Some methods of training radial basis neural networks in solving the Navier‐Stokes equations

The purpose of this research is to analyze the application of neural networks and specific features of training radial basis functions for solving 2‐dimensional Navier‐Stokes equations. The authors developed an algorithm for solving hydrodynamic equations with representation of their solution by the method of weighted residuals upon the general neural network approximation throughout the entire computational domain. The article deals with testing of the developed algorithm through solving the 2‐dimensional Navier‐Stokes equations. Artificial neural networks are widely used for solving problems of mathematical physics; however, their use for modeling of hydrodynamic problems is very limited. At the same time, the problem of hydrodynamic modeling can be solved through neural network modeling, and our study demonstrates an example of its solution. The choice of neural networks based on radial basis functions is due to the ease of implementation and organization of the training process, the accuracy of the approximations, and smoothness of solutions. Radial basis neural networks in the solution of differential equations in partial derivatives allow obtaining a sufficiently accurate solution with a relatively small size of the neural network model. The authors propose to consider the neural network as an approximation of the unknown solution of the equation. The Gaussian distribution is used as the activation function.     

Mesomorphic structure peculiarities of two mix-substituted phthalocyanines of the A3B type

Mesomorphic properties and structures of two mix-substituted lipophilic phthalocyanine derivatives of the A₃B type, with a different ratio of electron-donating (hexadecyloxy-) and electron-withdrawing (Cl-) substituents on the isoindol fragments ‘A’ and ‘B’, correspondingly, were studied by polarising optical microscopy, differential scanning calorimetry and small-angle X-ray scattering. Both compounds display columnar mesophases, and the type of organisation of the columns in the mesomorphic state was found to strongly depend on the number of peripheral chlorine substituents in the molecule. The di-chloro-substituted phthalocyanine forms a solid pasty lamellar phase at room temperature, which on heating undergoes successive transitions to two large-lattice columnar mesophases (2D-Col_h and 3D-M_Col) arising from the aggregation of several phthalocyanine-containing piles. On the contrary, aggregation of columns does not occur for the tetra-chloro-substituted phthalocyanine, which forms a nematic columnar mesophase of single phthalocyanine piles (1D-N_Col). While the di-chloro-compound partly crystallises on cooling, the nematic phase of the tetra-chloro-compound freezes at room temperature. The reasons for this different self-organisation behaviour are not yet fully understood, but some hints may be deduced from the proposed supramolecular models.     

Dioximes of 1,6-heptanediones from acetylene and ketones: only three atom-economic steps

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Facile Separation,Spectroscopic Identification,and Electrochemical Properties of Higher Trifluoromethylated Derivatives of [70]Fullerene

We survey the structure and electronic properties of the family of higher trifluoromethylated C₇₀(CF₃)_n molecules with n=14, 16, 18, and 20. Twenty‐two available compounds, of which thirteen are newly obtained and characterized, demonstrate the broad diversity of π‐system topologies, which enabled us to study the interplay between the CF₃ addition pattern and the electronic properties. UV/Vis spectroscopic and cyclic voltammetric studies demonstrate the importance of the exact addition pattern rather than the plain number of addends. Of particular interest is the skew pentagonal pyramid (SPP) addition pattern, which enables formation of closed‐shell cyclopentadienyl anions C₇₀(CF₃)_{n? 1} ^? through CF₃ detachment upon electron transfer. A detailed study of the process is presented for a SPP‐C₇₀(CF₃)₁₆ where potentiostatic electrolysis at the second reduction potential gives C₇₀(CF₃)₁₅^? oxidizable to a persistent C₇₀(CF₃)₁₅^· radical. Together with the literature data for the lower C₇₀(CF₃)_n compounds with n=2–12, the present results show good correlation between the experimental boundary level positions and the DFT predictions. The compounds turn out to be electron acceptor molecular semiconductors with experimental LUMO energies and HOMO–LUMO gaps within the ranges of ?4.3 to ?3.7 eV and 1.6 to 3.3 eV, respectively, depending on the shape of the conjugated fragments. The HOMO levels fall within the range of ?5.6 to ?6.9 eV and show linear correlation with the number of addends.     

