Mathematics

We consider quasi-perfect codes in Z over the `p metric, 2 ≤ p <∞. Through a computational approach, we determine all radii for which there are linear quasi-perfect codes for p = 2 and n = 2, 3. Moreover, we study codes with a certain degree of imperfection, a notion that generalizes the quasi-perfect codes. Numerical results concerning the codes with the smallest degree of imperfection are presented. ———————————————————————keywords:Tilings, Lattices, Quasi-perfect Codes, `p metric

In this paper, we construct some families of rotated unimodular lattices and rotated direct sum of Barnes–Wall lattices [Formula: see text] for [Formula: see text] and [Formula: see text] via ideals of the ring of the integers [Formula: see text] for [Formula: see text] and [Formula: see text]. We also construct rotated [Formula: see text] and [Formula: see text]-lattices via [Formula: see text]-submodules of [Formula: see text]. Our focus is on totally real number fields since the associated lattices have full diversity and then may be suitable for signal transmission over both Gaussian and Rayleigh fading channels. The minimum product distances of such constructions are also presented here.

A technique is described for calculating illuminance, equivalent sphere illumination (ESI), and the indirect effect on visual comfort probability due to the presence of daylighting in interior spaces. Finite Fourier series techniques are used to generate functions that describe the effects of differential elements of windows or skylights. The form of these functions allows for easy integration with resulting simple form to the final equations and also provides for computationally efficient algorithms. The equations are applied to the determination of the interreflected and direct components of illuminance and ESI due to windows or skylights. It is shown how to account for the effects of drapes, shades and overhangs on windows. Further, it is shown how to efficiently treat skylights that are recessed up into wells.

ABSTRACT Spiking neural P systems (in short, SNP systems) are parallel, distributed, and nondeterministic computing devices inspired by biological spiking neurons. Recently, a class of SNP systems known as SNP systems with structural plasticity (in short, SNPSP systems) was introduced. SNPSP systems represent a class of SNP systems that have dynamism applied to the synapses, i.e. neurons can use plasticity rules to create or remove synapses. In this work, we impose the restriction of sequentiality on SNPSP systems, using four modes: max, min, max-pseudo-, and min-pseudo-sequentiality. We also impose a normal form for SNPSP systems as number acceptors and generators. Conditions for (non)universality are then provided. Specifically, acceptors are universal in all modes, while generators need a nondeterminism source in two modes, which in this work is provided by the plasticity rules.

: A prototype computer program has been written to calculate three dimensional viscous compressible flow past bodies in relative motion. The program solves the Navier-Stokes equations using multiple zones of mesh. During the Phase I research and development effort, routines were written to allow the meshes to move and to couple the solutions in adjacent zones along sliding boundaries. The importance of a well planned software structure was demonstrated. The code a was applied to a turbine rotor/stator interaction problem. Keywords: Three dimensional flow; Navier Stokes; Viscous flow; Compressible flow; Zonal flow; Unsteady flow; Computer programming.

The functional box plot is generalized to provide a holistic view of the four dimensional space-time field data resulting from unsteady Computational Fluid Dynamics simulations. It displays the variation of five common statistics - minimum, first-quartile, median, third-quartile, and maximum - projected onto the three-dimensional spatial sub-space. Visual analysis using the generalized box plot is demonstrated for the unsteady flows past a swept cylinder and a wind turbine.

A recently developed computer program for hypersonic vehicle flow analysis is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together

Uncertainty is a pervasive feature of the domains in which expert systems are designed to function. Research design to test uncertain inference methods for accuracy and robustness, in accordance with standard engineering practice is reviewed. Several studies were conducted to assess how well various methods perform on problems constructed so that correct answers are known, and to find out what underlying features of a problem cause strong or weak performance. For each method studied, situations were identified in which performance deteriorates dramatically. Over a broad range of problems, some well known methods do only about as well as a simple linear regression model, and often much worse than a simple independence probability model. The results indicate that some commercially available expert system shells should be used with caution, because the uncertain inference models that they implement can yield rather inaccurate results.

Uncertainty is a pervasive feature of the domains in which expert systems are supposed to function. There are several mechanisms for handling uncertainty, of which the oldest and most widely used is probability theory. It is the only one which is derived from a formal description of rational behavior. For use in patten-directed inference systems, or rule-based inference engines, artificial intelligence researchers have favored others, largely for reasons of simplicity and speed. We have developed techniques which measure how these alternatives approximate the results of probability theory, assess how well they perform by those measures, and find out what underlying features of a problem affect performance. Because the amount of data required to fully specify a probability distribution is enormous, some technique must be used to estimate a distribution when only partial information is given. We give intuitive and axiomatic arguments, algebraic analysis, and numerical examples, that f...