In this paper, in order to numerically solve for multiple positive solutions to a singularly perturbed Neumann boundary value problem in mathematical biology and other applications, a local minimax method is modified with new local mesh refinement and other strategies. Algorithm convergence and other related properties are verified. Motivated by the numerical algorithm and convinced by the nume...

The Raman response function and Raman nonlinear index of phosphosilicate fibers are calculated for several P2O5 concentrations. The nonlinear index of phosphosilicate fiber is estimated by using the Boling formula, and it is used to calculate the Raman fraction of the nonlinear index. On the other hand, the Raman response function of the phosphosilicate fibers is fitted to a superposition of si...

We report the numerical analysis of gradient index (GRIN) lens-based optical coherence tomography imaging probes to derive optimal design parameters. Long and short working distance probes with a small focal spot are considered. In each model, the working distance and beam waist are characterized and compared for different values of length and refractive index of the probe components. We also e...

In this paper we consider the numerical solution of initial value delay-diierential-algebraic equations (DDAEs) of retarded and neutral types, with a structure corresponding to that of Hessenberg DAEs. We give conditions under which the DDAE is well-conditioned, and show how the DDAE is related to an underlying retarded or neutral delay-ODE (DODE). We present convergence results for linear mult...

In some data envelopment analysis (DEA) applications, some inputs of DMUs have negative values with positive cost. This paper generalizes the global cost Malmquist productivity index to compare the productivity of dierent DMUs with negative inputs in any two periods of times under variable returns to scale (VRS) technology, and then the generalized index is decomposed to several components. The...

In the last few years there has been considerable research on numerical methods for diierential algebraic equations (DAEs) f(x 0 ; x; t) = 0 where f x 0 is identically singular. The index provides one measure of the singularity of a DAE. Most of the numerical analysis literature on DAEs to date has dealt with DAEs with indices no larger than three. Even in this case, the systems were often assu...

This work presents the use of longitudinal refractive index modulation (apodization) in photosensitive glass for improved sidelobe suppression in volume holographic optical elements. We develop a numerical model for both uniform and apodized volume holograms based on rigorous coupled-wave analysis. We validate the model by comparison with a transmissive 1.55- mum uniform volume grating in photo...

The idea of the index of a differential algebraic equation (DAE) (or implicit differential equation) has played a fundamental role in both the analysis of DAEs and the development of numerical algorithms for DAEs. DAEs frequently arise as partial discretizations of partial differential equations (PDEs). In order to relate properties of the PDE to those of the resulting DAE it is necessary to ha...

Differential-algebraic equations (DAEs) naturally arise in many applications, but present numerical and analytical difficulties. The index of a DAE is a measure of the degree of numerical difficulty. In general, the higher the index is, the more difficult it is to solve the DAE. Therefore, it is desirable to transform the original DAE into an equivalent DAE with lower index. In this paper, we p...

Majority of the million plus cities in India are facing serious problems of traffic congestion and pollution due to the unprecedented and rapid pace of urbanization in last decade. City planners are providing solution to these twin problems by developing Mass Rapid Transit System including Metro and BRT in many Indian Metropolitan cities. The availability of transit network and pedestrian acces...