Algebraic models defined over Q of differential manifolds

Here we prove that every compact differential manifold has a smooth algebraic model defined over Q. In dimension 2 we find an algebraic model (may be singular) defined over Q and birational over Q to the projective plane.     

Well posed cauchy problems for complex nonlinear equations must be semilinear

The first author was supported in part by CNPq     

On the Behaviour of the First Eigenfunction of the p-Laplacian Near its Critical Points

In this paper, the behaviour of the positive eigenfunction of in u_| = 0, p > 1, isstudied near its critical points. Under some convexity and symmetryassumptions on , is seen to have a unique critical point atx = 0; also, the behaviour of both and is determined nearby.Positive solutions u to some general problems –_pu = f(u)in , u_| = 0, are also considered, with some convexity restrictionson u. 2000 Mathematics Subject Classification 35B05 (primary),35J65, 35J70 (secondary).     

Ordinary differential operators in Hilbert spaces and Fredholm pairs

Let be a path of bounded operators on a real Hilbert space, hyperbolic at . We study the Fredholm theory of the operator . We relate the Fredholm property of to the stable and unstable linear spaces of the associated system . Several examples are included to point out the differences with respect to the finite dimensional case, in particular concerning the role of the spectral flow. We define a general class of paths A for which many properties typical of the finite dimensional framework still hold. Our motivation is to develop the linear theory which is necessary for the set-up of Morse homology on Hilbert manifolds. Received: 9 March 2001; in final form: 1 March 2002 / Published online: 2 December 2002     

Intra- and intersubject variability in acoustic measures of normal voice

Twenty-four normal adult women read part of the Rainbow Passage and sustained vowels three trials each. Utterances were assessed for selected parameters measured by Visi-Pitch (average and SD of fundamental frequency (F₀), average and SD of dBA, perturbation, and percent voiced/unvoiced/pause). Assessment of each parameter included measures of central tendency, dispersion, and distribution characteristics (skewness and kurtosis) of the data and of the ranges of values that would include 95% of the scores (95% fiduciary limits). Generally, differences for the group between the three trials were not significant. Intersubject variability for only a few parameters was less than 20% of the parameter's mean. For vowels, variability of jitter was 30–48% of the mean. Eight subjects provided performances 2 months later to obtain an estimate of intrasubject variability over time. There were desirable intrasubject correlations between performances for mean F₀, jitter in reading and on vowels /i/ and /a/, and percent of voicing. Inter- and intrasubject variability seems restricted and the data appear to resemble a normally distributed function for mean F₀ on reading, jitter on /i/, and percent of voicing. Thus, these parameters may have statistical merit for use in vocal testing.     

Initial data truncation for multivariate output of discrete-event simulations using the Kalman filter

Data truncation is a commonly accepted method of dealing with initialization bias in discrete-event simulation. An algorithm for determining the appropriate initial-data truncation point for multivariate output is proposed. The technique entails averaging across independent replications and estimating a steady-state output model in a state-space framework. A Bayesian technique called Multiple Model Adaptive Estimation (MMAE) is applied to compute a time varying estimate of the output's steady-state mean vector. This MMAE implementation features the use, in paralle, of a bank of Kalman filters. Each filter is constructed under a different assumption concerning the output's steady-state mean vector. One of the filters assumes that the steady-state mean vector is accurately reflected by an estimate, called the assumed steady-state mean vector, taken from the last half of the simulation data. As the filters process the output through the effective transient, this particular filter becomes more likely (in a Bayesian sense) to be the best filter to represent the data and the MMAE mean estimator is influenced increasingly towards the assumed steady-state mean vector. The estimated truncation point is selected when a norm of the MMAE mean vector estimate is within a small tolerance of the assumed steady-state mean vector. A Monte Carlo analysis using data from simulations of open and closed queueing models is used to evaluate the technique. The evaluation criteria include the ability to construct accurate and reliable confidence regions for the mean response vector based on the truncated sequences.     

Light on light: A response to Grøn

Einstein's second postulate (light-speed constancy) is modified in the following manner:(1) as to motion of light emitters, no modification is made;(2) as to motion of light absorbers, if the absorber moves with velocityv with respect to the observer, that observer will attribute to light the velocity (c+v). It is shown, with reference to the original Einstein train example, that such a modification of the second postulate restores to kinematics a concept of distant simultaneity. Thus is indicated the complicated (acausal) behavior that must be attributed to light in order that the simple behavior earlier attributed ⁽¹⁾ to matter (nonoccurrence of the Lorentz contraction) may be consistent with all known facts. A reply is made to Grøn's critique ⁽²⁾ of the earlier paper on metric standards. It is concluded that further experimental data are needed to decide the simple-light-complicated-matter versus complicated-light-simple-matter issue.