On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

A Linear Time Algorithm for Computing Longest Paths in Cactus Graphs

ACM Computing Classification System (1998): G.2.2.

A New Method for Computing the Eccentric Connectivity Index of Fullerenes

ACM Computing Classification System (1998): G.2.2, G.2.3.

Financial Decisions via Methods of Guaranteed Control Theory

AMS subject classification: 93C95, 90A09.

Viability, Optimality and Stability of Dynamical Systems and Estimation of Convergence of Numerical Schemes

AMS subject classification: 49N35,49N55,65Lxx.

Hausdorff Approximation of Functions Different from Zero at One Point - Implementation in Programming Environment Mathematica

ACM Computing Classification System (1998): G.1.2.

Benchmarking of distributed computing engines spark and GraphLab for big data analytics

In this paper we evaluate and compare two representativeand popular distributed processing engines for large scalebig data analytics, Spark and graph based engine GraphLab. Wedesign a benchmark suite including representative algorithmsand datasets to compare the performances of the computingengines, from performance aspects of running time, memory andCPU usage, network and I/O overhead. The benchmark suite istested on both local computer cluster and virtual machines oncloud. By varying the number of computers and memory weexamine the scalability of the computing engines with increasingcomputing resources (such as CPU and memory). We also runcross-evaluation of generic and graph based analytic algorithmsover graph processing and generic platforms to identify thepotential performance degradation if only one processing engineis available. It is observed that both computing engines showgood scalability with increase of computing resources. WhileGraphLab largely outperforms Spark for graph algorithms, ithas close running time performance as Spark for non-graphalgorithms. Additionally the running time with Spark for graphalgorithms over cloud virtual machines is observed to increaseby almost 100% compared to over local computer clusters.

Műszaki és gazdasági hatékonyság Koopmans termeléselméletében (Technical and economic efficiency in Koopmans' theory of production)

Koopmans gyakorlati problémák megoldása során szerzett tapasztalatait általánosítva fogott hozzá a lineáris tevékenységelemzési modell kidolgozásához. Meglepődve tapasztalta, hogy a korabeli közgazdaságtan nem rendelkezett egységes, kellően egzakt termeléselmélettel és fogalomrendszerrel. Úttörő dolgozatában ezért - mintegy a lineáris tevékenységelemzési modell elméleti kereteként - lerakta a technológiai halmazok fogalmán nyugvó axiomatikus termeléselmélet alapjait is. Nevéhez fűződik a termelési hatékonyság és a hatékonysági árak fogalmának egzakt definíciója, s az egymást kölcsönösen feltételező viszonyuk igazolása a lineáris tevékenységelemzési modell keretében. A hatékonyság manapság használatos, pusztán műszaki szempontból értelmezett definícióját Koopmans csak sajátos esetként tárgyalta, célja a gazdasági hatékonyság fogalmának a bevezetése és elemzése volt. Dolgozatunkban a lineáris programozás dualitási tételei segítségével rekonstruáljuk ez utóbbira vonatkozó eredményeit. Megmutatjuk, hogy egyrészt bizonyításai egyenértékűek a lineáris programozás dualitási tételeinek igazolásával, másrészt a gazdasági hatékonysági árak voltaképpen a mai értelemben vett árnyékárak. Rámutatunk arra is, hogy a gazdasági hatékonyság értelmezéséhez megfogalmazott modellje az Arrow-Debreu-McKenzie-féle általános egyensúlyelméleti modellek közvetlen előzményének tekinthető, tartalmazta azok szinte minden lényeges elemét és fogalmát - az egyensúlyi árak nem mások, mint a Koopmans-féle hatékonysági árak. Végezetül újraértelmezzük Koopmans modelljét a vállalati technológiai mikroökonómiai leírásának lehetséges eszközeként. Journal of Economic Literature (JEL) kód: B23, B41, C61, D20, D50. /===/ Generalizing from his experience in solving practical problems, Koopmans set about devising a linear model for analysing activity. Surprisingly, he found that economics at that time possessed no uniform, sufficiently exact theory of production or system of concepts for it. He set out in a pioneering study to provide a theoretical framework for a linear model for analysing activity by expressing first the axiomatic bases of production theory, which rest on the concept of technological sets. He is associated with exact definition of the concept of production efficiency and efficiency prices, and confirmation of their relation as mutual postulates within the linear model of activity analysis. Koopmans saw the present, purely technical definition of efficiency as a special case; he aimed to introduce and analyse the concept of economic efficiency. The study uses the duality precepts of linear programming to reconstruct the results for the latter. It is shown first that evidence confirming the duality precepts of linear programming is equal in value, and secondly that efficiency prices are really shadow prices in today's sense. Furthermore, the model for the interpretation of economic efficiency can be seen as a direct predecessor of the Arrow–Debreu–McKenzie models of general equilibrium theory, as it contained almost every essential element and concept of them—equilibrium prices are nothing other than Koopmans' efficiency prices. Finally Koopmans' model is reinterpreted as a necessary tool for microeconomic description of enterprise technology.

