Analysis of non-overlapping domain decomposition algorithms with inexact solves

In this paper we construct and analyze new non-overlapping domain decomposition preconditioners for the solution of second-order elliptic and parabolic boundary value problems. The preconditioners are developed using uniform preconditioners on the subdomains instead of exact solves. They exhibit the same asymptotic condition number growth as the corresponding preconditioners with exact subdomain solves and are much more efficient computationally. Moreover, this asymptotic condition number growth is bounded independently of jumps in the operator coefficients across subdomain boundaries. We also show that our preconditioners fit into the additive Schwarz framework with appropriately chosen subspace decompositions. Condition numbers associated with the new algorithms are computed numerically in several cases and compared with those of the corresponding algorithms in which exact subdomain solves are used.

     

Thermochemische Untersuchungen zum System Bi/Se/O. I. Das Phasendreieck Bi2Se3/Bi2O2Se/Se

Thermochemical Investigation on the System Bi/Se/O. I The Phase Triangle Bi₂Se₃/Bi₂O₂Se/Se By total pressure measurements of compositions in the subsystem Bi₂Se₃/Bi₂O₂Se/Se was shown, that in thermodynamic equilibrium the three phases Bi₂Se₃/Bi₂O₂Se/Se coexist. The barogram of the triangle reduces to the barogram of the line Bi₂Se₃? Se, the compound Bi₂O₂Se is not from influence of the total pressure in the investigated temperature range.     

Infrared spectra and configuration of N,N'-diaryl-thioureas

The conformation of the —NH—CS—NH— grouping in a series of N,N'-diarylthioureas some of which possess a marked anti-viral activity is studied using IR spectral data. The results indicate that in organic solvents (CCl₄, CHCl₃, C₂C1₄, CH₂C1₂) the compounds studied participate in an equilibrium between several isomeric forms arising from the possibility of a cis or trans structure of the —CS—NH— groups. The increased solvent polarity favours the cis conformation.     

A Study of the Reaction of Phosphorus Trichloride with Paraformaldehyde in the Presence of Carboxylic Acids

Abstract

We investigated the mechanism of the reaction of paraformaldehyde with phosphorus trichloride in the presence of carboxylic acids (acetic, propanoic, and formic). Our results revealed that bisphosphonic acids were obtained without the use of water. The structures of the reaction products were studied by 1D and 2D homonuclear and heteronuclear ¹H-, ¹³C-, ³¹P- NMR spectroscopy.

[Supplementary materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfer, and Silicon and the Related Elements for the following free supplemental files: Additional tables.]     

Structure on the set of closure operations of a commutative ring

We investigate the algebraic structure on the set of closure operations of a ring. We show the set of closure operations is not a monoid under composition for a discrete valuation ring. Even the set of semiprime operations over a DVR is not a monoid; however, it is the union of two monoids, one being the left but not right act of the other. We also determine all semiprime operations over the ring $K?t^2,t^3?$.     

Conformal paracontact curvature and the local flatness theorem

A curvature-type tensor invariant called para contact (pc) conformal curvature is defined on a paracontact manifold. It is shown that a paracontact manifold is locally paracontact conformal to the hyperbolic Heisenberg group or to a hyperquadric of neutral signature iff the pc conformal curvature vanishes. In the three dimensional case the corresponding result is achieved through employing a certain symmetric (0,2) tensor. The well known result of Cartan–Chern–Moser giving necessary and sufficient condition a CR-structure to be CR equivalent to a hyperquadric in \mathbbCⁿ⁺¹{\mathbb{C}^{n+1}} is presented in-line with the paracontact case. An explicit formula for the regular part of a solution to the sub-ultrahyperbolic Yamabe equation on the hyperbolic Heisenberg group is shown.     

Test ideals in quotients of -finite regular local rings

Let be an -finite regular local ring and an ideal contained in . Let . Fedder proved that is -pure if and only if . We have noted a new proof for his criterion, along with showing that , where is the pullback of the test ideal for . Combining the the -purity criterion and the above result we see that if is -pure then is also -pure. In fact, we can form a filtration of , that stabilizes such that each is -pure and its test ideal is . To find examples of these filtrations we have made explicit calculations of test ideals in the following setting: Let , where is either a polynomial or a power series ring and is generated by monomials and the are regular. Set . Then .

     

Phase equilibria in the CdI2-Ag2Se system

The phase diagram of the system CdI₂-Ag₂Se is studied by means of X-ray diffraction, differential thermal analysis and measurements of the density of the material. The unit cell parameters of the intermediate phase 2CdI₂·3Ag₂Se were determined a = 0.6387 Å, b = 4.311 Å, c = 4.044 Å; α = 113.72°, β = 90.27° and γ = 94.85°. The intermediate phase 2CdI₂·3Ag₂Se has a polymorphic transition at 125 °C. It melts incongruently at 660 °C.