High-frequency conductivity of a two-dimensional electron gas with impurity electron states

The high-frequency conductivity tensor for a two-dimensional electron gas with short-range-acting impurity atoms has been computed. Spatial dispersion of the conductivity was taken into account. The threshold and maxima of the dissipative part of the conductivity arising from ionization of the impurity atoms by the field of electromagnetic waves were found. Numerical calculations of the conductivity were carried out for semiconductor structures with a two-dimensional electron gas. Khar’kov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 91–94, July, 1997.     

Defect capture under rapid solidification of the melt induced by the action of femtosecond laser pulses and formation of periodic surface structures on a semiconductor surface

A theory of defect-strain instability with formation of periodic surface relief in semiconductors irradiated by ultra-short (τ_p=10^-13 s) powerful laser pulses is developed. The period and time of formation of surface relief are calculated. Regimes of multi-pulse laser ablation leading to formation of either a smooth surface or arrays of surface-relief spikes are pointed out and corresponding experimental results are interpreted from the viewpoint of the developed theory. Received: 4 December 2000 / Accepted: 23 July 2001 / Published online: 11 February 2002     

Sharp MSE Bounds for Proximal Denoising

Denoising has to do with estimating a signal \(\mathbf {x}_0\) from its noisy observations \(\mathbf {y}=\mathbf {x}_0+\mathbf {z}\). In this paper, we focus on the “structured denoising problem,” where the signal \(\mathbf {x}_0\) possesses a certain structure and \(\mathbf {z}\) has independent normally distributed entries with mean zero and variance \(\sigma ^2\). We employ a structure-inducing convex function \(f(\cdot )\) and solve \(\min _\mathbf {x}\{\frac{1}{2}\Vert \mathbf {y}-\mathbf {x}\Vert _2^2+\sigma {\lambda }f(\mathbf {x})\}\) to estimate \(\mathbf {x}_0\), for some \(\lambda >0\). Common choices for \(f(\cdot )\) include the \(\ell _1\) norm for sparse vectors, the \(\ell _1-\ell _2\) norm for block-sparse signals and the nuclear norm for low-rank matrices. The metric we use to evaluate the performance of an estimate \(\mathbf {x}^*\) is the normalized mean-squared error \(\text {NMSE}(\sigma )=\frac{{\mathbb {E}}\Vert \mathbf {x}^*-\mathbf {x}_0\Vert _2^2}{\sigma ^2}\). We show that NMSE is maximized as \(\sigma \rightarrow 0\) and we find the exact worst-case NMSE, which has a simple geometric interpretation: the mean-squared distance of a standard normal vector to the \({\lambda }\)-scaled subdifferential \({\lambda }\partial f(\mathbf {x}_0)\). When \({\lambda }\) is optimally tuned to minimize the worst-case NMSE, our results can be related to the constrained denoising problem \(\min _{f(\mathbf {x})\le f(\mathbf {x}_0)}\{\Vert \mathbf {y}-\mathbf {x}\Vert _2\}\). The paper also connects these results to the generalized LASSO problem, in which one solves \(\min _{f(\mathbf {x})\le f(\mathbf {x}_0)}\{\Vert \mathbf {y}-{\mathbf {A}}\mathbf {x}\Vert _2\}\) to estimate \(\mathbf {x}_0\) from noisy linear observations \(\mathbf {y}={\mathbf {A}}\mathbf {x}_0+\mathbf {z}\). We show that certain properties of the LASSO problem are closely related to the denoising problem. In particular, we characterize the normalized LASSO cost and show that it exhibits a “phase transition” as a function of number of observations. We also provide an order-optimal bound for the LASSO error in terms of the mean-squared distance. Our results are significant in two ways. First, we find a simple formula for the performance of a general convex estimator. Secondly, we establish a connection between the denoising and linear inverse problems.     

Fluorinated porphyrin tweezer: a powerful reporter of absolute configuration for erythro and threo diols, amino alcohols, and diamines

A general and sensitive nonempirical protocol to determine the absolute configurations of erythro and threo diols, amino alcohols, and diamines is reported. Binding of diols to the porphyrin tweezer system is greatly enhanced by increasing the Lewis acidity of the metalloporphyrin. Supramolecular complexes formed between the porphyrin tweezer host and chiral substrates exhibited exciton-coupled bisignate CD spectra with predictable signs based on the substituents on the chiral center. The working model suggests that the observed helicity of the porphyrin tweezer is dictated via steric differentiation experienced by the porphyrin ring bound to each chiral center. A variety of erythro and threo substrates were investigated to verify this chiroptical method. Their absolute configurations were unequivocally determined, and thus a general mnemonic is provided for the assignment of chirality.     

