A Posteriori analysis of discontinuous Galerkin schemes for systems of hyperbolic conservation laws

In this work we construct reliable a posteriori estimates for some semi- (spatially) discrete discontinuous Galerkin schemes applied to nonlinear systems of hyperbolic conservation laws. We make use of appropriate reconstructions of the discrete solution together with the relative entropy stability framework, which leads to error control in the case of smooth solutions. The methodology we use is quite general and allows for a posteriori control of discontinuous Galerkin schemes with standard flux choices which appear in the approximation of conservation laws. In addition to the analysis, we conduct some numerical benchmarking to test the robustness of the resultant estimator.

On aposteriori error analysis of dG schemes approximating hyperbolic conservation laws

This contribution is concerned with aposteriori error analysis of discontinuous Galerkin (dG) schemes approximating hyperbolic conservation laws. In the scalar case the aposteriori analysis is based on the L1 contraction property and the doubling of variables technique. In the system case the appropriate stability framework is in L2, based on relative entropies. It is only applicable if one of the solutions, which are compared to each other, is Lipschitz. For dG schemes approximating hyperbolic conservation laws neither the entropy solution nor the numerical solution need to be Lipschitz. We explain how this obstacle can be overcome using a reconstruction approach which leads to an aposteriori error estimate.

Do laws influence the cost of real estate brokerage services? A state fixed effects approach

A FTC-DOJ study argues that state laws and regulations may inhibit the unbundling of real estate brokerage services in response to new technology. Our data show that 18 states have changed laws in ways that promote unbundling since 2000. We model brokerage costs as measured by number of agents in a state-level annual panel vector autoregressive framework, a novel way of analyzing wasteful competition. Our findings support a positive relationship between brokerage costs and lagged house price and transactions. We find that change in full-service brokers responds negatively (by well over two percentage points per year) to legal changes facilitating unbundling

Transmathematical basis of infinitely scalable pipeline machines

We describe infinitely scalable pipeline machines with perfect parallelism, in the sense that every instruction of an inline program is executed, on successive data, on every clock tick. Programs with shared data effectively execute in less than a clock tick. We show that pipeline machines are faster than single or multi-core, von Neumann machines for sufficiently many program runs of a sufficiently time consuming program. Our pipeline machines exploit the totality of transreal arithmetic and the known waiting time of statically compiled programs to deliver the interesting property that they need no hardware or software exception handling.

Family-friendly employment laws (re)assessed: the potential of care ethics

In light of various reforms in recent years, this article provides a (re)assessment of the broad package of family-friendly employment rights and relevant dispute resolution procedure now available to pregnant workers and working carers. It exposes how the realities of working life for many pregnant workers and carers and the long standing desire to promote gender equality in informal care-work remain at odds with the legal framework. An argument is presented in favour of an approach that, based upon the concept of care ethics, better engages with the impact of the provisions upon crucial interdependent care relationships.

Soluble one-dimensional particle conservation models with infinitely many absorbing states

Particle conservation lattice-gas models with infinitely many absorbing states are studied on a one-dimensional lattice. As one increases the particle density, they exhibit a phase transition from an absorbing to an active phase. The models are solved exactly by the use of the transfer matrix technique from which the critical behavior was obtained. We have found that the exponent related to the order parameter, the density of active sites, is 1 for all studied models except one of them with exponent 2.

Conservation laws and tachyon potentials in the sliver frame

Conservation laws have provided an elegant and efficient tool to evaluate the open string field theory interaction vertex, they have been originally implemented in the case where the string field is expanded in the Virasoro basis. In this work we derive conservation laws in the case where the string field is expanded in the so-called sliver L(0)-basis. As an application of this new set of conservation laws, we compute the open string field action relevant to the tachyon condensation and in order to present not only an illustration but also an additional information, we evaluate the action without imposing a gauge choice.

ENO adaptive method for solving one-dimensional conservation laws

In this work an efficient third order non-linear finite difference scheme for solving adaptively hyperbolic systems of one-dimensional conservation laws is developed. The method is based oil applying to the solution of the differential equation an interpolating wavelet transform at each time step, generating a multilevel representation for the solution, which is thresholded and a sparse point representation is generated. The numerical fluxes obtained by a Lax-Friedrichs flux splitting are evaluated oil the sparse grid by an essentially non-oscillatory (ENO) approximation, which chooses the locally smoothest stencil among all the possibilities for each point of the sparse grid. The time evolution of the differential operator is done on this sparse representation by a total variation diminishing (TVD) Runge-Kutta method. Four classical examples of initial value problems for the Euler equations of gas dynamics are accurately solved and their sparse solutions are analyzed with respect to the threshold parameters, confirming the efficiency of the wavelet transform as an adaptive grid generation technique. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.

Equilibrium theory with asymmetric information and infinitely many states

Radner (1968) proved the existence of a competitive equilibrium for differential information economies with finitely many states. We extend this result to economies with infinitely many states of nature.

Disputing the application of laws: the constitutionality of the Brazilian Statute against domestic violence in the courts

This study aimed to map the key positions regarding the constitutionality of the Maria da Penha Law (Law 11.340/2006) in the Brazilian judicial system. The law, the result of political struggles by the Brazilian feminist movement, has been the subject of discussions in the public sphere and actions aimed at consolidating its constitutionality before the Federal Supreme Court. We examined and discussed the arguments used in the Courts, intending to show that the creation of law is not limited to the legislative moment, but rather that its social meaning is also constituted through disputes within the Judiciary.

A metafísica de Isaac Newton

The general objective of this dissertation is to analyze the metaphysical aspects of "rational mechanics" of Isaac Newton, clarifying, by scientific and philosophical discourse, their main elements, with emphasis to the presence of one entity infinitely rational behind all the phenomena of nature, and to the Newton's insight as certain empiricist which, however, accepts deductions metaphysics; a philosopher-scientist. The specific objectives are detailed below: a) brief presentation of the development of modern science, since the Pre-Socratics, seeking to understand the historical conjecture that enabled the rise of Newtonian mechanics; b) presentation of the elements of scientific methodology and philosophical, aimed at comprehension of certain "Newtonian methodology", understanding how this specific methodology able to present empirical aspects, mathematics, philosophic and religious in communion; c) to understand, from the Newtonian concepts, both concerning man's role in the world as the "notional notions" of mass, space, time and movement, necessary for analysis and understanding of certain metaphysical aspects in the Newtonian physics; d) to present the Newtonian concepts related to the ether, to understand why it necessarily assumes metaphysics characteristics and mediation between the bodies; e) to present and understand the factors that lead the empiricist Newton to assume the religion in his mechanics, as well as, the existence and functions of God in nature, to object to the higher content of his metaphysics; f) to highlight the metaphysical elements of his classical mechanics, that confirm the presence of concepts like God Creator and Preserver of the natural laws; g) at last, to analyze the importance of Newton to the modern metaphysics and the legacy to philosophy of science at sec. XVII to science contemporary