Explicit Quantities Research Articles

Optimal inverse problems of potentials for two given eigenvalues of Sturm–Liouville problems

The present paper is concerned with the infimum of the norm of potentials for Sturm–Liouville eigenvalue problems with Dirichlet boundary condition such that the first two eigenvalues are known. The explicit quantity of the infimum is given by the two eigenvalues.

Modeling the propagation of riots, collective behaviors and epidemics

<abstract> This paper is concerned with a family of Reaction-Diffusion systems that we introduced in ^{[<xref ref-type="bibr" rid="b15">15</xref>]}, and that generalizes the <italic>SIR</italic> type models from epidemiology. Such systems are now also used to describe collective behaviors. In this paper, we propose a modeling approach for these apparently diverse phenomena through the example of the dynamics of social unrest. The model involves two quantities: the level of social unrest, or more generally activity, $ u $, and a field of social tension $ v $, which play asymmetric roles. We think of $ u $ as the actually observed or explicit quantity while $ v $ is an ambient, sometimes implicit, field of susceptibility that modulates the dynamics of $ u $. In this article, we explore this class of model and prove several theoretical results based on the framework developed in ^{[<xref ref-type="bibr" rid="b15">15</xref>]}, of which the present work is a companion paper. We particularly emphasize here two subclasses of systems: <italic>tension inhibiting</italic> and <italic>tension enhancing</italic>. These are characterized by respectively a negative or a positive feedback of the unrest on social tension. We establish several properties for these classes and also study some extensions. In particular, we describe the behavior of the system following an initial surge of activity. We show that the model can give rise to many diverse qualitative dynamics. We also provide a variety of numerical simulations to illustrate our results and to reveal further properties and open questions. </abstract>

On the integer part of the reciprocal of the Riemann zeta function tail at certain rational numbers in the critical strip

We prove that the integer part of the reciprocal of the tail of zeta (s) at a rational number s=frac{1}{p} for any integer with p geq 5 or s=frac{2}{p} for any odd integer with p geq 5 can be described essentially as the integer part of an explicit quantity corresponding to it. To deal with the case when s=frac{2}{p}, we use a result on the finiteness of integral points of certain curves over mathbb{Q}.

ЧИННИКИ ФУНКЦІОНУВАННЯ ТА ВИЗНАЧЕННЯ МАСШТАБІВ І ПЕРСПЕКТИВ РОЗВИТКУ ФІНАНСОВОГО СЕКТОРУ

Уточнено чинники функціонування і підходи до визначення масштабів і перспектив розвитку фінансового сектору національної економіки. Запропоновано авторське бачення детермінант функціонування і розвиненості фінансового сектору національної економіки. Проаналізовано підходи до визначення впливу розмірів фінансового сектору на стан національної економіки. Наведено чинники суттєвого розриву між фінансовим і реальним секторами національної економіки та погляди дослідників на вимірники розвитку фінансового сектору національної економіки й представлено авторську позицію стосовно показників такого розвитку.

Stochastic Lotka-Volterra food chains.

We study the persistence and extinction of species in a simple food chain that is modelled by a Lotka-Volterra system with environmental stochasticity. There exist sharp results for deterministic Lotka-Volterra systems in the literature but few for their stochastic counterparts. The food chain we analyze consists of one prey and [Formula: see text] predators. The jth predator eats the [Formula: see text]th species and is eaten by the [Formula: see text]th predator; this way each species only interacts with at most two other species-the ones that are immediately above or below it in the trophic chain. We show that one can classify, based on an explicit quantity depending on the interaction coefficients of the system, which species go extinct and which converge to their unique invariant probability measure. Our work can be seen as a natural extension of the deterministic results of Gard and Hallam '79 to a stochastic setting. As one consequence we show that environmental stochasticity makes species more likely to go extinct. However, if the environmental fluctuations are small, persistence in the deterministic setting is preserved in the stochastic system. Our analysis also shows that the addition of a new apex predator makes, as expected, the different species more prone to extinction. Another novelty of our analysis is the fact that we can describe the behavior of the system when the noise is degenerate. This is relevant because of the possibility of strong correlations between the effects of the environment on the different species.

