Asymptotic properties of Rao's test for testing hypotheses in discrete parameter stochastic processes

Summary In this note some asymptotically optimum tests for testing hypotheses concerning parameters when the observations are dependent are obtained. Test statistics based on the score functions, similar to the one proposed by Rao in the case when the observations are i.i.d. are proposed. Asymptotically UMP tests for one sided hypotheses against one sided alternatives and asymptotically UMP unbiased test for a simple hypothesis against two sided alternatives are derived. In the multiparameter case tests for simple hypotheses that have asymptotically best constant power on some family of surfaces in the parameter space are derived.     

A new type of symmetrical banana-shaped material based on N-methyldiphenylamine as a core moiety exhibiting an Ad→A2 transition

The synthesis and characterization of a homologous series of Schiff bases consisting of an N-methyldiphenylamine moiety as the central core is reported, which exhibits smectic A phase and transitions from the partial bilayer SmA_d phase to the bilayer SmA₂ phase as the temperature is lowered.     

Using discrete optimization algorithms to find minimum energy configurations of slender cantilever beams with non-convex energy functions

This paper deals with a new solution technique for approximately solving certain variational problems in elasticity by using discrete optimization techniques that were originally used in information theory. This allows us to easily and approximately solve large deformation buckling problems for slender cantilever beams (including post-buckling behavior) as well as problems where the strain energy function is non-convex.The core idea is to quantize or discretize the variables describing the possible configurations of the body. This, when combined with the fact that the variational problem has an inherent Markov structure allows us to use computationally efficient search techniques based on dynamic programming (equivalent to finding the shortest path in a weighted directed graph) to find optimal solutions within the quantized state space. The results can be used in two ways: (1) directly as a fast approximate solution to the variational problem (2) As a means for finding very good (nearly minimum energy) initial configurations for application of conventional minimization techniques, which might otherwise fail because of a poor starting configurations which are far from the global minimum. We demonstrate both these uses in the paper.     

Heat transfer and pressure drop studies in a circular tube fitted with straight full twist

Experimental investigation of heat transfer characteristics of circular tube fitted with straight full twist insert has been presented. The heat transfer coefficient increases with Reynolds number and decreasing spacer distance with maximum being 2 in. spacer distance for both the type of twist inserts. Also, there is no appreciable increase in heat transfer enhancement in straight full twist insert with 2 in. spacer distance. Experiments were carried out in turbulent flow using straight full twist insert with 4 in. spacer and similar trend of increasing Nusselt number with Reynolds number was observed. Performance evaluation analysis was made and the maximum performance ratio was obtained for each twist insert corresponding to the Reynolds number of 2550.     

Synthesis,characterization, DNA binding and nuclease activity of binuclear copper(II) complexes of cuminaldehyde thiosemicarbazones

Binuclear copper(II) complexes of thiosemicarbazones derived from cuminaldehyde (p-isopropyl benzaldehyde) and substituted thiosemicarbazides NH₂NHC(S)NHR, where R = H, Me, Et or Ph have been synthesized and characterized. The ESR indicates that the dissociation of dimeric complex into mononuclear [Cu(L)Cl(DMSO)₃] units in polar solvents like DMSO, where L = monoanionic thiosemicarbazone. The molecular ion peak in the LC-MS coincides with the formula weight of the complexes. The absorption titration studies revealed that each of these complexes is an avid binder to calf thymus-DNA. The apparent binding constants are in the order of 10⁷–10⁸ M⁻¹. The nucleolytic cleavage activities of the ligands and their complexes were assayed on pUC18 plasmid DNA using gel electrophoresis in the presence and absence of H₂O₂. The ligands showed increased nuclease activity when administered as copper complexes. All these copper(II) complexes behave as an efficient chemical nucleases with hydrogen peroxide activation. These studies revealed that the complexes exhibit both oxidative and hydrolytic chemistry in DNA cleavage.     

Theoretical study of14N pure quadrupole resonance in amino acids

The theoretical hybridization model of Vega is adapted to the tetrahedral environment around the nitrogen nucleus in eleven amino acids to estimate the orbital occupation numbers using the experimental values of the quadrupole coupling constant and asymmetry parameter of¹⁴N quadrupole resonance and the results are discussed.     

利普希茨伪紧缩映射下的利普希茨摄动迭代的Bruck公式

在非线性分析中,处理伪紧缩算子及其变形的解(不动点)存在性和近似性,从而使演化方程的求解已经发展成为一个独立的理论.使用近似不动点技术,采用摄动迭代方法,目的是证明利普希茨伪紧缩映射序列的收敛性.该迭代方法适用于比利普希茨伪紧缩算子更一般的非线性算子以及Bruck迭代法无法证明其收敛性的情况.推广了Chidume和Zegeye的结果.