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]

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

Cephalometric evaluation of Class II malocclusion treatment with cervical headgear and mandibular fixed appliances

The present study aimed to evaluate the cephalometric changes in Class II patients treated exclusively with cervical headgear (CHG) in the maxillary arch and fixed appliances in the mandibular arch as compared with a control group. The sample comprised 82 lateral cephalograms obtained pre- (T1) and post- (T2) treatment/observation of 41 subjects, divided into two groups: group 1-25 Class II division 1 patients (20 females and five males), with a mean pre-treatment age of 10.4 years, treated for a mean period of 2.5 years and group 2-16 Class II untreated subjects (12 females and four males), with a mean initial age of 9.9 years, followed for a mean period of 2.2 years. Treatment changes between the groups were compared by means of t-tests. The results showed restriction of maxillary forward displacement and also a restriction in maxillary length growth, improvement in the maxillomandibular relationship, restriction of mandibular incisor vertical development, reduction in overjet and overbite, and improvement in molar relationship. It was concluded that this treatment protocol corrected the Class II malocclusion characteristics primarily through maxillary forward growth restriction.

A general Trotter-Kato formula for a class of evolution operators

In this article we prove new results concerning the existence and various properties of an evolution system U(A+B)(t, s)0 <= s <= t <= T generated by the sum -(A(t) + B(t)) of two linear, time-dependent, and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing L(B) for the algebra of all linear bounded operators on B, we can express U(A+B)(t, s)0 <= s <= t <= T as the strong limit in C(8) of a product of the holomorphic contraction semigroups generated by -A (t) and - B(t), respectively, thereby proving a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t) + B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND(t is an element of)[0,T] D(A(t) + B(t)) everywhere dense in B. We obtain a special case of our formula when B(t) = 0, which, in effect, allows us to reconstruct U(A)(t, s)0 <=(s)<=(t)<=(T) very simply in terms of the semigroup generated by -A(t). We then illustrate our results by considering various examples of nonautonomous parabolic initial-boundary value problems, including one related to the theory of timedependent singular perturbations of self-adjoint operators. We finally mention what we think remains an open problem for the corresponding equations of Schrodinger type in quantum mechanics.

A Trotter-Kato product formula for a class of non-autonomous evolution equations

In this article dedicated to Professor V. Lakshmikantham on the occasion of the celebration of his 84th birthday, we announce new results concerning the existence and various properties of an evolution system UA+B(t, s)(0 <= s <= t <= T) generated by the sum -(A(t)+B(t)) of two linear, time-dependent and generally unbounded operators defined on time-dependent domains in a complex and separable Banach space B. In particular, writing G(B) for the algebra of all linear bounded operators on B, we can express UA+B(t, s)(0 <= s <= t <= T) as the strong limit in L(B) of a product of the holomorphic contraction semigroups generated by -A(t) and -B(t), thereby getting a product formula of the Trotter-Kato type under very general conditions which allow the domain D(A(t)+B(t)) to evolve with time provided there exists a fixed set D subset of boolean AND D-t epsilon[0,D-T](A(t)+B(t)) everywhere dense in B. We then mention several possible applications of our product formula to various classes of non-autonomous parabolic initial-boundary value problems, as well as to evolution problems of Schrodinger type related to the theory of time-dependent singular perturbations of self-adjoint operators in quantum mechanics. We defer all the proofs and all the details of the applications to a separate publication. (C) 2008 Elsevier Ltd. All rights reserved.

SPECTRUM OF SCREENING MASSES FOR SU(2) GAUGE THEORY: UNIVERSALITY CLASS

In this work we study the spectrum of the lowest screening masses for Yang-Mills theories on the lattice. We used the SU(2) gauge group in (3 + 1) dmensions. We adopted the multiple exponential method and the so-called ""variational"" method, in order to detect possible excited states. The calculations were done near the critical temperature of the confinement-deconfinement phase transition. We obtained values for the ratios of the screening masses consistent with predictions from universality arguments. A Monte Carlo evolution of the screening masses in the gauge theory confirms the validity of the predictions.

Wavelet regression with correlated errors on a piecewise Holder class

This paper generalizes the methodology of Cat and Brown [Cai, T., Brown, L.D., 1998. Wavelet shrinkage for nonequispaced samples. The Annals of Statistics 26, 1783-1799] for wavelet shrinkage for nonequispaced samples, but in the presence of correlated stationary Gaussian errors. If the true function is a member of a piecewise Holder class, it is shown that, even for long memory errors, the rate of convergence of the procedure is almost-minimax relative to the independent and identically distributed errors case. (c) 2008 Elsevier B.V. All rights reserved.

Local solvability for a class of evolution equations

Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider it class of evolution operators with real-analytic coefficients and study their local solvability both in L(2) and in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg-Treves condition (psi) which is suitable to our study. (C) 2009 Published by Elsevier Inc.

d-Koszul algebras, 2-d-determined algebras and 2-d-Koszul algebras

The relationship between an algebra and its associated monomial algebra is investigated when at least one of the algebras is d-Koszul It is shown that an algebra which has a reduced Grobnerbasis that is composed of homogeneous elements of degree d is d-Koszul if and only if its associated monomial algebra is d-Koszul The class of 2-d-determined algebras and the class 2-d-Koszul algebras are introduced In particular it is shown that 2-d-determined monomial algebras are 2-d-Koszul algebras and the structure of the ideal of relations of such an algebra is completely determined (C) 2010 Elsevier B V All rights reserved

Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

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.

Maxillary protraction after surgically assisted maxillary expansion

This case report describes the orthodontic treatment of a 32-year-old woman with a Class III malocclusion, whose chief compliant was her dentofacial esthetics. The pretreatment lateral cephalometric tracings showed the presence of a Class III dentoskeletal malocclusion with components of maxillary deficiency. After discussion with the patient, the treatment option included surgically assisted rapid maxillary expansion (SARME) followed by orthopedic protraction (Sky Hook) and Class III elastics. Patient compliance was excellent and satisfactory dentofacial esthetics was achieved after treatment completion.

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.