The Trapping Effect on Degenerate Horizons

We show that degenerate horizons exhibit a new trapping effect. Specifically, we obtain a non-degenerate Morawetz estimate for the wave equation in the domain of outer communications of extremal Reissner-Nordstrom up to and including the future event horizon. We show that such an estimate requires 1) a higher degree of regularity for the initial data, reminiscent of the regularity loss in the high-frequency trapping estimates on the photon sphere, and 2) the vanishing of an explicit quantity that depends on the restriction of the initial data on the horizon. The latter condition demonstrates that degenerate horizons exhibit a global trapping effect (in the sense that this effect is not due to individual underlying null geodesics as in the case of the photon sphere). We moreover uncover a new stable higher-order trapping effect; we show that higher-order estimates do not hold regardless of the degree of regularity and the support of the initial data. We connect our findings to the spectrum of the stability operator in the theory of marginally outer trapped surfaces (MOTS). Our methods and results play a crucial role in our upcoming works on linear and non-linear wave equations on extremal black hole backgrounds.

Linking indices for biodiversity monitoring to extinction risk theory.

Biodiversity indices often combine data from different species when used in monitoring programs. Heuristic properties can suggest preferred indices, but we lack objective ways to discriminate between indices with similar heuristics. Biodiversity indices can be evaluated by determining how well they reflect management objectives that a monitoring program aims to support. For example, the Convention on Biological Diversity requires reporting about extinction rates, so simple indices that reflect extinction risk would be valuable. We developed 3 biodiversity indices that are based on simple models of population viability that relate extinction risk to abundance. We based the first index on the geometric mean abundance of species and the second on a more general power mean. In a third index, we integrated the geometric mean abundance and trend. These indices require the same data as previous indices, but they also relate directly to extinction risk. Field data for butterflies and woodland plants and experimental studies of protozoan communities show that the indices correlate with local extinction rates. Applying the index based on the geometric mean to global data on changes in avian abundance suggested that the average extinction probability of birds has increased approximately 1% from 1970 to 2009.Conectando Índices para el Monitoreo de la Biodiversidad con la Teoría de Riesgo de ExtinciónResumenLos índices de biodiversidad combinan frecuentemente los datos de diferentes especies cuando se usan en los programas de monitoreo. Las propiedades heurísticas pueden sugerir índices preferidos, pero carecemos de medios objetivos para discriminar a los índices con propiedades heurísticas similares. Los índices de biodiversidad pueden evaluarse al determinar qué tan bien reflejan los objetivos de manejo que un programa de monitoreo busca apoyar. Por ejemplo, la Convención sobre la Diversidad Biológica requiere reportar las tasas de extinción, así que los índices que reflejan el riesgo de extinción serían valiosos. Desarrollamos 3 índices de biodiversidad que se basan en modelos sencillos de viabilidad de población y que relacionan el riesgo de extinción con la abundancia. Basamos el primer índice en la media geométrica de la abundancia de especies, y el segundo en una media de poder más general. En el tercer índice integramos la media geométrica y la tendencia. Estos índices requieren los mismos datos que índices previos, pero también se relacionan directamente con el riesgo de extinción. La información de campo sobre mariposas y plantas de bosque, y los estudios experimentales de comunidades protozoarias, muestran que los índices se correlacionan con las tasas locales de extinción. Al aplicar el índice basado en la media geométrica sobre los datos globales de los cambios en la abundancia de aves, sugirió que la probabilidad de extinción promedio de aves ha incrementado aproximadamente 1% desde 1970 hasta 2009.Palabras ClaveÍndice de biodiversidad, media geométrica, medida de la biodiversidad, riesgo de extinción

Complement set focus without explicit quantity

Production and comprehension of pronominal references may vary depending on whether this is preceded by a statement including a positive or a negative natural language quantifier (NLQ). After a negative NLQ there is a preference to refer to the complement set, a set not explicitly mentioned (Moxey & Sanford, 1987). We report two experiments which examine whether a property of the NLQ, or some alternative factor is responsible for this pattern of reference. According to the Presupposition Denial Account, complement set reference arises when the shortfall between a previously expected amount and a smaller amount, denoted by an NLQ, is made salient (Moxey, 2006). Using a character's implicit desire and positive versus negative emotion words, we manipulate the prominence of the shortfall. Results from a language production task show that when there is a large difference between what a character is likely to want and the amount that can be inferred from a negative emotion word there is an increase in production of complement set references. An eye movement study shows that, if a shortfall has been made salient in this way, a reference set reference leads to disruption during reading. These results are consistent with the Presupposition Denial Account.

