Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...

Any line bundle L on a smooth curve C of genus g with degL ≥ 2g+1 is normally generated, i.e., φL(C) ⊆ PH(C,L) is projectively normal. However, it has known that more various line bundles of degree d failing to be normally generated appear on multiple coverings of genus g as d becomes smaller than 2g+1. Thus, investigating the normal generation of line bundles on multiple coverings can be an ef...

In cells of Leuconostoc oenos, the fermentation of L-malic acid generates both a transmembrane pH gradient, inside alkaline, and an electrical potential gradient, inside negative. In resting cells, the proton motive force ranged from -170 mV to -88 mV between pH 3.1 and 5.6 in the presence Of L-malate. Membrane potentials were calculated by using a model for probe binding that accounted for the...

Let G be a finitely generated infinite group and let p > 1. In this paper we make a connection between the first L-cohomology space of G and p-harmonic functions on G. We also describe the elements in the first Lcohomology space of groups with polynomial growth, and we give an inclusion result for nonamenable groups.

Our understanding of the mechanisms used by Mycobacterium tuberculosis to persist in a "dormant" state is essential to the development of therapies effective in sterilizing tissues. Gene expression profiling in model systems has revealed a complex adaptive response thought to endow M. tuberculosis with the capacity to survive several months of combinatorial antibiotic treatment. We show here th...

Allee effects are important dynamical mechanisms in small-density populations in which per capita population growth rate increases with density. When positive density dependence is sufficiently severe (a 'strong' Allee effect), a critical density arises below which populations do not persist. For spatially distributed populations subject to dispersal, theory predicts that the occupied area also...

Background: In earlier work, inversion of S matrix for 330 MeV O on C resulted in highly undulatory potentials; the S matrix resulted from the inclusion of strong coupling to states of projectile and target nuclei. L-independent S-matrix equivalent potentials for other explicitly L-dependent potentials have been found to be undulatory. Purpose: To investigate the possible implications of the un...

L-Systems have been extensively utilized in plant modeling and music rendering. However, the music generated was not very pleasant as the grammars used are very simple. This paper describes a hybrid method that generates more complex grammars for L-Systems in a visual language framework for music rendering so that the musical sounds generated can be improved and fine-tuned. The method which use...