An interval-valued distribution is a fmite sequence of intervals ([Pl1 ,Pu1 ], ... ,[Pln,Pun]) n n such that O$Plj$Put�l, E Puj�l, and E Plj$1. Interval distributions generalize realj=l j=l valued probability distributions and arise naturally in many situations. They may represent collections of confidence intervals derived from frequency data, imprecisely stated subjective probabilities, known...

In this paper, linear second-order differential equations of Sturm-Liouville type having a finite number of singularities and turning points in a finite interval are investigated. First, we obtain the dual equations associated with the Sturm-Liouville equation. Then, we prove the uniqueness theorem for the solutions of dual initial value problems.

We consider a problem of an optimal consumption strategy on the infinite time horizon when the short-rate is a diffusion process. General existence and uniqueness theorem is illustrated by the Vasicek and so-called invariant interval models. We show also that when the short-rate dynamics is given by a Brownian motion or a geometric Brownian motion, then the value function is infinite.

The problem of robust state feedback design for a linear dynamical system with uncertain (interval) parameters is considered. The designed state feedback controller has to place all the coefficients of the closed loop system characteristic polynomial within assigned closed loop interval characteristic polynomial. A condition is derived using certain known facts about matrix minors and its chara...

We are concerned with the numerical exact controllability of semilinear wave equation on interval (0, 1). introduce a Picard iterative scheme yielding sequence approximated solutions which converges towards solution null problem, provided that initial data small enough. The boundary control, is applied at endpoint $$x=1$$ , taken in space $$H^1_0(0,T)$$ for $$T=2$$ . For linear part, control in...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

This paper is concerned with the observability problem of a parallelow twouid heat exchanger equation with di usion term. First, the case where two uid temperatures are measured at the outlet is considered. It is shown that the observed system with the measurements becomes observable on any interval of time through a concrete series expression of the solution. Next, the two cases where each one...

A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

this paper presents a probabilistic confidence-interval based method for optimal placement of shunt capacitors in distribution networks by considering probabilistic characteristics of loads. the main objective function are reducing loss and improving the voltage profile. backward forward sweep method has been employed to obtain the power flow results in distribution system. in addition, integer...