Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

A geometric mass-preserving redistancing scheme for the level set function

In this paper we describe and evaluate a geometric mass-preserving redistancing procedure for the level set function on general structured grids. The proposed algorithm is adapted from a recent finite element-based method and preserves the mass by means of a localized mass correction. A salient feature of the scheme is the absence of adjustable parameters. The algorithm is tested in two and three spatial dimensions and compared with the widely used partial differential equation (PDE)-based redistancing method using structured Cartesian grids. Through the use of quantitative error measures of interest in level set methods, we show that the overall performance of the proposed geometric procedure is better than PDE-based reinitialization schemes, since it is more robust with comparable accuracy. We also show that the algorithm is well-suited for the highly stretched curvilinear grids used in CFD simulations. Copyright (C) 2010 John Wiley & Sons, Ltd.

A Direct Numerov Sixth-order Numerical Scheme to Accurately Solve the Unidimensional Poisson Equation with Dirichlet Boundary Conditions

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.

A DISCRETIZATION SCHEME FOR AN ONE-DIMENSIONAL REACTION-DIFFUSION EQUATION WITH DELAY AND ITS DYNAMICS

The goal of this paper is to present an approximation scheme for a reaction-diffusion equation with finite delay, which has been used as a model to study the evolution of a population with density distribution u, in such a way that the resulting finite dimensional ordinary differential system contains the same asymptotic dynamics as the reaction-diffusion equation.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

Differential regulation of PGC-1 alpha expression in rat liver and skeletal muscle in response to voluntary running

Background: The beneficial actions of exercise training on lipid, glucose and energy metabolism and insulin sensitivity appear to be in part mediated by PGC-1 alpha. Previous studies have shown that spontaneously exercised rats show at rest enhanced responsiveness to exogenous insulin, lower plasma insulin levels and increased skeletal muscle insulin sensitivity. This study was initiated to examine the functional interaction between exercise-induced modulation of skeletal muscle and liver PGC-1 alpha protein expression, whole body insulin sensitivity, and circulating FFA levels as a measure of whole body fatty acid (lipid) metabolism. Methods: Two groups of male Wistar rats (2 Mo of age, 188.82 +/- 2.77 g BW) were used in this study. One group consisted of control rats placed in standard laboratory cages. Exercising rats were housed individually in cages equipped with running wheels and allowed to run at their own pace for 5 weeks. At the end of exercise training, insulin sensitivity was evaluated by comparing steady-state plasma glucose (SSPG) concentrations at constant plasma insulin levels attained during the continuous infusion of glucose and insulin to each experimental group. Subsequently, soleus and plantaris muscle and liver samples were collected and quantified for PGC-1 alpha protein expression by Western blotting. Collected blood samples were analyzed for glucose, insulin and FFA concentrations. Results: Rats housed in the exercise wheel cages demonstrated almost linear increases in running activity with advancing time reaching to maximum value around 4 weeks. On an average, the rats ran a mean (Mean +/- SE) of 4.102 +/- 0.747 km/day and consumed significantly more food as compared to sedentary controls (P < 0.001) in order to meet their increased caloric requirement. Mean plasma insulin (P < 0.001) and FFA (P < 0.006) concentrations were lower in the exercise-trained rats as compared to sedentary controls. Mean steady state plasma insulin (SSPI) and glucose (SSPG) concentrations were not significantly different in sedentary control rats as compared to exercise-trained animals. Plantaris PGC-1 alpha protein expression increased significantly from a 1.11 +/- 0.12 in the sedentary rats to 1.74 +/- 0.09 in exercising rats (P < 0.001). However, exercise had no effect on PGC-1 alpha protein content in either soleus muscle or liver tissue. These results indicate that exercise training selectively up regulates the PGC-1 alpha protein expression in high-oxidative fast skeletal muscle type such as plantaris muscle. Conclusion: These data suggest that PGC-1 alpha most likely plays a restricted role in exercise-mediated improvements in insulin resistance (sensitivity) and lowering of circulating FFA levels.

Analysis of the histologic features in the differential diagnosis of intrahepatic neonatal cholestasis

AIM: To compare the histologic features of the liver in intrahepatic neonatal cholestasis (IHNC) with infectious, genetic-endocrine-metabolic, and idiopathic etiologies. METHODS: Liver biopsies from 86 infants with IHNC were evaluated. The inclusion criteria consisted of jaundice beginning at 3 mo of age and a hepatic biopsy during the 1st year of life. The following histologic features were evaluated: cholestasis, eosinophilia, giant cells, erythropoiesis, siderosis, portal fibrosis, and the presence of a septum. RESULTS: Based on the diagnosis, patients were classified into three groups: group 1 (infectious; n = 18), group 2 (genetic-endocrine-metabolic; n = 18), and group 3 (idiopathic; n = 50). There were no significant differences with respect to the following variables: cholestasis, eosinophilia, giant cells, siderosis, portal fibrosis, and presence of a septum. A significant difference was observed with respect to erythropoiesis, which was more severe in group 1 (Fisher's exact test, P = 0.016). CONCLUSION: A significant difference was observed in IHNC of infectious etiology, in which erythropoiesis was more severe than that in genetic-endocrine-metabolic and idiopathic etiologies, whereas there were no significant differences among cholestasis, eosinophilia, giant cells, siderosis, portal fibrosis, and the presence of a septum. (C) 2009 The WIG Press and Baishideng. All rights reserved.

