An irreducibility criterion for group representations, with arithmetic applications

We prove a criterion for the irreducibility of an integral group representation p over the fraction field of a noetherian domain R in terms of suitably defined reductions of p at prime ideals of R. As applications, we give irreducibility results for universal deformations of residual representations, with a special attention to universal deformations of residual Galois representations associated with modular forms of weight at least 2.

The mapping of the local contributions of Fermi and Coulomb correlation into intracule and extracule density distributions

The contributions of the correlated and uncorrelated components of the electron-pair density to atomic and molecular intracule I(r) and extracule E(R) densities and its Laplacian functions ∇2I(r) and ∇2E(R) are analyzed at the Hartree-Fock (HF) and configuration interaction (CI) levels of theory. The topologies of the uncorrelated components of these functions can be rationalized in terms of the corresponding one-electron densities. In contrast, by analyzing the correlated components of I(r) and E(R), namely, IC(r) and EC(R), the effect of electron Fermi and Coulomb correlation can be assessed at the HF and CI levels of theory. Moreover, the contribution of Coulomb correlation can be isolated by means of difference maps between IC(r) and EC(R) distributions calculated at the two levels of theory. As application examples, the He, Ne, and Ar atomic series, the C2-2, N2, O2+2 molecular series, and the C2H4 molecule have been investigated. For these atoms and molecules, it is found that Fermi correlation accounts for the main characteristics of IC(r) and EC(R), with Coulomb correlation increasing slightly the locality of these functions at the CI level of theory. Furthermore, IC(r), EC(R), and the associated Laplacian functions, reveal the short-ranged nature and high isotropy of Fermi and Coulomb correlation in atoms and molecules

Second differential of the entropy as a criterion for the stability in low-dimensional climate models

The second differential of the entropy is used for analysing the stability of a thermodynamic climatic model. A delay time for the heat flux is introduced whereby it becomes an independent variable. Two different expressions for the second differential of the entropy are used: one follows classical irreversible thermodynamics theory; the second is related to the introduction of response time and is due to the extended irreversible thermodynamics theory. the second differential of the classical entropy leads to unstable solutions for high values of delay times. the extended expression always implies stable states for an ice-free earth. When the ice-albedo feedback is included, a discontinuous distribution of stable states is found for high response times. Following the thermodynamic analysis of the model, the maximum rates of entropy production at the steady state are obtained. A latitudinally isothermal earth produces the extremum in global entropy production. the material contribution to entropy production (by which we mean the production of entropy by material transport of heat) is a maximum when the latitudinal distribution of temperatures becomes less homogeneous than present values

Semiclassical theory of shot noise in ballistic n+in+ semiconductor structures: relevance of Pauli and long range Coulomb interactions

We work out a semiclassical theory of shot noise in ballistic n+-i-n+ semiconductor structures aiming at studying two fundamental physical correlations coming from Pauli exclusion principle and long-range Coulomb interaction. The theory provides a unifying scheme which, in addition to the current-voltage characteristics, describes the suppression of shot noise due to Pauli and Coulomb correlations in the whole range of system parameters and applied bias. The whole scenario is summarized by a phase diagram in the plane of two dimensionless variables related to the sample length and contact chemical potential. Here different regions of physical interest can be identified where only Coulomb or only Pauli correlations are active, or where both are present with different relevance. The predictions of the theory are proven to be fully corroborated by Monte Carlo simulations.

The role of energy correlations on Coulomb suppression in ballistic conductors contacted to degenerate reservoirs

Coulomb suppression of shot noise in a ballistic diode connected to degenerate ideal contacts is analyzed in terms of the correlations taking place between current fluctuations due to carriers injected with different energies. By using Monte Carlo simulations we show that at low frequencies the origin of Coulomb suppression can be traced back to the negative correlations existing between electrons injected with an energy close to that of the potential barrier present in the diode active region and all other carriers injected with higher energies. Correlations between electrons with energy above the potential barrier with the rest of electrons are found to influence significantly the spectra at high frequency in the cutoff region.

A measure of stability as a criterion for the verification and analysis of simulation models

The aim of this study is to define a new statistic, PVL, based on the relative distance between the likelihood associated with the simulation replications and the likelihood of the conceptual model. Our results coming from several simulation experiments of a clinical trial show that the PVL statistic range can be a good measure of stability to establish when a computational model verifies the underlying conceptual model. PVL improves also the analysis of simulation replications because only one statistic is associated with all the simulation replications. As well it presents several verification scenarios, obtained by altering the simulation model, that show the usefulness of PVL. Further simulation experiments suggest that a 0 to 20 % range may define adequate limits for the verification problem, if considered from the viewpoint of an equivalence test.

Effect of long-range Coulomb interaction on shot-noise suppression in ballistic transport

We present a microscopic analysis of shot-noise suppression due to long-range Coulomb interaction in semiconductor devices under ballistic transport conditions. An ensemble Monte Carlo simulator self-consistently coupled with a Poisson solver is used for the calculations. A wide range of injection-rate densities leading to different degrees of suppression is investigated. A sharp tendency of noise suppression at increasing injection densities is found to scale with a dimensionless Debye length related to the importance of space-charge effects in the structure.

Theory of surface noise under Coulomb correlations between carriers and surface states

We present a theory of the surface noise in a nonhomogeneous conductive channel adjacent to an insulating layer. The theory is based on the Langevin approach which accounts for the microscopic sources of fluctuations originated from trapping¿detrapping processes at the interface and intrachannel electron scattering. The general formulas for the fluctuations of the electron concentration, electric field as well as the current-noise spectral density have been derived. We show that due to the self-consistent electrostatic interaction, the current noise originating from different regions of the conductive channel appears to be spatially correlated on the length scale correspondent to the Debye screening length in the channel. The expression for the Hooge parameter for 1/f noise, modified by the presence of Coulomb interactions, has been derived

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.

Self-selection consistent functions

This paper studies collective choice rules whose outcomes consist of a collection of simultaneous decisions, each one of which is the only concern of some group of individuals in society. The need for such rules arises in different contexts, including the establishment of jurisdictions, the location of multiple public facilities, or the election of representative committees. We define a notion of allocation consistency requiring that each partial aspect of the global decision taken by society as a whole should be ratified by the group of agents who are directly concerned with this particular aspect. We investigate the possibility of designing envy-free allocation consistent rules, we also explore whether such rules may also respect the Condorcet criterion.

Freedom of choice as control over outcomes

As interactions between individuals are introduced into the freedom of choice literature by the mean of game forms, new issues appear. In particular, in this paper it is argued that individuals face uncertainty with respect to outcomes as they lose the control they implicitely exert over options in the opportunity set framework. A criterion is proposed as to compare alternative game forms in terms of the control they offer to individuals. The CardMin criterion suggests that any game form should be judged on the basis of the strategy offering the lowest number of pairwise different outcomes. An axiomatic characterization is provided in the case of two individuals.