A finitely generated $R$-module is said to be a module of type ($F_r$) if its $(r-1)$-th Fitting ideal is the zero ideal and its $r$-th Fitting ideal is a regular ideal. Let $R$ be a commutative ring and $N$ be a submodule of  $R^n$ which is generated by columns of  a matrix $A=(a_{ij})$ with $a_{ij}in R$ for all $1leq ileq n$, $jin Lambda$, where $Lambda $ is a (possibly infinite) index set.  ...

In antenna theory, antenna parameters are directly related to the wavelength lambda of incident radiation, but this scaling fails at optical frequencies where metals behave as strongly coupled plasmas. In this Letter we show that antenna designs can be transferred to the optical frequency regime by replacing lambda by a linearly scaled effective wavelength lambda(eff)=n(1)+n(2)lambda/lambda(p),...

We study the optimal distance in networks, l(opt), defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that l(opt) approximately N(1/3) in both Erdos-Rényi (ER) and Watts-Strogatz (WS) networks. ...

BACKGROUND A randomized, double-blind, multinational, phase 3 study was conducted comparing the efficacy and safety of peginterferon lambda-1a (Lambda)/ribavirin (RBV)/telaprevir (TVR) vs. peginterferon alfa-2a (Alfa)/RBV/TVR in patients with chronic hepatitis C virus (HCV) genotype-1 (GT-1) infection. METHODS Patients (treatment-naïve or relapsers on prior Alfa/RBV treatment) were randomly a...

Physical and chemical properties that may be used to determine the purity of several Fusarium mycotoxins have been investigated. A combination of analytical procedures, which include high performance thin-layer chromatography (HPTLC), liquid chromatography (LC), gas chromatography (GC), gas chromatography/mass spectrometry (GC/MS), ultraviolet spectrometry (UV), and nuclear magnetic resonance (...

The paper describes an application of logic programming to the modeling of difficult combinatorial properties of lambda terms, with focus on the class of simply typed terms. Lambda terms in de Bruijn notation are Motzkin trees (also called binary-unary trees) with indices at their leaves counting up on the path to the root the steps to their lambda binder. As a generalization of affine lambda t...