The alicyclic ring contraction of perfluoro-1-phenyltetralin in reaction with antimony pentafluoride

Perfluoro-1-phenyltetralin (1) heated with antimony pentafluoride at 130 °C, then treated with water, gave a mixture of perfluorinated 3-methyl-2-phenylindenone (3), 3-methyl-2-phenylindene (4), 3-hydroxy-1-methyl-3-phenylindan (5), 1-methyl-3-phenylindan (6), 9-methyl-1,2,3,4,5,6,7,8-octahydroanthracene (7), and 1,9-dimethyl-5,6,7,8-tetrahydro-β-naphthindan (8). When heated with SbF₅ in the presence of HF, then treated with water, compound 1 is transformed to a mixture of products 3-6. The reaction at 170 and 200 °C forms compounds 3-6 together with perfluoro-2-(cyclohexen-1-yl)-3-methylindene (10).     

Corrected results for the influence of size,zeta potential,and state of motion of dispersed particles on the conductivity of a colloidal suspension

A correction of a recent work on the dependence of the DC conductivity of diluted colloidal suspensions on the size, zeta potential, and state of motion of dispersed particles (C. Grosse, S. Pedrosa, V.N. Shilov, J. Colloid Interface Sci. 251 (2002) 304) is presented. It is shown that the procedure used in that work to calculate the contribution of the particles to the conductivity of the suspension leads to a result that includes the variation of the conductivity of the dispersion medium. Revised analytical and numerical calculations are presented, which strongly reinforce the conclusions reached in the original work: The expression for the conductivity increment based on the value of the dipolar coefficient of the suspended particles (calculated taking into account their electrophoretic motion) appears to be valid over the whole range of particle sizes.     

Study of Wave Functions and Radiation Transitions in a Rydberg Polar Cluster Using the Continuum Model

A continuum model describing highly excited (Rydberg) electronic states in clusters composed of polar molecules was proposed. On the basis of this model, the wave functions of Rydberg electronic states of clusters were calculated for a wide range of characteristic cluster parameters. These states are not hydrogen-like and can be described using the quantum defect theory. This fact indicates that radiative transitions can be forbidden within certain ranges of cluster parameters. The quantum defects in clusters and the lifetimes of different states were calculated. The possibility of formation of metastable Rydberg states and anomalous spectral characteristics of Rydberg clusters was shown.     

Effects of Added Surfactant on the Dynamic Interfacial Tension Behavior of Acidic Oil/Alkaline Systems

The effects of a ready-made surfactant (sodium dodecyl sulfate) on the dynamic interfacial tension between a model acidic oil (linoleic acid dissolved in paraffin oil) and various aqueous alkaline (NaOH) systems have been studied using pendant drop tensiometry at surfactant concentrations both below and above the critical micelle concentration (CMC). Below the CMC the added surfactant contributes significantly to a further reduction of interfacial tension of the reacting acid/alkaline system, whereas above the CMC the added surfactant plays an important role in damping the dynamic trends observed for the reactive system alone. Copyright 2001 Academic Press.     

Network manipulation algorithm based on inexact alternating minimization

In this paper, we present a network manipulation algorithm based on an alternating minimization scheme from Nesterov (Soft Comput 1–12, 2020). In our context, the alternative process mimics the natural behavior of agents and organizations operating on a network. By selecting starting distributions, the organizations determine the short-term dynamics of the network. While choosing an organization in accordance with their manipulation goals, agents are prone to errors. This rational inattentive behavior leads to discrete choice probabilities. We extend the analysis of our algorithm to the inexact case, where the corresponding subproblems can only be solved with numerical inaccuracies. The parameters reflecting the imperfect behavior of agents and the credibility of organizations, as well as the condition number of the network transition matrix have a significant impact on the convergence of our algorithm. Namely, they turn out not only to improve the rate of convergence, but also to reduce the accumulated errors. From the mathematical perspective, this is due to the induced strong convexity of an appropriate potential function.

     

On equivalence of Floer's and quantum cohomology

We show that the Floer cohomology and quantum cohomology rings of the almost Kähler manifoldM, both defined over the Novikov ring of the loop space M, are isomorphic. We do it using a BRST trivial deformation of the topological A-model. The relevant aspect of noncompactness of the moduli of pseudoholomorphic instantons is discussed. It is shown nonperturbatively that any BRST trivial deformation of A model which does not change the dimensions of BRST cohomology does not change the topological correlation functions either.     

On the Discrete Hardy Inequality

Necessary and sufficient conditions for the boundedness of thediscrete Hardy operator of the form , from to when 0 < q < 1 <p , is given.     

Weakly compactly generated Banach spaces and the strong law of large numbers

IfB is a weakly compactly generated Banach space andf: (S,S, ) satisfies the strong law of large numbers, thenf=f ₁+f ₂, wheref ₁ is Bochner -integrable andf ₂ is Pettis -integrable with Pettis norm 0. The decomposition is unique.     

Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.