Extensions of homogeneous polynomials ON c(0)(l(2)(i))

We show that a 2-homogeneous polynomial on the complex Banach space c(0)(l(2)(i)) is norm attaining if and only if it is finite (i.e, depends only on finite coordinates). As the consequence, we show that there exists a unique norm-preserving extension for norm-attaining 2-homogeneous polynomials on c(0)(l(2)(i)).

The univalent polynomial of Suffridge as a summability kernel

A positive summability trigonometric kernel {K(n)(theta)}(infinity)(n=1) is generated through a sequence of univalent polynomials constructed by Suffridge. We prove that the convolution {K(n) * f} approximates every continuous 2 pi-periodic function f with the rate omega(f, 1/n), where omega(f, delta) denotes the modulus of continuity, and this provides a new proof of the classical Jackson`s theorem. Despite that it turns out that K(n)(theta) coincide with positive cosine polynomials generated by Fejer, our proof differs from others known in the literature.

A full family of multimodal maps on the circle

We exhibit a family of trigonometric polynomials inducing a family of 2m-multimodal maps on the circle which contains all relevant dynamical behavior.

Chronic Suppurative Otitis Media in Cleft Palate: Microorganism Etiology and Susceptibilities

Objective: To investigate the microbial etiology of suppurative chronic otitis media (SCOM) in patients with complete cleft lip and palate and isolated cleft palate and to determine the sensitivity of isolated microorganisms to antibiotics by drug diffusion from impregnated discs in agar and the minimum inhibitory concentration of each drug to these microorganisms by drug dilution in agar. Design/Patients: Effusion samples of SCOM obtained from 40 patients with cleft lip and palate registered at the Hospital for Rehabilitation of Craniofacial Anomalies, University of Sao Paulo, at Bauru, Brazil, were bacteriologically analyzed by cultures. The isolated bacteria were submitted to an in vitro susceptibility test to clinically used drugs. Results: Positive cultures were obtained in 100% of studied cases. Among the 57 strains observed, the most frequent were Pseudomonas aeruginosa (35%), Staphylococcus aureus (15.5%), Enterococcus faecalis (14%), and Proteus mirabilis (12%). The frequency of Gram-negative bacilli (enterobacteriaceae and nonfermentative bacilli) was 67%. Pseudomonas aeruginosa presented the highest sensitivity to ciprofloxacin, and enterobacteriaceae exhibited the highest sensitivity to gentamicin. The strains of S. aureus and E. faecalis presented the highest sensitivity to imipenem and sulfamethoxazole/trimethoprim, respectively. Conclusion: Patients with cleft lip and palate presenting with SCOM exhibited 100% positive cultures, with the highest frequency of Pseudomonas and enterobacteriaceae. With regard to the action of antibiotics, imipenem was effective against the four species of isolated microorganisms, followed by ciprofloxacin, which was effective against 75% of isolated species.

Melatonin inhibits LPS-induced NO production in rat endothelial cells

Endothelial cells produce NO by activation of constitutive nitric oxide synthase (NOS) and transcription of inducible NOS (iNOS). We have previously shown that melatonin, in the nanomolar range, inhibits activation of constitutive NOS, and in the present paper, we evaluated whether it could interfere with the expression of iNOS, which is activated by lipopolysaccharide (LPS), a major component of gram-negative bacteria cell walls. Primary cultures of rat endothelial cells were loaded with fluorescent probe for NO detection. Nuclear factor kappa B (NF-kappa B) translocation in endothelial cells elicited by LPS was measured by electromobility shift assay, and the vasodilation of aortic rings was accessed by recording isometric contraction. Melatonin in a micromolar but not in a nanomolar range inhibits the NO production induced by LPS. This effect is not dependent on the activation of G protein-coupled melatonin receptors. The nuclear NF-kappa B translocation is a process necessary for iNOS transcription, and melatonin also inhibits its translocation. LPS induced vasodilation only in endothelium-intact aortic rings, and melatonin (10 mu m) inhibits the vasodilation. Here, we show that concentrations compatible with nocturnal melatonin surge (nm) did not interfere with the activity of iNOS. Considering that micromolar melatonin concentrations could be locally achieved through production by activated immune competent cells, extra-pineal melatonin could have a protective effect against tissue injury. We propose that melatonin blocked the LPS-induced vasodilation by inhibiting the NF-kappa B pathway. Finally, we propose that the effect of melatonin on vascular reactivity is one of the mechanisms that underlies the protective effect of this indolamine against LPS.

