Given the central role that software development plays in the delivery and application of information technology, managers are increasingly focusing on process improvement in the software development area. This demand has spurred the provision of a number of new and/or improved approaches to software development, with perhaps the most prominent being object-orientation (OO). In addition, the focus on process improvement has increased the demand for software measures, or metrics with which to manage the process. The need for such metrics is particularly acute when an organization is adopting a new technology for which established practices have yet to be developed. This research addresses these needs through the development and implementation of a new suite of metrics for OO design. Metrics developed in previous research, while contributing to the field's understanding of software development processes, have generally been subject to serious criticisms, including the lack of a theoretical base. Following Wand and Weber (1989), the theoretical base chosen for the metrics was the ontology of Bunge (1977). Six design metrics are developed, and then analytically evaluated against Weyuker's (1988) proposed set of measurement principles. An automated data collection tool was then developed and implemented to collect an empirical sample of these metrics at two field sites in order to demonstrate their feasibility and suggest ways in which managers may use these metrics for process improvement. >

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A metrics suite for object oriented design

Analytic Combinatorics is a self-contained treatment of the mathematics underlying the analysis of discrete structures, which has emerged over the past several decades as an essential tool in the understanding of properties of computer programs and scientific models with applications in physics, biology and chemistry. Thorough treatment of a large number of classical applications is an essential aspect of the presentation. Written by the leaders in the field of analytic combinatorics, this text is certain to become the definitive reference on the topic. The text is complemented with exercises, examples, appendices and notes to aid understanding therefore, it can be used as the basis for an advanced undergraduate or a graduate course on the subject, or for self-study.

Analytic Combinatorics

The classic problem of stimulus-response (S-R) compatibility (SRC) is addressed. A cognitive model is proposed that views the stimulus and response sets in S-R ensembles as categories with dimensions that may or may not overlap. If they do overlap, the task may be compatible or incompatible, depending on the assigned S-R mapping. If they do not overlap, the task is noncompatible regardless of the assigned mapping. The overlapping dimensions may be relevant or not. The model provides a systematic account of SRC effects, a taxonomy of simple performance tasks that were hitherto thought to be unrelated, and suggestive parallels between these tasks and the experimental paradigms that have traditionally been used to study attentional, controlled, and automatic processes. In this article, we address the classic problem of stimulusresponse (S-R) compatibility (SRC). A model is proposed that attempts to provide a systematic account of performance in highly compatible, incompatible, and noncompatible tasks. At the core of our model is the idea that when a particular S-R ensemble produces either high or low compatibility effects, it is because the stimulus and response sets in the ensemble have properties in common, and elements in the stimulus set automatically activate corresponding elements in the response set. Noncompatible tasks are those in which the stimulus and response sets have nothing in common. If the activated response is the required one, it will be executed rapidly and correctly; if it is not, then it will be relatively slow and error prone. Whether a particular S-R ensemble will produce compatibility effects is often quite easy to determine because of the relationship between the stimulus and response sets. In the part of the model that treats the representational aspects of the problem, we postulate that this relationship is based on the commonality, simi

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Dimensional overlap: cognitive basis for stimulus-response compatibility--a model and taxonomy.

"Dimensional overlap: Cognitive basis for stimulus-response compatibility--A model and taxonomy": Correction to Kornblum et al

The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as they often yield valuable information about the large fluctuations of a random system around its most probable state or trajectory. In the context of equilibrium statistical mechanics, the theory of large deviations provides exponential-order estimates of probabilities that refine and generalize Einstein's theory of fluctuations. This review explores this and other connections between large deviation theory and statistical mechanics, in an effort to show that the mathematical language of statistical mechanics is the language of large deviation theory. The first part of the review presents the basics of large deviation theory, and works out many of its classical applications related to sums of random variables and Markov processes. The second part goes through many problems and results of statistical mechanics, and shows how these can be formulated and derived within the context of large deviation theory. The problems and results treated cover a wide range of physical systems, including equilibrium many-particle systems, noise-perturbed dynamics, nonequilibrium systems, as well as multifractals, disordered systems, and chaotic systems. This review also covers many fundamental aspects of statistical mechanics, such as the derivation of variational principles characterizing equilibrium and nonequilibrium states, the breaking of the Legendre transform for nonconcave entropies, and the characterization of nonequilibrium fluctuations through fluctuation relations.

The large deviation approach to statistical mechanics

Encyclopedia of Mathematics and its Applications.

1. Introduction 2. Elementary Properties of Continued Fractions 3. Continued Fractions 4. Convergence of Continued Fractions 5. Methods for Representing Analytic Functions by Continued Fractions 6. Representations of Analytic Functions by Continued Fractions 7. Types of Corresponding Continued Fractions and Related Algorithms 8. Truncation-Error Analysis 9. Asymptotic Expansions and Moment Problems 10. Numerical Stability in Evaluating Continued Fractions 11. Application of Continued Fractions to Birth-Death Processes 12. Miscellaneous Results.

Continued Fractions: Analytic Theory and Applications

Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!

https://gendocs.ru/docs/28/27781/conv_1/file1.pdf

Handbook of Continued Fractions for Special Functions

Etude des relations entre la theorie des moments, les polynomes orthogonaux, la quadrature et les fractions continues associees au cercle-unite. Revue d'ensemble des resultats generaux

Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle

This paper is concerned with double sequences of complex numbers C = [cn}^x and with formal Laurent series Lq(C) = 2f c_mzm and /.„(C) = 2o°cmz~m generated by them. We investigate the following related problems: (1) Does there exist a holomorphic function having L0(C) and LX(C) as asymptotic expansions at z — 0 and z = oo, respectively? (2) Does there exist a real-valued bounded, monotonically increasing function <f>(f) with infinitely many points of increase on [0, oo) such that, for every integer n, c„ = / 5°(-0\" dty(t)l The latter problem is called the strong Stieltjes moment problem. We also consider a modified moment problem in which the function ¡f/(t) has at most a finite number of points of increase. Our approach is made through the study of a special class of continued fractions (called positive 7\"-fractions) which correspond to L0(C) at z = 0 and LX(C) at z = oo. Necessary and sufficient conditions are given for the existence of these corresponding continued fractions. It is further shown that the even and odd parts of these continued fractions always converge to holomorphic functions which have Lq(C) and LX(C) as asymptotic expansions. Moreover, these holomorphic functions are shown to be represented by Stieltjes integral transforms whose distributions ^°\\t) and ^'\"'(O solve the strong Stieltjes moment problem. Necessary and sufficient conditions are given for the existence of a solution to the strong Stieltjes moment problem. This moment problem is shown to have a unique solution if and only if the related continued fraction is convergent. Finally it is shown that the modified moment problem has a unique solution if and only if there exists a terminating positive T-fraction that corresponds to both Lq(C) and ¿„(C). References are given to other moment problems and to investigations in which negative, as well as positive, moments have been used.

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William B. Jones

Papers

Encyclopedia of Mathematics and its Applications.

Continued Fractions: Analytic Theory and Applications

Handbook of Continued Fractions for Special Functions

Moment Theory, Orthogonal Polynomials, Quadrature, and Continued Fractions Associated with the unit Circle

A strong Stieltjes moment problem