Consider $\beta > 1$ and $\lfloor \beta \rfloor$ its integer part. It is widely known that any real number $\alpha \in \Bigl[0, \frac{\lfloor \rfloor}{\beta - 1}\Bigr]$ can be represented in base $\beta$ using a development series of the form = \sum_{n 1}^\infty x_n\beta^{-n}$, where $x (x_n)_{n \geq 1}$ sequence taking values into alphabet $\{0,\; ...\; ,\; \lfloor \rfloor\}$. The so called $\...

Mutagenesis studies and alignments of homologous sequences have demonstrated that protein function typically is compatible with a variety of amino-acid residues at most exterior non-active-site positions. These observations have led to the current view that functional constraints on sequence are minimal at these positions. Here, it is shown that this inference assumes that the set of acceptable...

– Recently an extension of beta function is defined by introducing an extra parameter is proved to be useful earlier (Aslam Chaudhry 1997 [8] and A. R. Miller 1998 [1]). In this research note, we generalize the incomplete beta function and obtained the various integral representations and properties. Furthermore, we obtained the beta distribution for generalized beta function. Keywords––Incompl...

Wild-type strains of Escherichia coli are normally unable to metabolize cellobiose. However, cellobiose-positive (Cel(+)) mutants arise upon prolonged incubation on media containing cellobiose as the sole carbon source. We show that the Cel(+) derivatives carry two classes of mutations that act concertedly to alter the regulation of the chb operon involved in the utilization of N,N'-diacetylchi...

beta-Amyloid peptide is the major protein component of Alzheimer's plaques. When aggregated into amyloid fibrils, the peptide is toxic to neuronal cells. Here, an approach to the design of inhibitors of beta-amyloid toxicity is described; in this strategy, a recognition element, which interacts specifically with beta-amyloid, is combined with a disrupting element, which alters beta-amyloid aggr...

In the context of AdS/CFT with flavor, we consider the type IIB supergravity solution corresponding to a fully localized D3/D7 intersection. We complete the standard metric ansatz by providing an analytic expression for the warp factor, under the assumption of a logarithmically running axion-dilaton. From the gauge dual perspective, this behavior is related to the positive beta function of the ...

A bstract Extending earlier work, we find the two-loop term in beta-function for scalar coupling ? a generalized Wilson loop operator of $$ \mathcal{N} N = 4 SYM theory, working planar weak-coupling expansion. The has fixed points at ±1 and 0, corresponding respectively to supersymmetric Wilson-Maldacena stan...