We consider an M/G/1 queue with balking based on the workload. An arriving customer joins the queue and stays until served only if the system workload is below a fixed level at the time of arrival. We use level-crossing argument to derive an integral equation for the steady state workload distribution. We describe a procedure to solve the equation for general distributions and we solve the equa...

The mechanical behavior of the tympanic membrane displays both non-linearity and viscoelasticity. Previous finite-element models of the tympanic membrane, however, have been either non-linear or viscoelastic but not both. In this study, these two features are combined in a non-linear viscoelastic model. The constitutive equation of this model is a convolution integral composed of a non-linear e...

Two classes of nonlinear coefficient Inverse Problems (IP) for differential equations are considered. The first class of the IP corresponds to the case of a stationary process, is described by an elliptic equation with some boundary conditions. The problem of the coefficient reconstruction, using measurements on a boundary only, corresponds to the Electrical Tomography. Known methods for the el...

We consider a sequence of blowup solutions of a two dimensional, second order elliptic equation with exponential nonlinearity and singular data. This equation has a rich background in physics and geometry. In a work of Bartolucci-Chen-Lin-Tarantello it is proved that the profile of the solutions differs from global solutions of a Liouville type equation only by a uniformly bounded term. The pre...

In this paper, we proposed a numerical integration method for the solution of singularly perturbed delay differential equation with dual layer behaviour. In this method, an asymptotically equivalent first order neutral type delay differential equation is obtained from the second order singularly perturbed delay differential equation and employed Trapezoidal rule on it. Then, linear interpolatio...

The Hirota–Miwa equation (also known as the discrete KP equation, or the octahedron recurrence) is a bilinear partial difference equation in three independent variables. It is integrable in the sense that it arises as the compatibility condition of a linear system (Lax pair). The Hirota–Miwa equation has infinitely many reductions of plane wave type (including a quadratic exponential gauge tran...

Accurate biomechanical characteristics of tissues are essential for developing realistic virtual reality surgical simulators utilizing haptic feedback. Surgical simulation technology has progressed rapidly but lacks a comprehensive database of soft tissue mechanical properties with which to incorporate. Simulators are often designed purely based on what "feels right;" quantitative empirical dat...

In this work we study the optimality of increasing stability inverse boundary value problem (IBVP) for Schr\"{o}dinger equation. The rigorous justification IBVP equation were established by Isakov \cite{Isa11} and Isakov, Nagayasu, Uhlmann, Wang paper \cite{INUW14}. \cite{Isa11}, \cite{INUW14}, authors showed that increases as frequency in sense estimate changes from a logarithmic type to H\"{o...

Interest in Sobolev type equations has recently increased signi cantly, moreover, there arose a necessity for their consideration in quasi-Banach spaces. The need is dictated not so much by the desire to ll up the theory but by the aspiration to comprehend nonclassical models of mathematical physics in quasi-Banach spaces. Notice that the Sobolev type equations are called evolutionary if soluti...

The purpose of this paper is to analysis the viscoelastic models under dynamic loading. A five-parameter model is chosen for study exhibits elastic, viscous, and retarded elastic response to shearing stress. The viscoelastic specimen is chosen which closely approximates the actual behavior of a polymer. The module of elasticity and viscosity coefficients are assumed to be space dependent i.e. f...