Theory and practice in the field of foresight

Purpose – The paper aims to explore the gap between theory and practice in foresight and to give some suggestions on how to reduce it. Design/methodology/approach – Analysis of practical foresight activities and suggestions are based on a literature review, the author's own research and practice in the field of foresight and futures studies, and her participation in the work of a European project (COST A22). Findings – Two different types of practical foresight activities have developed. One of them, the practice of foresight of critical futures studies (FCFS) is an application of a theory of futures studies. The other, termed here as praxis foresight (PF), has no theoretical basis and responds directly to practical needs. At present a gap can be perceived between theory and practice. PF distinguishes itself from the practice and theory of FCFS and narrows the construction space of futures. Neither FCFS nor PF deals with content issues of the outer world. Reducing the gap depends on renewal of joint discourses and research about experience of different practical foresight activities and manageability of complex dynamics in foresight. Production and feedback of self-reflective and reflective foresight knowledge could improve theory and practice. Originality/value – Contemporary practical foresight activities are analysed and suggestions to reduce the gap are developed in the context of the linkage between theory and practice. This paper is thought provoking for futurists, foresight managers and university researchers.

Bródy András gazdaságiciklus-elmélete (András Bródy's theory of economic cycles)

Bródy András kutatásainak egyik központi témaköre a gazdasági mozgás vizsgálata volt. Írásunkban Bródy elméletét kívánjuk röviden áttekinteni és összefoglalni. A termelés sokszektoros leírása egyben árelméletét (értékelméletét, méréselméletét) is keretbe foglalja. Ebben a keretben a gazdasági mozgás összetett ingadozása technológiai alapon elemezhető. Bródy megközelítésében a gazdasági ciklust nem külső megrázkódások magyarázzák, hanem a termelési rendszer belső arányai és kapcsolatai. A termelési struktúrát az árak és a volumenek egyformán alakítják, ezek között nincsen kitüntetett vagy domináns tényező. Az árak és a volumenek a köztük lévő duális kapcsolatban alakulnak ki. A gazdaság mozgásegyenleteit technológiai mérlegösszefüggések, valamint a piaci csere útján a gazdaságban újraelosztásra (újratermelésre) kerülő termékek felhasználása és az eszközlekötés változása írja le. Az így meghatározott mozgásegyenletek a gazdaság természetes mozgását ciklusmozgás alakjában írják le. A technológia vagy az értékviszonyok megváltozása (sokkok) a gazdaság ciklikus mozgásának megváltozásában tükröződik. Bródy munkáiban technológiai megalapozást nyer a történelemből ismert számos jellegzetes gazdasági ciklus. / === / Economic motion and dynamics are at the heart of Andras Brody's creative output. This paper attempts a bird's-eye view of his theory of economic cycles. Brody's multi-sector modelling of production has provided a framework for price theory (the theory of value and measurement). His theory of economic motion with cyclical characteristics is technology driven. It argues that the complex web of economic cycles is determined by the proportions and interrelationships of the system of production, not by arbitrary external shocks. The structure's behaviour are driven by prices and proportions, with the duality of prices and proportions as a dominant feature. These are features in common with the Leontief models, which Brody extended to economic cycles. Brody saw economic cycles as natural motions of economic systems with accumulated assets (time lags) and market exchange of goods (demand and supply adjustment). Changes in technology or valuations (shocks) are reflected in changing patterns of motion. His model of the economy is a fine instrument that enabled him to show how the technological parameters of its system determine the frequency and other characteristics of various economic cycles identified in economic history.

