A homological version of the implicit function theorem

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.

Effect of continuous and pulsed therapeutic ultrasound in the appearance of local recurrence of mammary cancer in rats

Purpose: Ultrasound (US) therapy is an elect rot hermotherapeutic modality that uses US energy to provoke physical and chemical alterations. US therapy has been widely used in physical therapy. However in clinical practice, it is contra-indicated in cancer patients due to the possibility of exacerbating tumor growth.Methods: Sixty-eight female Sprague-Dawley rats bred in UNIFAE vivarium were studied. At 50 days of age, 7, 12-dimetylbenz(a)anthracene (7, 12-DMBA) was administered to 35 rats by gastric gavage to induce mammary cancer After 90 days the mammary glands of the rats belonging to the group with mammary cancer induction and stimulated by US were removed. Animals received either continuous or pulsed US. US waves were generated at a frequency of 1 MHz during 10 days, with an intensity dose of 0.5 W in the continuous group, and 0.9 W (duty cycle: 20%) in the pulsed group.Results: Among the rats treated with continuous US, 44.4% developed local recurrence, while among the rats treated with pulsed US, 22.2% had local tumor recurrence (p < 0.05). No evidence of distant metastases was shown in any of the rats studied.Conclusion: The use ofcontinuous and pulsed therapeutic US promoted the development of local recurrence of mammary cancer in female Sprague-Dawley rats in the postoperative period.

The Noether theorem for geometric actions and area preserving diffeomorphisms on the torus

We find that within the formalism of coadjoint orbits of the infinite dimensional Lie group the Noether procedure leads, for a special class of transformations, to the constant of motion given by the fundamental group one-cocycle S. Use is made of the simplified formula giving the symplectic action in terms of S and the Maurer-Cartan one-form. The area preserving diffeomorphisms on the torus T2=S1⊗S1 constitute an algebra with central extension, given by the Floratos-Iliopoulos cocycle. We apply our general treatment based on the symplectic analysis of coadjoint orbits of Lie groups to write the symplectic action for this model and study its invariance. We find an interesting abelian symmetry structure of this non-linear problem.

Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfests theorem

The electron-diffraction pattern for two slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern that is asymmetric but has a symmetric envelope. In general, both the expected displacement and the kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless, Ehrenfests theorems and the conservation of momentum are satisfied. © 1992 The American Physical Society.

A refinement of the gauss-lucas theorem

The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial p lie in the convex hull H of the zeros of p. It is proved that, actually, a subdomain of H contains the critical points of p. ©1998 American Mathematical Society.

Invex nonsmooth alternative theorem and applications

An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion's approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

Reversible Hamiltonian Liapunov center theorem

We study the existence of periodic solutions in the neighbourhood of symmetric (partially) elliptic equilibria in purely reversible Hamiltonian vector fields. These are Hamiltonian vector fields with an involutory reversing symmetry R. We contrast the cases where R acts symplectically and anti-symplectically. In case R acts anti-symplectically, generically purely imaginary eigenvalues are isolated, and the equilibrium is contained in a local two-dimensional invariant manifold containing symmetric periodic solutions encircling the equilibrium point. In case R acts symplectically, generically purely imaginary eigenvalues are doubly degenerate, and the equilibrium is contained in two two-dimensional invariant manifolds containing nonsymmetric periodic solutions encircling the equilibrium point. In addition, there exists a three-dimensional invariant surface containing a two-parameter family of symmetric periodic solutions.

Secretion of middle ear in infants - Occurrence, recurrence and related factors

Objective: The present study aimed at evaluating the occurrence and recurrence of middle ear effusion and possible associated factors in the first two years of life of 190 newborns and infants, participants in the interdisciplinary prevention, detection, and intervention program at the Clínica de Educação para Saúde of Universidade do Sagrado Coração, Methods: Newborns and infants were monthly submitted to anamneses, otoscopy, behavioral hearing assessment using sound instruments and pure tones (pediatric audiometry) and tympanometry. Results: The results revealed that 68.4% of infants presented one or more episodes of middle ear effusion during their two first years, with more recurrence among males. Peak occurrence was between four and 12 months of age and, the earlier the first episode, the higher the probability of recurrence. Greatest incidence was during May and August. It was found that, of the variables investigated, the period of exclusive breastfeeding actuated as a protector factor. With respect of risk factors, it was observed that passive smoking, gastro-esophageal reflux and respiratory allergy were related with the recurrences of effusion. Conclusion: Findings revealed the importance of periodic auditory follow-up for infants during their first two years of life, considered to be the critical period of auditory system maturation, during which sensory deprivation can be responsible for damage to the development of speech, language and other auditory abilities. Copyright © 2005 by Sociedade Brasileira de Pediatria.

