A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Antigenic determinants at the carboxy terminus of chicken egg white riboflavin carrier protein (RCP): Epitope mapping and antibody-mediated pregnancy curtailment in rodents

The epitopic core sequences recognized by three monoclonal antibodies raised to chicken riboflavin carrier protein (RCP) were mapped to the C-terminal tail-end of the protein using the pepscan method A 21-residue synthetic peptide corresponding to residues 200-219 of the protein and comprising the regions corresponding to the antibodies was synthesized. Administration of polyclonal antibodies specific to this peptide led to termination of early pregnancy in mice. Also, active immunization of rats with the peptide-purified protein derivative conjugate inhibited establishment of pregnancy. These results demonstrate the functional importance of the C-terminal 200-219 region of chicken RCP. Copyright (C) 1996 Elsevier Science Ltd.

Automatic identification of modal damping from Floquet analysis

A practical method is proposed to identify the mode associated with the frequency part of the eigenvalue of the Floquet transition matrix (FTM). From the FTM eigenvector, which contains the states and their derivatives, the ratio of the derivative and the state corresponding to the largest component is computed. The method exploits the fact that the imaginary part of this (complex) ratio closely approximates the frequency of the mode. It also lends itself well to automation and has been tested over a large number of FTMs of order as high as 250.

Phosphate derivatives of 123 cuprates of the formula LnSr(2)Cu(3)O(7) (Ln=Gd, Dy, Ho)

Partial substitution of Cu in the chain by the phosphate ion stabilizes LnSr(2)Cu(3)O(7) (Ln = Gd, Dy or Ho) in the 123 structure. The LnSr(2)Cu(2.8)(PO4)(0.2)O-y derivatives exhibit incommensurately modulated structures. The holmium oxy-phosphate derivative has been rendered superconducting by the partial substitution of Ho by Ca.

Potassamide induced in situ alkylation of 5,6-dihydroisoquinoline with allyl bromide and Michael acceptors

Potassamide induced in situ alkylation of 4-cyano-3-methoxy-1-methyl-5, 6-dihydroisoquinoline (1a) with allyl bromide gives the 5-allyl- and 5,9-diallyl-5,6-dihydroisoquinolines (1c and 1d), isoquinoline derivative 2 and 4-allyl-1, 2, 3, 4-tetrahydroisoquinolin-3(2H)-one (3a). However, potassamide induced in situ alkylation of In with buten-2-one, mesityl oxide and acrylonitrile results in the formation of only 5-alkylated 5,6-dihydroisoquinoline derivatives 1e-g along with fully aromatised compound 2.

Structural variants of hyperbranched polyesters

Hyperbranched polyesters based on 3,5-dihydroxybenzoic acid and its derivatives were prepared by self-condensation of the corresponding ester under standard trans-esterification conditions. The spacer segment length that connects the branching points was systematically varied by starting from the appropriate ethyl 3,5-bis(omega-hydroxyoligo(ethyleneoxy))benzoate. The thermal properties of the hyperbranched polyesters were studied using DSC, and they have been compared with those of the linear analogues prepared from the corresponding p-hydroxybenzoic acid derivatives and also with the molecularly ''kinked'' analogues prepared from the meta isomers. These hyperbranched polyesters were also terminally functionalized by using a potentially mesogenic 4-butoxybiphenylcarboxylic acid derivative in an attempt to prepare novel hyperbranched liquid crystalline polyesters. This was achieved by copolymerization of the AB(2) monomer with the mesogenic A-type capping unit. These polymers were found to be amorphous and did not exhibit any liquid crystalline phases, probably due to the random distribution of the mesogenic segments on the polymer framework, making it difficult to both crystallize and form mesophases.

Structure, Spectra and Redox Behaviour of Copper(11) Complexes of Bis( benzimidazoly1)diamine Ligands

