Ricardian Equivalence revisited: introductory notes

ABSTRACT These notes aim to revisit the debate, the model, the results, and main objections to the validity of the Ricardian Equivalence Theorem as presented in Barro (1974). It is intended to explore his thesis that tax and debt are equivalent and have no real effect on perceived wealth, demand, the real interest rate or on the economy. The thesis refers to the analysis of the ways of financing debt at a given level of government expenditure and does not address the effects of an expansion of this volume of spending, nor it specifically analyzes the effects of an increase in public debt due to a tax reduction policy. After this presentation, the thesis is debated, consolidating some of the premises that are necessary to validate it. The purpose of the paper is to explore the first round of debates on the theme, explaining the restrictions to which the Barro-Ricardo Theorem or the Ricardian Equivalence Theorem is subject, based on the publications by Barro (1976), Buchanan (1976) and Feldstein (1976), all of them within the ‘realm’ of economic orthodoxy. The final section presents some remarks and an analysis of Barro’s later work (1989 and 1996).

Thermodynamics of galaxy clusters in modified Newtonian potential

We study the thermodynamics of galaxy clusters in a modified Newtonian potential motivated by a general solution to Newton’s “sphere-point” equivalence theorem. We obtain the N particle partition function by evaluating the configurational integral while accounting for the extended nature of galaxies (via the inclusion of the softening parameter ε into the potential energy function). This softening parameter takes care of the galaxy-halos whose effect on structuring the shape of the galactic disc has been found recently. The spatial distribution of the particles (galaxies) is also studied in this framework. A comparison of the new clustering parameter b + to the original clustering parameters is presented in order to visualize the effect of the modified gravity. We also discuss the possibility of system symmetry breaking via the behavior of the specific heat as a function of temperature.

Basic Bidding Formats: Characteristics and Differences

In standard auction theory, the ‘revenue equivalence theorem’ asserts that the outcomes of the elementary allocation methods coincide. However, bidding processes differ fundamentally with regard to the decision situation of the participants: Is it at all imperative to take into consideration the number of competitors (‘stochastic’ strategy) or not (‘deterministic’ course of action)? Furthermore, established auction theory neglects the operating modes of procurement alternatives under uncertainty. Apart from the lacking knowledge how many rivals have to be beaten, tenderers regularly are ignorant of the buyer’s reserve price. Then it is even more tentative to calculate an offer based on probability theory. Consequently, the suppliers’ propensity to collude increases.

The Abelian Higgs model under a gauge invariant looking glass: exploiting new Ward identities for gauge invariant operators and the Equivalence Theorem

The content of two additional Ward identities exhibited by the U(1) Higgs model is exploited. These novel Ward identities can be derived only when a pair of local composite operators providing a gauge invariant setup for the Higgs particle and the massive vector boson is introduced in the theory from the beginning. Among the results obtained from the above mentioned Ward identities, we underline a new exact relationship between the stationary condition for the vacuum energy, the vanishing of the tadpoles and the vacuum expectation value of the gauge invariant scalar operator. We also present a characterization of the two-point correlation function of the composite operator corresponding to the vector boson in terms of the two-point function of the elementary gauge fields. Finally, a discussion on the connection between the cartesian and the polar parametrization of the complex scalar field is presented in the light of the Equivalence Theorem. The latter can in the current case be understood in the language of a constrained cohomology, which also allows to rewrite the action in terms of the aforementioned gauge invariant operators. We also comment on the diminished role of the global U(1) symmetry and its breaking.

Generalization of the Lax–Ryabenky–Philippov theorem to nonlinear problems

In this paper, Lax’s equivalence theorem, which states that stability is a necessary and sufficient condition for its convergence in the presence of an approximation of a difference scheme, is generalized to abstract nonlinear difference problems with operators acting in finite dimensional Banach spaces. In contrast to linear finite-difference methods, such a criterion in the nonlinear case can be established only for unconditionally stable computational methods, when the corresponding a priori estimates take place for sufficiently small |h| ≤ h0. In this case, the value of h0 depends both on the consistency of discrete and continuous norms in Banach spaces, and on the magnitude of the perturbation of the input data of the problem. The proven convergence criterion is used to study the stability of difference schemes approximating quasilinear parabolic equations with nonlinearities of unbounded growth with respect to the initial data.

A Single-shot Field Measurement Procedure for Radiated Emissions using Equivalent Surface Dipoles

The new generation of communication devices operating in higher frequency bands is constantly pushing the complexity of field measurements for electromagnetic compliance and the design of field probes. These compliance are to be met for both electric and magnetic fields which demands repeating the same measurement procedure using different probes. The main objective of this paper is to provide a procedure which provides both fields in a single shot measurement using a single probe based on source reconstruction algorithm. The algorithm is based on a novel way of placing single dipole per point tangentially to a fictitious surface based on surface equivalence theorem instead of three orthogonal dipoles per point in earlier works. The control of overall accuracy by varying dipole and measurement point density is also demonstrated. We also prove the existence, uniqueness and the error bounds involved in the inverse problem rigorously. The numerical results corroborates the effectiveness of the proposed procedure in obtaining accurate fields and also locating the regions of the Device Under Test responsible for overshooting the interference limits.

A Single-shot Field Measurement Procedure for Radiated Emissions using Equivalent Surface Dipoles

The new generation of communication devices operating in higher frequency bands is constantly pushing the complexity of field measurements for electromagnetic compliance and the design of field probes. These compliance are to be met for both electric and magnetic fields which demands repeating the same measurement procedure using different probes. The main objective of this paper is to provide a procedure which provides both fields in a single shot measurement using a single probe based on source reconstruction algorithm. The algorithm is based on a novel way of placing single dipole per point tangentially to a fictitious surface based on surface equivalence theorem instead of three orthogonal dipoles per point in earlier works. The control of overall accuracy by varying dipole and measurement point density is also demonstrated. We also prove the existence, uniqueness and the error bounds involved in the inverse problem rigorously. The numerical results corroborates the effectiveness of the proposed procedure in obtaining accurate fields and also locating the regions of the Device Under Test responsible for overshooting the interference limits.