points. The mapping properties of single and double layer bihar-monic potentials, of the Calderon projections and the Poincar e-Steklov operators for such domains are analysed. We derive direct boundary integra...

AbsErad This paper presents a method of designing Proportional-Integral-DiEerential (PIID) Controllers for single-input, singleoutput (SISQ) systems. We used a Genetic Algorithm implemented in hardware for setting the K values of the PID Controller and ~ ~ ~ ~ ~ ~ i z ~ n g the integral error in the system. The system have been applied to a PID ~ o ~ t ~ Q l ~ e r system with variable plant tra...

Branciari [1] obtained a fixed point result for a single mapping satisfying an analogue of Banach’s contraction principle for an integral-type inequality. The second author [3] proved two fixed point theorems involving more general contractive conditions. In this paper, we establish a general principle, which makes it possible to prove many fixed point theorems for a pair of maps of integral ty...

We study the Dirichlet problem for the equation Δu − k2u = 0 in the exterior of nonclosed Lipschitz surfaces in R. The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single-layer potential. The density in the po...

We show that for a natural polynomial Hamiltonian system the existence of a single Darboux polynomial (a partial polynomial first integral) is equivalent to the existence of an additional first integral functionally independent with the Hamiltonian function. Moreover, we show that, in a case when the degree of potential is odd, the system does not admit any proper Darboux polynomial, i.e., the ...

We study the 2-loop part of the rational Kontsevich integral of a knot in an integer homology sphere. We give a general formula which explains how the 2-loop part of the Kontsevich integral of a knot changes after surgery on a single clasper whose leaves are not linked to the knot. As an application, we relate this formula with a conjecture of L. Rozansky about integrality of the 2-loop polynom...