The negative answer to Kameko's conjecture on the hit problem

The goal of this paper is to give a negative answer to Kameko's conjecture on the hit problem stating that the cardinal of a minimal set of generators for the polynomial algebra P k , considered as a module over the Steenrod algebra A , is dominated by an explicit quantity depending on the number of the polynomial algebra's variables k. The conjecture was shown by Kameko himself for k ⩽ 3 in his PhD thesis in the Johns Hopkins University in 1990, and recently proved by us and Kameko for k = 4 . However, we claim that it turns out to be wrong for any k > 4 . In order to deny Kameko's conjecture we study a minimal set of generators for A -module P k in some so-call generic degrees. What we mean by generic degrees is a bit different from that of other authors in the fields such as Crabb–Hubbuck, Nam, Repka–Selick, Wood …We prove an inductive formula for the cardinal of the minimal set of generators in these generic degrees when the number of the variables, k, increases. As an immediate consequence of this inductive formula, we recognize that Kameko's conjecture is no longer true for any k > 4 .

Nonequilibrium Linear Response for Markov Dynamics, I: Jump Processes and Overdamped Diffusions

Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of these quantities. The first term corresponds to the correlation between observable and excess entropy flux yielding a relation with energy dissipation like in equilibrium. The second term comes with a new meaning: it is the correlation between the observable and the excess in dynamical activity or reactivity, playing an important role in dynamical fluctuation theory out-of-equilibrium. It appears as a generalized escape rate in the occupation statistics. The resulting response formula holds for all observables and allows direct numerical or experimental evaluation, for example in the discussion of effective temperatures, as it only involves the statistical averaging of explicit quantities, e.g. without needing an expression for the nonequilibrium distribution. The physical interpretation and the mathematical derivation are independent of many details of the dynamics, but in this first part they are restricted to Markov jump processes and overdamped diffusions.

A characterization of dynamic reasoning: Reasoning with time as parameter

Students incorporate and use the implicit and explicit parameter time to support their mathematical reasoning and deepen their understandings as they participate in a differential equations class during instruction on solutions to systems of differential equations. Therefore, dynamic reasoning is defined as developing and using conceptualizations about time as a parameter that implicitly or explicitly coordinates with other quantities to understand and solve problems. Students participate in the following types of mathematical activity related to dynamic reasoning: making time an explicit quantity, using the metaphor of time as “unidimensional space”, using time to reason both quantitatively and qualitatively, using three-dimensional visualization of time related functions, fusing context and representation of time related functions, and using the fictive motion metaphor for function. The purpose of this article is to present a characterization of dynamic reasoning and promote more explicit attention to this type of reasoning by teachers in K-16 mathematics in order to improve student understanding in time related areas of mathematics.

Reliability analysis of linear dynamical systems using approximate representations of performance functions

A method to carry out reliability analysis of linear systems with random structural parameters and random excitation is presented. Probability that design conditions are satisfied within a given time period is used as a measure of system reliability. An efficient importance sampling technique is used to estimate the failure probabilities. This technique is combined with high quality approximations of the performance functions in terms of uncertain structural parameters. The number of dynamic analyses required during the estimation process is minimized since the simulations are carried out by evaluating explicit expressions. The explicit quantities correspond to approximate representations of the performance functions in terms of the uncertain structural parameters. A numerical example corresponding to problem 2, sub-case 2 of the benchmark study is presented to illustrate the accuracy and computational efficiency of the proposed computational procedure.