Spontaneous order and social norms. Hayek’s theory of socio-cultural evolution

Hayek’s theory of socio-cultural evolution is a generalization of his theory on spontaneous market order. Hayek explains both the emergence of market and social institutions serving as a social basis for that order within the framework of a unified evolutionary logic. This logic interprets the emergence and survival of spontaneous order and group-level rules of conduct as an unintended consequence of human action. In order to explain the emergence of social norms exclusively on the basis of methodological individualism, one would have to give up an exclusively evolutionary explanation of these norms. Since Hayek applies the invisible-hand explanation to the investigation of social norms, he combines the position of methodological individualism with functionalist-evolutionary arguments in his analysis. Hayek’s theory of socio-cultural evolution represents a theory in the framework of which methodological individualism and functionalism do not crowd out but complement each other.

Spontaneous order and social norms. Hayek’s theory of socio-cultural evolution

Hayek's theory of socio-cultural evolution is a generalization of his theory on spontaneous market order. Hayek explains both the emergence of market and social institutions serving as a social basis for that order within the framework of a unified evolutionary logic. This logic interprets the emergence and survival of spontaneous order and group-level rules of conduct as an unintended consequence of human action. In order to explain the emergence of social norms exclusively on the basis of methodological individualism, one would have to give up an exclusively evolutionary explanation of these norms. Since Hayek applies the invisiblehand explanation to the investigation of social norms, he combines the position of methodological individualism with functionalist-evolutionary arguments in his analysis. Hayek's theory of socio-cultural evolution represents a theory in the framework of which methodological individualism and functionalism do not crowd out but complement each other.

Piaci rend és társadalmi normák. Hayek elmélete a társadalmi evolúcióról (Market order and social norms Hayek's theory of social evolution)

A hayeki szociokulturális evolúció elmélete a piaci rend elemzésének általánosítása. Hayek mind a piaci rend, mind a piaci rend alapzatául szolgáló társadalmi intézmények kialakulását és működését azonos logika alapján magyarázza. Ez a logika az egyéni cselekvések nem szándékolt következményeként értelmezi a spontán rend és a csoportszintű magatartásszabályok kialakulását és fennmaradását. A társadalmi normák magyarázatában a módszertani individualizmus elveinek érvényesítéséért az evolucionista perspektíva feladásával kellene fizetni. Hayek azonban a társadalmi normák magyarázatára is az evolucionista megközelítést alkalmazza, ezért egészíti ki a módszertani individualista megközelítést funkcionalista-evolucionista érvekkel. A szociokulturális evolúció hayeki elmélete példa arra, hogy a módszertani individualizmusra épülő magyarázat és a funkcionalista érvelés nem kiszorítja, hanem kiegészíti egymást. _____ Hayek's theory of socio-cultural evolution is a generalization of his theory of market order. He explains in the same way the development and operation of market order and those of the social institutions on which market order is based. This logic interprets the development and persistence of spontaneous order and group-level behaviour rules as an unintentional consequence of individual actions. In his explanation of social norms, enforcement of the principles of methodological individualism has to be paid for by abandoning the evolutionist perspective. But Hayek also employs an evolutionist approach in his explanation of social norms, and so he augments his methodological individualist approach with some functionalist-cum-evolutionist arguments. Hayek's theory of sociocultural evolution, for instance, exemplifies how an explanation resting on methodological individualism and a functionalist argument can complement, not preclude each other.