The linear quadridentate ligand N,N'-bis(benzimidazoI-2-ylethyl)ethane-l,2-diamine (L') and its 1 - methylbenzimidazole analogue (L2) and homologues form 1 : 1 complexes with Cu(CIO,),; L' also forms complexes of the types CuL'X, where X = NO,, PF,, Br or CI and CuL'(X)Y where X = CI or Br and Y = CIO, or Br. Deep blue CuL1Br,*2H20 crystallizes in the monoclinic space group C2/c with Z = 4, a = 9.91 9(2), b = 16.626(3), c = 14.1 02(3) le\ and p = 94.39(2)". The structure was solved by Patterson and Fourier difference methods and refined by the least-squares technique to R = 0.064 for 2195 independent reflections with / > 1.50(/). The molecule lies on a two-fold axis symmetrically around Cu". The co-ordination around Cu" is found to be square planar with two amino nitrogens and two benzimidazole nitrogens forming the equatorial plane [CU-N 1.983(3) and 2.037(4) A]. The bromides are at longer distances [3.349(1) A] in axial sites. Ligand field and EPR spectra indicate that one bromide or chloride ion is axially co-ordinated to Cu" in [CuL1l2+. This ion exhibits quasi-reversible redox behaviour. Electrochemical studies of the dihalides in methanol have established the presence of [CuL'X,], [CuL'(X)]+ and [CuL'I2+ in equilibrium. In complexes with 565 [CuL4I2+ [L4 = N,Nbis( benzimidazol-2-ylmethyl)ethane-l,2-diamine] and 555 [CuL3] [L3 = N,N'-bis(1 -methylbenzimidazol- 2-ylmethyl)propane-l,3-diamine] chelate rings, Cull does not seem to lie in the N, square plane, as revealed by their low A values and irreversible electrochemical behaviour. The Cu"-Cu' redox potentials in methanol are in the order [CuL1I2+ < [CuL3I2+ < [CuL4I2+; this illustrates that sixmembered chelate rings are suitable to stabilize Cu", when CU-N 0 interactions are favourable.

Facial Coordination in BIS[BIS(Benzimidazol-2-Ylmethyl)Amine]Copper(II) Perchlorate Dihydrate - Synthesis, Structure, Spectra and Redox Behavior

The 1:1 and 1:2 cooper(II) complexes with the tridentate compound bis(benzimidazol-2-ylmethyl)amine (L(1)) and its benzimidazole (L(2)) and amine (L(3)) N-methyl-substituted derivatives have been prepared and their spectroscopic properties studied. While the 1:1 complexes are of the type CuLX(2) nH(2)O (X = C/O-4(-), NO3-, Cl- or Br-), the 1:2 complexes are of the type CuL(2) (ClO4)(2) nH(2)O (L = L(1) or L(3), n = 0-4). In all these complexes L acts as a tridentate ligand with the amine nitrogen and both the benzimidazole nitrogens co-ordinating to Cu-II. The complex [CuL(2)(1)][ClO4](2) 2H(2)O crystallises in the monoclinic space group P2(1)/c with a = 9.828(2), b = 9.546(2) and c = 19.906(2) Angstrom and beta = 95.71(1)degrees, for Z = 2. The R value is 0.0635 for 2180 significant reflections. The copper(II) ion has an elongated octahedral geometry with four equatorial benzimidazole and two long-distance axial amine N donors. The Cu-N-bzim and Cu-N-amine distances are 2.011(4) and 2.597(6) Angstrom respectively. Factors favouring facial co-ordination to tridentate ligands are discussed. The 1:1 complexes involve meridonal co-ordination of the ligands, with square-based geometry as revealed by ligand-field and EPR spectral properties. The NMe substitution as in CuL(3)(ClO4)(2) confers low V ($) over tilde$$(max) and high E(1/2) for the cu(II)-Cu-I couple. Most of the 1:1 complexes are less reversible but exhibit E(1/2) values more positive than those of the corresponding 1:2 complexes.

Synthesis Based on Cyclohexadienes. 5. A New Approach to the Synthesis of a-Ring Aromatic Steroids - a Formal Total Synthesis of (+/-)-Estrone

A new strategy for the construction of A-ring aromatic steroids which resulted in the formal total synthesis of estrone is described. Thus reaction of the adduct (9), obtained from 1-methoxy-4-methylcyclohexa-1,4-diene and acrolein, with 3-(m-methoxyphenyl)propylmagnesium bromide followed by oxidation afforded the bicyclo[2.2.2]octene derivative (14). Acid-catalysed rearrangement of (14) followed by an intramolecular Michael addition resulted in the cis tetraenone (18) which was dehydrogenated with palladium chloride to the pentaenone (22). Li/NH3 reduction of (22) gave 3-methoxy-D-homoestra-1,3,5(10)-trien-16-one (31) which has been converted into the methyl ether (37) of marrianolic acid, and its methyl ester (38).

Synthesis based on cyclohexadienes. Part 17. Total synthesis of the sesquiterpenes of Eremophila georgei diels

The first stereoselective total synthesis of the novel sesquiterpenes 1 and 2 is described. The preparation of the key intermediate 27 involved a rearrangement of a bicyclo[3.2.1] octane framework to an isomeric bicyclo[3.2.1]octane skeleton via a bicyclo[2.2.2]octane derivative.

