Some fragments of second-order logic over the reals for which satisfiability and equivalence are (un)decidable

We consider the Σ1 0-fragment of second-order logic over the vocabulary h+, ×, 0, 1, <, S1, ..., Ski, interpreted over the reals, where the predicate symbols Si are interpreted as semi-algebraic sets. We show that, in this context, satisfiability of formulas is decidable for the first-order ∃ ∗ - quantifier fragment and undecidable for the ∃ ∗∀- and ∀ ∗ -fragments. We also show that for these three fragments the same (un)decidability results hold for containment and equivalence of formulas.Fil: Grimson, Rafael. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Kuijpers, Bart. Hasselt University; Bélgic

Magneto-Electric Effect for Multiferroic Thin Film by Monte Carlo Simulation

Magneto-electric effect in a multiferroic heterostructure film, i.e. a coupled ferromagnetic-ferroelectric thin film, has been investigated through the use of the Metropolis algorithm in Monte Carlo simulations. A classical Heisenberg model describes the energy stored in the ferromagnetic film, and we use a pseudo-spin model with a transverse Ising Hamiltonian to characterise the energy of electric dipoles in the ferroelectric film. The purpose of this article is to demonstrate the dynamic response of polarisation is driven by an external magnetic field, when there is a linear magneto-electric coupling at the interface between the ferromagnetic and ferroelectric components.Comment: 5 pages, 8 figures, The 3rd Advanced Electromagnetics Symposium, Citation: Eur. Phys. J. Appl. Phys., Volume 70, Number 3, (2015

Evaluating geometric queries using few arithmetic operations

Let \cp:=(P_1,...,P_s) be a given family of $n$-variate polynomials with integer coefficients and suppose that the degrees and logarithmic heights of these polynomials are bounded by $d$ and $h$, respectively. Suppose furthermore that for each $1\leq i\leq s$ the polynomial $P_i$ can be evaluated using $L$ arithmetic operations (additions, subtractions, multiplications and the constants 0 and 1). Assume that the family \cp is in a suitable sense \emph{generic}. We construct a database $\cal D$, supported by an algebraic computation tree, such that for each $x\in [0,1]^n$ the query for the signs of $P_1(x),...,P_s(x)$ can be answered using h d^{\cO(n^2)} comparisons and $nL$ arithmetic operations between real numbers. The arithmetic-geometric tools developed for the construction of $\cal D$ are then employed to exhibit example classes of systems of $n$ polynomial equations in $n$ unknowns whose consistency may be checked using only few arithmetic operations, admitting however an exponential number of comparisons

Letter from Langer to G. Grimson Regarding D**-Stepp Case

Letter from Attorney General to G. Grimson saying that, given both Judge Kneeshaw\u27s and Grimson\u27s satisfaction with the way the case was handled, and in view of the statements of Mrs. D** and her daughter, he knows of nothing he can do for them and views the case terminated. See also: 1100, 1141https://commons.und.edu/langer-papers/1105/thumbnail.jp

CD ROMs at the University of Wollongong: a case study

The University of Wollongong Library purchased 21 bibliographic databases on CD-ROM during 1988, 1989 and 1990 covering the disciplines of business, psychology, medicine, geography, sociology, education, science, nursing, engineering, mathematics and occupational health and safety. The databases are available for use by all students and staff, and their use is continuing to be evaluated. The introduction of the CD··ROM service has had significant implications for library users and staff, e. g . the number of online searches has reduced, the use of serial literature has increased, the use of hard copy indexes has changed and staff involvement in the training of how to use the databases has been unexpectedly high. In order to more formally evaluate the service, student and staff use of the databases was surveyed during early 1990. This paper will focus on the findings of the survey, presenting recommendations for the continued use of the CD-ROM databases