A class of hypergeometric polynomials with zeros on the unit circle: Extremal and orthogonal properties and quadrature formulas

The class of hypergeometric polynomials F12(-m,b;b+b̄;1-z) with respect to the parameter b=λ+iη, where λ>0, are known to have all their zeros simple and exactly on the unit circle |z|=1. In this note we look at some of the associated extremal and orthogonal properties on the unit circle and on the interval (-1,1). We also give the associated Gaussian type quadrature formulas. © 2012 IMACS.

Comparisons between Bio-Oss® and Straumann® Bone Ceramic in immediate and staged implant placement in dogs mandible bone defects

Objective: To compare immediate and staged approach implant placement in circumferential defects treated with deproteinized bovine bone mineral (DBBM); hidroxyapatite/tricalcium phosphate (HA/TP); autogenous bone (Ab); and coagulum (Cg); upon implant stability, osseointegration and alveolar crest maintenance. Materials and methods: Six dogs underwent extractions of lower premolars, bilaterally. Twelve weeks later four bone defects (6 mm wide/4 mm long) were drilled at one side and randomly filled with DBBM; HA/TP; Ab; and Cg, respectively, and left to heal (staged approach). Eight weeks later one implant (Osseospeed™, AstraTech) was placed in experimental sites. At the same session four defects were drilled on contra-lateral side and implants were inserted immediately after biomaterials grafting (immediate approach). Animals were euthanized 8 weeks later. Implant stability was measured by resonance frequency analysis (RFA) at installation and after sacrifice. Ground sections were prepared for bone contact (BIC); bone area (BA); distance implant shoulder-bone crest (IS-C); distance implant shoulder first bone contact (IS-B); and areas occupied by soft tissue. Results: The BA and BIC were superior in the staged approach. The Cg exhibited higher BIC and BA as compared with other materials at the total implant body (P = 0.004 and 0.012, respectively). The DBBM, HA/TP and Ab groups rendered similar BA and BIC. The immediate approach resulted in less crest resorption compared to staged approach. The biomaterials did not affect the IS-C and IS-B measurements. Particles area tended to be higher in DBBM group than HA/TP (P = 0.15), while soft tissue infiltrate was higher in DBBM group when used in the immediate approach (P = 0.04). The RFA indicated gain in stability in the staged approach (P = 0.002). The correlation test between RFA vs. BIC and BA demonstrated inferior stability for DBBM group in immediate approach (P = 0.01). Conclusions: Implants placed in healed defects resulted in better stability as a consequence of higher BIC and BA. The Cg alone rendered increased BIC compared to other materials in both approaches. Immediate approach should be preferable to staged approach in terms of alveolar crest maintenance. The BIC and BA values did not vary between micro and macro-threads in this experimental model. Implants installed in sites filled with DBBM in immediate approach were less stable. © 2011 John Wiley & Sons A/S.

Incomplete mandibular fracture after lateralization of the inferior alveolar nerve for implant placement

PURPOSE: The present case describes an inferior alveolar nerve lateralization for implant placement that caused mandible fracture a few days after surgery. CLINICAL REPORT: In this case, a 56-year-old female patient who had a severely atrophied jaw and showing bone height less than 7 mm from the bone crest and the mandibular canal was submitted to surgery lateralization of the inferior alveolar conducted with piezzo. Even with all postoperative care, the patient suffered an incomplete fracture of the mandible a few days after lateralization of the inferior alveolar nerve for implant placement. The patient was treated with soft diet and medications for pain and antibiotics, besides removing the implant associated with the fracture. CONCLUSION: It is suggested that this procedure may be conducted in 2 operative periods: firstly, the lateralization of the inferior alveolar; and secondly, after a period of 3 months, the implant placement in a situation of more bone stability. Copyright © 2013 by Mutaz B. Habal, MD.

The success rate of immediate implant placement of mandibular molars: A clinical and radiographic retrospective evaluation between 2 and 8 years

Background: Dental implants, indicated for re-establishing both mastigatory and aesthetic functions, can be placed in the sockets immediately after tooth extraction. Most studies investigate the anterior and upper regions of the dental arch, whereas few examine longitudinal appraisal of immediate implant installation in the mandibular molar region. Objective: The aim of this retrospective study was to evaluate the success rate of immediate dental implants placement in mandibular molars within a follow-up period as long as 8 years. Materials and methods: Seventy-four mandibular molar implants after non-traumatic tooth extraction between 2002 and 2008 were examined in the study. All implants were evaluated radiographically immediately after prosthesis placement, 1 year after implantation, and by the end of the experimental period, in 2010. Clinical evaluation was done according to [Albrektsson et al. (1986) The International Journal of Oral & Maxillofacial Implants, 1, 11-25] success criteria for marginal bone loss. The mean bone losses, calculated as the difference between the final evaluation measures and those taken by the end of the first year of implant, were compared using Kruskal-Wallis test with a significance level of 5%. Results: All implants presented clinical and radiographic stable conditions, that is, 100% success rate. Significant bone loss was not found between final evaluation and that of the first functional year (P > 0.05). Conclusion: Immediate implant placement of mandibular molars proved to be a viable surgical treatment given the high success rate up to 8 years after implantation. © 2012 John Wiley & Sons A/S.

Zeros of a family of hypergeometric para-orthogonal polynomials on the unit circle

Para-orthogonal polynomials derived from orthogonal polynomials on the unit circle are known to have all their zeros on the unit circle. In this note we study the zeros of a family of hypergeometric para-orthogonal polynomials. As tools to study these polynomials, we obtain new results which can be considered as extensions of certain classical results associated with three term recurrence relations and differential equations satisfied by orthogonal polynomials on the real line. One of these results which might be considered as an extension of the classical Sturm comparison theorem, enables us to obtain monotonicity with respect to the parameters for the zeros of these para-orthogonal polynomials. Finally, a monotonicity of the zeros of Meixner-Pollaczek polynomials is proved. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Interlacing of zeros of orthogonal polynomials under modification of the measure

We investigate the mutual location of the zeros of two families of orthogonal polynomials. One of the families is orthogonal with respect to the measure dμ (x), supported on the interval (a, b) and the other with respect to the measure |x -c|τ|x -d|γdμ (x), where c and d are outside (a, b) We prove that the zeros of these polynomials, if they are of equal or consecutive degrees, interlace when either 0 < τ, γ ≤ 1 or γ = 0 and 0 < τ ≤ 2. This result is inspired by an open question of Richard Askey and it generalizes recent results on some families of orthogonal polynomials. Moreover, we obtain further statements on interlacing of zeros of specific orthogonal polynomials, such as the Askey-Wilson ones. © 2013 Elsevier Inc.

Teoria do potencial logarítmico e zeros de polinômios

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Controle ótimo H 'INFINITO' com modificação de zeros para o problema de rastreamento em sistemas discretos usando LMI

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Uso de modelos inflacionados de zeros na análise de questionários de frequência alimentar

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Posição e densidade dos zeros de Yang-Lee do modelo de Blume-Emery-Griffiths unidimensional sobre anéis conexos e desconexos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Limitantes para os zeros de polinômios gerados por uma relação de recorrência de três termos

Pós-graduação em Matemática - IBILCE

Interpretação eletrostática e zeros de polinômios

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Teorema de Sturm e zeros de polinômios ortogonais

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Polinômios algébricos e trigonométricos com zeros reais

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

Monotonicidade de zeros de polinômios ortogonais clássicos

Pós-graduação em Matematica Aplicada e Computacional - FCT