Embedding theorems of funcitional classes, III

In this paper we obtain the necessary and sufficient conditions for embedding results of different function classes. The main result is a criterion for embedding theorems for the so-called generalized Weyl-Nikol'skii class and the generalized Lipschitz class. To define the Weyl-Nikol'skii class, we use the concept of a (λ,β)-derivative, which is a generalization of the derivative in the sense of Weyl. As corollaries, we give estimates of norms and moduli of smoothness of transformed Fourier series.

Environment conditions and biological innovations in the european agrarian growth, 1819-1939

The circumstances that were the driving forces behind Europe's economic growth beginning in the 19th century are diverse, and not easily prioritized. Until the 1970's, specifically, in Economy and Economic History, attention was focused on different institutional and technological variables, and various regularities were proposed. Nevertheless, new studies also underlined that the evolution of economic activity could not be understood considering only the new production possibilities offered by market economies. As a result, today it is also accepted that those processes can not be explained without considering two additional circumstances: the energy flows that sustained them, and the changes undergone in their transformation In this context, a question arises that takes on special importance. Which was the influence of the biological change in the economic growth?. A part of the flows of energy must be made into food, and this transformation can only happen with the participation.

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Fair and efficient student placement with couples

We study situations of allocating positions or jobs to students or workers based on priorities. An example is the assignment of medical students to hospital residencies on the basis of one or several entrance exams. For markets without couples, e.g., for ``undergraduate student placement,'' acyclicity is a necessary and sufficient condition for the existence of a fair and efficient placement mechanism (Ergin, 2002). We show that in the presence of couples, which introduces complementarities into the students' preferences, acyclicity is still necessary, but not sufficient (Theorem 4.1). A second necessary condition (Theorem 4.2) is ``priority-togetherness'' of couples. A priority structure that satisfies both necessary conditions is called pt-acyclic. For student placement problems where all quotas are equal to one we characterize pt-acyclicity (Lemma 5.1) and show that it is a sufficient condition for the existence of a fair and efficient placement mechanism (Theorem 5.1). If in addition to pt-acyclicity we require ``reallocation-'' and ``vacancy-fairness'' for couples, the so-called dictator-bidictator placement mechanism is the unique fair and efficient placement mechanism (Theorem 5.2). Finally, for general student placement problems, we show that pt-acyclicity may not be sufficient for the existence of a fair and efficient placement mechanism (Examples 5.4, 5.5, and 5.6). We identify a sufficient condition such that the so-called sequential placement mechanism produces a fair and efficient allocation (Theorem 5.3).

Do market conditions affect gift exchange? Evidence from experimental markets with excess supply and excess demand

We study whether people's behavior in unbalanced gift exchange markets with repeated interaction are affected by whether they are on the excess supply side or the excess demand side of the market. Our analysis is based on the comparison of behavior between two types of experimental gift exchange markets, which vary only with respect to whether first or second movers are on the long side of the market. The direction of market imbalance could influence subjects' behavior, as second movers (workers) might react differently to favorable actions by first movers (firms) in the two cases. While our data show strong deviations from the standard game-theoretic prediction, we find mainly secondary treatment effects. Wage offers are not higher when there is an excess supply of firms, and workers do not respond more favorably to a given wage when there is an excess supply of labor. The state of competition does not appear to have strong effects in our data. We also present data from single-period sessions that show substantial gift exchange even without repeated interactions.

General equilibrium with asymmetric information: a dual approach

We study markets where the characteristics or decisions of certain agents are relevant but not known to their trading partners. Assuming exclusive transactions, the environment is described as a continuum economy with indivisible commodities. We characterize incentive efficient allocations as solutions to linear programming problems and appeal to duality theory to demonstrate the generic existence of external effects in these markets. Because under certain conditions such effects may generate non-convexities, randomization emerges as a theoretic possibility. In characterizing market equilibria we show that, consistently with the personalized nature of transactions, prices are generally non-linear in the underlying consumption. On the other hand, external effects may have critical implications for market efficiency. With adverse selection, in fact, cross-subsidization across agents with different private information may be necessary for optimality, and so, the market need not even achieve an incentive efficient allocation. In contrast, for the case of a single commodity, we find that when informational asymmetries arise after the trading period (e.g. moral hazard; ex post hidden types) external effects are fully internalized at a market equilibrium.

Generalized backward doubly stochastic differential equations and SPDEs with nonlinear Neumann boundary conditions

In this paper, a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for viscosity solutions of semi-linear stochastic partial differential equations with a Neumann boundary condition is given.

Weak systems of Gandy, Jensen and Devlin

In Part I, we formulate and examine some systems that have arisen in the study of the constructible hierarchy; we find numerous transitive models for them, among which are supertransitive models containing all ordinals that show that Devlin's system BS lies strictly between Gandy's systems PZ and BST'; and we use our models to show that BS fails to handle even the simplest rudimentary functions, and is thus inadequate for the use intended for it in Devlin's treatise. In Part II we propose and study an enhancement of the underlying logic of these systems, build further models to show where the previous hierarchy of systems is preserved by our enhancement; and consider three systems that might serve for Devlin's purposes: one the enhancement of a version of BS, one a formulation of Gandy-Jensen set theory, and the third a subsystem common to those two. In Part III we give new proofs of results of Boffa by constructing three models in which, respectively, TCo, AxPair and AxSing fail; we give some sufficient conditions for a set not to belong to the rudimentary closure of another set, and thus answer a question of McAloon; and we comment on Gandy's numerals and correct and sharpen other of his observations.

