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.

An Application of the Subordination Chains

MSC 2010: 30C45, 30A20, 34A30

Invariants of Unipotent Transformations Acting on Noetherian Relatively Free Algebras

2000 Mathematics Subject Classification: 16R10, 16R30.

Binomial Skew Polynomial Rings, Artin-Schelter Regularity, and Binomial Solutions of the Yang-Baxter Equation

2000 Mathematics Subject Classification: Primary 81R50, 16W50, 16S36, 16S37.

Windowed-Wigner Representations, Interferences and Operators

2010 Mathematics Subject Classification: 42B10, 47A07, 35S05.

Hyperbolic Fibrations and PDE

2010 Mathematics Subject Classification: 35L10, 35L90.

Solvability of an Infinite System of Singular Integral Equations

2000 Mathematics Subject Classification: 45G15, 26A33, 32A55, 46E15.

Pseudodifferential Operators and Weighted Normed Symbol Spaces

2000 Mathematics Subject Classification: 35S05.

Units of F5kD10

2000 Mathematics Subject Classification: 20C05, 16U60, 16S84, 15A33.

Outer endomorphisms of free metabelian Lie algebras

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.

Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions

2010 Mathematics Subject Classification: 47B33, 47B38.

A fizikai matematika legújabb eredményei mint a közgazdaság-tudomány lehetséges vizsgálati eszközei (The newest results of physical mathematics as the possible investigation tools of economics)

A közgazdaság-tudomány számos problémája a fizika analóg modelljeinek segítségével nyert megoldást. A közgazdászok körében erőteljesen megoszlanak a vélemények, hogy a közgazdasági modellek mennyire redukálhatók a fizika, vagy más természettudományok eredményeire. Vannak,akik pontosan ezzel magyarázzák,hogy a mai mainstream közgazdasági elmélet átalakult alkalmazott matematikává,ami a gazdasági kérdéseket csak a társadalom-tudományi vonatkozásaitól eltekintve képes vizsgálni. Mások, e tanulmányszerzője is, viszont úgy vélekednek, hogy a közgazdasági problémák egy része, ahol lehetőség van a mérésre, jól modellezhetők a természettudományok technikai arzenáljával. A másik része, amelyekben nem lehet mérni,s tipikusan ilyenek a társadalomtudományi kérdések, ott sokkal komplexebb technikákra lesz szükség. Etanulmány célkitűzése, hogy felvázolja a fizika legújabb, az irreverzibilis dinamika, a relativitáselmélet és a kvantummechanika sztochasztikus matematikai összefüggéseit, amelyekből a közgazdászok választhatnak egy-egy probléma megfogalmazásában és megoldásában. Például az időoperátorok pontos értelmezése jelentős fordulatot hozhat a makroökonómiai elméletekben; vagy az eddigi statikus egyensúlyi referencia pontokat felválthatják a dinamikus,időben változó sztochasztikus egyensúlyi referenciafüggvények, ami forradalmian új megvilágításba helyezhet számos társadalomtudományi, s főleg nemegyensúlyi közgazdasági kérdést.A termodinamika és a biológiai evolúció fogalmait és definícióit Paul A. Samuelson (1947) már adaptálta a közgazdaságtanban, viszont a kvantummechanika legújabb eredményeit, az időoperátorokat stb. nem érintette. E cikk azokat a legújabb fizikai, kémiai és biológiai matematikai összefüggéseket foglalja össze,amelyek hasznosak lehetnek a közgazdasági modellek komplexebb megfogalmazásához. ___________________ The aim of this paper is to out line the newest results of physics,i.e.,the stochastic mathematical relations of relativity theory and quantum mechanics as well as irreversible dynamics which can be applied for some economic problems.For example,the correct interpretation of time operators using for the macroeconomic theories may provide a serious improvement in approach to the reality.The stochastic dynamic equilibrium reference functions will take over the role of recent static equilibrium reference points,which may also reveal some nonequilibrium questions of macroeconomics.The concepts and definitions of thermodynamics and biological evolution have been adopted in economics by Paul A. Samuelson, but he did not concern the newest results of quantum mechanics, e.g., the time operators. Now we do it.In addition, following Samuelson,we show that von Neumann growth model cannot be explained as a peculiar extension of thermodynamic irreversibility.

