Abstract Let R be an integral domain with $qf(R)=K$ , and let $F(R)$ the set of nonzero fractional ideals . Call a dually compact (DCD) if, for each $I\in F(R)$ ideal $I_{v}=(I^{-1})^{-1}$ is finite intersection principal ideals. We characterize DCDs show that class properly contains various classes domains, such as Noetherian, Mori, Krull domains. In addition, we Schreier DCD greatest common d...

We study the cutting and packing C&P problems in two dimensions by using phi-functions. Our phi-functions describe the layout of given objects; they allow us to construct a mathematical model inwhich C&P problems become constrained optimization problems. Herewe define for the first time a complete class of basic phi-functions which allow us to derive phi-functions for all 2D objects that are fo...

Caulobacter phage phi Cr30T, a temperature-sensitive derivative of the lytic, generalized transducing phage phi Cr30, was isolated as a double temperature-sensitive recombinant in a cross between phi Cr30ts1 and phi Cr30ts2, phi Cr30T mediated generalized transduction of Caulobacter crescentus at frequencies comparable to those of phi Cr30 and eliminated the requirement for irradiation of trans...

In this note, we show that cite[Corollary 3.2]{sad} is not always true. In fact, we characterize essential left $phi$-contractibility of the group algebras in terms of compactness of its related locally compact group. Also, we show that for any compact commutative group $G$, $L^{2}(G)$ is always essentially left $phi$-contractible. We discuss the essential left $phi$-contractibility of some Fou...

in this paper we study the module contractibility ofbanach algebras and characterize them in terms the conceptssplitting and admissibility of short exact sequences. also weinvestigate module contractibility of banach algebras with theconcept of the module diagonal.

New low-lying excitations are observed by inelastic light scattering at filling factors nu=p/(phip+/-1) of the fractional quantum Hall regime with phi=4. Coexisting with these modes throughout the range nu < or =1/3 are phi=2 excitations seen at 1/3. Both phi=2 and phi=4 excitations have distinct behaviors with temperature and filling factor. The abrupt first appearance of the new modes in the ...