The projective method for solving linear matrix inequalities

Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest in LMI-based design techniques has really surged with the introduction of efficient interior-point methods for solving LMIs with a polynomial-time complexity. This paper describes one particular method called the Projective Method. Simple geometrical arguments are used to clarify the strategy and convergence mechanism of the Projective algorithm. A complexity analysis is provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed.     

On safe tractable approximations of chance constraints

A natural way to handle optimization problem with data affected by stochastic uncertainty is to pass to a chance constrained version of the problem, where candidate solutions should satisfy the randomly perturbed constraints with probability at least 1 − ?. While being attractive from modeling viewpoint, chance constrained problems “as they are” are, in general, computationally intractable. In this survey paper, we overview several simulation-based and simulation-free computationally tractable approximations of chance constrained convex programs, primarily, those of chance constrained linear, conic quadratic and semidefinite programming.     

Metal-stabilized phenoxonium cation

An unprecedented metal-stabilized phenoxonium cation was prepared by a process involving dearomatization of a phenoxy complex. The unique eta2 C=O-metal (iridium) coordination mode leaves the positive charge delocalized within the former aromatic ring. The X-ray structure and conversion into eta2 C=O-coordinated metal-quinone complex are described.     

Self-Concordant Barriers for Convex Approximations of Structured Convex Sets

We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with explicitly given and efficient (if the accuracy of the approximation is moderate) self-concordant barriers. This approach extends the reach of the modern theory of interior-point methods, and lays the foundation for new ways to treat structured convex optimization problems with a very large number of constraints. Moreover, our approach provides a strong connection from the theory of self-concordant barriers to the combinatorial optimization literature on solving packing and covering problems.     

光学特异材料的设计

In this contribution we review our latest achievements of combined experimental and theoretical studies to tailor the properties of optical metamaterials（MMs） at will. We give three examples of metamaterial designs that have been realized by means of electron-beam lithography and whose spectroscopic characteristics have been comprehensively investigated. In every case, our experiments are complemented by rigorous numer ical simulations. Particular emphasis is put on the significance of such tailored effective properties of optical MMs     

Nonaqueous CE using contactless conductivity detection and ionic liquids as BGEs in ACN

N,N'-Alkylmethylimidazolium cations have been separated in NACE when one of the N,N'-dialkylimidazolium salts (ionic liquids (ILs)) was used as an electrolyte additive to the organic solvent separation medium. The separated species were 1-methyl-, 1-ethyl-, 1-butyl-, 1-octyl-, 1-decyl-3-methylimidazolium and N-butyl-3-methylpyridinium cations and BGE composed of 1-ethyl-3-methylimidazolium ethylsulfate or 1-butyl-3-methylimidazolium trifluoroacetate [BMIm][FAcO] (A6; B2) diluted in ACN. It was demonstrated that contactless conductivity detection (CCD) may be applied to monitoring the separation process in nonaqueous separation media, allowing to use the UV light-absorbing imidazolium-based electrolyte additives. There could be marked three concentration regions of added ILs; at first ionic strength of BGE below 1-2 mM, and then the actual electrophoretic mobility of analytes rises from 0. At concentrations above 1-2 mM, the added IL facilitated separation. In concentration region of 1-20 mM, the actual electrophoretic mobility of analyzed imidazolium cations was increasing with decrease in separation medium ionic strength. At higher concentrations of BGE (above 30 mM), the conductivity of the separation media became too high for this detector. Some organic dyes were also successfully separated and detected by contactless conductivity detector in a 20 mM A6 separation electrolyte in ACN.     

Hypokinetic stress and neuronal porosome complex in the rat brain: the electron microscopic study

Porosomes are the universal secretory machinery in cells, where membrane-bound secretory vesicles transiently dock and fuse to release intravesicular contents to the outside of the cell during cell secretion. Studies using atomic force microscopy, electron microscopy, electron density and 3D contour mapping, provided rich nanoscale information on the structure and assembly of proteins within the neuronal porosome complex in normal brain. However it remains uncertain whether pathological conditions that alter process of neurotransmission, provoke alterations in the porosome structure also. To determine if porosomes are altered in disease states, the current study was undertaken for first time using high resolution electron microscope. One of pathologies that produce subtle alteration at the presynaptic terminals has been demonstrated to be hypokinetic stress. The central nucleus of amygdale is the brain region, where such alterations are mostly expressed. We have examined the width and depth of the neuronal porosome complex and their alterations provoked by chronic hypokinetic stress in above mentioned limbic region. Specifically, we have demonstrated that despite alterations in the presynaptic terminals and synaptic transmission provoked by this pathological condition in this region, the final step/structure in neurosecretion--the porosome--remains unaffected: the morphometric analysis of the depth and diameter of this cup-shaped structure at the presynaptic membrane point out to the heterogeneity of porosome dimensions, but with unchanged fluctuation in norm and pathology.