Oriented Percolation in One-dimensional 1/vertical bar x-y vertical bar(2) Percolation Models

We consider independent edge percolation models on Z, with edge occupation probabilities. We prove that oriented percolation occurs when beta > 1 provided p is chosen sufficiently close to 1, answering a question posed in Newman and Schulman (Commun. Math. Phys. 104: 547, 1986). The proof is based on multi-scale analysis.

Description of costandard modules for Schur superalgebra S(2 vertical bar 1) in positive characteristic

We describe the characters of simple modules and composition factors of costandard modules for S(2 vertical bar 1) in positive characteristics and verify a conjecture of La Scala-Zubkov regarding polynomial superinvariants for GL(2 vertical bar 1).

Ex Vivo Accuracy of an Apex Locator Using Digital Signal Processing in Primary Teeth

The purpose of this study was to evaluate ex vivo the accuracy an electronic apex locator during root canal length determination in primary molars. Methods: One calibrated examiner determined the root canal length in 15 primary molars (total=34 root canals) with different stages of root resorption. Root canal length was measured both visually, with the placement of a K-file 1 mm short of the apical foramen or the apical resorption bevel, and electronically using an electronic apex locator (Digital Signal Processing). Data were analyzed statistically using the intraclass correlation (ICC) test. Results: Comparing the actual and electronic root canal length measurements in the primary teeth showed a high correlation (ICC=0.95) Conclusions: The Digital Signal Processing apex locator is useful and accurate for apex foramen location during root canal length measurement in primary molars. (Pediatr Dent 200937:320-2) Received April 75, 2008 vertical bar Lost Revision August 21, 2008 vertical bar Revision Accepted August 22, 2008

Chronic ouabain treatment exacerbates blood pressure elevation in spontaneously hypertensive rats: the role of vascular mechanisms

Objective Hypertensive rats are more sensitive to the pressor effects of acute ouabain than normotensive rats. We analyzed the effect of chronic ouabain (similar to 8.0 mu g/day, 5 weeks) treatment on the blood pressure of spontaneously hypertensive rats (SHRs) and Wistar-Kyoto rats and the contribution of vascular mechanisms. Methods Responses to acetylcholine and phenylephrine were analyzed in isolated tail arteries. Protein expression of endothelial nitric oxide synthase and cyclooxygenase-2 (COX-2) were also investigated. Results Ouabain treatment enhanced blood pressure only in SHRs. The pD(2) for acetylcholine was decreased in arteries from SHRs compared with Wistar-Kyoto rats, and ouabain did not change this parameter. However, ouabain was able to increase the pD(2) to phenylephrine in SHRs. Nitric oxide synthase inhibition with N(G)-nitro-L-arginine methyl ester or potassium channel blockade by tetraetylamonium increased the response to phenylephrine in SHRs, with a smaller increase in response observed in ouabain-treated SHRs. In addition, indomethacin (a COX inhibitor) and ridogrel (a thromboxane A(2) synthase inhibitor and prostaglandin H(2)/thromboxane A(2) receptor antagonist) decreased contraction to phenylephrine in tail rings from ouabain-treated SHRs. Protein expression of endothelial nitric oxide synthase was unaltered following ouabain treatment in SHRs, whereas COX-2 expression was increased. Conclusion Chronic ouabain treatment further increases the raised blood pressure of SHRs. This appears to involve a vascular mechanism, related to a reduced vasodilator influence of nitric oxide and endothelium-derived hyperpolarizing factor and increased production of vasoconstrictor prostanoids by COX-2. These data suggest that the increased plasma levels of ouabain could play an important role in the maintenance of hypertension and the impairment of endothelial function. J Hypertens 27:1233-1242 (C) 2009 Wolters Kluwer Health vertical bar Lippincott Williams & Wilkins.

