A gas-kinetic scheme for shallow-water equations with source terms

In this paper, the Kinetic Flux Vector Splitting (KFVS) scheme is extended to solving the shallow water equations with source terms. To develop a well-balanced scheme between the source term and the flow convection, the source term effect is accounted in the flux evaluation across cell interfaces. This leads to a modified gas-kinetic scheme with particular application to the shallow water equations with bottom topography. Numerical experiments show better resolution of the unsteady solution than conventional finite difference method and KFVS method with little additional cost. Moreover, some positivity properties of the gas-kinetic scheme is established.     

Michael and ring expansion reactions of 6-carboethoxy-3,5-diaryl-2-cyclohexen-1-ones

When 64n853265325683/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-keto-ester1 a was reacted with dimethyl acetylenedicarboxylate ring expansion occurred to give substituted cyclooctadienones.Michael reactions of the title compounds1 with unsaturated ketones gave adducts, some of which underwent further cyclization reactions. A new route to 64n853265325683/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-tetralone ring system10 via cyclization of the intermediateMichael adduct9 is described.

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Michael- und Ringerweiterungsreaktionen von 6-Carboethoxy-3,5-diaryl-2-cyclohexen-1-onen

Zusammenfassung Bei der Reaktion von 64n853265325683/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-Keto-ester1 a mit Dimethyl-acetylendicarboxylat wurden unter Ringerweiterung substituierte Cyclooctadienone erhalten. DieMichael-Reaktion der Titelverbindung1 mit ungesättigten Ketonen ergab Addukte, von denen einige weitere Cyclisierungsreaktionen eingingen. Es wird ein neuer Weg zum 64n853265325683/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">-Tetralonsystem10 über die Cyclisierung des intermediärenMichael-Addukts9 beschrieben.

     

Base-catalyzed cyclization of β-(2-arylaminoethoxy)styrenes

64/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-(2-Arylaminoethoxy)styrenes undergo cyclization in the presence of KOH to giveN-aryl-2-benzyloxazolidines inca. 90 % yield. The structures of the products were confirmed by IR and NMR spectroscopy.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 340–341, February, 1994.     

Inclusion of α-phenyl-N-p-methylphenyl Nitrone in β- Cyclodextrin: Formation of 1G : 1H and 1G : 2H Complexes and the Remarkably Fast 1,3-Dipolar Cycloaddition of the 1G : 2H Complex with Olefins in the Solid State

The nitrone is found to be included in the 64t061577226184/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0">-cyclodextrin cavity in two different stoichiometries viz., 1G : 1H and 1G : 2H – the existence of which is proved by physical methods. The 1G : 2H complex of the nitrone serves as a good potent dipolarophile in the 1,3-dipolar cycloaddition reactions with olefins resulting in rate acceleration and regioselection.     

The spherical limit forn-vector correlations

We investigate then64/xxlarge8594.gif" alt="rarr" align="BASELINE" BORDER="0"> 64/xxlarge8734.gif" alt="infin" align="MIDDLE" BORDER="0"> limit of then-vector model single-spin and pairspin correlation functions. In this limit we show that the correlation functions become those of the corresponding spherical model.     

Crystal Structures of [Ni(Phen)(i‐Bu2PS2)2] and [Ni(Phen)3](i‐Bu2PS2)2 Complexes and Interaction between Coordinated 1,10‐Phenanthroline Molecules

