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.

Integration of polyharmonic functions

The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.

Estimates of covariance functions for growth from birth to 630 days of age in Nelore cattle

Weight records of Brazilian Nelore cattle, from birth to 630 d of age, recorded every 3 mo, were analyzed using random regression models. Independent variables were Legendre polynomials of age at recording. The model of analysis included contemporary groups as fixed effects and age of dam as a linear and quadratic covariable. Mean trends were modeled through a cubic regression on orthogonal polynomials of age. Up to four sets of random regression coefficients were fitted for animals' direct and maternal, additive genetic, and permanent environmental effects. Changes in measurement error variances with age were modeled through a variance function. Orders of polyno-mial fit from three to six were considered, resulting in up to 77 parameters to be estimated. Models fitting random regressions modeled the pattern of variances in the data adequately, with estimates similar to those from corresponding univariate analysis. Direct heritability estimates decreased after birth and tended to be lowest at ages at which maternal effect estimates tended to be highest. Maternal heritability estimates increased after birth to a peak around 110 to 120 d of age and decreased thereafter. Additive genetic direct correlation estimates between weights at standard ages (birth, weaning, yearling, and final weight) were moderate to high and maternal genetic and environmental correlations were consistently high. © 2001 American Society of Animal Science. All rights reserved.

Relation between speaking space of the /s/ sound and freeway space in dentate and edentate subjects.

The purpose of this study is to assess the relation between the speaking space of the /s/ sound and the freeway space in two subject groups. One group had natural dentition (Group I, n = 61) and the other comprised complete denture wearers (Group II, n = 33). The analysis was done by means of a jaw-tracking device (K6-I Diagnostic System, Myotronics Research Inc., Seattle, WA, USA). Freeway space was determined by asking the subjects to occlude from the postural rest position. Speaking space of /s/ was measured during the pronunciation of the word seis and comprised the mean distance from the /s/ speaking position to maximal intercuspation. A weak correlation was found between the speaking space of /s/ and the freeway space in Group I (r = 0.41, p < 0.01), but in Group II, the correlation was stronger (r = 0.75, p < 0.01). The speaking space of /s/ and freeway space were different in Group I, but statistically similar in Group II (paired t-test, alpha = 0.05). It can be suggested that anatomic changes following prosthetic procedures caused a functional adaptation which resulted in more similar values for the speaking space of /s/ and the freeway space.

A comparison of human and porcine acellular dermal tissues in the subcutaneous space of a rat model

The study compared the host response to a human and a porcine acellular dermal tissue implanted in the subcutaneous space of a rat model. The human and porcine acellular grafts were surgically implanted in the subcutaneous tissue of rats (5 rats/group) and the materials were evaluated at 7, 15, 30, 60 and 180 postoperative days (PO). The histological immune response was quantified using a digital image analysis system, which evaluated the number of vessels present in the implants and in the surrounding soft tissue, the area of inflammatory cell infiltration in the grafts, the width of the capsular formation present around the tissues and the area of implants absorbed. The data were submitted to statistical analysis. Light microscopy showed mononuclear cellular infiltration, the presence of a capsular formation surrounding the grafts and the presence of vacuolar structures (optically empty spaces) inside the implants. The image analysis comparing both materials showed significant inflammatory cells in the human graft at 15 and 30 PO, thicker capsular formation in the porcine tissue at 60 PO, increased number of vessels inside the implants and in the surrounding tissues in the porcine graft and a similar absorption pattern in both materials at 180 PO. The histological findings showed that both tissues were well-tolerated when implanted in the subcutaneous tissue of rats, allowing us to consider the porcine acellular dermal graft as a provisional alternative material for reconstructive plastic surgery. Copyright © 2005 Taylor & Francis LLC.

The Lamination of Infinitely Renormalizable Dissipative Gap Maps: Analyticity, Holonomies and Conjugacies

Motivated by return maps near saddles for three-dimensional flows and also by return maps in the torus associated to Cherry flows, we study gap maps with derivative positive and smaller than one outside the discontinuity point. We prove that the lamination of infinitely renormalizable maps (or else maps with irrational rotation numbers) has analytic leaves in a natural subset of a Banach space of analytic maps of this kind. With maps having Hölder continuous derivative and derivative bounded away from zero, we also prove Hölder continuity of holonomies of the lamination and also of conjugacies between maps having the same combinatorics. © 2011 Springer Basel AG.

Optimal low-cost transfer to L4 and L5 lagrangian points based on G-family of periodic orbits

An alternative transfer strategy to send spacecrafts to stable orbits around the Lagrangian equilibrium points L4 and L5 based in trajectories derived from the periodic orbits around LI is presented in this work. The trajectories derived, called Trajectories G, are described and studied in terms of the initial generation requirements and their energy variations relative to the Earth through the passage by the lunar sphere of influence. Missions for insertion of spacecrafts in elliptic orbits around L4 and L5 are analysed considering the Restricted Three-Body Problem Earth- Moon-particle and the results are discussed starting from the thrust, time of flight and energy variation relative to the Earth. Copyright© (2012) by the International Astronautical Federation.

Strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem

This paper proposes strategies to reduce the number of variables and the combinatorial search space of the multistage transmission expansion planning problem (TEP). The concept of the binary numeral system (BNS) is used to reduce the number of binary and continuous variables related to the candidate transmission lines and network constraints that are connected with them. The construction phase of greedy randomized adaptive search procedure (GRASP-CP) and additional constraints, obtained from power flow equilibrium in an electric power system are employed for more reduction in search space. The multistage TEP problem is modeled like a mixed binary linear programming problem and solved using a commercial solver with a low computational time. The results of one test system and two real systems are presented in order to show the efficiency of the proposed solution technique. © 1969-2012 IEEE.

