Phosphorylated Aminoacetal in the Synthesis of New Acyclic,Cyclic, and Heterocyclic Polyphenol Structures

New phosphorylated aminoacetal has been synthesized by the Kabachnik–Fields reaction; its reactivity has been studied in acid‐catalyzed condensation with linear polyphenols (2‐methylresorcinol, resorcinol, pyrogallol) and the Mannich reaction with macrocyclic polyphenol (calix[4]resorcinol). It has been determined for the first time that acid‐catalyzed reaction of phosphorus‐containing acetal with resorcinol and its derivatives in ethanol in the presence of hydrochloric acid gives new phosphorylated piperazines in addition to the compounds of diarylmethane series. Condensation of macrocyclic polyphenol (calix[4]resorcinol) with formaldehyde and N‐((dihexylphosphoryl)methyl)‐2, 2‐dimethoxyethylamine (the Mannich reaction) has resulted in novel tetrasubstituted calixarene containing aminophosphine oxide and acetal groups on the “upper rim” of molecule.     

Level-Rank Duality via Tensor Categories

We give a new way to derive branching rules for the conformal embedding $$(\hat{\mathfrak{sl}}_n)_m\oplus(\hat{\mathfrak{sl}}_m)_n\subset(\hat{\mathfrak{sl}}_{nm})_1. $$ In addition, we show that the category ${\mathcal{C}(\hat{\mathfrak{sl}}_n)_m^0}$ of degree zero integrable highest weight ${(\hat{\mathfrak{sl}}_n)_m}$ -representations is braided equivalent to ${\mathcal{C}(\hat{\mathfrak{sl}}_m)_n^0}$ with the reversed braiding.     

Renormalization of Critical Gaussian Multiplicative Chaos and KPZ Relation

Gaussian Multiplicative Chaos is a way to produce a measure on \({\mathbb{R}^d}\) (or subdomain of \({\mathbb{R}^d}\) ) of the form \({e^{\gamma X(x)} dx}\) , where X is a log-correlated Gaussian field and \({\gamma \in [0, \sqrt{2d})}\) is a fixed constant. A renormalization procedure is needed to make this precise, since X oscillates between ?∞ and ∞ and is not a function in the usual sense. This procedure yields the zero measure when \({\gamma = \sqrt{2d}}\) . Two methods have been proposed to produce a non-trivial measure when \({\gamma = \sqrt{2d}}\) . The first involves taking a derivative at \({\gamma = \sqrt{2d}}\) (and was studied in an earlier paper by the current authors), while the second involves a modified renormalization scheme. We show here that the two constructions are equivalent and use this fact to deduce several quantitative properties of the random measure. In particular, we complete the study of the moments of the derivative multiplicative chaos, which allows us to establish the KPZ formula at criticality. The case of two-dimensional (massless or massive) Gaussian free fields is also covered.     

Utilization of a multimembrane inlet and a cyclic sudden sampling introduction mode in membrane inlet mass spectrometry

Sudden sampling introduction into a membrane inlet mass spectrometer (MIMS) considerably improves the selectivity of the membrane inlet and is therefore applicable even for compounds with low permeabilities through a silicone membrane. In this study the basics of cyclic non-steady-state sudden increase sample injection were studied using a three-membrane inlet and a portable sector double-focusing mass spectrometer. The operational parameters of the inlet system providing the most efficient enrichment of volatile organic compounds (VOCs) in air were defined. Simulation of the diffusion process following sudden sample introduction into the three-membrane inlet was also carried out. Experimental testing of the three-membrane inlet system with the cyclic sudden sample injection mode for benzene, toluene, styrene, and xylene in air was performed. The simulation and the experimental results demonstrated that, when this mode is used, the VOCs/nitrogen relative enrichment factor of samples introduced into the mass spectrometer equipped with a three-membrane inlet is increased by a factor of approximately 10(5) compared with a direct introduction method. This effect may be used to decrease detection limits of compounds obtained with mass spectrometry to decrease matrix flow through the inlet at the same detection limits.     

Steric interference modification of the hammerhead ribozyme

Although the structure of the hammerhead ribozyme is well characterized, many questions remain about its catalytic mechanism. Extensive evidence suggests the necessity of a conformational change en route to the transition state. We report a steric interference modification approach for investigating this change. By placing large 2' modifications at residues insensitive to structurally conservative 2'-deoxy modifications, we hoped to discover structural effects distal to the site of modification. Of twenty residues tested, six were identified where the addition of 2' bulk inhibits cleavage, even though these bulky modifications could be accommodated in the crystal structure without steric clash. It is proposed that these 2'-modifications inhibit cleavage by preventing formation of the alternate, active conformation. Since these 2' effects are present in both domain I and domain II of the hammerhead, the entire catalytic core must undergo conformational changes during catalysis.     

Features of X-ray fluorescence determination of rock-forming elements in powder samples of peat sediments

The features of rock-forming elements determination in powder samples of peat sediments are considered. Based on theoretical calculations and experimental data, the mineralogical and particle size effects on the X-ray fluorescence intensity have been estimated. For routine analysis, powder rock samples are usually milled to a particle size of 10–60 μm. Theoretically, estimated variations of rock-forming elements analytical lines intensities in different minerals are up to 30%, and the particle size effect cannot be eliminated simultaneously for all rock-forming elements. Experimental estimation shows that the impossibility of the particle size distribution control can lead to significant variations in the intensities of the analytical lines (3%–18%) that is mainly corresponding to theoretical estimation. Fine milling allowed us to achieve an average particle size of fewer than 20 μm and reduce the measurement uncertainty by 1.5–2 times. 12 samples of peat sediments with organic matter content up to 70 wt% were analyzed by X-ray fluorescence analysis using different sample preparation techniques, as well as by certified methods. The accuracy of X-ray fluorescence analysis of peat sediments prepared as pressed pellets varies from 1.5 to 11 rel% depending on compound contents. It is more than for samples prepared as fused beads, however, the proposed method can be used to determine the variations of rock-forming elements contents in peat sediments where the content variations exceed the measurement uncertainty, and accuracy of analysis is sufficient for further paleoecological reconstructions.     

Vibration Analysis of Non-linear 6-parameter Prestressed Shells

Within the framework of the nonlinear six-parameter shell theory we discuss the influence of initial (residual) stresses on the eigen-frequencies. We derive the linearized boundary-value problems and formulate the Rayleigh variational principle which gives the possibility to estimate the eigen-frequencies of the prestressed shell. The Rayleigh quotient of the shell with initial stresses is represented as a sum of two terms. The first term depends on elastic moduli of the shell while the second one is determined by initial stress and couple stress tensors acting on the shell.     

Static equilibrium of a thermoelastic half-plane: Green’s functions and solutions in integrals

This article presents in a closed form new influence functions of a unit point heat source on the displacements for three boundary value problems of thermoelasticity for a half-plane. We also obtain the corresponding new integral formulas of Green’s and Poisson’s types that directly determine the thermoelastic displacements and stresses in the form of integrals of the products of specified internal heat sources or prescribed boundary temperature and constructed already thermoelastic influence functions (kernels). All these results are presented in terms of elementary functions in the form of three theorems. Based on these theorems and on derived early by author the general Green-type integral formula, we obtain in elementary functions new solutions to two particular boundary value problems of thermoelasticity for half-plane. The graphical presentation of the temperature and thermal stresses of one concrete boundary value problems of thermoelasticity for half-plane also is included. The proposed method of constructing thermoelastic Green’s functions and integral formulas is applicable not only for a half-plane, but also for many other two- and three-dimensional canonical domains of different orthogonal coordinate systems.