SOME PROPERTIES OF THE MULTIPLICITY SEQUENCE FOR ARBITRARY IDEALS

In this work we prove that the Achilles-Manaresi multiplicity sequence, like the classical Hilbert-Samuel multiplicity, is additive with respect to the exact sequence of modules. We also prove the associativity formula for his mulitplicity sequence. As a consequence, we give new proofs for two results already known. First, the Achilles-Manaresi multiplicity sequence is an invariant up to reduction, a result first proved by Ciuperca. Second, I subset of J is a reduction of (J,M) if and only if c(0)(I(p), M(p)) = c(0)(J(p), M(p)) for all p is an element of Spec(A), a result first proved by Flenner and Manaresi.

C(0) and bi-Lipschitz K-equivalence of mappings

In this paper we investigate the classification of mappings up to K-equivalence. We give several results of this type. We study semialgebraic deformations up to semialgebraic C(0) K-equivalence and bi-Lipschitz K-equivalence. We give an algebraic criterion for bi-Lipschitz K-triviality in terms of semi-integral closure (Theorem 3.5). We also give a new proof of a result of Nishimura: we show that two germs of smooth mappings f, g : R(n) -> R(n), finitely determined with respect to K-equivalence are C(0)-K-equivalent if and only if they have the same degree in absolute value.

Integral Piezoactuator System with Optimum Placement of Functionally Graded Material - A Topology Optimization Paradigm

Piezoactuators consist of compliant mechanisms actuated by two or more piezoceramic devices. During the assembling process, such flexible structures are usually bonded to the piezoceramics. The thin bonding layer(s) between the compliant mechanism and the piezoceramic may induce undesirable behavior, including unusual interfacial nonlinearities. This constitutes a drawback of piezoelectric actuators and, in some applications, such as those associated to vibration control and structural health monitoring (e. g., aircraft industry), their use may become either unfeasible or at least limited. A possible solution to this standing problem can be achieved through the functionally graded material concept and consists of developing `integral piezoactuators`, that is those with no bonding layer(s) and whose performance can be improved by tailoring their structural topology and material gradation. Thus, a topology optimization formulation is developed, which allows simultaneous distribution of void and functionally graded piezoelectric materials (including both piezo and non-piezoelectric materials) in the design domain in order to achieve certain specified actuation movements. Two concurrent design problems are considered, that is the optimum design of the piezoceramic property gradation, and the design of the functionally graded structural topology. Two-dimensional piezoactuator designs are investigated because the applications of interest consist of planar devices. Moreover, material gradation is considered in only one direction in order to account for manufacturability issues. To broaden the range of such devices in the field of smart structures, the design of integral Moonie-type functionally graded piezoactuators is provided according to specified performance requirements.

Gasless fetoscopy: A new approach to endoscopic closure of a lumbar skin defect in fetal sheep

Objective: To develop a new endoscopic approach to the correction of a myelomeningocele-like defect in fetal sheep. Methods: The fetuses of 9 pregnant ewes, with an average gestational age of 115 days, were subjected to a 3.0 x 2.0 cm removal of the skin over the lumbar spine, performed through hysterotomy. The uterus was closed, and three 5-mm endoscopic cannulas, without valve mechanisms, were inserted. In the pilot phase (2 animals), we initially worked exclusively in the amniotic fluid space. In the study phase, we partially withdrew the fetus from the amniotic fluid to completely expose its back. By simply allowing air to enter the amniotic cavity (without gas injection), a working space was created using a uterine lift device. The skin around the defect was dissected, and a biosynthetic cellulose material was applied to cover the area. A continuous suture of the skin was performed to completely hide the material. Results: The combined air/fluid space allowed the skin to be successfully closed in 6 out of 7 cases in the study phase. All fetuses were alive at the end of the procedures. Time to complete the endoscopic part of the procedure fell from 3 to 1 h by the end of this series. Premature birth occurred in 2 of the 4 cases allowed to continue with the pregnancy. Conclusion: A new gasless fetoscopic surgery technique was developed as an alternative to current techniques used for fetal endoscopic surgery. Copyright (C) 2008 S. Karger AG, Basel.

Neoskin development in the fetus with the use of a three-layer graft: an animal model for in utero closure of large skin defects

Objective: To assess the ability of a three-layer graft in the closuse of large fetal skin defects. Methods: Ovine fetuses underwent a large (4 x 3 cm) full-thickness skin defect over the lumbar region at 105 days` gestation (term = 140 days). A bilaminar artificial skin was placed over a cellulose interface to cover the defect (3-layer graft). The skin was partially reapproximated with a continuous nylon suture. Pregnancy was allowed to continue and the surgical site was submitted to histopathological analysis at different post-operative intervals. Results: Seven fetuses underwent surgery. One maternal/fetal death occurred, and the remaining 6 fetuses were analyzed. Artificial skin adherence to the wound edges was observed in cases that remained in utero for at least 15 days. Neoskin was present beneath the silicone layer of the bilaminar artificial skin. Conclusions: Our study shows that neoskin can develop in the fetus using a 3-layer graft, including epidermal growth beneath the silicone layer of the bilaminar skin graft. These findings suggest that the fetus is able to reepithelialise even large skin defects. Further experience is necessary to assess the quality of this repair.

