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.     

The half-life of the 1437 keV 11/2− state in97Mo

Using the (,n) reaction, the half-life of the first 11/2^– level in⁹⁷Mo has been determined as T_1/2(1437.0 keV)=2.5±0.3 ns by means of the pulsed beam method. The experimentally obtainedB(M2) value between theh _11/2 andg _7/2 configurations in⁹⁷Mo has been satisfactorily described within the quasiparticle-phonon model usingg _s ^eff =0.6g _s ^free . Similar calculations and comparisons with experminental data have been performed also for^95,99Mo as well as for⁹⁹Ru and¹⁰¹Pd.This work is partly supported by the Bulgarian National Research Foundation     

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.     

Preparation, crystallographic characterization and theoretical study of two isomers of C70(CF3)12

Two isomers of C70(CF3)12 have been isolated from a mixture obtained by trifluoromethylation of C70 with CF3I; their molecular structures determined by X-ray crystallography are in good agreement with the results of theoretical DFT calculations for the most stable C70(CF3)12 isomers.     

Capturing C90 Isomers as CF3 Derivatives: C90(30)(CF3)14, C90(35)(CF3)16/18, and C90(45)(CF3)16/18

High‐temperature trifluoromethylation of a C₉₀ isomeric mixture with CF₃I followed by HPLC separation of C₉₀(CF₃)_n isomers resulted in the isolation of several individual C₉₀(CF₃)_14?18 compounds. Single crystal X‐ray diffraction with the use of synchrotron radiation resulted in the structure determination of C₉₀(30)(CF₃)₁₄, C₉₀(35)(CF₃)_16/18, and C₉₀(45)(CF₃)_16/18. Their addition patterns are discussed and compared with the known isomers C₉₀(30)(CF₃)₁₈ and C₉₀(35)(CF₃)₁₄, respectively. The presence of the most stable C₉₀ isomer, C₉₀(45), in the fullerene soot has been confirmed for the first time.     

Abnormal reactions of 2‐methoxy‐4,9‐dimethyl‐1‐nitroacridine with selenous acid and selenium(IV) oxide. Synthesis of 1H‐selenopheno[2,3,4‐k,l]acridine‐1‐one: A new seleno‐containing ring system

Unusual course of the reaction was revealed on the oxidation of functionally substituted acridine containing the activated methyl groups by well‐known oxidants, such as selenous acid and selenium(IV) oxide. Treatment of 2‐methoxy‐4,9‐dimethyl‐1‐nitroacridine ( 5 ) with an excess of H₂SeO₃ in boiling ethanol gave a mixture of the normal reaction products, 2‐methoxy‐4‐methyl‐1‐nitro‐9‐formylacridine ( 11 ) (isolated yield 29%) and 2‐methoxy‐4‐methyl‐1‐nitroacridine‐9‐carboxylic acid ( 12 ) (36%), together with an abnormal product, 3‐methoxy‐5‐methyl‐1H‐selenopheno[2,3,4‐k,l]acridine‐1‐one ( 13 ) (21%), which is the first example of a new seleno‐containing ring system. With the use of SeO₂ the yield of selenolactone 13 was much lower. J. Heterocyclic Chem., 2011.     

Hydrolytic metal-mediated coupling of dialkylcyanamides at a Pt(IV) center giving a new family of diimino ligands

Addition of excess R(2)NCN to an aqueous solution of K(2)[PtCl(4)] led to the precipitation of [PtCl(2)(NCNR(2))(2)] (R(2) = Me(2) 1; Et(2) 2; C(5)H(10) 3; C(4)H(8)O, 4) in a cis/trans isomeric ratio which depends on temperature. Pure isomers cis-1-3 and trans-1-3 were separated by column chromatography on SiO(2), while trans-4 was obtained by recrystallization. Complexes cis-1-3 isomerize to trans-1-3 on heating in the solid phase at 110 degrees C; trans-1 has been characterized by X-ray crystallography. Chlorination of the platinum(II) complexes cis-1-3 and trans-1-4 gives the appropriate platinum(IV) complexes [PtCl(4)(NCNR(2))(2)] (cis-5-7 and trans-5-8). The compound cis-6 was also obtained by treatment of [PtCl(4)(NCMe)(2)] with neat Et(2)NCN. The platinum(IV) complex trans-[PtCl(4)(NCNMe(2))(2)] (trans-5) in a mixture of undried Et(2)O and CH(2)Cl(2) undergoes facile hydrolysis to give trans-[PtCl(4)[(H)=C(NMe(2))OH](2)] (9; X-ray structure has been determined). The hydrolysis went to another direction with the cis-[PtCl(4)(NCNR(2))(2)] (cis-5-7) which were converted to the metallacycles [PtCl(4)[NH=C(NR(2))OC(NR(2))=NH]] (11-13) due to the unprecedented hydrolytic coupling of the two adjacent dialkylcyanamide ligands giving a novel (for both coordination and organic chemistry) diimino linkage. Compounds 11-13 and also 14 (R(2) = C(4)H(8)O) were alternatively obtained by the reaction between cis-[PtCl(4)(MeCN)(2)] and neat undried NCNR(2). The structures of complexes 11, 13, and 14 were determined by X-ray single-crystal diffraction. All the platinum compounds were additionally characterized by elemental analyses, FAB mass-spectrometry, and IR and (1)H and (13)C[(1)H] NMR spectroscopies.     

Study of the system manganese(VII)-3,7-bis(dimethylamino)-phenothiazin-5-ium chloride-water-1,2-dichloroethane Using UV-spectrophotometry

The system manganese(VII)-3,7-bis(dimethylamino)-phenothiazin-5-ium chloride (MB)-water-1,2-dichloroethane has been studied using UV-spectrophotometry. The molar absorptivity of the complex is (3.86 ± 0.06) × 10⁴ L mol^?1 cm^?1 at 290 nm and the system obeys Beer??s law in the range 0.1?C0.99 ??g mL^?1 Mn(VII). The detection limit (DL) and quantitation limit (QL) of Mn(VII) determination were found to be 0.0146 and 0.049 ??g mL^?1, respectively. The composition of the complex is established as MB: MnO ₄ ^? = 1: 1. Extraction investigations of the system discussed were carried out. The characteristic values for the extraction equilibrium and the equilibrium in the aqueous phase was determined: extraction constant K_ex = (1.12 ± 0.05) × 10⁵, distribution constant K_D = 75.61 ± 0.1 and association constant ?? = (1.48 ± 0.08) × 10³. A new method has been developed for the microdetermination of manganese(VII) in plants and steels.