Single crystals of [Ni(Phen)(i64h8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">Bu₂PS₂)₂] (I) and [Ni(Phen)₃](i64h8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">Bu₂PS₂)₂ (III) compounds were grown, and their structures were determined by X64h8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">ray diffraction analysis (CAD64h8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">4 diffractometer, MoK _{64h8/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0">} radiation, 3336 F _hkl , R = 0.0373 for I and 2575 F _hkl for III). The crystals of complex I have a triclinic unit cell with the following parameters: a = 11.097(1) 64h8/xxlarge8491.gif" alt="angst" align="MIDDLE" BORDER="0">, b = 14.903(2) 64h8/xxlarge8491.gif" alt="angst" align="MIDDLE" BORDER="0">, c = 22.650(3)64h8/xxlarge8491.gif" alt="angst" align="MIDDLE" BORDER="0">; 64h8/xxlarge945.gif" alt="agr" align="BASELINE" BORDER="0"> = 75.18(1)°, 64h8/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = 80.50(1)°, 64h8/xxlarge947.gif" alt="gamma" align="MIDDLE" BORDER="0"> = 75.07(1)°, V = 3479.2(7)64h8/xxlarge8491.gif" alt="angst" align="MIDDLE" BORDER="0">³, Z = 4, 64h8/xxlarge961.gif" alt="rgr" align="MIDDLE" BORDER="0">_calc = 1.255 g/cm³, and space group 64h8/10947_2004_Article_474369_TeX2GIFIE1.gif" alt=" $$\bar P$$ " align="middle" border="0"> 1; the crystals of III have a monoclinic unit cell with the following parameters: a = 19.010(3)64h8/xxlarge8491.gif" alt="angst" align="MIDDLE" BORDER="0">, b = 15.481(1) 64h8/xxlarge8491.gif" alt="angst" align="MIDDLE" BORDER="0">, c = 17.940(3)64h8/xxlarge8491.gif" alt="angst" align="MIDDLE" BORDER="0">; 64h8/xxlarge946.gif" alt="beta" align="MIDDLE" BORDER="0"> = 97.58(1)°, V = 5233.5(12)64h8/xxlarge8491.gif" alt="angst" align="MIDDLE" BORDER="0">³, Z = 4, 64h8/xxlarge961.gif" alt="rgr" align="MIDDLE" BORDER="0">_calc = 1.292 g/cm³, and space group C2/c. The structure of complex I is built from mononuclear molecules, and the structure of III, from [Ni(Phen)₃]²⁺ complex cations and i64h8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0"> Bu₂PS₂ ^- outer64h8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">sphere anions. The NiN₂S₄ coordination polyhedra in the structure of I and NiN₆ in the structure of III are distorted octahedra. Based on structural data, the interaction between the coordinated Phen molecules of complexes I, [Ni(Phen)₂(i64h8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">Bu₂PS₂)](i64h8/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">Bu₂PS₂) (II), and III is considered, as well as the packing modes of these complexes.     

Synthesis of 4,4′-bis(4-aminophenoxy)benzophenone and polyimides based on this compound

Synthesis of 4,464x432/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-bis(4-aminophenoxy)benzophenone was performed starting from chloral. Various polyimides were obtained by reactions of 4,4 64x432/xxlarge8242.gif" alt="prime" align="BASELINE" BORDER="0">-bis(4-aminophenoxy)benzophenone with aromatic tetracarboxylic acid dianhydrides. Some of the polyimides obtained are crystalline compounds.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 673–676, March, 1996.     

On the homogeneity of additive mappings

LetK be a ring with an identity 1 0 andM, L two unitaryK-modules. Then, for any additive mappingf:M L, the setH _f :={ K f(x)=f(x) for allx M} forms a subring ofK, the homogeneity ring off. It is shown that, forM {0},L {0} and any subringS ofK for whichM is a freeS-module, there exists an additive mappingf:ML such thatH _f =S. This result is applied to the four Cauchy functional equations, and it leads also to an answer to the question as to whether it is possible to introduce onM a multiplication ·:M × M M makingM into a ring but not into aK-algebra.     

Radiotracer Investigation of the Copper Ore Concentration Process

One of the most difficult operations for control and identification in copper ore concentration process is grain classification in hydrocyclone batteries. In the paper radiotracer investigations of the classification process immediately give values of hydrocyclones parameters with higher accuracy than obtained from conventional methods. Presented paper includes the results of the investigation which was carried out in “Lubin” Copper Mine in Poland.