Generic properties of the complementarity problem

Givenf: R ₊ ⁿ R ⁿ , the complementarity problem is to find a solution tox 0,f(x) 0, and x, f(x) = 0. Under the condition thatf is continuously differentiable, we prove that for a generic set of such anf, the problem has a discrete solution set. Also, under a set of generic nondegeneracy conditions and a condition that implies existence, we prove that the problem has an odd number of solutions.This work was partially supported by N.S.F. Grants GP-8007 and 010185.     

Computing nonlinear network equilibria

This paper examines the problem of computing nonlinear network equilibria using a ‘Newton’ iteration. By exploiting the network structure, we are able to show that the iteration is globally convergent, monotonic, and (locally) quadratically convergent using only simple algebraic arguments.     

High‐throughput functional marker assay for detection of Xa/xa and fgr genes in rice (Oryza sativa L.)

We apply CE for high‐throughput analysis of functional markers for marker‐assisted selection in rice. The accuracy, throughput and reproducibility of CE analysis for sequence‐tagged site (STS) and simple sequence repeat (SSR) markers for bacterial blight resistance and aroma genes are demonstrated by using a CE system. Multiplex PCR products displayed well‐differentiated allelic variants using different STS and SSR markers for identification of xa13, Xa21 and fgr genes using the CE system compared to 1.2% agarose gel images. Moreover, consumption of PCR product is much less in the CE system compared to traditional agarose gel systems. Sample consumption is less than 0.1 μL per analysis, thereby conserving samples for further downstream analysis. Out of 29 genotypes in BC₁F₃ generation, 16 plants were found homozygous for all the three genes, viz., xa13, Xa21 and fgr. These homozygous lines can be used as potential donors in rice breeding programmes.     

Electrostatic instability in magnetically confined inhomogeneous plasma driven by nonlinear force

A theoretical investigation on amplification of electrostatic ion acoustic wave in magnetically confined plasma has been presented in this paper. This investigation considers nonlinear wave–particle interaction process, called plasma maser effect, in presence of drift wave turbulence supported by magnetically confined inhomogeneous plasma. The role of associated nonlinear dissipative force in this effect in a confined plasma has been analyzed. The nonlinear force, which arises as a result of resonant interaction between electrons and modulated fields, is shown to drive the instability. Using the ion fluid equation and the ion equation of continuity, the nonlinear dispersion relation of a test ion acoustic wave has been derived, and the growth rate of ion acoustic wave in presence of low frequency drift wave turbulence has been estimated using Helimak data.     

A facile one-pot synthesis of 7-substituted pyrazolo[1,5-a]pyrimidines by base induced three-component reaction

The preparation of steroid/nonsteroid fused 7-substituted pyrazolo[1,5-a]pyrimidines is described by a one-pot reaction of steroidal/nonsteroidal ketones, aromatic aldehydes and 3-amino-1H-pyrazoles/5-amino-1H-pyrazoles in the presence of potassium tert-butoxide in good yield under reflux condition in ethanol.     

A facile method for the synthesis of steroidal and nonsteroidal 5-methyl pyrazolo[1,5-a]pyrimidines

The steroidal and nonsteroidal 5-methyl pyrazolo[1,5-a]pyrimidines were synthesized by the reaction of steroidal/nonsteroidal α,β-unsaturated ketones and 3-amino-1H-pyrazoles/5-amino-1H-pyrazoles in the presence of KO^tBu in ethanol under reflux condition.