An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

On the mixing property for a class of states of relativistic quantum fields

Let omega be a factor state on the quasilocal algebra A of observables generated by a relativistic quantum field, which, in addition, satisfies certain regularity conditions [satisfied by ground states and the recently constructed thermal states of the P(phi)(2) theory]. We prove that there exist space- and time-translation invariant states, some of which are arbitrarily close to omega in the weak * topology, for which the time evolution is weakly asymptotically Abelian. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3372623]

Direct Measurement of the Bose-Einstein Condensation Universality Class in NiCl(2)-4SC(NH(2))(2) at Ultralow Temperatures

In this work, we demonstrate field-induced Bose-Einstein condensation (BEC) in the organic compound NiCl(2)-4SC(NH(2))(2) using ac susceptibility measurements down to 1 mK. The Ni S=1 spins exhibit 3D XY antiferromagnetism between a lower critical field H(c1)similar to 2 T and a upper critical field H(c2)similar to 12 T. The results show a power-law temperature dependence of the phase transition line H(c1)(T)-H(c1)(0)=aT(alpha) with alpha=1.47 +/- 0.10 and H(c1)(0)=2.053 T, consistent with the 3D BEC universality class. Near H(c2), a kink was found in the phase boundary at approximately 150 mK.

Intermediate motions as studied by solid-state separated local field NMR experiments

In this report, the application of a class of separated local field NMR experiments named dipolar chemical shift correlation (DIPSHIFT) for probing motions in the intermediate regime is discussed. Simple analytical procedures based on the Anderson-Weiss (AW) approximation are presented. In order to establish limits of validity of the AW based formulas, a comparison with spin dynamics simulations based on the solution of the stochastic Liouville-von-Neumann equation is presented. It is shown that at short evolution times (less than 30% of the rotor period), the AW based formulas are suitable for fitting the DIPSHIFT curves and extracting kinetic parameters even in the case of jumplike motions. However, full spin dynamics simulations provide a more reliable treatment and extend the frequency range of the molecular motions accessible by DIPSHIFT experiments. As an experimental test, molecular jumps of imidazol methyl sulfonate and trimethylsulfoxonium iodide, as well as the side-chain motions in the photoluminescent polymer poly[2-methoxy-5-(2(')-ethylhexyloxy)-1,4-phenylenevinylene], were characterized. Possible extensions are also discussed. (c) 2008 American Institute of Physics.

ON TWO-DIMENSIONAL QUASITOPOLOGICAL FIELD THEORIES

We study a class of lattice field theories in two dimensions that includes gauge theories. We show that in these theories it is possible to implement a broader notion of local symmetry, based on semisimple Hopf algebras. A character expansion is developed for the quasitopological field theories, and partition functions are calculated with this tool. Expected values of generalized Wilson loops are defined and studied with the character expansion.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

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.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Approach to Equilibrium for a Class of Random Quantum Models of Infinite Range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalizations allow a neat extension from the class l (1) of absolutely summable lattice potentials to the optimal class l (2) of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom l (1) case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class l (2) in the Bernoulli case. Open problems are discussed.

A new class of survival regression models with heavy-tailed errors: robustness and diagnostics

Birnbaum-Saunders models have largely been applied in material fatigue studies and reliability analyses to relate the total time until failure with some type of cumulative damage. In many problems related to the medical field, such as chronic cardiac diseases and different types of cancer, a cumulative damage caused by several risk factors might cause some degradation that leads to a fatigue process. In these cases, BS models can be suitable for describing the propagation lifetime. However, since the cumulative damage is assumed to be normally distributed in the BS distribution, the parameter estimates from this model can be sensitive to outlying observations. In order to attenuate this influence, we present in this paper BS models, in which a Student-t distribution is assumed to explain the cumulative damage. In particular, we show that the maximum likelihood estimates of the Student-t log-BS models attribute smaller weights to outlying observations, which produce robust parameter estimates. Also, some inferential results are presented. In addition, based on local influence and deviance component and martingale-type residuals, a diagnostics analysis is derived. Finally, a motivating example from the medical field is analyzed using log-BS regression models. Since the parameter estimates appear to be very sensitive to outlying and influential observations, the Student-t log-BS regression model should attenuate such influences. The model checking methodologies developed in this paper are used to compare the fitted models.