Reduced evolution equations for general motion of surfaces

The system of intrinsic evolution equations for general motion of a surface is analyzed locally for possible reductions to a smaller, but equivalent, system under the formal assumption that the coefficients of the surface metric must remain as explicit quantities. No other restrictions are imposed. Two alternative reduced systems valid for any general motion are found: first, of five equations for the coefficients of the Riemannian metric, mean curvature and angular velocity of the principal directions of the second fundamental form as the unknown quantities, and, second, of four equations for the coefficients of the metric and a distance function. The paper concludes with the discussion why reduction to four is ultimate under the above assumption.

Real Wages, Skill Mismatch and Unemployment Persistence France, 1962-1989

We develop a model of equilibrium unemployment with endogenous real wages and productivity. We use a framework with explicit quantity constraints and aggregation over micromarkets to derive a Beveridge curve and discuss the relationship between shifts in the Beveridge curve and equilibrium unemployment. We also distinguish skilled and unskilled labor, so that shifts in the aggregate UV-curve can be the outcome of either frictions on the skilled labor market or skill mismatch. Frictions are assumed to be exogenous and are estimated by a linear trend. Skill mismatch is endogenous and depends, a.o., on the skilled/unskilled relative wage. There is a tight relationship and interaction between skill mismatch and equilibrium unemployment. We estimate the model on French annual data, over the period 1962-89. We exploit these results to propose tentative explanations of observed unemployment rises and Beveridge curve shifts, and to discuss a few economic policy options.

Thermodynamics of open nonlinear systems far from equilibrium: The continuously stirred tank reactor

A thermodynamic analysis is made of a continuously stirred tank reactor (CSTR) which is fed with ideal gases and in which arbitrary types of chemical reactions take place. For stationary states and oscillatory ones in which limit cycles are established, expressions are derived which describe the change of entropy of the reactor contents relative to the feed in terms of explicit quantities, including the rate of entropy production due to the chemical reactions. This entropy change is shown to be always greater than what would be observed in closed systems under comparable circumstances. It is pointed out that this statement is beyond what the second law of thermodynamics can predict. In previous articles, entropy and entropy production have been found to follow certain systematic trends in some specific models based on the CSTR. That work is compared with the present theory.

Design sensitivity analysis for nonlinear thermal systems

The Lagrange multiplier method and convolution theory are used to formulate design sensitivities for nonlinear transient thermal systems. Variations of a general design functional are expressed in explicit form with respect to variations in structural shape and the conventional design quantities, i.e., material properties, applied loads, prescribed boundary conditions and initial conditions. The design functional depends on these explicit quantities and the implicit repsonse fields: temperature, temperature gradient, heat flux vector and reaction surface flux. A finite element implementation of the methodology illustrates the formulation.

Heat transfer between two fluid phases

The interface (or the surface phase) in an n-component fluid is studied on a model of the discontinuity surface in continuum. Balance equations, equations for entropy production, phenomenological equations and heat transfer equations are derived, which comprise bulk phase temperatures, the temperature of the interface (or the temperature of the surface phase), the surface heat conductivity coefficient and heat transfer coefficients as explicit quantities.

Analyzing the Use of Information in Investment Decision Making: A Methodological Proposal

Foresightful investment analysts have long recognized the need to understand more clearly the detailed processes underlying investment decisions-especially decisions made by acknowledged experts. For example, Bernhard observes that, if the mental processes of consistently successful investors are intuitional, that intuitional reasoning must be made understandable.' In a similar vein, others have argued that, by compelling the investment analyst to translate his vague attitudes, opinions, and reasons into explicit quantities, the analyst's thoughts are brought out into the open where they can be observed, evaluated, and tested.2 Researchers in the areas of economics, finance, and psychology have recently taken up the challenge of simulating and describing the judgment process. There are, at present, a number of methods that should be of interest to persons concerned with the dynamics of investment decisions. The objective of this paper is to provide a brief introduction to this work and to present an experiment that illustrates the use of one such method for quantitatively describing the use of information in investment decisions. Due to limitations of the sample of subjects and the particular cases being judged, the reader should view the experiment as a methodological illustration-not a finished empirical investigation.