Differential gene expression profiling in mucus glands of honey bee (Apis mellifera) drones during sexual maturation

The mating sign that each drone leaves when mating with a queen essentially consists of mucus gland proteins. We employed a Representational Difference Analysis (RDA) methodology to identify genes that are differentially expressed in mucus glands during sexual maturation of drones. The RDA library for mucus glands of newly emerged drones was more complex than that of 8 day-old drones, with matches to 20 predicted genes. Another 26 reads matched to the Apis genome but not to any predicted gene. Since these ESTs were located within ORFs they may represent novel honey bee genes, possibly fast evolving mucus gland proteins. In the RDA library for mucus glands of 8 day-old drones, most reads corresponded to a capsid protein of deformed wing virus, indicating high viral loads in these glands. The expression of two genes encoding venom allergens, acid phosphatase-1 and hyaluronidase, in drone mucus glands argues for their homology with the female venom glands, both associated with the reproductive system.

Differential expression of 12 histone deacetylase (HDAC) genes in astrocytomas and normal brain tissue: class II and IV are hypoexpressed in glioblastomas

Background: Glioblastoma is the most lethal primary malignant brain tumor. Although considerable progress has been made in the treatment of this aggressive tumor, the clinical outcome for patients remains poor. Histone deacetylases (HDACs) are recognized as promising targets for cancer treatment. In the past several years, HDAC inhibitors (HDACis) have been used as radiosensitizers in glioblastoma treatment. However, no study has demonstrated the status of global HDAC expression in gliomas and its possible correlation to the use of HDACis. The purpose of this study was to evaluate and compare mRNA and protein levels of class I, II and IV of HDACs in low grade and high grade astrocytomas and normal brain tissue and to correlate the findings with the malignancy in astrocytomas. Methods: Forty-three microdissected patient tumor samples were evaluated. The histopathologic diagnoses were 20 low-grade gliomas (13 grade I and 7 grade II) and 23 high-grade gliomas (5 grade III and 18 glioblastomas). Eleven normal cerebral tissue samples were also analyzed (54 total samples analyzed). mRNA expression of class I, II, and IV HDACs was studied by quantitative real-time polymerase chain reaction and normalized to the housekeeping gene beta-glucuronidase. Protein levels were evaluated by western blotting. Results: We found that mRNA levels of class II and IV HDACs were downregulated in glioblastomas compared to low-grade astrocytomas and normal brain tissue (7 in 8 genes, p < 0.05). The protein levels of class II HDAC9 were also lower in high-grade astrocytomas than in low-grade astrocytomas and normal brain tissue. Additionally, we found that histone H3 (but not histone H4) was more acetylated in glioblastomas than normal brain tissue. Conclusion: Our study establishes a negative correlation between HDAC gene expression and the glioma grade suggesting that class II and IV HDACs might play an important role in glioma malignancy. Evaluation of histone acetylation levels showed that histone H3 is more acetylated in glioblastomas than normal brain tissue confirming the downregulation of HDAC mRNA in glioblastomas.

Differential expression of microRNAs in mouse pain models

Background: MicroRNAs (miRNAs) are short non-coding RNAs that inhibit translation of target genes by binding to their mRNAs. The expression of numerous brain-specific miRNAs with a high degree of temporal and spatial specificity suggests that miRNAs play an important role in gene regulation in health and disease. Here we investigate the time course gene expression profile of miR-1, -16, and -206 in mouse dorsal root ganglion (DRG), and spinal cord dorsal horn under inflammatory and neuropathic pain conditions as well as following acute noxious stimulation. Results: Quantitative real-time polymerase chain reaction analyses showed that the mature form of miR-1, -16 and -206, is expressed in DRG and the dorsal horn of the spinal cord. Moreover, CFA-induced inflammation significantly reduced miRs-1 and -16 expression in DRG whereas miR-206 was downregulated in a time dependent manner. Conversely, in the spinal dorsal horn all three miRNAs monitored were upregulated. After sciatic nerve partial ligation, miR-1 and -206 were downregulated in DRG with no change in the spinal dorsal horn. On the other hand, axotomy increases the relative expression of miR-1, -16, and 206 in a time-dependent fashion while in the dorsal horn there was a significant downregulation of miR-1. Acute noxious stimulation with capsaicin also increased the expression of miR-1 and -16 in DRG cells but, on the other hand, in the spinal dorsal horn only a high dose of capsaicin was able to downregulate miR-206 expression. Conclusions: Our results indicate that miRNAs may participate in the regulatory mechanisms of genes associated with the pathophysiology of chronic pain as well as the nociceptive processing following acute noxious stimulation. We found substantial evidence that miRNAs are differentially regulated in DRG and the dorsal horn of the spinal cord under different pain states. Therefore, miRNA expression in the nociceptive system shows not only temporal and spatial specificity but is also stimulus-dependent.