The bar-radical of a class of almost alternative baric algebras

In this article we prove that, if (U, ) is a finite dimensional baric algebra of (gamma, delta) type over a field F of characteristic not equal 2,3,5 such that gamma(2) - delta(2) + delta = 1 and 0,1, then rad(U) = R(U)boolean AND(bar(U))(2), where R(U) is the nilradical (maximal nil ideal) of U.

Early treatment of Class III malocclusion: 10-year clinical follow-up

Angle Class III malocclusion has been a challenge for researchers concerning diagnosis, prognosis and treatment. It has a prevalence of 5% in the Brazilian population, and may have a genetic or environmental etiology. This malocclusion can be classified as dentoalveolar, skeletal or functional, which will determine the prognosis. Considering these topics, the aim of this study was to describe and discuss a clinical case with functional Class III malocclusion treated by a two-stage approach (interceptive and corrective), with a long-term follow-up. In this case, the patient was treated with a chincup and an Eschler arch, used simultaneously during 14 months, followed by corrective orthodontics. It should be noticed that, in this case, initial diagnosis at the centric relation allowed visualizing the anterior teeth in an edge-to-edge relationship, thereby favoring the prognosis. After completion of the treatment, the patient was followed for a 10-year period, and stability was observed. The clinical treatment results showed that it is possible to achieve favorable outcomes with early management in functional Class III malocclusion patients.

Class II malocclusion occlusal severity description

OBJECTIVES: It is well known that the efficacy and the efficiency of a Class II malocclusion treatment are aspects closely related to the severity of the dental anteroposterior discrepancy. Even though, sample selection based on cephalometric variables without considering the severity of the occlusal anteroposterior discrepancy is still common in current papers. In some of them, when occlusal parameters are chosen, the severity is often neglected. The purpose of this study is to verify the importance given to the classification of Class II malocclusion, based on the criteria used for sample selection in a great number of papers published in the orthodontic journal with the highest impact factor. MATERIAL AND METHODS: A search was performed in PubMed database for full-text research papers referencing Class II malocclusion in the history of the American Journal of Orthodontics and Dentofacial Orthopedics (AJO-DO). RESULTS: A total of 359 papers were retrieved, among which only 72 (20.06%) papers described the occlusal severity of the Class II malocclusion sample. In the other 287 (79.94%) papers that did not specify the anteroposterior discrepancy severity, description was considered to be crucial in 159 (55.40%) of them. CONCLUSIONS: Omission in describing the occlusal severity demands a cautious interpretation of 44.29% of the papers retrieved in this study.

Segmental LeFort I osteotomy for treatment of a class III malocclusion with temporomandibular disorder

This article reports the case of a 19-year-old young man with Class III malocclusion and posterior crossbite with concerns about temporomandibular disorder (TMD), esthetics and functional problems. Surgical-orthodontic treatment was carried out by decompensation of the mandibular incisors and segmentation of the maxilla in 4 pieces, which allowed expansion and advancement. Remission of the signs and symptoms occurred after surgical-orthodontic intervention. The maxillary dental arch presented normal transverse dimension. Satisfactory static and functional occlusion and esthetic results were achieved and remained stable. Three years after the surgical-orthodontic treatment, no TMD sign or symptom was observed and the occlusal results had not changed. When vertical or horizontal movements of the maxilla in the presence of moderate maxillary constriction are necessary, segmental LeFort I osteotomy can be an important part of treatment planning.

Orthodontic-surgical treatment of class III malocclusion with mandibular asymmetry

Class III skeletal malocclusion may present several etiologies, among which maxillary deficiency is the most frequent. Bone discrepancy may have an unfavorable impact on esthetics, which is frequently aggravated by the presence of accentuated facial asymmetries. This type of malocclusion is usually treated with association of Orthodontics and orthognathic surgery for correction of occlusion and facial esthetics. This report presents the treatment of a patient aged 15 years and 1 month with Class III skeletal malocclusion, having narrow maxilla, posterior open bite on the left side, anterior crossbite and unilateral posterior crossbite, accentuated negative dentoalveolar discrepancy in the maxillary arch, and maxillary and mandibular midline shift. Clinical examination also revealed maxillary hypoplasia, increased lower one third of the face, concave bone and facial profiles and facial asymmetry with mandibular deviation to the left side. The treatment was performed in three phases: presurgical orthodontic preparation, orthognathic surgery and orthodontic finishing. In reviewing the patient's final records, the major goals set at the beginning of treatment were successfully achieved, providing the patient with adequate masticatory function and pleasant facial esthetics.