Lp mean estimates for an operator preserving inequalities between polynomials

If $P(z)$ be a polynomial of degree at most $n$ which does not vanish in $|z| < 1$, it was recently formulated by Shah and Liman \cite[\textit{Integral estimates for the family of $B$-operators, Operators and Matrices,} \textbf{5}(2011), 79 - 87]{wl} that for every $R\geq 1$, $p\geq 1$, $$\left\|B[P\circ\sigma](z)\right\|_p \leq\frac{R^{n}|\Lambda_n|+|\lambda_{0}|}{\left\|1+z\right\|_p}\left\|P(z)\right\|_p,$$ where $B$ is a $\mathcal{B}_{n}$-operator with parameters $\lambda_{0}, \lambda_{1}, \lambda_{2}$ in the sense of Rahman \cite{qir}, $\sigma(z)=Rz$ and $\Lambda_n=\lambda_{0}+\lambda_{1}\frac{n^{2}}{2} +\lambda_{2}\frac{n^{3}(n-1)}{8}$. Unfortunately the proof of this result is not correct. In this paper, we present a more general sharp $L_p$-inequalities for $\mathcal{B}_{n}$-operators which not only provide a correct proof of the above inequality as a special case but also extend them for $0 \leq p <1$ as well.Comment: 16 Page

EVALUATION OF IN VITRO ANTIOXIDANT ACTIVITY AND ESTIMATION OF TOTAL PHENOL AND FLAVONOID CONTENT OF ETHANOLIC LEAF EXTRACT OF IRIS KASHMIRIANA

Objective: The main aim of this study was to determine the in vitro antioxidant activity of Iris kashmiriana ethanolic leaf extract and also total phenol and flavonoid content was evaluated.Methods: Total phenol content (TPC) was determined by Folin–Ciocalteu method, total flavonoid content (TFC) was estimated by aluminum trichloride spectrophotometer method. Furthermore, antioxidant activity was revealed by 1,1-diphenyl-2-picrylhydrazyl (DPPH) assay, hydrogen peroxide (H2O2) scavenging activity, and reducing power assay.Results: The ethanolic leaf extract of I. kashmiriana showed TPC of 13.25±0.57 μg/100 μg gallic acid equivalents and TFC of 33.61±3.37 μg/100 μg rutin equivalents. The DPPH assay revealed IC50 of 0.418 mg/ml and for H2O2 radical scavenging IC50 was 0.476 mg/ml for the plant extract while as reducing power assay revealed concentration-dependent absorption values which clearly determine the antioxidant property of plant.Conclusion: From the results, it is apparent that I. kashmiriana ethanolic leaf extract possessed potential antioxidant activity which can be used to cure wide range of diseases

ADHD presenting as recurrent epistaxis: a case report

Epistaxis is an important otorhinolaryngological emergency, which usually has an apparent etiology, frequently local trauma in children. Here we present a case report wherein the epistaxis was recalcitrant, and proved to have a psychiatric disorder as an underlying basis. The child was diagnosed with Attention Deficit/Hyperactivity Disorder, hyperactive type, which led to trauma to nasal mucosa due to frequent and uncontrolled nose picking. Treatment with atomoxetine controlled the patient's symptoms and led to a remission of epistaxis

A Negative Feedback Loop That Limits the Ectopic Activation of a Cell Type–Specific Sporulation Sigma Factor of Bacillus subtilis

