Counting Solutions to Binomial Complete Intersections

We study the problem of counting the total number of affine solutions of a system of n binomials in n variables over an algebraically closed field of characteristic zero. We show that we may decide in polynomial time if that number is finite. We give a combinatorial formula for computing the total number of affine solutions (with or without multiplicity) from which we deduce that this counting problem is #P-complete. We discuss special cases in which this formula may be computed in polynomial time; in particular, this is true for generic exponent vectors.Comment: Several minor improvements. Final version to appear in the J. of Complexit

Multi--hump soliton--like structures in interactions of lasers and Bose--Einstein condensates

An investigation is made of multi-hump and periodic solutions of the semi-classical coupled equations describing laser radiation copropagating with a Bose-Einstein condensate. Solutions reminiscent of optical vector solitons have been found and have been used to gain understanding of the dynamics observed in the numerical simulations, in particular to shed light on the phenomenon of jet emission from a condensate interacting with a laser.Comment: 6 pages, 4 figures; submitted to European Physics Letter

Two-surface wave decay: improved analytical theory and effects on electron acceleration

Two-surface wave decay (TSWD), i.e. the parametric excitation of electron surface waves, was recently proposed as an absorption mechanism in the interaction of ultrashort, intense laser pulses with solid targets. We present an extension of the fluid theory of TSWD to a warm plasma which treats boundary effects consistently. We also present test-particle simulations showing localized enhancement of electron acceleration by TSWD fields; this effect leads to a modulation of the current density entering into the target and may seed current filamentation instabilities.Comment: 4 figures, submitted to Appl.Phys.B (special issue from HFSW X conference, Biarritz, France, Oct 12-15 2003); slightly revised tex

Communicative and linguistic development in preterm children: a longitudinal study from 12 to 24 months.

BACKGROUND: Research conducted on preterm children's linguistic skills has provided varying pictures, and the question of whether and to what extent preterm children are delayed in early language acquisition remains largely unresolved. AIMS: To examine communicative and linguistic development during the second year in a group of Italian children born prematurely using the 'Primo Vocabolario del Bambino' (PVB), the Italian version of the MacArthur-Bates Communicative Development Inventory. The primary goal was to compare action/gesture production, word comprehension, and word production, and the relationship between these three domains in preterm children and to normative data obtained from a large sample of Italian children born at term. A second aim was to address the longstanding debate regarding the use of chronological versus corrected gestational age in the assessment of preterm children's abilities. METHODS & PROCEDURES: Parents of twelve preterm children completed the PVB questionnaire at five age points during the children's second year, and scores were compared with those from a normative sample of full-term children and those of 59 full-term children selected as a control group from the normative sample for the PVB. OUTCOMES & RESULTS: Preterm children exhibited a delay in all three aspects of communication and language. In particular, communicative-linguistic age tended to lag approximately 3 months behind chronological age when children were between the ages of 12 and 24 months. When chronological age was used, preterm children's percentile scores for all three components of communication and language fell within the lower limits of the normal range, while scores calculated using corrected age either fell at or above the 50th percentile. CONCLUSIONS & IMPLICATIONS: Findings suggest that despite the significant biological risk engendered by premature birth, early communicative and linguistic development appears to proceed in a relatively robust fashion among preterm children, with tight relations across communicative domains as in full-term children. Employing both chronological and corrected gestational age criteria in the evaluation of preterm children's abilities may provide important information about their progress in language acquisition. This may be especially important during the initial stages of communicative and linguistic development, inasmuch as comparisons of the two sets of scores may provide clinicians with a way to distinguish children who may be at risk for language problems from those who may be expected to progress normally

On the discrete harmonic wavelet transform

The discrete harmonic wavelet transform has been reviewed and applied towards given functions. The absolute error of reconstruction of the functions has been computed

Gravitational Waves from Wobbling Pulsars

The prospects for detection of gravitational waves from precessing pulsars have been considered by constructing fully relativistic rotating neutron star models and evaluating the expected wave amplitude $h$ from a galactic source. For a "typical" neutron matter equation of state and observed rotation rates, it is shown that moderate wobble angles may render an observable signal from a nearby source once the present generation of interferometric antennas becomes operative.Comment: PlainTex, 7 pp. , no figures, IAG/USP Rep. 6

On a mathematical model of immune competition

AbstractThis work deals with the qualitative analysis of a nonlinear integro-differential model of immune competition with special attention to the dynamics of tumor cells contrasted by the immune system. The analysis gives evidence of how initial conditions and parameters influence the asymptotic behavior of the solutions

On a Mathematical Model of Immune Competition

This work deals with the qualitative analysis of a nonlinear integro-differential model of immune competition with special attention to the dynamics of tumor cells contrasted by the immune system. The analysis gives evidence of how initial conditions and parameters influence the asymptotic behavior of the solutions