HARDY-LITTLEWOOD-POLYA INEQUALITY FOR A LINEAR DIFFERENTIAL OPERATOR AND SOME RELATED OPTIMAL PROBLEMS

In this paper a generalized version of the classical Hardy-Littlewood-Polya inequality is given.Furthermore,the Stechkin's problem for a linear differential operator is solved in L_2(R), and the optimal recovery problem for such differential operator is considered.

A UNIVERSAL APPROACH FOR CONTINUOUS OR DISCRETE NONLINEAR PROGRAMMINGS WITH MULTIPLE VARIABLES AND CONSTRAINTS

A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function, constraint functions and their First-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted.

Wavelets with Differential Relation

Divergence-free wavelets are successfully applied to numerical solutions of Navier-Stokes equation and to analysis of incompressible flows. They closely depend on a pair of one-dimensional wavelets with some differential relations. In this paper, we point out some restrictions of those wavelets and study scaling functions with the differential relation; Wavelets and their duals are discussed; In addition to the differential relation, we are particularly interested in a class of examples with the interpolatory property; It turns out there is a connection between our examples and Micchelli＇s work.

Preliminary studies on tin miners’ lung cancer tissue related genes by differential display mRNA

Objective To study the genes related to tin miners' lung cancer tissue Method Differential display mRNA Results Thirty cDNA fragments which differentially expressed in lung cancer tissues and the same patient's normal lung tissues were discovered Among these, 16 expressed in lung cancer tissues, not in normal lung tissues; fourteen expressed on the contrary Six cDNA fragment sequence was determined Five sequences CG2, CG7, CG8, CA5 and CC6 had less than 75% homology with known sequences in GenBank BLAST, so they were believed to be new sequences which we have recorded in Genbank Only one fragment coded CG3 had homology up to 95% with human ribosome protein L27a gene Conclusions mRNA differential display provides a unique and powerful experimental system to study differential gene expression in tin miners' lung cancer tissues and the same patient's normal lung tissues Using the system, differential expression of 30 cDNA fragments was observed Six of them may be used to study the molecular mechanism of miners' radon associated lung cancer

Genetic differentiation of grain, fodder and pod vegetable type cowpeas (Vigna unguiculata L.) identified through single nucleotide polymorphisms from genotyping-by-sequencing

The species Vigna unguiculata L.(Walp),commonly known as cowpea,is a multi-purpose legume that has been selected into three subspecies that are divided into grain,fodder and pod(yardlong bean)types.However,genetic bases for distinctions are not well understood.The purpose of this study was to apply genotyping-by-sequencing(GBS)and current reference genome for V.unguiculata to distinguish three subspecies and identify signatures of divergence.The collection of 130 accessions included 128 cultivated from:1)ssp.cylindrica,fodder type;2)ssp.sesquipedalis,pod vegetable type;and 3)ssp.unguiculata,grain type.Two wilds genotypes from spp.dekindtiana and spp.pubescens,were used to anchor phylogeny.A total of 11,083 highly informative single nucleotide polymorphisms(SNPs)were discovered.Wild accessions showed distinct genetic fingerprints and were separated from cultivated subspecies.Principal component analysis showed closer relationship between ssp.unguiculata and ssp.cylindrica compared to ssp.sesquipedalis.Relative differentiation of cultivated subspecies(with Fixation Index,FST)indicated the existence of discrete signatures of selection.This work clarifies the population structure,phylogeny,and domestication of cultivated cowpeas.Furthermore,significant genetic differences between grain and pod vegetable types can provide valuable information for future breeding in three cowpea groups.