Two highly similar RNA polymerase sigma subunits, σF and σG, govern the early and late phases of forespore-specific gene expression during spore differentiation in Bacillus subtilis. σF drives synthesis of σG but the latter only becomes active once engulfment of the forespore by the mother cell is completed, its levels rising quickly due to a positive feedback loop. The mechanisms that prevent premature or ectopic activation of σG while discriminating between σF and σG in the forespore are not fully comprehended. Here, we report that the substitution of an asparagine by a glutamic acid at position 45 of σG (N45E) strongly reduced binding by a previously characterized anti-sigma factor, CsfB (also known as Gin), in vitro, and increased the activity of σG in vivo. The N45E mutation caused the appearance of a sub-population of pre-divisional cells with strong activity of σG. CsfB is normally produced in the forespore, under σF control, but sigGN45E mutant cells also expressed csfB and did so in a σG-dependent manner, autonomously from σF. Thus, a negative feedback loop involving CsfB counteracts the positive feedback loop resulting from ectopic σG activity. N45 is invariant in the homologous position of σG orthologues, whereas its functional equivalent in σF proteins, E39, is highly conserved. While CsfB does not bind to wild-type σF, a E39N substitution in σF resulted in efficient binding of CsfB to σF. Moreover, under certain conditions, the E39N alteration strongly restrains the activity of σF in vivo, in a csfB-dependent manner, and the efficiency of sporulation. Therefore, a single amino residue, N45/E39, is sufficient for the ability of CsfB to discriminate between the two forespore-specific sigma factors in B. subtilis

CHARACTERIZATION OF THE CHROMOSOMAL AAC(6&apos;)-IC GENE FROM SERRATIA-MARCESCENS

The DNA sequence of the chromosomal aac(6’)-k gene from Serratia marcescens, which had been previously cloned (H. M. Champion, P. M. Bennett, D. A. Lewis, and D. S. Reeves, J. Antimicrob. Chemother. 22:587-596, 1988) was determined. High-pressure liquid chromatographic analysis of extracts prepared from Escherichia coli carrying the chromosomal aac(6’)-Ic gene on a plasmid confirmed the presence of 6’-N-acetyltransferase activity in this strain, which was suggested by the aminoglycoside resistance profile. DNA sequence analysis of the cloned 2,057-bp PstI fragment revealed several regions of homology to previously characterized sequences from GenBank, including the rpoD and tRNA-2 genes of E. coli. Subcloning experiments confirmed the coding sequence of the aac(6’)-Ic gene to be at positions 1554 to 1992. The predicted amino acid sequence of the AAC(6’)-Ic protein suggested that it was the third member of a family of AAC(6’) proteins which included a coding region identified between the aadB and aadA genes of Tn4000 and an AAC(6’) protein encoded by pUO490, which was isolated from Enterobacter cloacae. Primer extension analysis suggested that the -35 region of the aac(6’)-Ic promoter overlapped a large palindromic sequence which may be involved in the regulation of the aac(6’)-Ic gene. Hybridization experiments utilizing a restriction fragment from the aac(6’)-Ic gene showed that all S. marcescens organisms carried this gene whether or not the AAC(6’)-I resistance profile was expressed. Organisms other than Serratia spp. did not hybridize to this probe

An iron detection system determines bacterial swarming initiation and biofilm formation

Iron availability affects swarming and biofilm formation in various bacterial species. However, how bacteria sense iron and coordinate swarming and biofilm formation remains unclear. Using Serratia marcescens as a model organism, we identify here a stage-specific iron-regulatory machinery comprising a two-component system (TCS) and the TCS-regulated iron chelator 2-isocyano-6,7-dihydroxycoumarin (ICDH-Coumarin) that directly senses and modulates environmental ferric iron (Fe(3+)) availability to determine swarming initiation and biofilm formation. We demonstrate that the two-component system RssA-RssB (RssAB) directly senses environmental ferric iron (Fe(3+)) and transcriptionally modulates biosynthesis of flagella and the iron chelator ICDH-Coumarin whose production requires the pvc cluster. Addition of Fe(3+), or loss of ICDH-Coumarin due to pvc deletion results in prolonged RssAB signaling activation, leading to delayed swarming initiation and increased biofilm formation. We further show that ICDH-Coumarin is able to chelate Fe(3+) to switch off RssAB signaling, triggering swarming initiation and biofilm reduction. Our findings reveal a novel cellular system that senses iron levels to regulate bacterial surface lifestyle