Oxidative stress and inflammatory mediators contribute to endothelial dysfunction in high-fat diet-induced obesity in mice

Objective We investigated the effects of high-fat diet-induced obesity on vascular proinflammatory factors and oxidative stress on endothelium-dependent relaxation of the aorta. Methods Female Swiss mice were submitted to a high-fat diet for 16 weeks. At the end of the experimental period, we evaluated blood pressure, relaxation in response to acetylcholine in aortic rings in the absence and the presence of the superoxide anion scavenger, superoxide dismutase (SOD, 150 U/ml), and the nuclear factor (NF)-kappa B inhibitor, sodium salicylate (5 mmol/l). Aortic protein expression of endothelial nitric oxide synthase, Cu/Zn-SOD, NF-kappa B, I kappa B-alpha, and proinflammatory cytokines were also evaluated. Results Obese mice presented higher systolic and diastolic blood pressure than control mice (P<0.05). The relaxation of aortas to acetylcholine, but not to sodium nitroprusside, was significantly decreased in obese mice and was corrected by both SOD and sodium salicylate (P<0.05). The protein expression of endothelial nitric oxide synthase and Cu/Zn-SOD was significantly decreased in aorta from obese mice (P<0.05). Total p65 NF-kappa B subunit protein expression was not affected by obesity, but the protein expression of NF-kappa B inhibitor I kappa B-alpha was lower in aorta from obese mice (P<0.05). There were no significant differences in the interleukin (IL)-1 beta and IL-6 protein expression between groups. In contrast, the expression of TNF-alpha was significantly increased in aortas from obese mice. Conclusion Our resultssuggest that the reducedantioxidant defense and the local NF-kappa B pathway play an important role in the impairment of endothelium-dependent relaxation in aorta from obese mice. J Hypertens 28: 2111-2119 (C) 2010 Wolters Kluwer Health vertical bar Lippincott Williams & Wilkins.

Mesenchymal Stem Cells Attenuate Renal Fibrosis Through Immune Modulation and Remodeling Properties in a Rat Remnant Kidney Model

Mesenchymal stem cells (MSCs) have regenerative properties in acute kidney injury, but their role in chronic kidney diseases is still unknown. More specifically, it is not known whether MSCs halt fibrosis. The purpose of this work was to investigate the role of MSCs in fibrogenesis using a model of chronic renal failure. MSCs were obtained from the tibias and femurs of male Wistar-EPM rats. Female Wistar rats were subjected to the remnant model, and 2 vertical bar x vertical bar 10(5) MSCs were intravenously administrated to each rat every other week for 8 weeks or only once and followed for 12 weeks. SRY gene expression was observed in female rats treated with male MSCs, and immune localization of CD73(+)CD90(+) cells at 8 weeks was also assessed. Serum and urine analyses showed an amelioration of functional parameters in MSC-treated animals at 8 weeks, but not at 12 weeks. Masson`s trichrome and Sirius red staining demonstrated reduced levels of fibrosis in MSC-treated animals. These results were corroborated by reduced vimentin, type I collagen, transforming growth factor beta, fibroblast specific protein 1 (FSP-1), monocyte chemoattractant protein 1, and Smad3 mRNA expression and alpha smooth muscle actin and FSP-1 protein expression. Renal interleukin (IL)-6 and tumor necrosis factor alpha mRNA expression levels were significantly decreased after MSC treatment, whereas IL-4 and IL-10 expression levels were increased. All serum cytokine expression levels were decreased in MSC-treated animals. Taken together, these results suggested that MSC therapy can indeed modulate the inflammatory response that follows the initial phase of a chronic renal injury. The immunosuppressive and remodeling properties of MSCs may be involved in the decreased fibrosis in the kidney. STEM CELLS 2009;27:3063-3073

Dipeptidyl peptidase IV inhibition attenuates blood pressure rising in young spontaneously hypertensive rats

