In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

Extracting a subset of a given ontology that captures all the ontology’s knowledge about a specified set of terms is a well-understood task. This task can be based, for instance, on locality-based modules. However, a single module does not allow us to understand neither topicality, connectedness, structure, or superfluous parts of an ontology, nor agreement between actual and intended modeling....

various methods for parametric interpolation of nurbs curves have been proposed in the past. however, the errors caused by the approximate nature of the nurbs interpolator were rarely taken into account. this paper proposes an integrated look-ahead algorithm for parametric interpolation along nurbs curves. the algorithm interpolates the sharp corners on the curve with the pythagorean-hodograph ...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...

We introduce a versatile method to control the quality factor Q of a conducting cantilever in an atomic force microscope (AFM) via capacitive coupling to the local environment. Using this method, Q may be reversibly tuned to within 10% of any desired value over several orders of magnitude. A point-mass oscillator model describes the measured effect. Our simple Q control module increases the AFM...

The systematic comparison of the atomic structure of solids and clusters has become an important task in crystallography, chemistry, physics and materials science, in particular in the context of structure prediction and structure determination of nanomaterials. In this work, an efficient and robust algorithm for the comparison of cluster structures is presented, which is based on the mapping o...

We present the coupling of atomic force microscopy (AFM) and nuclear magnetic resonance (NMR) technologies to enable topographical, mechanical, and chemical profiling of biological samples. Here, we fabricate and perform proof-of-concept testing of radiofrequency planar microcoils on commercial AFM cantilevers. The sensitive region of the coil was estimated to cover an approximate volume of 19....

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...