Efficient algorithms for the recognition of topologically conjugate gradient-like diffeomorhisms

It is well known that the topological classification of structurally stable flows on surfaces as well as the topological classification of some multidimensional gradient-like systems can be reduced to a combinatorial problem of distinguishing graphs up to isomorphism. The isomorphism problem of general graphs obviously can be solved by a standard enumeration algorithm. However, an efficient algorithm (i. e., polynomial in the number of vertices) has not yet been developed for it, and the problem has not been proved to be intractable (i. e., NPcomplete). We give polynomial-time algorithms for recognition of the corresponding graphs for two gradient-like systems. Moreover, we present efficient algorithms for determining the orientability and the genus of the ambient surface. This result, in particular, sheds light on the classification of configurations that arise from simple, point-source potential-field models in efforts to determine the nature of the quiet-Sun magnetic field.     

Reverse fragment based drug discovery approach via simple estimation of fragment contributions

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N-Pyrrolidine-2-ylmethyl)-2-hydroxy-3-aminopinanes as novel organocatalysts for asymmetric conjugate additions of ketones to α-nitroalkenes

Novel stereoisomeric natural pinane-derived bifunctional catalysts 3a–d bearing a pyrrolidine unit have been synthesized and examined in the asymmetric conjugate additions of carbonyl compounds to α-nitroalkenes. Six-membered cyclic ketones react with β-nitrostyrene derivatives in the presence of (1R,2R,3R,5R)-2-hydroxy-3-((S)-pyrrolidin-2-ylmethylamino) pinane 3b (10 mol %) with high conversion to afford with diastereoselectivity (dr (syn/anti) up to 97/3), the corresponding Michael adducts with enantiomeric purities of up to 88% ee.     

Rearrangement of O,O’-bis(2-benzylideneaminophenyl) phenylphosphonite into 1,6,7-triphenyl-3,4:9,10-dibenzo-2,11-dioxa-5,8-diaza-1-phosphatricyclo[6.3.0.01,5]undeca-3,9-diene

Keeping of O,O’-bis(2-benzylideneaminophenyl) phenylphosphonite in a CCl4 solution for 50 days resulted in its spontaneous rearrangement into 1,6,7-triphenyl-3,4:9,10-dibenzo-2,11-dioxa-5,8-diaza-1-phosphatricyclo[6.3.0.01,5]undeca-3,9-diene, a representative of spirophosphoranes with P–N bonds.     

Spectral stability of periodic waves in the generalized reduced Ostrovsky equation

We consider stability of periodic travelling waves in the generalized reduced Ostrovsky equation with respect to co-periodic perturbations. Compared to the recent literature, we give a simple argument that proves spectral stability of all smooth periodic travelling waves independent of the nonlinearity power. The argument is based on the energy convexity and does not use coordinate transformations of the reduced Ostrovsky equations to the semi-linear equations of the Klein–Gordon type.     

Design and Synthesis of Nitrogen-Rich Azo-Bridged Furoxanylazoles as High-Performance Energetic Materials

A series of novel energetic materials comprising of azo-bridged furoxanylazoles enriched with energetic functionalities was designed and synthesized. These high-energy materials were thoroughly characterized by IR and multinuclear NMR (¹H, ¹³C, ¹⁴N) spectroscopy, high-resolution mass spectrometry, elemental analysis, and differential scanning calorimetry (DSC). The molecular structures of representative amino and azo oxadiazole assemblies were additionally confirmed by single-crystal X-ray diffraction and X-ray powder diffraction. A comparison of contributions of explosophoric moieties into the density of energetic materials revealed that furoxan and 1,2,4-oxadiazole rings are the densest motifs while the substitution of the azide and amino fragments on the nitro and azo ones leads to an increase of the density. Azo bridged energetic materials have high nitrogen-oxygen contents (68.8–76.9 %) and high thermal stability. The synthesized compounds exhibit good experimental densities (1.62–1.88 g cm⁻³), very high enthalpies of formation (846–1720 kJ mol⁻¹), and, as a result, excellent detonation performance (detonation velocities 7.66–9.09 km s⁻¹ and detonation pressures 25.0–37.7 GPa). From the application perspective, the detonation parameters of azo oxadiazole assemblies exceed those of the benchmark explosive RDX, while a combination of high detonation performance and acceptable friction sensitivity of azo(1,2,4-triazolylfuroxan) make it a promising potential alternative to PETN.     

Relaxation of vibrational nonequilibrium distributions: the effect of multiphoton excitation on relaxation behavior

A theoretical study has been made on the non-stationary relaxation of highly vibrationally excited molecules in the presence of a source, producing these molecules. Initially, the nonequilibrium vibrational distribution is created using multiphoton absorption of laser radiation. An exact, analytical solution to the master equation is derived in terms of Meixner polynomials with regard to VV- and VT-processes. The time-dependent distribution of the system “molecule + field” is used to give explicit expressions for the mean number of photons distributed among vibrational and translational degrees of freedom and for the time dependence of average energy transferred per collision.     

On the long‐range relativistic effects in the 15N NMR chemical shifts of halogenated azines

Long‐range β‐ and γ‐relativistic effects of halogens in ¹⁵N NMR chemical shifts of 20 halogenated azines (pyridines, pyrimidines, pyrazines, and 1,3,5‐triazines) are shown to be unessential for fluoro‐, chloro‐, and bromo‐derivatives (1–2 ppm in average). However, for iodocontaining compounds, β‐ and γ‐relativistic effects are important contributors to the accuracy of the ¹⁵N calculation. Taking into account long‐range relativistic effects slightly improves the agreement of calculation with experiment. Thus, mean average errors (MAE) of ¹⁵N NMR chemical shifts of the title compounds calculated at the non‐relativistic and full 4‐component relativistic levels in gas phase are accordingly 7.8 and 5.5 ppm for the range of about 150 ppm. Taking into account solvent effects within the polarizable continuum model scheme marginally improves agreement of computational results with experiment decreasing MAEs from 7.8 to 7.4 ppm and from 5.5 to 5.3 ppm at the non‐relativistic and relativistic levels, respectively. The best result (MAE: 5.3 ppm) is achieved at the 4‐component relativistic level using Keal and Tozer's KT3 functional used in combination with Dyall's relativistic basis set dyall.av3z with taking into account solvent effects within the polarizable continuum solvation model. The long‐range relativistic effects play a major role (of up to dozen of parts per million) in ¹⁵N NMR chemical shifts of halogenated nitrogen‐containing heterocycles, which is especially crucial for iodine derivatives. This effect should apparently be taken into account for practical purposes.