Local laws for non-Hermitian random matrices

The product of m ∈ N independent random square matrices whose elements are independent identically distributed random variables with zero mean and unit variance is considered. It is known that, as the size of the matrices increases to infinity, the empirical spectral measure of the normalized eigenvalues of the product converges with probability 1 to the distribution of the mth power of the random variable uniformly distributed on the unit disk of the complex plane. In particular, in the case of m = 1, the circular law holds. The purpose of this paper is to prove the validity of the local circular law (as well as its generalization to the case of any fixed m) in the case where the distribution of the matrix elements has finite absolute moment of order 4 + δ,δ > 0,. Recent results of Bourgade, Yau, and Yin, of Tao and Vu, and of Nemish are generalized.     

Novel silver(I)N-heterocyclic carbene complexes bearing 2-(4-hydroxyphenyl)ethyl group: Synthesis,characterization, and enzyme inhibition properties

Herein, novel silver-based N-heterocyclic carbene (NHC) complexes bearing 2-(4-hydroxyphenyl)ethyl group were synthesized. Novel Ag(I)NHC complexes were synthesized from the 2-(4-hydroxyphenyl)ethyl-substituted benzimidazolium salts and silver oxide via in situ deprotonation method. The successful formation of all Ag(I)NHC complexes was proved by using ¹H NMR, ¹³C NMR, FTIR spectroscopy, and elemental analysis techniques. In addition, their inhibitory effects have been investigated of these substances on acetylcholinesterase (AChE), α-glycosidase (α-Gly), human carbonic anhydrase I (hCA I), and human carbonic anhydrase II (hCA II) enzymes. It has been seen that all compounds have a better ability to inhibit compared with existing tried inhibitors. Among these, the best inhibitor against AChE enzyme is 1g (K_i : 9.54 ± 0.98 μM and IC₅₀ : 17.40), and against α-Gly, 1c showed the highest effect (K_i 3.09 ± 0.36 μM and IC₅₀ 7.91). The best inhibitor against hCA I and hCA II enzymes are 1c and 1g compounds. For hCA I and hCA II, IC₅₀ values were calculated as 17.85 and 9.06 μM and K_i values were measured as 5.45 ± 2.02 and 8.99 ± 2.02 μM, respectively.     

Silver as a capturing material for iodine released from lead–bismuth eutectic in various conditions

Journal of Radioanalytical and Nuclear Chemistry - The usage of silver as a filtering material for removal of iodine from the gas phase of a lead–bismuth eutectic based nuclear reactor was...     

Bistriazoles Connected Through a B−B Bridge,Synthesized by Highly Selective Dipolar Cycloaddition Reactions of a Diazido-diborane(4)

In this work we report the first cycloaddition reactions between a diazido diborane(4) and terminal alkynes, providing unique access to bis-1,2,3-triazoles connected by a B−B bridge. The catalyst-free reactions are highly selective, yielding exclusively the thermodynamically disfavored bis-1,4-triazoles. The reactions are enabled by the high thermal stability of the diazido-diborane [B(hpp)(N₃)]₂ (hpp=1,3,4,6,7,8-hexahydro-2H-pyrimido[1,2-α]pyrimidinate). Due to the tetra-coordinate boron atoms in this reagent, the reactions are tolerant with respect to the introduction of Lewis-basic groups at the alkyne. The scope and limitations of the new reactions are discussed.     

The influence of radiation on the temperature profile of an induced discharge in argon at atmospheric pressure

This study presents a quantitative evaluation of the influence of radiation upon the parameters of a long induced discharge in argon at atmospheric pressure. Radiation heat transfer in the optically transparent tin plasma layers with thickness of the order of several centimeters) and reabsorption spectral intervals is examined. Experimental error produced by inaccurate knowledge of the transfer and optical characteristics of the plasma is evaluated. The effect of convection on radial temperature profile is evaluated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiztki, No. 6, pp. 35–43, November–December, 1971.     

On the temperature rise at the tip of a fast running crack2

The high energy concentration at the tip of a running crack leads to irreversible deformations, and a great amount of the deformation energy is set free as heat. Assuming that this moving heat source is of circular shape, the temperature distribution around the crack tip has been calculated. The temperatures are dependent on the radius of the heat source and the crack velocity. Some examples for the material glass are given. The very high temperatures computed lead to the supposition that the observed light emission during fast fracture is of thermal origin.     

Méthodes d'approximation et d'itération pour les opérateurs monotones

Sans résumé Mémoire présenté par J. L. Lions     

Design and stress evaluation of a nonsymmetric pressure vessel

Presently, the large variation in demand for electrical power at different periods of the day imposes new considerations in the evaluation of pressure components in large steam-generating equipment. In the past, pressure components such as valve bodies have been designed for static pressure conditions against bursting with sufficient stiffness to assure operation ability. In today's plant operation, the response of the valve body to thermal transients will have a major influence on the life of the valve. Since the valve body is a compact nonsymmetric body, the direct calculation of stresses is very complex. The evaluation of the behavior of nonsymmetric pressure components under the loads imposed by various operational modes requires information from both analytical and experimental methods of analysis. The contributions from modern computer-calculation programs and three-dimensional photoelasticity are discussed as applied to the evaluation of a valve body used in a large, supercritical steam generator. In the analysis, computer procedures are used to develop the preliminary geometry for pressure loading. Because of the close proximity of the nonsymmetrical openings, a three-dimensional photoelastic analysis is used to calibrate the computer model. Once a satisfactory computer model has been developed for pressure loading, it is used to calculate the thermal stresses. Since stresses have little meaning in themselves, a design basis is necessary to evaluate the significance of the calculated stresses. The design basis must consider the types of failures which are possible and is thus dependent on the temperature at which the valve must operate. A design basis is discussed for the evaluation of pressure components in a boiler system.