Remarks on an S-shaped bifurcation curve

We study the non-negative solutions of the boundary value problem $\text{?Δu = λ [}\text{exp}\text{αu}\text{(α + u)}\text{]; x ? Ω. u = 0; x ? ?Ω,}\text{where}\text{α > 0, λ ? 0, Ω ? R}{}^{\mathrm{n}}$ is bounded with smooth boundary ?Ω.This problem arises in the theory of combustion. We study the estimates on the supremum norm of the solutions and estimates on the critical values of λ.     

Nonexistence results for classes of 3 × 3 elliptic systems

We consider the system

     

Structure and NMR properties of 6‐substituted‐5,6‐dihydrobenzo[c]phenanthridine alkaloids

We report a preparation of new 6‐substituted‐5,6‐dihydrobenzo[c]phenanthridines by the reaction of azoles with quaternary benzo[c]phenanthridine alkaloids sanguinarine and chelerythrine. The prepared compounds have been characterized by NMR spectroscopy, mass spectrometry, and single‐crystal X‐ray diffraction. Conformational behaviors of carbazole derivatives in solution have been investigated by low‐temperature NMR experiments. Barriers to rotation around newly formed C6–N bonds were determined to be 12–13 kcal/mol. Quantum chemical calculations have been used to reproduce the experimental observations. Large structural effects on several ¹H NMR resonances were observed experimentally, analyzed by Density Functional Theory (DFT) calculations at B3LYP/6‐311+G(d,p)/PCM level, and interpreted by ring‐current effects of the benzo[c]phenanthridine and carbazole units. Copyright © 2013 John Wiley & Sons, Ltd.     

On the Stochastic Non-sequential Production-planning Problem

This paper examines a stochastic non-sequential capacitated production-planning problem where the demand of each period is a continuous random variable. The stochastic non-sequential production-planning problem is examined with sequence-independent and then with sequence-dependent set-up costs, and the worst-case error determined when an approximate solution is obtained by solving the deterministic equivalent. We prove in general that the worst-case error is not dependent on the nature of the set-up cost, and identify a family of approximations for the stochastic non-sequential production-planning problem.     

Gold-catalyzed glycosidations: synthesis of 1,6-anhydro saccharides

Various 1,6-anhydro sugars are synthesized utilizing salient features of gold-catalyzed glycosidations. All the reactions occurred under mild conditions in the presence of 7 mol % of AuBr₃ enabling easy synthesis of 1,6-anhydro sugars from corresponding 6-hydroxy propargyl/methyl monosaccharides, disaccharides, and trisaccharides in good yields.     

Hydrothermal Assisted Synthesis of Micro-Bricks Shaped WO3 for Electrochemical Oxidation of Paracetamol: A Microstructured Paracetamol Sensor

Russian Journal of Electrochemistry - A micro-bricks shaped tungsten oxide (WO3) was prepared by hydrothermal method. The prepared material was characterized by field emission scanning electron...     

A Facile One‐Pot Synthesis of 3,5‐Disubstituted Isoxazole Derivatives Using Hydroxy (Tosyloxy) Iodobenzene

Hydroxy (tosyloxy) iodobenzene (HTIB), a hypervalent iodine reagent, has been extensively used for oxidative transformations. We have developed a one‐pot synthesis wherein aldoximes when reacted with alkynes in the presence of HTIB result in the direct formation of isoxazoles. This simple and straightforward reaction allows for ease of purification while leading to the formation of high purity 3,5‐disubstituted isoxazoles in moderate yields.