Objectives The present study aimed to assess the effect of the specific dipeptidyl peptidase IV (DPPIV) inhibitor sitagliptin on blood pressure and renal function in young prehypertensive (5-week-old) and adult spontaneously hypertensive rats (SHRs; 14-week-old). Methods Sitagliptin (40 mg/kg twice daily) was given by oral gavage to young (Y-SHR + IDPPIV) and adult (A-SHR R IDPPIV) SHRs for 8 days. Kidney function was assessed daily and compared with age-matched vehicle-treated SHR (Y-SHR and A-SHR) and with normotensive Wistar-Kyoto rats (Y-WKY and A-WKY). Arterial blood pressure was measured in these animals at the end of the experimental protocol. Additionally, Na(+)/H(+) exchanger isoform 3 (NHE3) function and expression in microvilli membrane vesicles were assessed in young animals. Results Mean arterial blood pressure of Y-SHR + IDPPIV was significantly lower than that of Y-SHR (104 +/- 3 vs. 123 +/- 5 mmHg, P < 0.01) and was similar to Y-WKY (94 +/- 4 mmHg, P > 0.05). Compared to Y-SHR, Y-SHR + IDPPIV exhibited enhanced cumulative urinary flow and sodium excretion and decreased NHE3 activity and expression in proximal tubule microvilli. In the A-SHR, sitagliptin treatment had no significant effect on either renal function or arterial blood pressure. Conclusion Our data suggest that DPPIV inhibition attenuates blood pressure rising in young prehypertensive SHRs, partially by inhibiting NHE3 activity in renal proximal tubule. J Hypertens 29:520-528 (C) 2011 Wolters Kluwer Health vertical bar Lippincott Williams & Wilkins.

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.

ON INTEGRABLE CODIMENSION ONE ANOSOV ACTIONS OF R(k)

In this paper, we consider codimension one Anosov actions of R(k), k >= 1, on closed connected orientable manifolds of dimension n vertical bar k with n >= 3. We show that the fundamental group of the ambient manifold is solvable if and only if the weak foliation of codimension one is transversely affine. We also study the situation where one 1-parameter subgroup of R(k) admits a cross-section, and compare this to the case where the whole action is transverse to a fibration over a manifold of dimension n. As a byproduct, generalizing a Theorem by Ghys in the case k = 1, we show that, under some assumptions about the smoothness of the sub-bundle E(ss) circle plus E(uu), and in the case where the action preserves the volume, it is topologically equivalent to a suspension of a linear Anosov action of Z(k) on T(n).

Global attractor for a model of extensible beam with nonlinear damping and source terms

This paper is concerned with the existence of a global attractor for the nonlinear beam equation, with nonlinear damping and source terms, u(tt) + Delta(2)u -M (integral(Omega)vertical bar del u vertical bar(2)dx) Delta u + f(u) + g(u(t)) = h in Omega x R(+), where Omega is a bounded domain of R(N), M is a nonnegative real function and h is an element of L(2)(Omega). The nonlinearities f(u) and g(u(t)) are essentially vertical bar u vertical bar(rho) u - vertical bar u vertical bar(sigma) u and vertical bar u(t)vertical bar(r) u(t) respectively, with rho, sigma, r > 0 and sigma < rho. This kind of problem models vibrations of extensible beams and plates. (C) 2010 Elsevier Ltd. All rights reserved.

MULTIPLICITY OF POSITIVE SOLUTIONS FOR A CLASS OF NONLINEAR SCHRODINGER EQUATIONS

This paper proves the multiplicity of positive solutions for the following class of quasilinear problems: {-epsilon(p)Delta(p)u+(lambda A(x) + 1)vertical bar u vertical bar(p-2)u = f(u), R(N) u(x)>0 in R(N), where Delta(p) is the p-Laplacian operator, N > p >= 2, lambda and epsilon are positive parameters, A is a nonnegative continuous function and f is a continuous function with subcritical growth. Here, we use variational methods to get multiplicity of positive solutions involving the Lusternick-Schnirelman category of intA(-1)(0) for all sufficiently large lambda and small epsilon.