Near-infrared integral field spectroscopy of the Homunculus nebula around eta Carinae using Gemini/CIRPASS

This work presents the first integral field spectroscopy of the Homunculus nebula around eta Carinae in the near-infrared spectral region (J band). We confirmed the presence of a hole on the polar region of each lobe, as indicated by previous near-IR long-slit spectra and mid-IR images. The holes can be described as a cylinder of height (i.e. the thickness of the lobe) and diameter of 6.5 and 6.0 x 10(16) cm, respectively. We also mapped the blue-shifted component of He I lambda 10830 seen towards the NW lobe. Contrary to previous works, we suggested that this blue-shifted component is not related to the Paddle but it is indeed in the equatorial disc. We confirmed the claim of N. Smith and showed that the spatial extent of the Little Homunculus matches remarkably well the radio continuum emission at 3 cm, indicating that the Little Homunculus can be regarded as a small H II region. Therefore, we used the optically thin 1.3 mm radio flux to derive a lower limit for the number of Lyman-continuum photons of the central source in eta Car. In the context of a binary system, and assuming that the ionizing flux comes entirely from the hot companion star, the lower limit for its spectral type and luminosity class ranges from O5.5 III to O7 I. Moreover, we showed that the radio peak at 1.7 arcsec NW from the central star is in the same line-of-sight of the `Sr-filament` but they are obviously spatially separated, while the blue-shifted component of He I lambda 10830 may be related to the radio peak and can be explained by the ultraviolet radiation from the companion star.

Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 3

In this paper, we classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 3. (C) 2008 Elsevier Ltd. All rights reserved.

Measurement of thermal neutron cross section and resonance integral for the (165)Ho(n, gamma)(166g)Ho reaction

The ground state thermal neutron cross section and the resonance integral for the (165)Ho(n, gamma)(166)Ho reaction in thermal and 1/E regions, respectively, of a thermal reactor neutron spectrum have been measured experimentally by activation technique. The reaction product, (166)Ho in the ground state, is gaining considerable importance as a therapeutic radionuclide and precisely measured data of the reaction are of significance from the fundamental point of view as well as for application. In this work, the spectrographically pure holmium oxide (Ho(2)O(3)) powder samples were irradiated with and without cadmium covers at the IEA-RI reactor (IPEN, Sao Paulo), Brazil. The deviation of the neutron spectrum shape from 1/E law was measured by co-irradiating Co, Zn, Zr and Au activation detectors with thermal and epithermal neutrons followed by regression and iterative procedures. The magnitudes of the discrepancies that can occur in measurements made with the ideal 1/E law considerations in the epithermal range were studied. The measured thermal neutron cross section at the Maxwellian averaged thermal energy of 0.0253 eV is 59.0 +/- 2.1 b and for the resonance integral 657 +/- 36b. The results are measured with good precision and indicated a consistency trend to resolve the discrepant status of the literature data. The results are compared with the values in main libraries such as ENDF/B-VII, JEF-2.2 and JENDL-3.2, and with other measurements in the literature.

Pseudoclassical description of scalar particle in non-abelian background and path-integral representations

Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then quantized to prove their consistency.

Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action

It is known that the actions of field theories on a noncommutative space-time can be written as some modified (we call them theta-modified) classical actions already on the commutative space-time (introducing a star product). Then the quantization of such modified actions reproduces both space-time noncommutativity and the usual quantum mechanical features of the corresponding field theory. In the present article, we discuss the problem of constructing theta-modified actions for relativistic QM. We construct such actions for relativistic spinless and spinning particles. The key idea is to extract theta-modified actions of the relativistic particles from path-integral representations of the corresponding noncommutative field theory propagators. We consider the Klein-Gordon and Dirac equations for the causal propagators in such theories. Then we construct for the propagators path-integral representations. Effective actions in such representations we treat as theta-modified actions of the relativistic particles. To confirm the interpretation, we canonically quantize these actions. Thus, we obtain the Klein-Gordon and Dirac equations in the noncommutative field theories. The theta-modified action of the relativistic spinning particle is just a generalization of the Berezin-Marinov pseudoclassical action for the noncommutative case.

Integral group ring of the Suzuki sporadic simple group

Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle`s conjecture on prime graphs.

INVOLUTIONS AND FREE PAIRS OF BASS CYCLIC UNITS IN INTEGRAL GROUP RINGS

Let ZG be the integral group ring of the finite nonabelian group G over the ring of integers Z, and let * be an involution of ZG that extends one of G. If x and y are elements of G, we investigate when pairs of the form (u(k,m)(x*), u(k,m)(x*)) or (u(k,m)(x), u(k,m)(y)), formed respectively by Bass cyclic and *-symmetric Bass cyclic units, generate a free noncyclic subgroup of the unit group of ZG.

CENTRAL UNITS IN METACYCLIC INTEGRAL GROUP RINGS

In this article, we give a method to compute the rank of the subgroup of central units of ZG, for a finite metacyclic group, G, by means of Q-classes and R-classes. Then we construct a multiplicatively independent set u subset of Z(U(ZC(p,q))) and by applying our results, we prove that u generates a subgroup of finite index.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.