An unequivocal synthesis of some substituted 1,2,4-triazolo[1,5-a]pyrimidines

An unequivocal synthesis of 5-chloro-7-methyl- (8) and 7-methyl-1,2,4-triazolo[1,5-a]pyrimidine (10) from 2-amino-4-chloro-6-methylpyrimidine (5) through the corresponding amidine6 and formamide oxime7 was developed. It was unambigously shown by comparison of the chemical shifts and the magnitude of coupling constants that the compounds obtained by condensation of 3-amino-1,2,4-triazole (12) and ethyl acetoacetate (13) and some further transformations are isomeric 5-methyl substituted 1,2,4-triazolo[1,5-a]pyrimidines1,9, and11.

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Eine eindeutige Synthese einiger substituierter 1,2,4-Triazolo[1,5-a]pyrimidine

Zusammenfassung Es wurde ein eindeutiger Syntheseweg für 5-Chlor-7-methyl- (8) und 7-Methyl-1,2,4-triazolo[1,5-a]pyrimidin (10) ausgehend von 2-Amino-4-chlor-6-methylpyrimidin (5) über das entsprechende Amidin6 und das Formamidoxim7 entwickelt. Durch Vergleich von chemischen Verschiebungen und Kopplungskonstanten konnte eindeutig gezeigt werden, daß die Verbindungen, die bei der Kondensation von 3-Amino-1,2,4-triazol (12) and Ethylacetoacetat (13), sowie einige weitere Transformationsprodukte, isomere 5-Methylsubstituierte 1,2,4-Triazolo[1,5-a]pyrimidine sind (1,9,11).

     

Synthesis and X-ray crystal structure of oxamido-bridged heterobinuclear Ni(Ⅱ)-Cu(Ⅱ) complexes

The two complexes [Ni(oxen)Cu(L)2](ClO4)2.xH2O (L=2,2'-bipyridyl(bpy), 1,10-phenanthroline(phen)) have been synthesized, where oxen is N,N'-bis(2-aminoethyl)oxamido di-anion. The crystal structure of [Ni(oxen)Cu(bpy)2](ClO4)2.CH3OH has been determined by X-ray diffraction method. The crystal is triclinic system, space group P1 with a=12.179(1),b=12.298(2), c=11.476(2) A, a=97.57(1), B=97.52(1), 7=80.29(2), V=1669.04(67) A3, Z=2, Dcalcd=1.667 g/cm3. The structure has been refined to final R of 0.076 and Rw of 0.080, respectively. The complexes have an extended oxamido-bridged structure and consist of Ni(Ⅱ) ion in a square planar environment and Cu(Ⅱ) ion in a distorted octahedral environment.     

On a numerical approach to Stefan-like problems

Summary This paper is devoted to the numerical analysis of a bidimensional two-phase Stefan problem. We approximate the enthalpy formulation byC ⁰ piecewise linear finite elements in space combined with a semi-implicit scheme in time. Under some restrictions related to the finite element mesh and to the timestep, we prove positivity, stability and convergence results. Various numerial tests are presented and discussed in order to show the accuracy of our scheme.This work is supported by the Fonds National Suisse pour la Recherche Scientifique.     

Numerical implementation of coherence for the example of the “Swiss Cross”

Summary We consider the two-dimensional Helmholtz equation u+u=0 inD with the boundary conditionsu=0 on D. D is the Swiss Cross — a region consisting of five unit squares. A method based on the concept of Coherence is utilized to determine an approximation for the first eigenvalue= ₁ more accurate than calculated by classical difference methods. The numerical result is used to illustrate isoperimetric upper and lower bounds for ₁, and to test some conjectures on its relations with torsional rigidity.Dedicated to the memory of Professor Lathar Collatz     

On the implementation of Sμ U(2) action in the irreducible representations of twisted canonical commutation relations

The natural S U(2) action on the creation and annihilation operators satisfying twisted canonical commutation relations (TCCR) is investigated. It is shown that the Fock representation is the only covariant irreducible representation of TCCR.Partially supported by the program RP.1.10.     

Differential calculus on quantized simple lie groups

Differential calculi, generalizations of Woronowicz's four-dimensional calculus on SU _q (2), are introduced for quantized classical simple Lie groups in a constructive way. For this purpose, the approach of Faddeev and his collaborators to quantum groups was used. An equivalence of Woronowicz's enveloping algebra generated by the dual space to the left-invariant differential forms and the corresponding quantized universal enveloping algebra, is obtained for our differential calculi. Real forms for q are also discussed.     

A remark on compact matrix quantum groups

A simpler set of axioms of the theory of compact matrix quantum groups (pseudogroups) is found.Supported by Japan Society for Promoting Science. On leave from the Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Hoa 74, 00-682 Warsaw, Poland.     

A study of the density of gap states in amorphous semiconductors from thermostimulated conductivity spectra

A theoretical analysis of thermostimulated conductivity spectra _TSC(T) has been applied to determine the density of gap states g(E) in a-Si: H and a-Si: H/a-SiN _x : H multilayer structures. The results for g(E) are consistent with the results deduced from Fritzsche's analytical approach as well as other methods. A comparison has been made between the two different analytical approaches for _TSC(T). We discuss the relationship between the energy of maximum thermostimulated current emission E _m and quasi-Fermi level E _q. We demonstrate that E _q could be a better parameter than E _m in the general theoretical treatment of thermostimulated conductivity.     

Convergence rate estimate for a domain decomposition method

Summary We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ². We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.This author was supported by the National Science Foundation under contract numbers DCR-8521451 and ECS-8957475, by the IBM Corporation, and by the 3M Company, while in residence at Yale UniversityThis author was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy under Contract W-31-109-Eng-38This author was supported by the National Science Foundation under contract number ECS-8957475, by the IBM Corporation, and by the 3M Company     

The finite element method with non-uniform mesh sizes applied to the exterior Helmholtz problem

Summary The finite element method with non-uniform mesh sizes is employed to approximately solve Helmholtz type equations in unbounded domains. The given problem on an unbounded domain is replaced by an approximate problem on a bounded domain with the radiation condition replaced by an approximate radiation boundary condition on the artificial boundary. This approximate problem is then solved using the finite element method with the mesh graded systematically in such a way that the element mesh sizes are increased as the distance from the origin increases. This results in a great reduction in the number of equations to be solved. It is proved that optimal error estimates hold inL ²,H ¹ andL , provided that certain relationships hold between the frequency, mesh size and outer radius.