Search results for "Abstract"
showing 10 items of 1959 documents
Numerical approach for signal delay in general distributed networks
2003
The authors consider a general network with telegraph equations modelling distributed elements and having, additionally, nonlinear capacitors. A global asymptotic exponential stability of the solution is given. A simple computable upper bound of the delay time is given. Numerical examples illustrate the usefulness of the results. >
Cubic Local Splines on Non-uniform Grid
2015
In this chapter, two types of local cubic splines on non-uniform grids are described: 1. The simplest variation-diminishing splines and 2. The quasi-interpolating splines. The splines are computed by a simple fast computational algorithms that utilizes a relation between the splines and cubic interpolation polynomials. Those splines can serve as an efficient tool for real-time signal processing. As an input, they use either clean or noised arbitrarily-spaced samples. On the other hand, the capability to adapt the grid to the structure of an object and minimal requirements to the operating memory are great advantages for off-line processing of signals and multidimensional data arrays.
Local Splines on Non-uniform Grid
2018
In this Chapter and in the next Chap. 7, we deal with continuous rather than discrete and discrete-time splines. In these and only these chapters, we abandon the assumption that the grid, on which the splines are constructed, is uniform and consider splines on arbitrary grids. Two types of local cubic and quadratic splines on non-uniform grids are described: 1. The simplest variation-diminishing splines and 2. The quasi-interpolating splines. The splines are computed by simple fast computational algorithms that utilize relations between the splines and interpolation polynomials. In addition, these relations provide sharp estimations of splines’ approximation accuracy. These splines can serv…
Sputtered SiOxNy thin films: improving optical efficiency of liquid crystal diffuser elements in multi-focal near-to-eye display architecture
2021
In this work we present reactive sputtered SiOxNy films with a variable refractive index as a convienent solution for contrast improvement of liquid crystal diffuser multi stacks in near-to-eye AR/VR displays. The focus concerns minimization of light reflections between internal structures, in particular ITO, by optimizing internal layers through tailored properties of thin film coatings, as well as subsequent laser patterning of thin film stack. Inorganic thin films have been deposited on glass by physical vapor deposition. Corresponding refractive index, thickness, uniformity and dielectric characteristics and other electro-optical properties have been measured and their impact on the res…
Generalized singly-implicit Runge-Kutta methods with arbitrary knots
1985
The aim of this paper is to derive Butcher's generalization of singly-implicit methods without restrictions on the knots. Our analysis yields explicit computable expressions for the similarity transformations involved which allow the efficient implementation of the first phase of the method, i.e. the solution of the nonlinear equations. Furthermore, simple formulas for the second phase of the method, i.e. computation of the approximations at the next nodal point, are established. Finally, the matrix which governs the stability of the method is studied.
Harmonic maps and singularities of period mappings
2015
We use simple methods from harmonic maps to investigate singularities of period mappings at infinity. More precisely, we derive a harmonic map version of Schmid’s nilpotent orbit theorem. MSC Classification 14M27, 58E20
Atomic and electronic structure of gold clusters: understanding flakes, cages and superatoms from simple concepts.
2008
Atomic structure and electronic structure are intimately interrelated properties of nanoclusters and nanoparticles, defining their stability, electronic, optical and chemical properties, in other words, their usability as potential components for nanoscale devices. This tutorial review attempts to describe the development in understanding the structures of bare and ligand-protected gold clusters over the past decade, based on selected density-functional-theory calculations. This review should be of interest both to newcomers in the field and to an interdisciplinary community of researchers working in synthesis, characterization and utilization of ligand-protected gold clusters.
Preparation of Indoles from α-Aminonitriles: A Short Synthesis of FGIN-1-27
2006
α-Aminonitriles derived from 2-aminocinnamic acid esters and amides can be cyclized under basic conditions to furnish substituted indole-3-acetic acid derivatives in quantitative yield. The reaction provides a simple access to a class of biologically active compounds.
A Simple Characterization of Differentiation
2013
AbstractIn this short note we will give a result that can be treated as a characterization of differentiation.
Superposing significant interaction rules (SSIR) method: a simple procedure for rapid ranking of congeneric compounds
2020
The Superposing Significant Interaction Rules (SSIR) method is revised and implemented. The method is a simple combinatorial procedure, which deals with in situ generated rules among a dichotomized congeneric molecular family, selecting the most probabilistically relevant ones. The mere counting of the number of relevant rules attached to new compounds generates a molecular ranking useful for database filtering, refinement and prediction. The algorithm only needs for a symbolic molecular representation and this allows for mining the database in a confidential manner. Third parties will not know the real compounds that are on the way to be worked out. The procedure is tested for a complete s…