Aqueous solutions of ionic liquids: study of the solution/vapor interface using molecular dynamics simulations

We performed a detailed molecular dynamics study of the interfacial structure of aqueous solutions of 1-butyl-3-methylimidazolium tetrafluoroborate in order to explain the anomalous dependence of the surface tension on concentration. At low concentrations the surface tension decreases with concentration. At higher concentrations the surface becomes saturated; a plateau is observed in simulations with a non-polarizable force field while a possible increase is detected in simulations with a polarizable force field. The structure is characterized by a surplus of cations at the surface (with hydrophobic butyl chains pointing toward vacuum) which at low concentrations is only partly compensated by the anions because of asymmetric solvation. A more hydrophobic 1-butyl-3-methylimidazolium hexafluorophosphate is also simulated for comparison.     

Separation performance of foils from Pd—In(6%)—Ru(0.5%), Pd—Ru(6%), and Pd—Ru(10%) alloys and influence of CO<Subscript>2</Subscript>, CH<Subscript>4</Subscript>, and water vapor on the H<Subscript>2</Subscript> flow rate through the test membranes

The H₂ flow rate through the 30-μm thick foil from Pd—Ru(6%) and Pd—Ru(10%) alloys at 673 and 773 K was found to be controlled by the diffusion of H atoms in the foil bulk. The interrelation between hydrogen permeability through the Pd—In(6%)—Ru(0.5%), Pd—Ru(10%), Pd—Ru(6%), and Pd—Ag(23%) membranes and the permeability pre-exponential factors in the Sieverts equation in the 573—773 K temperature interval indicated that the hydrogen permeability depended on the structural characteristics of palladium alloys. The influence of the CO₂, CH₄, and water vapor impurities on the H₂ flow rate through the studied membranes depended on the driving force nature (the sweep gas or transmembrane pressure) used for the development of the partial hydrogen pressure difference across the membrane. The negative influence of CH₄ and CO₂ was observed only when using a transmembrane pressure and at the impurity content of 20% or more. This effect increased with increasing temperature in the 573—773 K range, with the influence of CO₂ being more pronounced due to its reaction with hydrogen leading to the formation of CO. The influence of water vapor was studied at its 11—23% content in hydrogen and at 573 and 773 K of temperature. The negative influence of water vapor was found to subside as its content in the hydrogen mixture decreased and the temperature increased. It was shown that water vapor can be used as a sweep gas and at T = 773 K its influence on the H₂ flow rate through the membrane was almost the same as that of N₂.     

Multi-mode resource-constrained project scheduling problem with material ordering under bonus–penalty policies

This study emphasizes that project scheduling and material ordering (time and quantity of an order) must be considered simultaneously to minimize the total cost, as setting the material ordering decisions after the project scheduling phase leads to non-optimal solutions. Hence, this paper mathematically formulates the model for the multi-mode resource-constrained project scheduling with material ordering (MRCPSMO) problem. In order to be more realistic, bonus and penalty policies are included for the project. The objective function of the model consists of four elements: the material holding cost, the material ordering cost, the bonus paid by the client and the cost of delay in the project completion. Since MRCPSMO is NP-hard, the paper proposes three hybrid meta-heuristic algorithms called PSO-GA, GA-GA and SA-GA to obtain near-optimal solutions. In addition, the design of experiments and Taguchi method is used to tune the algorithms’ parameters. The proposed algorithms consist of two components: an outside search, in which the algorithm searches for the best schedule and mode assignment, and the inside search, which determines the time and quantity of orders of the nonrenewable resources. First, a comparison is made for each individual component with the exact or best solutions available in the literature. Then, a set of standard PROGEN test problems is solved by the proposed hybrid algorithms under fixed CPU time. The results reveal that the PSO-GA algorithm outperforms both GA-GA and SA-GA algorithms and provides good solutions in a reasonable time.     

Sensing Remote Chirality: Stereochemical Determination of β‐, γ‐, and δ‐Chiral Carboxylic Acids

Determining the absolute stereochemisty of small molecules bearing remote nonfunctionalizable stereocenters is a challenging task. Presented is a solution in which appropriately substituted bis(porphyrin) tweezers are used. Complexation of a suitably derivatized β‐, γ‐, or δ‐chiral carboxylic acid to the tweezer induces a predictable helicity of the bis(porphyrin), which is detected as a bisignate Cotton Effect (ECCD). The sign of the ECCD curve is correlated with the absolute stereochemistry of the substrate based on the derived working mnemonics in a predictable manner.     

Silica Chloride Nano Particle Catalyzed Ring Opening of Epoxides by Aromatic Amines

Silica chloride nano particle (nano SiO₂‐Cl), has been found to be heterogeneous catalyst for facile, simple and mild ring opening of epoxides with aromatic amines to afford β‐amino alcohols in dry CH₂Cl₂ at room temperature.     

Organic reactions in water: an efficient method for the synthesis of 1,2,4-oxadiazoles in water

A simple and efficient process has been developed for the synthesis of 1,2,4-oxadiazoles in good yields through the reaction of amidoximes with anhydrides under catalyst-free conditions in water.