On the Dimension of the Space of Dark States in the Tavis–Cummings Model

Mathematical Notes - The space of minimal energy of a qubit system is the dark subspace of quantum states of a system of two-level atoms in the finite-dimensional Tavis–Cummings (TC) model of...     

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Notices bibliographiques

     

NMR-Spektren vontrans—Chalcon-oxim,-semicarbazon und-thiosemicarbazon und ihren cyclischen Isomeren (3,5-Diphenyl-2-isoxazolin und 1-substituierte 3,5-Diphenyl-2-pyrazoline)

Zusammenfassung Frühere Strukturvorschläge für dastrans-Chalcon-oxim, semicarbazon und thiosemicarbazon¹ werden mit Hilfe von NMR-Spektren richtiggestellt: Die sauer katalysierte Reaktion führt zwar zum Oxim, Semicarbazon und Thiosemicarbazon destrans-Chalcons; basische Katalysatoren bewirken dagegen eine interne Cyclisierung zu 3,5-Diphenyl-2-isoxazolin bzw. zu 1-substituierten 3,5-Diphenyl-2-pyrazolinen. Die Zuordnungen in den NMR-Spektren wurden durch Vergleich mittrans-Dypnon und seinem Semicarbazon getroffen.

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NMR spectra of trans-chalcone oxime, semicarbazone and thiosemicarbazone and their cyclic isomers (3,5-diphenyl-2-isoxazoline and 1-substituted 3,5-diphenyl-2-pyrazolines)

Earlier tentatively assigned structures fortrans-chalcone oxime, semicarbazone and thiosemicarbazone, resp., have been corrected by means of NMR spectra: open-chain structures have been found for the title compounds formed in the acid catalyzed reaction, whereas basic catalysts lead to intramolecular cyclization with formation of 3,5-diphenyl-2-isoxazoline and 1-substituted 3,5-diphenyl-2-pyrazolines resp. Assignments in the NMR spectra were made by comparison with those from authentic samples oftrans-dypnone and its semicarbazone.

     

Temperature stresses in plates made of reinforced laminated material

The heat conduction equations and the basic equations of the quasi-static axisymmetric problem of thermoelasticity are obtained for thin plates with heat transfer and cylindrical anisotropy. The nonsteady temperature stresses are determined for an infinite plate with a circular opening and an annular plate, both made of reinforced laminated material.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Translated from Mekhanika Polimerov, No. 4, pp. 721–726, July–August, 1970.     

Effects of hydraulic pressure on the stability and transition of wetting modes of superhydrophobic surfaces

The underlying mechanisms of stability, metastability, or instability of the Cassie-Baxter and Wenzel wetting modes and their transitions on superhydrophobic surfaces decorated with periodic micropillars are quantitatively studied in this article. Hydraulic pressure, which may be generated by the water-air interfacial tension of water droplets or external factors such as raining impact, is shown to be a key to understanding these mechanisms. A detailed transition process driven by increasing hydraulic pressure is numerically simulated. The maximum sustainable or critical pressure of the Cassie-Baxter wetting state on a pillarlike microstructural surface is formulated for the first time in a simple, unified, and precise form. This analytic result reveals the fact that reducing the microstructural scales (e.g., the pillars' diameters and spacing) is probably the most efficient measure needed to enlarge the critical pressure significantly. We also introduce a dimensionless parameter, the pillar slenderness ratio, to characterize the stability of either the Cassie-Baxter or the Wenzel wetting state and show that the energy barrier for transitioning from the Cassie-Baxter to the Wenzel wetting mode is proportional to both the slenderness ratio and the area fraction. Thus, the Cassie-Baxter wetting mode may collapse under a hydraulic pressure lower than the critical one if the slenderness ratio is improperly small. This quantitative study explains fairly well some experimental observations of contact angles that can be modeled by neither Wenzel nor Cassie-Baxter contact angles and eventually leads to our proposals for a mixed (or coexisting) wetting mode.     

Generalized-hypergeometric solutions of the biconfluent Heun equation

The Ramanujan Journal - Infinitely many cases for which two independent fundamental solutions of the biconfluent Heun equation can each be presented as an irreducible linear combination of two...     

Sub-Riemannian Cartan Sphere

Doklady Mathematics - The structure of the intersection of the sub-Riemannian sphere on the Cartan group with a 3-dimensional invariant manifold of main symmetries is described.     

A High-Accuracy Algorithm for Solving Problems of Electrostatics in a Nonhomogeneous Spatially Periodic Dielectric Medium

Doklady Mathematics - A high-accuracy economical iterative method is proposed for calculating the potential and the strength of the electric field in a three-dimensional inhomogeneous spatially...     

Optimization of Oscillations of Mechanical Systems

Doklady Mathematics - The problem of controlling oscillations near the equilibrium position of a scleronomic mechanical system with several degrees of freedom is solved. One degree of freedom is...