DAMPED WAVE EQUATIONS WITH FAST GROWING DISSIPATIVE NONLINEARITIES

Let a > 0, Omega subset of R(N) be a bounded smooth domain and - A denotes the Laplace operator with Dirichlet boundary condition in L(2)(Omega). We study the damped wave problem {u(tt) + au(t) + Au - f(u), t > 0, u(0) = u(0) is an element of H(0)(1)(Omega), u(t)(0) = v(0) is an element of L(2)(Omega), where f : R -> R is a continuously differentiable function satisfying the growth condition vertical bar f(s) - f (t)vertical bar <= C vertical bar s - t vertical bar(1 + vertical bar s vertical bar(rho-1) + vertical bar t vertical bar(rho-1)), 1 < rho < (N - 2)/(N + 2), (N >= 3), and the dissipativeness condition limsup(vertical bar s vertical bar ->infinity) s/f(s) < lambda(1) with lambda(1) being the first eigenvalue of A. We construct the global weak solutions of this problem as the limits as eta -> 0(+) of the solutions of wave equations involving the strong damping term 2 eta A(1/2)u with eta > 0. We define a subclass LS subset of C ([0, infinity), L(2)(Omega) x H(-1)(Omega)) boolean AND L(infinity)([0, infinity), H(0)(1)(Omega) x L(2)(Omega)) of the `limit` solutions such that through each initial condition from H(0)(1)(Omega) x L(2)(Omega) passes at least one solution of the class LS. We show that the class LS has bounded dissipativeness property in H(0)(1)(Omega) x L(2)(Omega) and we construct a closed bounded invariant subset A of H(0)(1)(Omega) x L(2)(Omega), which is weakly compact in H(0)(1)(Omega) x L(2)(Omega) and compact in H({I})(s)(Omega) x H(s-1)(Omega), s is an element of [0, 1). Furthermore A attracts bounded subsets of H(0)(1)(Omega) x L(2)(Omega) in H({I})(s)(Omega) x H(s-1)(Omega), for each s is an element of [0, 1). For N = 3, 4, 5 we also prove a local uniqueness result for the case of smooth initial data.

The curve selection lemma and the Morse-Sard theorem

We use an inequality due to Bochnak and Lojasiewicz, which follows from the Curve Selection Lemma of real algebraic geometry in order to prove that, given a C(r) function f : U subset of R(m) -> R, we have lim(y -> xy is an element of crit(f)) vertical bar f(y) - f(x)vertical bar/vertical bar y - x vertical bar(r) = 0, for all x is an element of crit(f)` boolean AND U, where crit( f) = {x is an element of U vertical bar df ( x) = 0}. This shows that the so-called Morse decomposition of the critical set, used in the classical proof of the Morse-Sard theorem, is not necessary: the conclusion of the Morse decomposition lemma holds for the whole critical set. We use this result to give a simple proof of the classical Morse-Sard theorem ( with sharp differentiability assumptions).

Semilinear elliptic problems near resonance with a nonprincipal eigenvalue

We consider the Dirichlet problem for the equation -Delta u = lambda u +/- (x, u) + h(x) in a bounded domain, where f has a sublinear growth and h is an element of L-2. We find suitable conditions on f and It in order to have at least two solutions for X near to an eigenvalue of -Delta. A typical example to which our results apply is when f (x, u) behaves at infinity like a(x)vertical bar u vertical bar(q-2)u, with M > a(x) > delta > 0, and I < q < 2. (C) 2007 Elsevier Inc. All rights reserved.

Regularity of solutions on the global attractor for a semilinear damped wave equation

We consider attractors A(eta), eta epsilon [0, 1], corresponding to a singularly perturbed damped wave equation u(tt) + 2 eta A(1/2)u(t) + au(t) + Au = f (u) in H-0(1)(Omega) x L-2 (Omega), where Omega is a bounded smooth domain in R-3. For dissipative nonlinearity f epsilon C-2(R, R) satisfying vertical bar f ``(s)vertical bar <= c(1 + vertical bar s vertical bar) with some c > 0, we prove that the family of attractors {A(eta), eta >= 0} is upper semicontinuous at eta = 0 in H1+s (Omega) x H-s (Omega) for any s epsilon (0, 1). For dissipative f epsilon C-3 (R, R) satisfying lim(vertical bar s vertical bar) (->) (infinity) f ``(s)/s = 0 we prove that the attractor A(0) for the damped wave equation u(tt) + au(t) + Au = f (u) (case eta = 0) is bounded in H-4(Omega) x H-3(Omega) and thus is compact in the Holder spaces C2+mu ((Omega) over bar) x C1+mu((Omega) over bar) for every mu epsilon (0, 1/2). As a consequence of the uniform bounds we obtain that the family of attractors {A(eta), eta epsilon [0, 1]} is upper and lower semicontinuous in C2+mu ((Omega) over bar) x C1+mu ((Omega) over bar) for every mu epsilon (0, 1/2). (c) 2007 Elsevier Inc. All rights reserved.