Existence and multiplicity results for quasilinear elliptic equations

The goal of this paper is to study the multiplicity of positive solutions of a class of quasilinear elliptic equations. Based on the mountain pass theorems and sub-and supersolutions argument for p-Laplacian operators, under suitable conditions on nonlinearity f (x, s), we show the following problem: -Delta(p)u = lambda f(x,u) in Omega, u/(partial derivative Omega) = 0, where Omega is a bounded open subset of R-N, N >= 2, with smooth boundary, lambda is a positive parameter and Delta(p) is the p-Laplacian operator with p > 1, possesses at least two positive solutions for large lambda.

Multiplicity results for second-order two-point boundary value problems with nonlinearities across several eigenvalues

We consider the boundary value problems for nonlinear second-order differential equations of the form u '' + a(t)f (u) = 0, 0 < t < 1, u(0) = u (1) = 0. We give conditions on the ratio f (s)/s at infinity and zero that guarantee the existence of solutions with prescribed nodal properties. Then we establish existence and multiplicity results for nodal solutions to the problem. The proofs of our main results are based upon bifurcation techniques. (c) 2004 Elsevier Ltd. All rights reserved.

Multiplicity results for second-order two-point boundary value problems with superlinear or sublinear nonlinearities

We consider boundary value problems for nonlinear second order differential equations of the form u + a(t) f(u) = 0, t epsilon (0, 1), u(0) = u(1) = 0, where a epsilon C([0, 1], (0, infinity)) and f : R --> R is continuous and satisfies f (s)s > 0 for s not equal 0. We establish existence and multiplicity results for nodal solutions to the problems if either f(0) = 0, f(infinity) = infinity or f(0) = infinity, f(0) = 0, where f (s)/s approaches f(0) and f(infinity) as s approaches 0 and infinity, respectively. We use bifurcation techniques to prove our main results. (C) 2004 Elsevier Inc. All rights reserved.

El Niño Southern Oscillation and Ross River Virus Outbreaks in Australia

Various authors have suggested a general predictive value of climatic indices of El Nino/Southem Oscillation events as indicators of outbreaks of arbovirus disease, particularly Ross River virus in Australia. By analyzing over 100 years of historical outbreak data on Ross River virus disease, our data indicate that, although high Southern Oscillation Index and La Nina conditions are potentially important predictors for the Murray Darling River region, this is not the case for the other four ecological zones in Australia. Our study, therefore, cautions against overgeneralization and suggests that, since climate and weather exert different influences and have different biological implications for the multiplicity of vectors involved, it is logical that predictors should be heterogeneous.

Application of mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

A physiological product-release model for baculovirus infected insect cells

Existing models describe the product release from baculovirus infected insect cells as an unspecific protein leakage occurring in parallel with protein production. The model presented here shows that the observed product release of normally non-secreted proteins can be described through cell death alone. This model avoids the implicit non-physiological assumption of previous models that cells permeable to recombinant protein as well as trypan blue continue to produce protein. (c) 2005 Wiley Periodicals, Inc.

Using mixture models to detect differentially expressed genes

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local false discovery rate is provided for each gene, and it can be implemented so that the implied global false discovery rate is bounded as with the Benjamini-Hochberg methodology based on tail areas. The latter procedure is too conservative, unless it is modified according to the prior probability that a gene is not differentially expressed. An attractive feature of the mixture model approach is that it provides a framework for the estimation of this probability and its subsequent use in forming a decision rule. The rule can also be formed to take the false negative rate into account.

A note on bifurcation from an interval

We study the global bifurcation of nonlinear Sturm-Liouville problems of the form -(pu')' + qu = lambda a(x)f(u), b(0)u(0) - c(0)u' (0) = 0, b(1)u(1) + c(1)u'(1) = 0 which are not linearizable in any neighborhood of the origin. (c) 2005 Published by Elsevier Ltd.

Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

Folate: Methods of analysis

Folates and its derivatives occur as polyglutamates in nature. The multiplicity of forms and the generally low levels in foods makes quantitative analysis of folate a difficult task. The assay of folates from foods generally involves three steps: liberation of folates from the cellular matrix; deconjugation from the polyglutamate to the mono and di-glutamate forms; and the detection of the biological activity or chemical concentration of the resulting folates. The detection methods used are the microbiological assay relying on the turbidimetric bacterial growth of Lactobacillus rhamnosus which is by far the most commonly used method; the HPLC and LC/MS techniques and bio-specific procedures. This review attempts to describe the methods along with the merits and demerits of using each of these methods.

Operation of polymer electrolyte membrane fuel cells with dry feeds: Design and operating strategies

The operation of polymer electrolyte membrane fuel cells (PEMFCs) with dry feeds has been examined with different fuel cell flow channel designs as functions of pressure, temperature and flow rate. Auto-humidified (or self-humidifying) PEMFC operation is improved at higher pressures and low gas velocities where axial dispersion enhances back-mixing of the product water with the dry feed. We demonstrate auto-humidified operation of the channel-less, self-draining fuel cell, based on a stirred tank reactor; data is presented showing auto-humidified operation from 25 to 115 degrees C at 1 and 3 atm. Design and operating requirements are derived for the auto-humidified operation of the channel-less, self-draining fuel cell. The auto-humidified self-draining fuel cell outperforms a fully humidified serpentine flow channel fuel cell at high current densities. The new design offers substantial benefits for simplicity of operation and control including: the ability to self-drain reducing flooding, the ability to uniformly disperse water removing current gradients and the ability to operate on dry feeds eliminating the need for humidifiers. Additionally, the design lends itself well to a modular design concept. (c) 2005 Elsevier B.V. All rights reserved.

Mixture models for detecting differentially expressed genes in microarrays

An important and common problem in microarray experiments is the detection of genes that are differentially expressed in a given number of classes. As this problem concerns the selection of significant genes from a large pool of candidate genes, it needs to be carried out within the framework of multiple hypothesis testing. In this paper, we focus on the use of mixture models to handle the multiplicity issue. With this approach, a measure of the local FDR (false discovery rate) is provided for each gene. An attractive feature of the mixture model approach is that it provides a framework for the estimation of the prior probability that a gene is not differentially expressed, and this probability can subsequently be used in forming a decision rule. The rule can also be formed to take the false negative rate into account. We apply this approach to a well-known publicly available data set on breast cancer, and discuss our findings with reference to other approaches.

Towards more personalized web: Extraction and integration of dynamic content from the Web

Information and content integration are believed to be a possible solution to the problem of information overload in the Internet. The article is an overview of a simple solution for integration of information and content on the Web. Previous approaches to content extraction and integration are discussed, followed by introduction of a novel technology to deal with the problems, based on XML processing. The article includes lessons learned from solving issues of changing webpage layout, incompatibility with HTML standards and multiplicity of the results returned. The method adopting relative XPath queries over DOM tree proves to be more robust than previous approaches to Web information integration. Furthermore, the prototype implementation demonstrates the simplicity that enables non-professional users to easily adopt this approach in their day-to-day information management routines.