On the intersection of two particular convex sets

In this note, necessary and sufficient conditions are given for the intersection of them?1 simplex co {ξ¹,...,ξ ^m } ofm affinely independent vectors ξ¹,...,ξ ^m of ? ⁿ and the negative orthant ? _? ⁿ to be empty, i.e., $$co\{ \xi ^1 ,...,\xi ^m \} \cap \mathbb{R}_ - ^n = \emptyset ,$$ wherem≤n. It is also shown that the special casem=2 can be checked easily. These results suggest that the above-mentioned emptiness can be checked recursively. Some numerical examples are given to illustrate the results. Potential applications of these results include the compatible multicommodity flow problems and satisficing solution problems.     

High resolution FTIR spectrum of the nu1 band of DCOOD

Accurate spectral information on formic acid has wide application to radioastronomy since it was the first organic acid found in interstellar space. In this work, the infrared absorption spectrum of the nu1 band of deuterated formic acid (DCOOD) has been measured on a Bomem DA3.002 Fourier transform spectrometer in the wavenumber region 2560-2690 cm(-1) with a resolution of 0.004 cm(-1). A total of 292 infrared transitions have been assigned in this hybrid type A and B band centred at 2631.8736 +/- 0.0004 cm(-1). The assigned transitions have been fitted to give a set of eight rovibrational constants for the nu1 = 1 state with a standard deviation of 0.00078 cm(-1).     

Minor methylated pyranoamentoflavones from Calophyllum venulosum

Two new biflavonoids, pyranoamentoflavone 7-methyl ether (1) and pyranoamentoflavone 4'-methyl ether (2), have been isolated from the leaves of Calophyllum venulosum. The structures of these two new compounds were elucidated by spectroscopic data.     

Characterisation of an extract and fractions of Azadirachta indica flower on cholesterol lowering property and intestinal motility

Azadirachta indica has long been used in traditional medicine. This study focused on isolation and characterisation of active ingredients in the extract, its fractions (NF-EA, NF-AQ, NF-G) and its effect on the cholesterol absorption activity. The NF-EA fraction was identified by marker compounds by LC-ESI-QTOF/MS. Cholesterol absorption activity was performed by measuring the solubility and size of cholesterol micelles. The intestinal motility was also examined by isolated rat’s ileum to test the contraction. The extract and its fractions consist of flavonoids and phenolic compounds, like quercetin, kaempferol and myricetin. We found that A. indica extract and NF-EA increase cholesterol micelles size, while the extract, NF-AQ, myricetin and quercetin, reduced the solubility of cholesterol in micelles. The extract and quercetin inhibited the contraction induced by KCl up to 29 and 18%, respectively, and also decreased CaCl₂-induced contraction. This finding is in support to traditional uses of A. indica as cholesterol-lowering agents and regulator of gastrointestinal motility.     

A Modelling Study of Machine-Service Operation in an Electronics Industry

Optimal scheduling of machine-service crew is an important issue in a manufacturing company. This paper discusses the use of two quantitative techniques, the mixed integer linear-programming approach and the queueing cost-analysis approach, to schedule the machine-service crew of an electronics manufacturing and testing company. Potential productivity improvement in the company is demonstrated by numerical results.     

Synthesis and aggregation of poly(valine)‐poly (ethylene glycol) block copolymers

The solubility nature of many medicines presents a challenge for successful delivery of these drugs to the body. Polymeric carriers are potentially viable as vessels for both the protection and transport of these medicinal substances. In an effort to generate polymeric materials for this desired application, A‐B‐A triblock copolymers have been synthesized with a central block composed of hydrophilic poly (ethylene glycol) (PEG) and flanking hydrophobic sequences composed of five valine units terminated with end groups of varying hydrophobicity. These copolymers were constructed by adding amino acids stepwise to the hydrophilic block using solution phase chemistry. The self‐assembly behavior of all polymers was investigated using fluorimetry with a pyrene probe. In general, copolymers with more hydrophobic end groups exhibited lower critical aggregation concentrations (CACs). Fmoc‐terminated copolymers displayed the lowest CAC of 0.032 mg/mL and demonstrated little cytotoxicity when exposed to SW620 colorectal cancer cells. Transmission electron micrographs show the presence of multiple compartments within these spherical assemblies, which may prove useful in encapsulating medicinal substances. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5381–5389, 2008     

Convergence of Algorithms in Optimization and Solutions of Nonlinear Equations

It is desirable that an algorithm in unconstrained optimization converges when the guessed initial position is anywhere in a large region containing a minimum point. Furthermore, it is useful to have a measure of the rate of convergence which can easily be computed at every point along a trajectory to a minimum point. The Lyapunov function method provides a powerful tool to study convergence of iterative equations for computing a minimum point of a nonlinear unconstrained function or a solution of a system of nonlinear equations. It is surprising that this popular and powerful tool in the study of dynamical systems is not used directly to analyze the convergence properties of algorithms in optimization. We describe the Lyapunov function method and demonstrate how it can be used to study convergence of algorithms in optimization and in solutions of nonlinear equations. We develop an index which can measure the rate of convergence at all points along a trajectory to a minimum point and not just at points in a small neighborhood of a minimum point. Furthermore this index can be computed when the calculations are being carried out.     

On the Semismoothness of Projection Mappings and Maximum Eigenvalue Functions

This paper analyses the properties of the projection mapping over a set defined by a constraint function whose image is possibly a nonpolyhedral convex set. Under some nondegeneracy assumptions, we prove the (strong) semismoothness of the projection mapping. In particular, we derive the strong semismoothness of the projection mapping when the nonpolyhedral convex set under consideration is taken to be the second-order cone or the semidefinite cone. We also derive the semismoothness of the solution to the Moreau–Yosida regularization of the maximum eigenvalue function.