Multiple positive solutions for singular anisotropic Dirichlet problems

We consider a nonlinear Dirichlet problem driven by the variable exponent (anisotropic) p-Laplacian and a reaction that has the competing effects of a singular term and of a superlinear perturbation. There is no parameter in the equation (nonparametric problem). Using variational tools together with truncation and comparison techniques, we show that the problem has at least two positive smooth solutions

Dirichlet problems with unbalanced growth and convection

We consider a double phase Dirichlet problem with a gradient dependent reaction term (convection). Using the theory of nonlinear operators of monotone type, we show the existence of a bounded strictly positive solution. Moreover, we show that the set of these solutions is compact in the corresponding generalized Sobolev–Orlicz space

Singular anisotropic equations with a sign-changing perturbation

We consider an anisotropic Dirichlet problem driven by the variable (p, q)-Laplacian (double phase problem). In the reaction, we have the competing effects of a singular term and of a superlinear perturbation. Contrary to most of the previous papers, we assume that the perturbation changes sign. We prove a multiplicity result producing two positive smooth solutions when the coefficient function in the singular term is small in the L∞-norm

A double phase equation with convection

We consider a double phase problem with a gradient dependent reaction (convection). Using the theory of nonlinear operators of monotone type, we show the existence of a nontrivial, positive, bounded solution

A simple, low-cost conductive composite material for 3D printing of electronic sensors

3D printing technology can produce complex objects directly from computer aided digital designs. The technology has traditionally been used by large companies to produce fit and form concept prototypes (‘rapid prototyping’) before production. In recent years however there has been a move to adopt the technology as full-scale manufacturing solution. The advent of low-cost, desktop 3D printers such as the RepRap and Fab@Home has meant a wider user base are now able to have access to desktop manufacturing platforms enabling them to produce highly customised products for personal use and sale. This uptake in usage has been coupled with a demand for printing technology and materials able to print functional elements such as electronic sensors. Here we present formulation of a simple conductive thermoplastic composite we term ‘carbomorph’ and demonstrate how it can be used in an unmodified low-cost 3D printer to print electronic sensors able to sense mechanical flexing and capacitance changes. We show how this capability can be used to produce custom sensing devices and user interface devices along with printed objects with embedded sensing capability. This advance in low-cost 3D printing with offer a new paradigm in the 3D printing field with printed sensors and electronics embedded inside 3D printed objects in a single build process without requiring complex or expensive materials incorporating additives such as carbon nanotubes

Elastocaloric determination of the phase diagram of Sr2_2RuO4_4

One of the main developments in unconventional superconductivity in the past two decades has been the discovery that most unconventional superconductors form phase diagrams that also contain other strongly correlated states. Many systems of interest are therefore close to more than one instability, and tuning between the resultant ordered phases is the subject of intense research1. In recent years, uniaxial pressure applied using piezoelectric-based devices has been shown to be a particularly versatile new method of tuning, leading to experiments that have advanced our understanding of the fascinating unconventional superconductor Sr$_2$RuO$_4$. Here we map out its phase diagram using high-precision measurements of the elastocaloric effect in what we believe to be the first such study including both the normal and the superconducting states. We observe a strong entropy quench on entering the superconducting state, in excellent agreement with a model calculation for pairing at the Van Hove point, and obtain a quantitative estimate of the entropy change associated with entry to a magnetic state that is observed in proximity to the superconductivity. The phase diagram is intriguing both for its similarity to those seen in other families of unconventional superconductors and for extra features unique, so far, to Sr$_2$RuO$_4$

ProFITS of maize: a database of protein families involved in the transduction of signalling in the maize genome

<p>Abstract</p> <p>Background</p> <p>Maize (<it>Zea mays </it>ssp. <it>mays </it>L.) is an important model for plant basic and applied research. In 2009, the B73 maize genome sequencing made a great step forward, using clone by clone strategy; however, functional annotation and gene classification of the maize genome are still limited. Thus, a well-annotated datasets and informative database will be important for further research discoveries. Signal transduction is a fundamental biological process in living cells, and many protein families participate in this process in sensing, amplifying and responding to various extracellular or internal stimuli. Therefore, it is a good starting point to integrate information on the maize functional genes involved in signal transduction.</p> <p>Results</p> <p>Here we introduce a comprehensive database 'ProFITS' (Protein Families Involved in the Transduction of Signalling), which endeavours to identify and classify protein kinases/phosphatases, transcription factors and ubiquitin-proteasome-system related genes in the B73 maize genome. Users can explore gene models, corresponding transcripts and FLcDNAs using the three abovementioned protein hierarchical categories, and visualize them using an AJAX-based genome browser (JBrowse) or Generic Genome Browser (GBrowse). Functional annotations such as GO annotation, protein signatures, protein best-hits in the <it>Arabidopsis </it>and rice genome are provided. In addition, pre-calculated transcription factor binding sites of each gene are generated and mutant information is incorporated into ProFITS. In short, ProFITS provides a user-friendly web interface for studies in signal transduction process in maize.</p> <p>Conclusion</p> <p>ProFITS, which utilizes both the B73 maize genome and full length cDNA (FLcDNA) datasets, provides users a comprehensive platform of maize annotation with specific focus on the categorization of families involved in the signal transduction process. ProFITS is designed as a user-friendly web interface and it is valuable for experimental researchers. It is freely available now to all users at <url>http://bioinfo.cau.edu.cn/ProFITS</url>.</p

Positive solutions for nonlinear singular elliptic equations of p-Laplacian type with dependence on the gradient

In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution set. Our approach is based on Leray-Schauder alternative principle, method of sub-supersolution, nonlinear regularity, truncation techniques, and set-valued analysis

3640 Unique EST Clusters from the Medaka Testis and Their Potential Use for Identifying Conserved Testicular Gene Expression in Fish and Mammals

BACKGROUND: The fish medaka is the first vertebrate capable of full spermatogenesis in vitro from self-renewing spermatogonial stem cells to motile test-tube sperm. Precise staging and molecular dissection of this process has been hampered by the lack of suitable molecular markers. METHODOLOGY AND PRINCIPAL FINDINGS: We have generated a normalized medaka testis cDNA library and obtained 7040 high quality sequences representing 3641 unique gene clusters. Among these, 1197 unique clusters are homologous to known genes, and 2444 appear to be novel genes. Ontology analysis shows that the 1197 gene products are implicated in diverse molecular and cellular processes. These genes include markers for all major types of testicular somatic and germ cells. Furthermore, markers were identified for major spermatogenic stages ranging from spermatogonial stem cell self-renewal to meiosis entry, progression and completion. Intriguingly, the medaka testis expresses at least 13 homologs of the 33 mouse X-chromosomal genes that are enriched in the testis. More importantly, we show that key components of several signaling pathways known to be important for testicular function in mammals are well represented in the medaka testicular EST collection. CONCLUSIONS/SIGNIFICANCE: Medaka exhibits a considerable similarity in testicular gene expression to mammals. The medaka testicular EST collection we obtained has wide range coverage and will not only consolidate our knowledge on the comparative analysis of known genes' functions in the testis but also provide a rich resource to dissect molecular events and mechanism of spermatogenesis in vivo and in vitro in medaka as an excellent vertebrate model