TLR4 and CD14 receptors expressed in rat pineal gland trigger NFKB pathway

Nuclear factor-kappa B (NFKB), a pivotal player in inflammatory responses, is constitutively expressed in the pineal gland. Corticosterone inhibits pineal NFKB leading to an enhancement of melatonin production, while tumor necrosis factor (TNF) leads to inhibition of Aa-nat transcription and the production of N-acetylserotonin in cultured glands. The reduction in nocturnal melatonin surge favors the mounting of the inflammatory response. Despite these data, there is no clear evidence of the ability of the pineal gland to recognize molecules that signal infection. This study investigated whether the rat pineal gland expresses receptors for lipopolysaccharide (LPS), the endotoxin from the membranes of Gram-negative bacteria, and to establish the mechanism of action of LPS. Here, we show that pineal glands possess both CD14 and toll-like receptor 4 (TLR4), membrane proteins that bind LPS and trigger the NFKB pathway. LPS induced the nuclear translocation of p50/p50 and p50/RELA dimers and the synthesis of TNF. The maximal expression of TNF in cultured glands coincides with an increase in the expression of TNF receptor 1 (TNFR1) in isolated pinealocytes. In addition, LPS inhibited the synthesis of N-acetylserotonin and melatonin. Therefore, the pineal gland transduces Gram-negative endotoxin stimulation by producing TNF and inhibiting melatonin synthesis. Here, we provide evidence to reinforce the idea of an immune-pineal axis, showing that the pineal gland is a constitutive player in the innate immune response.

Insulin suppresses LPS-induced iNOS and COX-2 expression and NF-kappa B activation in alveolar macrophages

The development of septic shock is a common and frequently lethal consequence of gram-negative infection. Mediators released by lung macrophages activated by bacterial products such as lipopolysaccharide (LPS) contribute to shock symptoms. We have shown that insulin downregulates LPS-induced TNF production by alveolar macrophages (AMs). In the present study, we investigated the effect of insulin on the LPS-induced production of nitric oxide (NO) and prostaglandin (PG)-E(2), on the expression of inducible nitric oxide synthase ( iNOS) and cyclooxygenase (COX)-2, and on nuclear factor kappa B (NF-kappa B) activation in AMs. Resident AMs from male Wistar rats were stimulated with LPS (100 ng/mL) for 30 minutes. Insulin (1 mU/mL) was added 10 min before LPS. Enzymes expression, NF-kappa B p65 activation and inhibitor of kappa B (I-kappa B) a phosphorylation were assessed by immunobloting; NO by Griess reaction and PGE(2) by enzyme immunoassay (EIA). LPS induced in AMs the expression of iNOS and COX-2 proteins and production of NO and PGE(2), and, in parallel, NF-kappa B p65 activation and cytoplasmic I-kappa B alpha phosphorylation. Administration of insulin before LPS suppressed the expression of iNOS and COX-2, of NO and PGE(2) production and Nuclear NF-kappa B p65 activation. Insulin also prevented cytoplasmic I-kappa Ba phosphorylation. These results show that in AMs stimulated by LPS, insulin prevents nuclear translocation of NF-kappa B, possibly by blocking I-kappa Ba degradation, and supresses the production of NO and PGE(2), two molecules that contribute to septic shock. Copyright (C) 2008 S. Karger AG, Basel.

Invariant theory and reversible-equivariant vector fields

In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants. (C) 2008 Elsevier B.V, All rights reserved.

Reaction-diffusion systems coupled at the boundary and the Morse-Smale property

We study an one-dimensional nonlinear reaction-diffusion system coupled on the boundary. Such system comes from modeling problems of temperature distribution on two bars of same length, jointed together, with different diffusion coefficients. We prove the transversality property of unstable and stable manifolds assuming all equilibrium points are hyperbolic. To this end, we write the system as an equation with noncontinuous diffusion coefficient. We then study the nonincreasing property of the number of zeros of a linearized nonautonomous equation as well as the Sturm-Liouville properties of the solutions of a linear elliptic problem. (C) 2008 Elsevier Inc. All rights reserved.

Finite-dimensional non-associative algebras and codimension growth

Let A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded. Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One of the main tools of independent interest is the construction in the free non-associative algebra of multialternating polynomials satisfying special properties. (C) 2010 Elsevier Inc. All rights reserved.

Positive solutions of the p-Laplacian involving a superlinear nonlinearity with zeros

Using a combination of several methods, such as variational methods. the sub and supersolutions method, comparison principles and a priori estimates. we study existence, multiplicity, and the behavior with respect to lambda of positive solutions of p-Laplace equations of the form -Delta(p)u = lambda h(x, u), where the nonlinear term has p-superlinear growth at infinity, is nonnegative, and satisfies h(x, a(x)) = 0 for a suitable positive function a. In order to manage the asymptotic behavior of the solutions we extend a result due to Redheffer and we establish a new Liouville-type theorem for the p-Laplacian operator, where the nonlinearity involved is superlinear, nonnegative, and has positive zeros. (C) 2009 Elsevier Inc. All rights reserved.

UNIQUENESS OF THE EXTENSION OF 2-HOMOGENEOUS POLYNOMIALS

Homogeneous polynomials of degree 2 on the complex Banach space c(0)(l(n)(2)) are shown to have unique norm-preserving extension to the bidual space. This is done by using M-projections and extends the analogous result for c(0) proved by P.-K. Lin.