Investigation into the impact of embedded generators on distribution system performance using theorem of superposition

Since the 1980s, huge efforts have been made to utilise renewable energy sources to generate electric power. One of the interesting issues about embedded generators is the question of optimal placement and sizing of the embedded generators. This paper reports an investigation of impact of the integration of embedded generators on the overall performances of the distribution networks in the steady state, using theorem of superposition. Set of distribution system indices is proposed to observe performances of the distribution networks with embedded generators. Results obtained from the case study using IEEE test network are presented and discussed.

Transmission analysis of candidate genes for nonsyndromic oral clefts in Brazilian parent-child triads with recurrence

Cleft lip and/or palate (CL/P) is a major congenital defect with complex etiology, including multiple genetic and environmental factors. Approximately two thirds of the cases are not accompanied by other anomalies and are called nonsyndromic (NS). In the present study, we performed transmission distortion analysis of the MSX1-CA, TGFB3-CA and MTHFR-C677T polymorphisms in 60 parent-child triads, in which the NS-CL/ P affected child had at least one affected parent. No association with genes MSX1 or TGFB3 was found, but the results were suggestive of an association of the MTHFR-C677T polymorphism with NS-CL/P. © 2006 Sociedade Brasileira de Genética.

Liouville's theorem and power series for quaternionic functions

In recent years quaternionic functions have been an intense and prosperous object of research, and important results were determined [1]-[6]. Some of these results are similar to well known cases in one complex variable, op. cit. [5], [6]. In this paper the hypercomplex expansion of a function in a power series as well as determination of a Liouville's type theorem have been investigated to the quaternionic functions. In this case, it is observed that the Liouville's type theorem is true for second order derivatives, which differs from its classical version. © 2011 Academic Publications, Ltd.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

High dosage folic acid supplementation, oral cleft recurrence and fetal growth

Objectives: To evaluate the effects of folic acid supplementation on isolated oral cleft recurrence and fetal growth. Patients and Methods: The study included 2,508 women who were at-risk for oral cleft recurrence and randomized into two folic acid supplementation groups: 0.4 and 4 mg per day before pregnancy and throughout the first trimester. The infant outcome data were based on 234 live births. In addition to oral cleft recurrence, several secondary outcomes were compared between the two folic acid groups. Cleft recurrence rates were also compared to historic recurrence rates. Results: The oral cleft recurrence rates were 2.9% and 2.5% in the 0.4 and 4 mg groups, respectively. The recurrence rates in the two folic acid groups both separately and combined were significantly different from the 6.3% historic recurrence rate post the folic acid fortification program for this population (p = 0.0009 when combining the two folic acid groups). The rate of cleft lip with palate recurrence was 2.9% in the 0.4 mg group and 0.8% in the 4 mg group. There were no elevated fetal growth complications in the 4 mg group compared to the 0.4 mg group. Conclusions: The study is the first double-blinded randomized clinical trial (RCT) to study the effect of high dosage folic acid supplementation on isolated oral cleft recurrence. The recurrence rates were similar between the two folic acid groups. However, the results are suggestive of a decrease in oral cleft recurrence compared to the historic recurrence rate. A RCT is still needed to identify the effect of folic acid on oral cleft recurrence given these suggestive results and the supportive results from previous interventional and observational studies, and the study offers suggestions for such future studies. The results also suggest that high dosage folic acid does not compromise fetal growth. © 2013 by the authors; licensee MDPI, Basel, Switzerland.

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometric para-orthogonal polynomials. As tools to study these polynomials, we obtain new results which can be considered as extensions of certain classical results associated with three term recurrence relations and differential equations satisfied by orthogonal polynomials on the real line. One of these results which might be considered as an extension of the classical Sturm comparison theorem, enables us to obtain monotonicity with respect to the parameters for the zeros of these para-orthogonal polynomials. Finally, a monotonicity of the zeros of Meixner-Pollaczek polynomials is proved. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.