Herbrand's Theorem and Equational Reasoning: Problems and Solutions

The famous Herbrand's theorem of mathematical logic plays an important role in automated theorem proving. In the first part of this article, we recall the theorem and formulate a number of natural decision problems related to it. Somewhat surprisingly, these problems happen to be equivalent. One of these problems is the so-called simultaneous rigid E-unification problem. In the second part, we survey recent result on the simultaneous rigid E-unification problem.

Central limit theorem for asymmetric kernel functionals

Asymmetric kernels are quite useful for the estimation of density functions with bounded support. Gamma kernels are designed to handle density functions whose supports are bounded from one end only, whereas beta kernels are particularly convenient for the estimation of density functions with compact support. These asymmetric kernels are nonnegative and free of boundary bias. Moreover, their shape varies according to the location of the data point, thus also changing the amount of smoothing. This paper applies the central limit theorem for degenerate U-statistics to compute the limiting distribution of a class of asymmetric kernel functionals.

A note on an application of Arrow's theorem: sufficient conditions for Lucas' inflation and welfare

Bellman's methods for dynamic optimization constitute the present mainstream in economics. However, some results associated with optimal controI can be particularly usefuI in certain problems. The purpose of this note is presenting such an example. The value function derived in Lucas' (2000) shopping-time economy in Infiation and Welfare need not be concave, leading this author to develop numerical analyses to determine if consumer utility is in fact maximized along the balanced path constructed from the first order conditions. We use Arrow's generalization of Mangasarian's results in optimal control theory and develop sufficient conditions for the problem. The analytical conclusions and the previous numerical results are compatible .

On the Impossibility of an Exact Imperfect Monitoring Folk Theorem

It is shown that, for almost every two-player game with imperfect monitoring, the conclusions of the classical folk theorem are false. So, even though these games admit a well-known approximate folk theorem, an exact folk theorem may only be obtained for a measure zero set of games. A complete characterization of the efficient equilibria of almost every such game is also given, along with an inefficiency result on the imperfect monitoring prisoner s dilemma.

Modulação quantizada para sistemas com codificação wavelet sujeitos ao desvanecimento rayleigh

Wavelet coding is an efficient technique to overcome the multipath fading effects, which are characterized by fluctuations in the intensity of the transmitted signals over wireless channels. Since the wavelet symbols are non-equiprobable, modulation schemes play a significant role in the overall performance of wavelet systems. Thus the development of an efficient design method is crucial to obtain modulation schemes suitable for wavelet systems, principally when these systems employ wavelet encoding matrixes of great dimensions. In this work, it is proposed a design methodology to obtain sub-optimum modulation schemes for wavelet systems over Rayleigh fading channels. In this context, novels signal constellations and quantization schemes are obtained via genetic algorithm and mathematical tools. Numerical results obtained from simulations show that the wavelet-coded systems derived here have very good performance characteristics over fading channels

On the zeros of polynomials: An extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier B.V. All rights reserved.

Stabilizing a class of time delay systems using the Hermite-Biehler theorem

In this paper we use the Hermite-Biehler theorem to establish results for the design of fixed order controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. (C) 2003 Elsevier B.V. All rights reserved.

An existence theorem for an analytic first order PDE in the framework of Colombeau's theory

We study the existence of a holomorphic generalized solution u of the PDE[GRAPHICS]where f is a given holomorphic generalized function and (alpha (1),...alpha (m)) is an element of C-m\{0}.

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Finiteness theorem for topological contact equivalence of map germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

RITZ ANALYSIS OF THE FOURIER SPECTRUM OF CH3OH BETWEEN 350 AND 950 CM(-1)

A new ''Ritz'' program has been used for revising and expanding the assignment of the Fourier transform infrared and far-infrared spectrum of CH3OH. This program evaluates the energy levels involved in the assigned transitions by the Rydberg-Ritz combination principle and can tackle such perturbations as Fermi-type resonances or Coriolis interactions. Up to now this program has evaluated the energies of 2768 levels belonging to A-type symmetry and 4133 levels belonging to E-type symmetry of CH3OH. Here we present the assignment of almost 9600 lines between 350 and 950 cm(-1). The Taylor expansion coefficients for evaluating the energies of the levels involved in the transitions are also given. All of the lines presented in this paper correspond to transitions involving torsionally excited levels within the ground vibrational state. (C) 1995 Academic Press, Inc.

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).