Higher order turän inequalities

The celebrated Turân inequalities P 2 n(x)-P n-x(x)P n+1(x) ≥ 0, x ε[-1,1], n ≥ 1, where P n(x) denotes the Legendre polynomial of degree n, are extended to inequalities for sums of products of four classical orthogonal polynomials. The proof is based on an extension of the inequalities γ 2 n - γ n-1γ n+1 ≥ 0, n ≥ 1, which hold for the Maclaurin coefficients of the real entire function ψ in the Laguerre-Pölya class, ψ(x) = ∑ ∞ n=0 γ nx n / n!. ©1998 American Mathematical Society.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

Laguerre polynomials as Jensen polynomials of Laguerre-Polya entire functions

We prove that the only Jensen polynomials associated with an entire function in the Laguerre-Polya class that are orthogonal are the Laguerre polynomials. (C) 2009 Elsevier B.V. All rights reserved.

Schur-Szegö composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

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

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

Schur-SzegA composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Higher order turán inequalities for the Riemann ξ-function

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Almost strict total positivity and a class of Hurwitz polynomials

We establish sufficient conditions for a matrix to be almost totally positive, thus extending a result of Craven and Csordas who proved that the corresponding conditions guarantee that a matrix is strictly totally positive. Then we apply our main result in order to obtain a new criteria for a real algebraic polynomial to be a Hurwitz one. The properties of the corresponding extremal Hurwitz polynomials are discussed. (C) 2004 Elsevier B.V. All rights reserved.

Equivalence of many-photon Green's functions in the Duffin-Kemmer-Petiau and Klein-Gordon-Fock statistical quantum field theories

Using the functional integral formalism for the statistical generating functional in the statistical (finite temperature) quantum field theory, we prove the equivalence of many-photon Greens functions in the Duffin-Kennner-Petiau and Klein-Gordon-Fock statistical quantum field theories. As an illustration, we calculate the one-loop polarization operators in both theories and demonstrate their coincidence.

Evaluation of anionic collagen membranes in the treatment of class II furcation lesions: an histometric analysis in dogs

This study aims to evaluate the effect of using anionic collagen membranes in guided tissue regeneration treatment of Class II furcation lesions in dogs. The defects were created in the buccal furcation of 16 mandibular premolars of four dogs. After 56 days without plaque control, the sites were scaled and divided into two groups according to the treatment applied: control sites, open flap debridement; and test sites, guided tissue regeneration treatment. The animals were killed after 3 months. Histological and histometrical analyses showed that the collagen membrane was better than open flap debridement in terms of newly formed cementum and epithelial migration prevention. It provided effective blockade of epithelial tissue and promoted regeneration of lost periodontal tissues, suggesting that the membrane warrants further study. (C) 1997 Elsevier B.V. Limited. All rights reserved.

Comparative study of the Frankel (FR-2) and bionator appliances in the treatment of Class II malocclusion

The purpose of this investigation was to compare the dentoalveolar and skeletal cephalometric changes produced by the Frankel (FR-2) and bionator appliances in persons with Class 11 malocclusion. Lateral cephalograms were available for 66 patients of both sexes, who were divided into 3 groups of 22. The control group included untreated Class 11 children, with an initial mean age of 8 years 7 months; they were followed without treatment for 13 months. The FR-2 appliance group had an initial mean age of 9 years; those children were treated for a mean period of 17 months. The bionator group initially had a mean age of 10 years 8 months; on average, they were treated for 16 months. The results demonstrated no significant changes in maxillary growth during the evaluation period. Both appliances showed statistically significant increases in mandibular growth and mandibular protrusion, with greater increases in patients treated in the bionator group. Both experimental groups showed an improvement in the maxillomandibular relationship. There were no significant changes in growth direction, while the bionator group had a greater increase in posterior facial height. Both appliances produced similar labial tipping and protrusion of the lower incisors, lingual inclination, retrusion of the upper incisors, and a significant increase in mandibular posterior dentoalveolar height. The major treatment effects of bionator and FR-2 appliances were dentoalveolar, with a smaller, but significant, skeletal effect.

Equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories

We prove the equivalence of many-gluon Green's functions in the Duffin-Kemmer-Petieu and Klein-Gordon-Fock statistical quantum field theories. The proof is based on the functional integral formulation for the statistical generating functional in a finite-temperature quantum field theory. As an illustration, we calculate one-loop polarization operators in both theories and show that their expressions indeed coincide.

GENERALIZED HEAVISIDE FUNCTIONS IN THE COLOMBEAU THEORY CONTEXT

We defined generalized Heaviside functions for a variable x in R-n, and for variables (x, t) in R-n x R-m. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

Autogenous bone graft with or without a calcium sulfate barrier in the treatment of class II furcation defects: A histologic and histometric study in dogs

Background: The purpose of this study was to histologically evaluate the healing of surgically created Class II furcation defects treated using an autogenous bone (AB) graft with or without a calcium sulfate (CS) barrier. Methods: The second, third, and fourth mandibular premolars (P2, P3, and P4) of six mongrel dogs were used in this study. Class II furcation defects (5 mm in height × 2 mm in depth) were surgically created and immediately treated. Teeth were randomly divided into three groups: group C (control), in which the defect was filled with blood clot; group AB, in which the defect was filled with AB graft; and group AB/CS, in which the defect was filled with AB graft and covered by a CS barrier. Elaps were repositioned to cover all defects. The animals were euthanized 90 days post-surgery. Mesio-distal serial sections were obtained and stained with either hematoxylin and eosin or Masson's trichrome. Histometric, using image-analysis software, and histologic analyses were performed. Linear and area measurements of periodontal healing were evaluated and calculated as a percentage of the original defect. Percentage data were transformed into arccosine for statistical analysis (analysis of variance; P<0.05). Results: Periodontal regeneration in the three groups was similar. Regeneration of bone and connective tissue in the furcation defects was incomplete in most of the specimens. Statistically significant differences were not found in any of the evaluated parameters among the groups. Conclusion: Periodontal healing was similar using surgical debridement alone, AB graft, or AB graft with a CS barrier in the treatment of Class II furcation defects.

Mandibular growth and dentoalveolar development in the treatment of Class II, division 1, malocclusion using Balters Bionator according to the skeletal maturation

OBJECTIVE: The purpose of the study was to evaluate the influence of the skeletal maturation in the mandibular and dentoalveolar growth and development during the Class II, division 1, malocclusion correction with Balters bionator. METHODS: Three groups of children with Class II, division 1, malocclusion were evaluated. Two of them were treated for one year with the bionator of Balters appliance in different skeletal ages (Group 1: 6 children, 7 to 8 years old and Group 2: 10 children, 9 to 10 years old) and the other one was followed without treatment (Control Group: 7 children, 8 to 9 years old). Lateral 45 degree cephalometric radiographs were used for the evaluation of the mandibular growth and dentoalveolar development. Tantalum metallic implants were used as fixed and stable references for radiograph superimposition and data acquisition. Student's t test was used in the statistical analysis of the displacement of the points in the condyle, ramus, mandibular base and dental points. Analysis of variance one-fixed criteria was used to evaluate group differences (95% of level of significance). RESULTS: The intragroup evaluation showed that all groups present significant skeletal growth for all points analyzed (1.2 to 3.7 mm), but in an intergroup comparison, the increment of the mandibular growth in the condyle, ramus and mandibular base were not statically different. For the dentoalveolar modifications, the less mature children showed greater labial inclination of the lower incisors (1.86 mm) and the most mature children showed greater first permanent molar extrusion (4.8 mm).