The fat body of termites: Functions and stored materials

The functions of the fat body in the different castes of termites, and accumulation of energy reserves, proteins and urates within this organ, are reviewed. The termite fat body is involved in multiple metabolic activities, including recycling of nitrogen. Termite fat body showed three different types of cells: adipocytes, urocytes and mycetocytes, the latter restricted to the species Mastotermes darwiniensis. Adipocytes synthesize and store lipids, glycogen and several proteins. These cells also elaborate important peptides, including some that act in immune processes. Urocytes are responsible for the storage of spherocrystals of urates, which vary quantitatively among the termite castes. The different metabolic functions of the fat body in the several castes and stages of termites are associated with specific adipocyte morphologies. The synthesis and storage of different compounds modify the structure of the fat body; this differentiation is coordinated by hormones involved with molting and reproductive cycles. © 2013 Elsevier Ltd.

Histologic Characterization of Engineered Tissues in the Canal Space of Closed-apex Teeth with Apical Periodontitis

Introduction: The aim of this study was to investigate the capacity of endodontic regenerative procedures combining an induced blood clot, platelet-rich plasma (PRP), and bone marrow aspirate (BMA) to regenerate dental pulp in canine closed-apex necrotic teeth. Methods: Apical periodontitis was induced in 20 upper and lower premolars of 2 dogs. After biomechanical preparation, enlargement to a #60 file, and disinfection with a triantibiotic paste for 28 days, the roots were randomly assigned to 4 treatment groups: blood clot (BC), BC + PRP gel, BC + BMA gel, and BC + BMA/PRP gel. Negative controls were also included. After a 3-month follow-up period, the animals were killed. Results: Histologic analysis showed the presence of newly formed vital tissues (connective, cement-like, and bone-like tissue) in 23 of the 32 treated roots (71.87%). There was no statistically significant difference between the treatment groups. Conclusions: New vital tissues were formed and characterized as connective, cementum-like, or bone-like, but not as pulp-like tissue; PRP and/or BMA did not improve the tissue ingrowth. © 2013 American Association of Endodontists.

Schur-Szegö composition of entire functions

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

Comparative study between powers of sigmoid functions, MLP-backpropagation and polynomials in function approximation problems

Function approximation is a very important task in environments where the computation has to be based on extracting information from data samples in real world processes. So, the development of new mathematical model is a very important activity to guarantee the evolution of the function approximation area. In this sense, we will present the Polynomials Powers of Sigmoid (PPS) as a linear neural network. In this paper, we will introduce one series of practical results for the Polynomials Powers of Sigmoid, where we will show some advantages of the use of the powers of sigmiod functions in relationship the traditional MLP-Backpropagation and Polynomials in functions approximation problems.

Estimates of covariance functions for growth from birth to 630 days of age in Nelore cattle

Weight records of Brazilian Nelore cattle, from birth to 630 d of age, recorded every 3 mo, were analyzed using random regression models. Independent variables were Legendre polynomials of age at recording. The model of analysis included contemporary groups as fixed effects and age of dam as a linear and quadratic covariable. Mean trends were modeled through a cubic regression on orthogonal polynomials of age. Up to four sets of random regression coefficients were fitted for animals' direct and maternal, additive genetic, and permanent environmental effects. Changes in measurement error variances with age were modeled through a variance function. Orders of polynomial fit from three to six were considered, resulting in up to 77 parameters to be estimated. Models fitting random regressions modeled the pattern of variances in the data adequately, with estimates similar to those from corresponding univariate analysis. Direct heritability estimates decreased after birth and tended to be lowest at ages at which maternal effect estimates tended to be highest. Maternal heritability estimates increased after birth to a peak around 110 to 120 d of age and decreased thereafter. Additive genetic direct correlation estimates between weights at standard ages (birth, weaning, yearling, and final weight) were moderate to high and maternal genetic and environmental correlations were consistently high.

Guidelines for the management and treatment of periodic fever syndromes Familial Mediterranean Fever

To establish guidelines based on scientific evidence for the management of familial Mediterranean fever. The Guideline was prepared from 5 clinical questions that were structured through PICO (Patient, Intervention or indicator, Comparison and Outcome), to search in key primary scientific information databases. After defining the potential studies to support the recommendations, these were graduated considering their strength of evidence and grade of recommendation. 10,341 articles were retrieved and evaluated by title and abstract; from these, 46 articles were selected to support the recommendations. 1. The diagnosis of FMF is based on clinical manifestations, characterized by recurrent febrile episodes associated with abdominal pain, chest or arthritis of large joints; 2. FMF is a genetic disease presenting an autosomal recessive trait, caused by mutation in the MEFV gene; 3. Laboratory tests are not specific, demonstrating high serum levels of inflammatory proteins in the acute phase of the disease, but also often showing high levels even between attacks. SAA serum levels may be especially useful in monitoring the effectiveness of treatment; 4. The therapy of choice is colchicine; this drug has proven effectiveness in preventing acute inflammatory episodes and progression towards amyloidosis in adults; 5. Based on the available information, the use of biological drugs appears to be an alternative for patients with FMF who do not respond or are intolerant to therapy with colchicine.

A discrete finite-dimensional phase space approach for the description of Fe8 magnetic clusters: Wigner and Husimi functions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)