New tetranorlabdanoic acid from aerial parts of Salvia aethiopis

Salvia aethiopis is a perennial plant native to Eurasia and known by the common names Mediterranean sage or African sage. This plant has been used in Iranian medicine as a carminative and tonic. The ethanolic extract of aerial part of S. aethiopis exhibited moderate to weak activity towards delta and kappa opioid receptors (46.3 and 45.3% displacement, respectively). Chromatographic purification of the ethanolic extract on silica gel column led to isolation of one new: 3α-hydroxy-8α-acetoxy-13,14,15,16-tetranorlabdan-12-oic acid (I) and three known compounds: sesquiterpene spathulenol (II), β-sitosterol (III) and β-sitosterol-3-O-glucoside (IV). The structures of all isolated compounds were elucidated by their NMR (1D and 2D) and MS spectral data. All the fractions and isolated compounds were tested for cannabinoid and opioid receptor binding assays.     

Synthesis, structure and theoretical study of mixed fluoro-trifluoromethyl derivatives of C60. Molecular structures of C60F18(CF3)6 and C60F16(CF3)6

A series of novel mixed C60Fn(CF3)m compounds has been produced by trifluoromethylation of C60F18 with CF3I in ampoules at 380-420 degrees C. Two of these compounds, C60F18(CF3)6 and C60F16(CF3)6, have been characterized by X-ray crystallography, which has revealed addition of six CF3 groups to the C3v-C60F18 for the former and replacement/elimination of two outermost F atoms in the latter. Quantum chemical calculations have been employed to predict the most stable possible isomers of C60F16/18(CF3)6 in order to rationalize the experimental results.     

Practical synthesis of 1,4-dioxane derivative of the closo-dodecaborate anion and its ring opening with acetylenic alkoxides

Practical method of synthesis of the 1,4-dioxane derivative of the closo-dodecaborate anion was developed. The cleavage of the dioxonium ring in [B₁₂H₁₁O(CH₂CH₂)₂O]⁻ with acetylenic alcohols gave rise to the preparation of closo-dodecaborate derivatives with terminal acetylene group. These compounds can be introduced into click reactions with phenylazide leading to the corresponding triazoles. The structures of (Bu₄N)[B₁₂H₁₁O(CH₂CH₂)₂O] and (Bu₄N)₂[B₁₂H₁₁(OCH₂CH₂)₂OCH₂CCH] · 0.5HOCH₂CCH were determined by single-crystal X-ray diffraction.     

Comparative analysis of hydrogen bonding with participation of the nitrogen, oxygen and sulfur atoms in the 2(2'-heteroaryl)pyrroles and their trifluoroacetyl derivatives based on the 1H, 13C, 15N spectroscopy and DFT calculations

The N-H...X (X = N,O,S) intramolecular hydrogen bond in the series of 2(2'-heteroaryl)pyrroles and their trifluoroacetyl derivatives is examined by the (1)H, (13)C, (15)N spectroscopy and density functional theory (DFT) calculations. The influence of the hydrogen bond on coupling and shielding constants is considered. It is shown that the N-H...N intramolecular hydrogen bond causes a larger increase in the absolute size of the (1)J(N,H) coupling constant and a larger deshielding of the bridge proton than the N-H...O hydrogen bond. The effect of the N-H...S interaction on the (1)J(N,H) coupling constant and the shielding of the bridge proton is small. The NMR parameter changes in the series of the 2(2'-heteroaryl)pyrroles due to N-H...X hydrogen bond and the series of the 1-vinyl-2-(2'-heteroaryl)-pyrroles due to C-H...X hydrogen bond have the same order. The proximity of the nitrogen, oxygen or sulfur lone pair to the F...H hydrogen bridge quenches the trans-hydrogen bond spin-spin couplings (1h)J(F,H-1) and (2h)J(F,N).     

HNO3 forming channel of the HO2 + NO reaction as a function of pressure and temperature in the ranges of 72-600 Torr and 223-323 K

A high-pressure turbulent flow reactor coupled with a chemical ionization mass-spectrometer was used to determine the branching ratio of the HO(2) + NO reaction: HO(2) + NO --> OH + NO(2) (1a), HO(2) + NO --> HNO(3) (1b). The branching ratio, beta = k(1b)/k(1a), was derived from the measurements of "chemically amplified" concentrations of the NO(2) and HNO(3) products in the presence of O(2) and CO. The pressure and temperature dependence of beta was determined in the pressure range of 72-600 Torr of N(2) carrier gas between 323 and 223 K. At each pressure, the branching ratio was found to increase with the decrease of temperature, the increase becoming less pronounced with the increase of pressure. In the 298-223 K range, the data could be fitted by the expression: beta(T,P) = (530 +/- 10)/T(K) + (6.4 +/- 1.3) x 10(-4)P(Torr) - (1.73 +/- 0.07), giving beta approximately 0.5% near the Earth's surface (298 K, 760 Torr) and 0.8% in the tropopause region (220 K, 200 Torr). The atmospheric implication of these results is briefly discussed.