Shape preserving approximation in vector ordered spaces

AbstractThe aim of this note is to extend some classical results on the shape preserving approximation of real functions (of real variables) to functions with values in ordered vector spaces

Geometric and approximation properties of some singular integrals in the unit disk

The purpose of this paper is to prove several results in approximation by complex Picard, Poisson-Cauchy, and Gauss-Weierstrass singular integrals with Jackson-type rate, having the quality of preservation of some properties in geometric function theory, like the preservation of coefficients' bounds, positive real part, bounded turn, starlikeness, and convexity. Also, some sufficient conditions for starlikeness and univalence of analytic functions are preserved.</p

E. R. LOVE TYPE LEFT FRACTIONAL INTEGRAL INEQUALITIES

Here first we derive a general reverse Minkowski integral inequality. Then motivated by the work of E. R. Love [4] on integral inequalities we produce general reverse and direct integral inequalities. We apply these to ordinary and left fractional integral inequalities. The last involve ordinary derivatives, left RiemannLiouville fractional integrals, left Caputo fractional derivatives, and left generalized fractional derivatives. These inequalities are of Opial type

Transient down-regulation of beta1 integrin subtypes on kidney carcinoma cells is induced by mechanical contact with endothelial cell membranes

Adhesion molecules of the integrin beta1 family are thought to be involved in the malignant progression renal cell carcinoma (RCC). Still, it is not clear how they contribute to this process. Since the hematogenous phase of tumour dissemination is the rate-limiting step in the metastatic process, we explored beta1 integrin alterations on several RCC cell lines (A498, Caki1, KTC26) before and after contacting vascular endothelium in a tumour-endothelium (HUVEC) co-culture assay. Notably, alpha2, alpha3 and alpha5 integrins became down-regulated immediately after the tumour cells attached to HUVEC, followed by re-expression shortly thereafter. Integrin down-regulation on RCC cells was caused by direct contact with endothelial cells, since the isolated endothelial membrane fragments but not the cell culture supernatant contributed to the observed effects. Integrin loss was accompanied by a reduced focal adhesion kinase (FAK) expression, FAK activity and diminished binding of tumour cells to matrix proteins. Furthermore, intracellular signalling proteins RCC cells were altered in the presence of HUVEC membrane fragments, in particular 14-3-3 epsilon, ERK2, PKCdelta, PKCepsilon and RACK1, which are involved in regulating tumour cell motility. We, therefore, speculate that contact of RCC cells with the vascular endothelium converts integrin-dependent adhesion to integrin-independent cell movement. The process of dynamic integrin regulation may be an important part in tumour cell migration strategy, switching the cells from being adhesive to becoming motile and invasive

Computational analysis of the synergy among multiple interacting genes

Diseases such as cancer are often related to collaborative effects involving interactions of multiple genes within complex pathways, or to combinations of multiple SNPs. To understand the structure of such mechanisms, it is helpful to analyze genes in terms of the purely cooperative, as opposed to independent, nature of their contributions towards a phenotype. Here, we present an information-theoretic analysis that provides a quantitative measure of the multivariate synergy and decomposes sets of genes into submodules each of which contains synergistically interacting genes. When the resulting computational tools are used for the analysis of gene expression or SNP data, this systems-based methodology provides insight into the biological mechanisms responsible for disease

Opial type L

This paper presents a class of Lp-type Opial inequalities for generalized fractional derivatives for integrable functions based on the results obtained earlier by the first author for continuous functions (1998). The novelty of our approach is the use of the index law for fractional derivatives in lieu of Taylor's formula, which enables us to relax restrictions on the orders of fractional derivatives