On Boas-Type Problem

R.P. Boas has found necessary and sufficient conditions of belonging of function to Lipschitz class. From his findings it turned out, that the conditions on sine and cosine coefficients for belonging of function to Lip α(0 & α & 1) are the same, but for Lip 1 are different. Later his results were generalized by many authors in the viewpoint of generalization of condition on the majorant of modulus of continuity. The aim of this paper is to obtain Boas-type theorems for generalized Lipschitz classes. To define generalized Lipschitz classes we use the concept of modulus of smoothness of fractional order.

Constrained school choice

Recently, several school districts in the US have adopted or consider adopting the Student-Optimal Stable Mechanism or the Top Trading Cycles Mechanism to assign children to public schools. There is clear evidence that for school districts that employ (variants of) the so-called Boston Mechanism the transition would lead to efficiency gains. The first two mechanisms are strategy-proof, but in practice student assignment procedures impede students to submit a preference list that contains all their acceptable schools. Therefore, any desirable property of the mechanisms is likely toget distorted. We study the non trivial preference revelation game where students can only declare up to a fixed number (quota) of schools to be acceptable. We focus on the stability of the Nash equilibrium outcomes. Our main results identify rather stringent necessary and sufficient conditions on the priorities to guaranteestability. This stands in sharp contrast with the Boston Mechanism which yields stable Nash equilibrium outcomes, independently of the quota. Hence, the transition to any of the two mechanisms is likely to come with a higher risk that students seek legal actionas lower priority students may occupy more preferred schools.

Norm inequalities in multidimensional Lorentz spaces

In this paper we obtain necessary and sufficient conditions for double trigonometric series to belong to generalized Lorentz spaces, not symmetric in general. Estimates for the norms are given in terms of coefficients.

Well-posedness and invariant measures for HJM models with deterministic volatility and Lévy noise

We give sufficient conditions for existence, uniqueness and ergodicity of invariant measures for Musiela's stochastic partial differential equation with deterministic volatility and a Hilbert space valued driving Lévy noise. Conditions for the absence of arbitrage and for the existence of mild solutions are also discussed.

Effects of atmospheric carbon dioxide fertilization on biomass and secondary metabolites of some plant species with pharmacological interes under greenhouse conditions

RESUMEN El aumento del CO2 atmosférico debido al cambio global y/o a las prácticas hortícolas promueve efectos directos sobre crecimiento vegetal y el desarrollo. Estas respuestas pueden ocurrir en ecosistemas naturales, pero también se pueden utilizar para aumentar la producción de algunas plantas y de algunos compuestos secundarios. El actual trabajo intenta estudiar los efectos del enriquecimiento atmosférico del CO2 bajo condiciones de invernadero en el crecimiento y la concentración y la composición de metabolitos secundarios de Taxus bacatta, Hypericum perforatum y Echinacea purpurea en condiciones ambientales mediterráneas. La fertilización del CO2 muestra perspectivas interesantes para la mejorara y aplicabilidad de técnicas hortícolas para aumentar productividad de plantas medicinales, a pesar de diferencias claras entre la especie. En general esta técnica promueve aumentos importantes y significativos en producción primaria y, en algunos casos, también en compuestos secundarios. Esto tiene una gran importancia hortícola porque la productividad a nivel de cosecha total aumenta, directamente porque se aumenta la concentración e indirectamente porque se aumenta la biomasa. SUMMARY The increase of atmospheric CO2 due to global change and/or horticultural practices promotes direct effects on plant growth and development. These responses may occur in natural ecosystems, but also can be used to increase the production of some plants and some secondary compounds. Present work tries to study the effects of atmospheric CO2 enrichment under greenhouse conditions on growth and in the concentration and composition of secondary metabolites of Taxus bacatta, Hypericum perforatum and Echinacea purpurea under Mediterranean environmental conditions. CO2 fertilization shows interesting perspectives to increase and improve horticultural techniques in order to increase plant medicinal productivity, in spite of clear differences among the species. In general this technique promotes important and significant increases in primary productivity and, in some cases, also in secondary compounds. This has a great horticultural relevance because the total productivity of this kind of products increase at crop level, directly because concentration is increased and /or indirectly because biomass is increased. RESUM L'augment del CO2 atmosfèric a causa del canvi global i/o a les pràctiques hortícoles promou efectes directes sobre creixement vegetal i el desenvolupament. Aquestes respostes poden ocórrer en ecosistemes naturals, però també es poden utilitzar per a augmentar la producció d'algunes plantes i d'alguns compostos secundaris. L'actual treball intenta estudiar els efectes de l'enriquiment atmosfèric del CO2 sota condicions d'hivernacle en el creixement i la concentració i la composició de metabòlits secundaris de Taxus bacatta, Hypericum perforatum i Echinacea purpurea en condicions ambientals mediterrànies. La fertilització del CO2 mostra perspectives interessants per a la millora i aplicabilitat de tècniques hortícoles per a augmentar productivitat de plantes medicinals, a pesar de diferències clares entre l'espècie. En general aquesta tècnica promou augments importants i significatius en producció primària i, en alguns casos, també en compostos secundaris. Això té una gran importància hortícola perquè la productivitat a nivell de collita total augmenta, directament perquè s'augmenta la concentració i indirectament perquè s'augmenta la biomassa.