The Use of the Internet in the U.S Lodging Industry

The internet has been heralded as the communications and marketing tool of the future for the hospitality industry. Both corporate executives and information technology experts feel the hotel of the future cannot do without a presence on the Web. Yet, do the actions of hospitality operators in the field reflect this optimism? This article reports on a study done among property managers in the U.S. lodging industry to determine the actual use of the internet in hotel properties of various types and sizes. Additionally, it addresses development and maintenance issues related to internet use.

Electoral rules and elite recruitment: A comparative analysis of the Bundestag and the U.S. House of Representatives

In this research, I analyze the effects of candidate nomination rules and campaign financing rules on elite recruitment into the national legislatures of Germany and the United States. This dissertation is both theory-driven and constitutes exploratory research, too. While the effects of electoral rules are frequently studied in political science, the emphasis is thereby on electoral rules that are set post-election. My focus, in contrast, is on electoral rules that have an effect prior to the election. Furthermore, my dissertation is comparative by design.^ The research question is twofold. Do electoral rules have an effect on elite recruitment, and does it matter? To answer these question, I create a large-N original data set, in which I code the behavior and recruitment paths and patterns of members of the American House of Representatives and the German Bundestag. Furthermore, I include interviews with members of the said two national legislatures. Both the statistical analyses and the interviews provide affirmative evidence for my working hypothesis that differences in electoral rules lead to a different type of elite recruitment. To that end, I use the active-politician concept, through which I dichotomously distinguish the economic behavior of politicians.^ Thanks to the exploratory nature of my research, I also discover the phenomenon of differential valence of local and state political office for entrance into national office in comparative perspective. By statistically identifying this hitherto unknown paradox, as well as evidencing the effects of electoral rules, I show that besides ideology and culture, institutional rules are key in shaping the ruling elite. The way institutional rules are set up, in particular electoral rules, does not only affect how the electorate will vote and how seats will be distributed, but it will also affect what type of people will end up in elected office.^

Investigating the Intrinsic and Extrinsic Drivers of Primate Heterothermy

Seasonal heterothermy—an orchestrated set of extreme physiological responses—is directly responsible for the over-winter survival of many mammalian groups living in seasonal environments. Historically, it was thought that the use of seasonal heterothermy (i.e. daily torpor and hibernation) was restricted to cold-adapted species; it is now known that such thermoregulatory strategies are used by more species than previously appreciated, including many tropical species. The dwarf and mouse lemurs (family Cheirogaleidae) are among the few primates known to use seasonal heterothermy to avoid Madagascar’s harsh and unpredictable environments. These primates provide an ideal study system for investigating a common mechanism of mammalian seasonal heterothermy. The overarching theme of this dissertation is to understand both the intrinsic and extrinsic drivers of heterothermy in three species of the family Cheirogaleidae. By using transcriptome sequencing to characterize gene expression in both captive and natural settings, we identify unique patterns of differential gene expression that are correlated with extreme changes in physiology in two species of dwarf lemurs: C. medius under captive conditions at the Duke Lemur Center and C. crossleyi studied under field conditions in Madagascar. Genes that are differentially expressed appear to be critical for maintaining the health of these animals when they undergo prolonged periods of metabolic depression concurrent with the hibernation phenotype. Further, a comparative analysis of previously studied mammalian heterotherms identifies shared genetic mechanisms underlying the hibernation phenotype across the phylogeny of mammals. Lastly, conducting a diet manipulation study with a captive colony of mouse lemurs (Microcebus murinus) at the Duke Lemur Center, we investigated the degree to which dietary effects influence torpor patterns. We find that tropical primate heterotherms may be exempt from the traditional paradigms governing cold-adapted heterothermy, having evolved different dietary strategies to tolerate circadian changes in body temperature.