A novel derivative free algorithm with seventh order convergence for solving systems of nonlinear equations

We present a seventh order iterative method for solving systems of nonlinear equations. The algorithm is derivative free per full iteration. A comparison between the computational efficiencies of proposed technique and existing techniques of similar nature is made. It is shown that for large system the new method is more efficient. The performance is tested through numerical experimentation which also confirms the theoretical results.     

Approximate controllability of retarded semilinear stochastic system with non local conditions

This paper deals with the approximate controllability of retarded semilinear stochastic system with nonlocal conditions in Hilbert Spaces under the assumption that the corresponding linear system is approximately controllable. The control function for this system is suitably constructed by using the infinite dimensional controllability operator. With this control function, the sufficient conditions for the approximate controllability of the proposed problem in Hilbert Space are established. The results are obtained by using Banach fixed point theorem. Finally, two examples are provided to illustrate the application of the obtained results.     

Regioselective Photocyclization Reactions of 3‐Allyloxy‐6‐chloro‐2‐(thiophen‐3‐yl)‐4H‐chromen‐4‐one: Solvent Effect

The photo‐irradiation of thienylchromenone resulted in the regioselective cyclization which is exclusively controlled by the nature of solvent used as reaction medium. Compared to nonpolar medium, polar solvent furnished a diverse array of novel angular tetracyclic photoproducts with gem‐dihydro functionality and exocyclic double bonds on the fused pyran ring, which is unprecedented to best of our knowledge.     

Synthesis of polyfunctional triethoxysilanes by ‘click silylation’

The copper-catalyzed ‘click silylation’ has been exploited for the chemical modification of γ-azidopropyltriethoxysilane (AzPTES) with a wide range of terminal alkynes (1a–1v) in a one-pot operation. The novel 1,2,3-triazole-triethoxysilane derivatives (2a–2v) were synthesized by this procedure and comprehensively characterized by IR spectra, ¹H and ¹³C NMR, and HRMS studies.     

A Facile Method for Detection and Speciation of Inorganic Selenium with Ion Chromatography

Chromatographia - In this work, we present a new method for the determination and speciation of selenium in water with ion chromatography (IC) using a conductometric detector. Chromatographic...     

Isolation,Purification, and Characterization of Antimicrobial Compound 6-[1,2-dimethyl-6-(2-methyl-allyloxy)-hexyl]-3-(2-methoxy-phenyl)-chromen-4-one from Penicillium sp. HT-28

A fungal culture (Penicillium sp., HT-28), isolated from soil has been evaluated for its bioactivity, which showed broad spectrum antimicrobial activity and was effective against methicillin-resistant Staphylococcus aureus (MRSA) also. Statistical optimization of the medium by response surface methodology (RSM) enhanced the antimicrobial activity up to 1.8-fold. Column chromatography was used to isolate the active compound (A), which was characterized to be 6-[1,2-dimethyl-6-(2-methyl-allyloxy)-hexyl]-3-(2-methoxy-phenyl)-chromen-4-one by various spectroscopic techniques such as infrared (IR), ¹H and ¹³C nuclear magnetic resonance (NMR) spectra, and mass spectroscopy. Minimum inhibitory concentration (MIC) of the active compound (A) ranged from 0.5 to 15 μg/mL. Viable cell count studies of the active compound (A) showed S. aureus, Escherichia coli, Staphylococcus epidermidis, and Salmonella typhimurium 1 to be the most sensitive. The compound retained its bioactivity after treating it at 100 °C for 1 h. Furthermore, the compound (A) when tested for its biosafety was found neither to be cytotoxic nor mutagenic. The study demonstrated that an apparently novel compound isolated from Penicillium sp. (HT-28) seems to be a stable and potent antimicrobial.     

Minimal quadratic residue cyclic codes of length 2 n

LetF be a finite field of prime power orderq(odd) and the multiplicative order ofq modulo 2 ⁿ (n>1) be ?(2 ⁿ )/2. Ifn>3, thenq is odd number(prime or prime power) of the form 8m±3. Ifq=8m?3, then the ring $$R_{2^n } = F\left[ x \right]/< x^{2^n } - 1 > $$ has 2n primitive idempotents. The explicit expressions for these primitive idempotents are obtained and the minimal QR cyclic codes of length 2 ⁿ generated by these idempotents are completely described. Ifq=8m+3 then the expressions for the 2n?1 primitive idempotents ofR ₂ ⁿ are obtained. The generating polynomials and the upper bounds of the minimum distance of minimal QR cyclic codes generated by these 2n?1 idempotents are also obtained. The casen=2, 3 is dealt separately.     

Skeletal muscle metabolism in Duchenne muscular dystrophy (DMD): an in-vitro proton NMR spectroscopy study

The metabolic differences in the skeletal muscle of patients with Duchenne muscular dystrophy (DMD) and normal subjects (controls) were investigated using in-vitro high-resolution proton NMR spectroscopy. In all, 56 metabolites were unambiguously identified in the perchloric acid extract of muscle tissue using one- and two-dimensional NMR. The concentrations of glycolytic substrate glucose (Glc; p < 0.05), gluconeogenic amino acids such as glutamine (Gln; p < 0.05) and alanine (Ala; p < 0.05) and the glycolytic product lactate (Lac; p < 0.05) were statistically significantly lower in DMD patients as compared to controls. A significant reduction in the concentrations of total creatine (TCr; p < 0.05), glycerophosphoryl choline + phosphoryl choline + carnitine (GPC/PC/Car; p < 0.05), choline (Cho; p < 0.05) and acetate (Ace; p < 0.05) was also observed in these patients. Decrease in the level of glucose may be attributed to the reduction in the concentrations of gluconeogenic substrates or membrane abnormalities in degenerated muscle of DMD patients. Lower levels of choline containing compounds indicate membrane abnormalities. Decrease in the concentration of lactate in the muscle of DMD patients may be due to the reduction in anaerobic glycolytic activity or lower substrate concentration. The decrease in the concentration of acetate may reflect reduced transport of fatty acids into mitochondria due to decreased concentration of carnitine in DMD patients. Kreb's cycle intermediate alpha-ketoglutarate was observed only in the diseased muscle, which is suggestive of predominant oxidative metabolism for energy generation.