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.

Healing of dehiscence defects following root surface demineralization with tetracycline: A histologic study in monkeys

Background: the purpose of this study was to histologically evaluate the healing of experimental dehiscence defects after surface demineralization with tetracycline hydrochloride.Methods: Six adult male monkeys (Cebus apella) were used in this study. Dehiscence defects were surgically created on the buccal aspect of the mandibular lateral incisors in all animals. The root surfaces were debrided and planed. In a split-mouth design, a 10% tetracycline hydrochloride solution was applied to one tooth for 4 minutes (T group), followed by irrigation with saline. The contralateral tooth served as a control (C group). The flaps were repositioned and sutured. The animals were sacrificed at 6 months postoperatively and histological sections were processed. Computer-assisted histomorphometric analysis was used to evaluate the formation of new cementum, new bone, new connective tissue attachment, and length of the epithelium (junctional and sulcular).Results: Bone regeneration was similar in both groups (1.5 +/- 0.3 mm for the T group and 1.5 +/- 0.6 mm for the C group). The C group showed more new cementum than the T group (2.3 +/- 0.3 mm versus 2.2 +/- 0.3 mm) as well as a longer epithelium (1.0 +/- 0.3 mm versus 0.9 +/- 0.2 mm). The T group presented more new connective tissue attachment (3.1 +/- 0.2 mm) than the C group (2.9 +/- 0.6 mm). However, no statistically significant differences were detected between the two groups.Conclusions: the amount of new attachment was similar in both groups. Root conditioning with 10% tetracycline solution did not produce any additional new attachment in comparison to the controls.

Dynamical capture in the Pluto-Charon system

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

Centers on center manifolds in the Lu system

We confirm a conjecture of Mello and Coelho [Phys. Lett. A 373 (2009) 1116] concerning the existence of centers on local center manifolds at equilibria of the Lu system of differential equations on R(3). Our proof shows that the local center manifolds are algebraic ruled surfaces, and are unique. (C) 2011 Elsevier B.V. All rights reserved.

Bone healing in critical-size defects treated with platelet-rich plasma: a histologic and histometric study in rat calvaria

Background and objective: The purpose of this study was to analyze histologically the influence of autologous platelet-rich plasma on bone healing in surgically created critical-size defects in rat calvaria.Material adn Methods: Thirty-two rats were divided into two groups: the control group (group C) and the platelet-rich plasma group. An 8-mm-diameter critical-size defect was created in the calvarium of each animal. In group C the defect was filled by a blood clot only. In the platelet-rich plasma group, 0.35 mL of platelet-rich plasma was placed in the defect and covered by 0.35 mL of platelet-poor plasma. Both groups were divided into subgroups (n = 8) and killed at either 4 or 12 wk postoperatively. Histometric (using image-analysis software) and histologic analyses were performed. The amount of new bone formed was calculated as a percentage of the total area of the original defect. Percentage data were transformed into arccosine for statistical analysis (analysis of variance, Tukey, p < 0.05).Results: No defect completely regenerated with bone. The platelet-rich plasma group had a statistically greater amount of bone formation than group C at both 4 wk (17.68% vs. 7.20%, respectively) and 12 wk (24.69% vs. 11.65%, respectively) postoperatively.Conclusion: Within the limits of this study, it can be concluded that platelet-rich plasma placed in the defects and covered by platelet-poor plasma significantly enhanced bone healing in critical-size defects in rat calvaria.

Influência da densidade de estocagem no desempenho produtivo do acará-bandeira (Pterophyllum scalare)

The present study aimed to evaluate the effects of three different stock densities (0.33; 0.67 e 1.00 fish L-1) on freshwater angelfish productive performance reared in aquarium. Fish were fed with commercial diets during 35 days in two diary meals. The experimental design was entirely randomized and for each density were used four replicates. Were evaluated physical-chemical water parameters: temperature, oxygen dissolved concentration and total ammonia concentration and growth performance parameters: weight gain, feed conversion, specific growth rate, final standard length, conduction factor and length uniformity. Results were submitted to variance analysis and means were compared by Tukey's test (alpha = 0.05), it was used the statistic program ESTAT 2.0. Mortality was not observed in any tested density. on physical-chemical water parameters, total ammonia level increased significantly with stock density increasing, but they did not showed clinical signs of ammonia toxicity. As there were no significant differences between treatments, stock density 1.00 fish L-1 is the most indicated because it allows higher production.

Thermal behaviour and analytical study of the production of TiSnOx from the mixed 8-hydroxyquinolinates

Solubility and pH precipitation studies were carried out to obtain the binuclear complex {[TiO(C9H6NO)2][Sn(C9H6NO) 2]} involving 8-hydroxyquinoline as chelating agent. The compound, the individual mononuclear complexes and their physical mixture were evaluated by means of techniques such as TG, DTA, elemental analysis, X-ray diffraction, IR spectroscopy. The properties of the original compounds and also the thermoanalytical conditions exerted a great influence on the degree of crystallinity and on the crystalline phase of the mixed oxide obtained as final product of the thermal decomposition.

BFFT quantization and dynamical solutions of a fluid field theory

We study a field theory formulation of a fluid mechanical model. We implement the Hamiltonian formalism by using the BFFT conjecture in order to build a gauge invariant fluid field theory. We also generalize previous known classical dynamical field solutions for the fluid model. ©2000 The American Physical Society.

