Expanding the class of conditionally exactly solvable potentials

Recently a class of quantum-mechanical potentials was presented that is characterized by the fact that they are exactly solvable only when some of their parameters are fixed to a convenient value, so they were christened as conditionally exactly solvable potentials. Here we intend to expand this class by introducing examples in two dimensions. As a byproduct of our search, we found also another exactly solvable potential. © 1994 The American Physical Society.

On the parameters of the Lewis metric for the Lewis class

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

In analogy with the Liouville case we study the sl3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W3 algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.

Tau-functions and dressing transformations for zero-curvature affine integrable equations

The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac-Moody algebras g. Their common feature is that they have some special vacuum solutions corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.

Constrained KP models as integrable matrix hierarchies

We formulate the constrained KP hierarchy (denoted by cKP K+1,M) as an affine sl(M + K+ 1) matrix integrable hierarchy generalizing the Drinfeld-Sokolov hierarchy. Using an algebraic approach, including the graded structure of the generalized Drinfeld-Sokolov hierarchy, we are able to find several new universal results valid for the cKP hierarchy. In particular, our method yields a closed expression for the second bracket obtained through Dirac reduction of any untwisted affine Kac-Moody current algebra. An explicit example is given for the case sl(M + K + 1), for which a closed expression for the general recursion operator is also obtained. We show how isospectral flows are characterized and grouped according to the semisimple non-regular element E of sl(M + K+ 1) and the content of the center of the kernel of E. © 1997 American Institute of Physics.

Some comments on the bi(tri)-Hamiltonian structure of generalized AKNS and DNLS hierarchies

We give the correct prescriptions for the terms involving ∂ -1 xδ(x - y), in the Hamiltonian structures of the AKNS and DNLS systems, necessary for the Jacobi identities to hold. We establish that the sl(2) and sl(3) AKNS systems are tri-Hamiltonians and construct two compatible Hamiltonian structures for the sl(n) AKNS system. We give a method for the derivation of the recursion operator for the sl(n + 1) DNLS system, and apply it explicitly to the sl(2) case, showing that such a system is tri-Hamiltonian. © 1998 Elsevier Science B.V.

Class of self-dual models in three dimensions

In the present paper we introduce a hierarchical class of self-dual models in three dimensions, inspired in the original self-dual theory of Towsend-Pilch-Nieuwenhuizen. The basic strategy is to explore the powerful property of the duality transformations in order to generate a new field. The generalized propagator can be written in terms of the primitive one (first order), and also the respective order and disorder correlation functions. Some conclusions about the charge screening and magnetic flux were established. ©1999 The American Physical Society.

Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Resistance to maxillary premolar fractures after restoration of class II preparations with resin composite or ceromer.

OBJECTIVE: The aim of this study was to evaluate the resistance to fracture of intact and restored human maxillary premolars. METHOD AND MATERIALS: Thirty noncarious human maxillary premolars, divided into three groups of 10, were submitted to mechanical tests to evaluate their resistance to fracture. Group 1 consisted of intact teeth. Teeth in group 2 received mesio-occlusodistal cavity preparations and were restored with direct resin composite restorations. Teeth in group 3 received mesio-occlusodistal cavity preparations and were restored with ceromer inlays placed with the indirect technique. After restoration, teeth were stored at 37 degrees C for 24 hours and then thermocycled for 500 cycles at temperatures of 5 degrees C and 55 degrees C. RESULTS: Statistical analysis revealed that group 3 (178.765 kgf) had a significantly greater maximum rupture load than did group 1 (120.040 kgf). There was no statistically significant difference between groups 1 and 2 or between groups 2 and 3. CONCLUSION: Class II cavity preparations restored with indirect ceromer inlays offered greater resistance to fracture than did intact teeth. The fracture resistance of teeth restored with resin composite was not significantly different from that of either the ceromer or intact teeth.

Treatment Effects Produced by Fränkel Appliance in Patients with Class II, Division 1 Malocclusion

The purpose of this investigation was to evaluate the dentoalveolar and skeletal cephalometric changes produced by the Fränkel appliance in individuals with a Class II, division 1 malocclusion. Lateral cephalograms of 44 patients of both sexes were divided in two groups of 22 each. The control group was comprised of untreated Class II children with an initial mean age of eight years and seven months who were followed without treatment for a period of 13 months. The Fränkel group had an initial mean age of nine years and was treated for a mean period of 17 months. Lateral cephalometric headfilms of each patient were obtained at the beginning and end of treatment. The Fränkel appliance produced no significant changes in maxillary growth during the evaluation period, while a statistically significant increase in mandibular length was observed. The maxillomandibular relationship improved mostly because of an increase in mandibular length. In addition, there were no statistically significant differences in the craniofacial growth direction between the Fränkel and the control group, both showing a slight downward rotation of the palatal plane. The Fränkel appliance produced a labial tipping of the lower incisors and a lingual inclination of the upper incisors as well as a significant increase in mandibular posterior dentoalveolar height. It was concluded that the main effects of the Fränkel appliance during this time period were mostly dentoalveolar with a smaller but significant skeletal mandibular effect.

Solutions for a class of integro-differential equations with time periodic coefficients

In this work, a series solution is found for the integro-differential equation y″ (t) = -(ω2 c + ω2 f sin2 ωpt)y(t) + ωf (sin ωpt) z′ (0) + ω2 fωp sin ωpt ∫t 0 (cos ωps) y(s)ds, which describes the charged particle motion for certain configurations of oscillating magnetic fields. As an interesting feature, the terms of the solution are related to distinct sequences of prime numbers.

Evaluation of marginal microleakage in Class II cavities: Effect of microhybrid, flowable, and compactable resins

Objective: The goal of the present study was to evaluate the microleakage on the cementum/dentin and enamel surfaces in Class II restorations, using different kinds of resin composite (microhybrid, flowable, and compactable). Method and materials: Forty human caries-free molars were extracted and selected. Eighty Class II standardized cavities were made in the cervical wall at the cementoenamel junction (CEJ) and at the mesial and distal surfaces. The teeth were divided into four groups: G1 - adhesive system + microhybrid resin composite Z100; G2 - adhesive system + compactable resin composite Prodigy Condensable; G3 - adhesive system + flowable resin composite Revolution + Z100 resin composite; G4 - adhesive system + Revolution fluid resin + compactable resin composite Prodigy Condensable. The adhesive system used in this study was Scotchbond Multi-Purpose Plus. The specimens were thermocycled in baths of 5°C and 55°C for 1,000 cycles and immersed in 50% silver nitrate solution. The specimens then were sectioned and evaluated on degree of dye penetration. Results: The results were evaluated using the nonparametric Kruskall-Wallis test, which showed a statistically significant difference between groups G1 and G4, G2 and G4, and G3 and G4. Conclusions: None of the materials was able to eliminate the marginal microleakage at the cervical wall; the application of a low-viscosity resin composite combined with a compactable resin composite significantly decreased the microleakage.

PI Stabilization of a Class of Time Delay Systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral (PI) controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. A signature for the quasipolynomials in this class is derived and used in the proposed approach which yields the complete set of the stabilizing PI controllers.

Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation

Supersymmetry is formulated for integrable models based on the sl(2 1) loop algebra endowed with a principal gradation. The symmetry transformations which have half-integer grades generate supersymmetry. The sl(2 1) loop algebra leads to N=2 supersymmetric mKdV and sinh-Gordon equations. The corresponding N=1 mKdV and sinh-Gordon equations are obtained via reduction induced by twisted automorphism. Our method allows for a description of a non-local symmetry structure of supersymmetric integrable models. © 2003 Elsevier B.V. All rights reserved.