Unusual ribose conformation in a ternary copper(II) 2?deoxyribonucleotide complex

The ternary metal deoxyribonucleotide complex [Cu(bzim)(5?-dGMP)(H2O)3](bzim = benzimidazole, 5?-dGMP = 2?-deoxyguanosine 5?-monophosphate) has been prepared and the structure analysed by X-ray diffraction. The compound crystallizes in the space group P1 with a= 7.069(6), b= 13.959(10), c= 14.204(12)Å, ?= 75.12(6), ?= 94.15(6), ?= 97.98(6)° and Z= 2. The structure was solved by the heavy-atom method and refined by full-matrix least-squares procedures on the basis of 2813 observed [I[gt-or-equal] 3?(I)] reflections to final R and R? values of 0.050 and 0.052 respectively. There are two independent molecules in the asymmetric unit and both copper(II) centres have square-pyramidal co-ordination geometry. An unusual feature of the structure is the co-ordination of the metal by N(7) of the base, in the presence of a ?-aromatic amine, bzim. The structure is stabilized by intermolecular base�bzim stacking. The nucleotides of both the molecules have an anti conformation about the glycosyl bond, and a gauche-gauche conformation about the C(4?)�C(5?) bond. A feature of particular interest is the unusual sugar conformation. The base furanose rings of the two nucleotide molecules adopt C(3?)-exo/C(2?)-endo pucker and C(3?)-exo pucker respectively.

Uniform algebras generated by holomorphic and close-to-harmonic functions

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc (D) over bar generated by z and h, where h is a nowhere-holomorphic harmonic function on D that is continuous up to partial derivative D, equals C((D) over bar). The abstract tools used by Axler and Shields make harmonicity of h an essential condition for their result. We use the concepts of plurisubharmonicity and polynomial convexity to show that, in fact, the same conclusion is reached if h is replaced by h + R, where R is a non-harmonic perturbation whose Laplacian is ``small'' in a certain sense.

Nonequilibrium-phase transition and 'specific-heat' singularity in the kinetic Ising model: A Monte Carlo study

The nonequilibrium-phase transition has been studied by Monte Carlo simulation in a ferromagnetically interacting (nearest-neighbour) kinetic Ising model in presence of a sinusoidally oscillating magnetic field. The ('specific-heat') temperature derivative of energies (averaged over a full cycle of the oscillating field) diverge near the dynamic transition point.

Synthesis and biological evaluation of novel 2-aralkyl-5-substituted-6-(4 `-fluorophenyl)-imidazo2,1-b]1,3,4]thiadiazole derivatives as potent anticancer agents

Levamisole, the imidazo2,1-b]thiazole derivative has been reported as a potential antitumor agent. In the present study, we synthesized, characterized and evaluated biological activity of its novel analogues with substitution in the aralkyl group and on imidazothiadiazole molecules with same chemical backbone but different side chains namely 2-aralkyl-6-(4'-fluorophenyl)-imidazo2,1-b]1,3,4]thiadiazoles (SCR1), 2-aralkyl-5-bromo-6-(4'-fluorophenyl)-imidazo2,1-b]1,3,4]-thiadiaz oles (SCR2), 2-aralkyl-5-formyl-6-(4'-fluorophenyl)-imidazo2,1-b]1,3,4]-thiadia zoles (SCR3) and 2-aralkyl-5-thiocyanato-6-(4'-fluorophenyl)-imidazo2,1-b]1,3,4]-th iadiazoles (SCR4) on leukemia cells. The cytotoxic studies showed that 3a, 4a, and 4c exhibited strong cytotoxicity while others had moderate cytotoxicity. Among these we chose 4a (IC50, 8 mu M) for understanding its mechanism of cytotoxicity. FACS analysis in conjunction with mitochondrial membrane potential and DNA fragmentation studies indicated that 4a induced apoptosis without cell cycle arrest suggesting that it could be used as a potential chemotherapeutic agent. (C) 2011 Elsevier Masson SAS. All rights reserved.

Synthesis based on cyclohexadienes .23. Total synthesis of 5-epi-pupukean-2-one

A new strategy for the construction of the isotwistane skeleton is reported from easily available cyclohexadienes which involves stereoselective alkylation of a bicyclooctenone derivative and a decarboxylative 5-exo-trig radical cyclisation as the key steps in the total synthesis of 5-epi-pupukean-2-one.