We present a ray-tracing application in the modeling of an optical detection element employed as a sensor of refractive index of surrounding fluids or gases. The detection element is a solid glass microstructure having a surface of the second order. We exploit the sensitivity of internal reflection of light on the element’s surface to the refractive index of the surrounding medium, operation ne...

In this research, we propose the string vector based KNN as the approach to the index optimization. The task may be viewed into an instance of word classification and the problems in encoding words or texts into numerical vectors were solved by encoding texts into string vectors in the previous works on text mining tasks. Influence by the previous works, we encode words into string vectors, as ...

Let M be a compact manifold. and D a Dirac type differential operator on M . Let A be a C ∗-algebra. Given a bundle W of A-modules over M (with connection), the operator D can be twisted with this bundle. One can then use a trace on A to define numerical indices of this twisted operator. We prove an explicit formula for this index. Our result does complement the Mishchenko-Fomenko index theorem...

In this paper we develop the idea introduced by Lipovetski and Conklin in 2002 of considering a pairwise comparison matrix (PCM) as a contingency table. Instead of focusing on outliers detection, we use the χ2 value as an index to evaluate the deviation of a pairwise comparison matrix from consistency. We verify by means of numerical simulations that our new index satisfies a set of five proper...

We have investigated the transmission and reflection properties of structures incorporating left-handed materials with graded index of refraction. We present an exact analytical solution to Helmholtz' equation for a graded index profile changing according to a hyperbolic tangent function along the propagation direction. We derive expressions for the field intensity along the graded index struct...

Apart from the well-known weaknesses of the standard Malmquist productivity index related to infeasibility and not accounting for slacks, already addressed in the literature, we identify a new and significant drawback of the Malmquist-Luenberger index decomposition that questions its validity as an empirical tool for environmental productivity measurement associated with the production of bad o...

We describe a novel scheme for obtaining a superhigh numerical aperture gradient-index (SHNA GRIN) lens from multiple thin layers of two or more materials with large refractive-index contrast. Design procedures for the lens are described, including variation of the layer thickness to achieve focusing and of the thickness limit to reduce scattering loss. We use an exact numerical solution by the...

We describe the new software package GELDA for the numerical solution of linear diierential{algebraic equations with variable coeecients. The implementation is based on the new discretization scheme introducedin 20]. It can deal with systems of arbitrary index and with systems that do not have unique solutions or inconsistencies in the initial values or the inhomogeneity. The package includes a...

By means of a surface-integral formalism we derive the integral equations for diffuse photon density waves with boundary conditions corresponding to a diffuse–diffuse interface with index mismatch and solve them numerically without any approximation. These numerical results are verified with Monte Carlo simulations for the planar interface case. Since the application of the boundary condition t...

We revisit the characterisation of modules over non-unital C∗-algebras analogous to modules of sections of vector bundles. A fullness condition on the associated multiplier module characterises a class of modules which closely mirror the commutative case. We also investigate the multiplier-module construction in the context of bi-Hilbertian bimodules, particularly those of finite numerical inde...