Paths through inverse limits

In Bani?, ?repnjak, Merhar and Milutinovi? (2010) [2] the authors proved that if a sequence of graphs of surjective upper semi-continuous set-valued functions fn:X→X² converges to the graph of a continuous single-valued function f:X→X, then the sequence of corresponding inverse limits obtained from fn converges to the inverse limit obtained from f. In this paper a more general result is presented in which surjectivity of fn is not required. The result is also generalized to the case of inverse sequences with non-constant sequences of bonding maps. Finally, these new theorems are applied to inverse limits with tent maps. Among other applications, it is shown that the inverse limits appearing in the Ingram conjecture (with a point added) form an arc.     

Convergence of multistep discretizations of DAEs

Standard ODE methods such as linear multistep methods encounter difficulties when applied to differential-algebraic equations (DAEs) of index greater than 1. In particular, previous results for index 2 DAEs have practically ruled out the use of all explicit methods and of implicit multistep methods other than backward difference formulas (BDFs) because of stability considerations. In this paper we embed known results for semi-explicit index 1 and 2 DAEs in a more comprehensive theory based on compound multistep and one-leg discretizations. This explains and characterizes the necessary requirements that a method must fulfill in order to be applicable to semi-explicit DAEs. Thus we conclude that the most useful discretizations are those that avoid discretization of the constraint. A freer use of e.g. explicit methods for the non-stiff differential part of the DAE is then possible.Dedicated to Germund Dahlquist on the occasion of his 70th birthdayThis author thanks the Centro de Estadística y Software Matemático de la Universidad Simón Bolivar (CESMa) for permitting her free use of its research facilities.Partial support by the Swedish Research Council for Engineering Sciences TFR under contract no. 222/91-405.     

Multi-cut solutions of Laplacian growth

A new class of solutions to Laplacian growth (LG) with zero surface tension is presented and shown to contain all other known solutions as special or limiting cases. These solutions, which are time-dependent conformal maps with branch cuts inside the unit circle, are governed by a nonlinear integral equation and describe oil fjords with non-parallel walls in viscous fingering experiments in Hele-Shaw cells. Integrals of motion for the multi-cut LG solutions in terms of singularities of the Schwarz function are found, and the dynamics of densities (jumps) on the cuts are derived. The subclass of these solutions with linear Cauchy densities on the cuts of the Schwarz function is of particular interest, because in this case the integral equation for the conformal map becomes linear. These solutions can also be of physical importance by representing oil/air interfaces, which form oil fjords with a constant opening angle, in accordance with recent experiments in a Hele-shaw cell.     

On integralEP r matrices

Periodica Mathematica Hungarica - This paper gives a characterization of integralEP r matrices and necessary and sufficient conditions for the generalized inverse of the product of two integralEP r...     

Static cylindrical matter shells

Static cylindrical shells composed of massive particles arising from matching of two different Levi–Civita space-times are studied for the shell satisfying either an isotropic or an anisotropic equation of state. We find that these solutions satisfy the energy conditions for certain ranges of the parameters.     

Brane world cosmology in Jordan-Brans-Dicke theory

We consider the embedding of 3+1 dimensional cosmology in 4+1 dimensional Jordan-Brans-Dicke theory. We show that exponentially growing and power law scale factors are implied. Whereas the 4+1 dimensional scalar field is approximately constant for each, the effective 3+1 dimensional scalar field is constant for exponentially growing scale factor and time dependent for power law scale factor.     

Conformational preferences driven by the C-methyl substituent in chelated o-diphenylphosphino-alpha-methyl-N,N-dimethylbenzylamine rhodium complexes

The stereochemistry of the chelate rings of a number of rhodium aminophosphine complexes is studied by NMR spectroscopy. The similarity in the variable-temperature behavior for the different compounds is consistent with them having in common highly preferred chelate ring conformations. The six-membered metallacycle of coordinated (R)-PN (PN = o-diphenylphosphino-alpha-methyl-N,N-dimethylbenzylamine) adopts a delta conformation in the solid state. NMR experiments indicate that this conformation is strongly favored in solution as well. The preferred sense of helicity is imposed by the absolute configuration of the stereogenic carbon atom on the ligand, which exerts an important steric control. The complex [Rh(TFB)((C(6)H(4)CHMeNMe(2))(2)P(C(6)H(4)CHMeNHMe(2)))](BF(4))(2).H(2)O.Me(2)CO crystallizes in the monoclinic space group P2(1) with a = 12.0548(11) A, b = 16.139(2) A, c = 12.1804(10) A, beta = 100.742(9) degrees, Z = 4.     

Synthesis,characterization and antimicrobial activity of pentagonal-bipyramidal isothiocyanato Co(II) and Ni(II) complexes with 2,6-diacetylpyridine bis(trimethylammoniumacetohydrazone)

Pentagonal-bipyramidal isothiocyanato Co(II) and Ni(II) complexes with condensation product of 2,6-diacetylpyridine and trimethylammoniumacetohydrazide (Girard’s T reagent) were synthesized and characterized by elemental analyses, IR and UV–vis spectra, molar conductivity, and magnetic susceptibility. Crystal structures of the Co(II) and Ni(II) complexes were also determined. Antimicrobial activities of the ligand and metal complexes were examined.