Interband photoconductivity of Ge/Si structures with self-organized quantum rings

At low temperatures a lateral photoconductivity (PC) of Ge/Si (1 0 0) self-organized quantum rings (QRs) structures as a function of interband light intensity has been investigated for different values of lateral voltage and temperature. In contrast to self-organized Ge/Si quantum dots (QDs) structures (grown at the same conditions) where the stepped PC was registered, for QRs structures essential smoothing of PC steps was observed. Such behavior is determined by decreasing of strain potential around QRs in conductive Si matrix due to a transfer of Ge atoms from the center of QDs to its periphery accompanied by Ge/Si intermixing.     

Spontaneous decay of an excited atom placed near a rectangular plate

Using the Born expansion of the Green tensor, we consider the spontaneous decay rate of an excited atom placed in the vicinity of a rectangular plate. We discuss the limitations of the commonly used simplifying assumption that the plate extends to infinity in the lateral directions and examine the effects of the atomic dipole moment orientation, atomic position, and plate boundary and thickness on the atomic decay rate. In particular, it is shown that due to the plate finite size, the spontaneous decay may be inhibited even when the atom is situated very close to the surface, and that in the boundary region, the spontaneous decay rate can be strongly modified.     

A uniform refinement property for congruence lattices

The Congruence Lattice Problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of a lattice. It was hoped that a positive solution would follow from E. T. Schmidt's construction or from the approach of P. Pudlák, M. Tischendorf, and J. Tuma. In a previous paper, we constructed a distributive algebraic lattice with compact elements that cannot be obtained by Schmidt's construction. In this paper, we show that the same lattice cannot be obtained using the Pudlák, Tischendorf, Tuma approach.

The basic idea is that every congruence lattice arising from either method satisfies the Uniform Refinement Property, that is not satisfied by our example. This yields, in turn, corresponding negative results about congruence lattices of sectionally complemented lattices and two-sided ideals of von Neumann regular rings.

     

Reactions of 1,4-dioxa-2-silacyclohexanes with acetyl chloride

The reactions of 1,4-dioxa-2-silacyclohexanes with acetyl chloride lead to the cleavage of the Si−O bond to form chlorotriorganosilanes containing the acetoxy group in the organic radical at the silicon atom. Hydrolysis of these chlorosilanes affords bis(acetoxy-alkoxy(aryloxy)methyl)disiloxanes, while the reactions with cage copper sodium phenylsiloxane give dodecaphenyl[dodeca(acetoxyorganodimethylsilyloxy)]cyclododecasiloxanes. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2527–2529, December, 1998.     

On the optimum design of piston rings

We study a family of control problems that arise in the design of dynamically loaded bearings which have a minimum power loss; in particular, we study the design of piston rings with minimum parasitic power loss.This research was partially supported by NSF Grant No. MCS-77-05624.     

Retention of configuration in the nucleophilic substitution reactions of some nine-membered ansa derivatives of cyclotriphosphazatriene

X-ray crystallographic evidence shows that nucleophilic substitution reactions of two different types of cyclophosphazene derivatives with relatively rigid nine-membered ansa rings leads to the first demonstration of retention of configuration in these molecular systems.     

Ideals in a perfect closure, linear growth of primary decompositions, and tight closure

This paper is concerned with tight closure in a commutative Noetherian ring of prime characteristic , and is motivated by an argument of K. E. Smith and I. Swanson that shows that, if the sequence of Frobenius powers of a proper ideal of has linear growth of primary decompositions, then tight closure (of ) `commutes with localization at the powers of a single element'. It is shown in this paper that, provided has a weak test element, linear growth of primary decompositions for other sequences of ideals of that approximate, in a certain sense, the sequence of Frobenius powers of would not only be just as good in this context, but, in the presence of a certain additional finiteness property, would actually imply that tight closure (of ) commutes with localization at an arbitrary multiplicatively closed subset of .

Work of M. Katzman on the localization problem for tight closure raised the question as to whether the union of the associated primes of the tight closures of the Frobenius powers of has only finitely many maximal members. This paper develops, through a careful analysis of the ideal theory of the perfect closure of , strategies for showing that tight closure (of a specified ideal of ) commutes with localization at an arbitrary multiplicatively closed subset of and for showing that the union of the associated primes of the tight closures of the Frobenius powers of is actually a finite set. Several applications of the strategies are presented; in most of them it was already known that tight closure commutes with localization, but the resulting affirmative answers to Katzman's question in the various situations considered are believed to be new.

     

Characterization of completions of reduced local rings

We find necessary and sufficient conditions for a complete local ring to be the completion of a reduced local ring. Explicitly, these conditions on a complete local ring with maximal ideal are (i) or , and (ii) for all , if is an integer of , then .

     

Commutativity of rings through a Streb's result

In this paper we investigate commutativity of rings with unity satisfying any one of the properties:

Undecidability of the word problem in relatively free rings

An example of a series of varieties of rings with the finite basis property is constructed for which the word problem in the relatively free ring of rankn in the variety is decidable if and only ifn <p. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 582–594, April, 2000.