Tachyon condensation in superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the D-brane-anti-D-brane pair or for the non-BPS D-brane of superstring theories, the negative energy density cancels the brane tensions. We study this conjecture using a Wess-Zumino-Witten-like open superstring field theory free of contact term divergences and recently shown to give 60% of the vacuum energy by condensation of the tachyon field alone. While the action is non-polynomial, the multiscalar tachyon potential to any fixed level involves only a finite number of interactions. We compute this potential to level three, obtaining 85% of the expected vacuum energy, a result consistent with convergence that can also be viewed as a successful test of the string field theory. The resulting effective tachyon potential is bounded below and has two degenerate global minima. We calculate the energy density of the kink solution interpolating between these minima finding good agreement with the tension of the D-brane of one lower dimension. © 2000 Elsevier Science B.V.

Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

The critical number of atoms for Bose-Einstein condensates with cylindrically symmetrical traps were calculated. The time evolution of the condensate was also studied at changing ground state. A conjecture on higher-order nonlinear effects was also discussed to determine its signal and strength. The results show that by exchanging frequencies, the geometry favors the condensation of larger number of particles.

Towards covariant quantization of the supermembrane

By replacing ten-dimensional pure spinors with eleven-dimensional pure spinors, the formalism recently developed for covariantly quantizing the d = 10 superparticle and superstring is extended to the d = 11 superparticle and supermembrane. In this formalism, kappa symmetry is replaced by a BRST-like invariance using the nilpotent operator Q = ∮ λ αdα where dα is the worldvolume variable corresponding to the d = 11 spacetime supersymmetric derivative and λα is an SO(10, 1) pure spinor variable satisfying λΓcλ = 0 for c = 1 to 11. Super-Poincaré covariant unintegrated and integrated supermembrane vertex operators are explicitly constructed which are in the cohomology of Q. After double-dimensional reduction of the eleventh dimension, these vertex operators are related to type-IIA superstring vertex operators where Q = QL + QR is the sum of the left and right-moving type-IIA BRST operators and the eleventh component of the pure spinor constraint, λΓ 11λ = 0, replaces the bL 0 - b R 0 constraint of the closed superstring. A conjecture is made for the computation of M-theory scattering amplitudes using these supermembrane vertex operators. © SISSA/ISAS 2002.

On the injectivity of C1 maps of the real plane

Let X : ℝ2 → ℝ2 be a C1 map. Denote by Spec(X) the set of (complex) eigenvalues of DXp when p varies in ℝ2. If there exists ε > 0 such that Spec(X) ∩ (-ε, ε) = ∅, then X is injective. Some applications of this result to the real Keller Jacobian conjecture are discussed.

Cubic twistorial string field theory

Witten has recently proposed a string theory in twistor space whose D-instanton contributions are conjectured to compute M = 4 super-Yang-Mills scattering amplitudes. An alternative string theory in twistor space was then proposed whose open string tree amplitudes reproduce the D-instanton computations of maximal degree in Witten's model. In this paper, a cubic open string field theory action is constructed for this alternative string in twistor space, and is shown to be invariant under parity transformations which exchange MHV and googly amplitudes. Since the string field theory action is gauge-invariant and reproduces the correct cubic super-Yang-Mills interactions, it provides strong support for the conjecture that the string theory correctly computes N-point super-Yang-Mills tree amplitudes. © SISSA/ISAS 2004.

Multiloop amplitudes and vanishing theorems using the pure spinor formalism for the superstring

A ten-dimensional super-Poincaré covariant formalism for the superstring was recently developed which involves a BRST operator constructed from superspace matter variables and a pure spinor ghost variable. A super-Poincaré covariant prescription was defined for computing tree amplitudes and was shown to coincide with the standard RNS prescription. In this paper, picture-changing operators are used to define functional integration over the pure spinor ghosts and and to construct a suitable b ghost. A super-Poincaré covariant prescription is then given for the computation of N-point multiloop amplitudes. One can easily prove that massless N-point multiloop amplitudes vanish for N < 4, confirming the perturbative finiteness of superstring theory. One can also prove the Type IIB S-duality conjecture that R4 terms in the effective action receive no perturbative contributions above one loop. © SISSA/ISAS 2004.

Bone healing in surgically created defects treated with either bioactive glass particles, a calcium sulfate barrier, or a combination of both materials: A histological and histometric study in rat tibias

Objective: The purpose of this study was to histologically analyze the influence of bioactive glass and/or a calcium sulfate barrier on bone healing in surgically created defects in rat tibias. Material and methods: Sixty-four rats were divided into 4 groups: C (control), CS (calcium sulfate), BG (bioactive glass), and BG/CS (bioactive glass/calcium sulfate). A surgical defect was created in the tibia of each animal. In Group CS, a calcium sulfate barrier was placed to cover the defect. In Group BG the defect was filled with bioactive glass. In Group BG/CS, it was filled with bioactive glass and protected by a barrier of calcium sulfate. Animals were sacrificed at 10 or 30 days post-operative. The formation of new bone in the cortical area of the defect was evaluated histomorphometrically. Results: At 10 days post-operative, Group C presented significantly more bone formation than Groups CS, BG, or BG/CS. No statistically significant differences were found between the experimental groups. At 30 days post-operative, Group C demonstrated significantly more bone formation than the experimental groups. Groups CS and BG/CS showed significantly more bone formation than Group BG. No statistically significant differences were found between Group CS and BG/CS. Conclusions: (a) the control groups had significantly more bone formation than the experimental groups; (b) at 10 days post-operative, no significant differences were found between any of the experimental groups; and (c) at 30 days post-operative, the groups with a calcium sulfate barrier had significantly more bone formation than the group that used bioactive glass only. Copyright © Blackwell Munksgaard 2005.