Characteristics of effective clinical and theory instructors as perceived by LPN to RN versus generic students in an associate degree nursing program

The purpose of this study was to compare the characteristics of effective clinical and theory instructors as perceived by LPN/RN versus generic students in an associate degree nursing program.^ Data were collected from 508 students during the 1996-7 academic year from three NLN accredited associate degree nursing programs. The researcher developed instrument consisted of three parts: (a) Whitehead Characteristics of Effective Clinical Instructor Rating Scale, (b) Whitehead Characteristics of Effective Theory Instructor Rating Scale, and (c) Demographic Data Sheet. The items were listed under five major categories identified in the review of the literature: (a) interpersonal relationships, (b) personality traits, (c) teaching practices, (d) knowledge and experience, and (e) evaluation procedures. The instrument was administered to LPN/RN students in their first semester and to generic students in the third semester of an associate degree nursing program.^ Data was analyzed using a one factor mutivariate analysis of variance (MANOVA). Further t tests were carried out to explore for possible differences between type of student and by group. Crosstabulations of the demographic data were analyzed.^ There were no significant differences found between the LPN/RN versus generic students on their perceptions of either effective theory or effective clinical instructor characteristics. There were significant differences between groups on several of the individual items. There was no significant interaction between group and ethnicity or group and age on the five major categories for either of the two instruments. There was a significant main effect of ethnicity on several of the individual items.^ The differences between the means and standard deviations on both instruments were small, suggesting that all of the characteristics listed for effective theory and clinical instructors were important to both groups of students. Effective teaching behaviors, as indicated on the survey instruments, should be taught to students in graduate teacher education programs. These behaviors should also be discussed by faculty coordinators supervising adjunct faculty. Nursing educators in associate degree nursing programs should understand theories of adult learning and implement instructional strategies to enhance minority student success. ^

Extending the Theory of Planned Behavior in the exercise domain: A study of community college students in an urban multicultural setting

The purpose of this study was to assess the intention to exercise among ethnically and racially diverse community college students using the Theory of Planned Behavior (TPB). In addition to identifying the variables associated with motivation or intention of college students to engage in physical activity, this study tested the model of the Theory of Planned Behavior, asking: Does the TPB model explain intention to exercise among a racially/ethnically diverse group of college students? ^ The relevant variables were the TPB constructs (behavioral beliefs, normative beliefs, and control beliefs), which combined to form a measure of intention to exercise. Structural Equation Modeling was used to test the predictive power of the TPB constructs for predicting intention to exercise. Following procedures described by Ajzen (2002), the researcher developed a questionnaire encompassing the external variables of student demographics (age, gender, work status, student status, socio-economic status, access to exercise facilities, and past behavior), major constructs of the TPB, and two questions from the Godin Leisure Time Questionnaire (GLTQ; Godin & Shephard, 1985). Participants were students (N = 255) who enrolled in an on-campus wellness course at an urban community college. ^ The demographic profile of the sample revealed a racially/ethnically diverse study population. The original model that was used to reflect the TPB as developed by Ajzen was not supported by the data analyzed using SEM; however, a revised model that the researcher thought was theoretically a more accurate reflection of the causal relations between the TPB constructs was supported. The GLTQ questions were problematic for some students; those data could not be used in the modeling efforts. The GLTQ measure, however, revealed a significant correlation with intention to exercise (r = .27, p = .001). Post-hoc comparisons revealed significant differences in normative beliefs and attitude toward exercising behavior between Black students and Hispanic students. Compared to Black students, Hispanic students were more likely to (a) perceive “friends” as approving of them being physically active and (b) rate being physically active for 30 minutes per day as “beneficial”. No statistically significant difference was found among groups on overall intention to exercise. ^