Photorefractive Four-Wave Mixing Switches Utilizing Pockels Effect -Longitudinal and Lateral Switches-

We carried out detailed calculations for photorefractive wave-mixing switches based on one of three crystals with high electro-optic coefficients, namely, BaTiO₃, Strontium Barium Niobate (SBN (0.75)), and Potasium Sodium Strontium Barium Niobate (KNSBN). A comparison of results for the three crystals shows that a 0_-cut BaTiO³ crystal is suitable for a longitudinal switch and requires a voltage of about 80 for a 2-mm-thick crystal to induce sufficient phase mismatch. The electrodes must be transparent for the incident and diffracted beams. A 45_-cut SBN (0.75) crystal, however, is suitable for a lateral switch and requires a voltage of about 150 for a 1-mm-wide crystal. The electrodes do not need to be transparent.     

Depolymerization Study of Pakistani Lignite Coal Influence of Pre‐treatments on Product Slate

Influence of pretreatments, i.e., demineralization and pre‐soaking in some solvents on the yields of liquefied products obtained from hydro‐depolymerization of Pakistani coal in a pool of hydrogen has been discussed. Results of hydrogenation experiments demonstrated that demineralizing the coal sample prior to liquefaction caused the yields to decrease compared with the virgin coal samples. The contribution of mineral matter of coal has been evaluated by comparing the yields of liquid products of virgin and leached samples. Increase in the yields obtained from the hydrogenation experiments of swollen coal samples was not satisfactorily significant.     

A Resin‐Linker‐Vector Approach to Radiopharmaceuticals Containing 18F: Application in the Synthesis of O‐(2‐[18F]‐Fluoroethyl)‐L‐tyrosine

A Resin‐linker‐vector (RLV) strategy is described for the radiosynthesis of tracer molecules containing the radionuclide ¹⁸F, which releases the labelled vector into solution upon nucleophilic substitution of a polystyrene‐bound arylsulfonate linker with [¹⁸F]‐fluoride ion. Three model linker‐vector molecules 7 a – c containing different alkyl spacer groups were assembled in solution from (4‐chlorosulfonylphenyl)alkanoate esters, exploiting a lipase‐catalysed chemoselective carboxylic ester hydrolysis in the presence of the sulfonate ester as a key step. The linker‐vector systems were attached to aminomethyl polystyrene resin through amide bond formation to give RLVs 8 a – c with acetate, butyrate and hexanoate spacers, which were characterised by using magic‐angle spinning (MAS) NMR spectroscopy. On fluoridolysis, the RLVs 8 a , b containing the longer spacers were shown to be more effective in the release of the fluorinated model vector (4‐fluorobutyl)phenylcarbamic acid tert‐butyl ester ( 9 ) in NMR kinetic studies and gave superior radiochemical yields (RCY≈60 %) of the ¹⁸F‐labelled vector. The approach was applied to the synthesis of the radiopharmaceutical O‐(2‐[¹⁸F]‐fluoroethyl)‐L ‐tyrosine ([¹⁸F]‐FET), delivering protected [¹⁸F]‐FET in >90 % RCY. Acid deprotection gave [¹⁸F]‐FET in an overall RCY of 41 % from the RLV.     

On Some Inequalities Concerning Rate of Growth of Polynomials

In this paper we consider a class of polynomials P(z) = a0+∑n v=t a v z v, t ≥ 1not vanishing in |z|k, k≥1 and investigate the dependence of max|z|=1|P(Rz)-P(rz)on max|z|=1|P(z)|, where 1 ≤ r R. Our result generalizes and refines some know polynomial inequalities.     

Spectral Analysis of Some Distillates from Asphalt Cracking and Evaluation of UTIMAC as Cracking Catalyst

This paper demonstrates the spectral analysis of some distillates obtained from asphalt cracking in the presence of a conventional expensive catalyst, i.e., HZSM‐5, and local cheap and readily available clay, i.e., UTIMAC. Each distillate was fractionated into pentane soluble (PI) and pentane insoluble (PI) fractions based on solubility in n, pentane. Both PS and PI obtained in the case of HZSM‐5 and UTIMAC were analyzed by ¹H‐NMR spectrophotometry using CDCl₃ as dissolving solvent and tetramethylsilane (TMS) as internal standard. It is evident from the profiles that both catalysts caused the generation of some peaks ascribed to methylene and methene configurations in the aliphatic region. Bands corresponding to aromatic configurations were also generated. The results indicate that the cheap local catalyst used has comparable suitability with the conventional expensive catalyst in terms of asphalt cracking.     

Enantioselective Synthesis of Spiroindenes by Enol‐Directed Rhodium(III)‐Catalyzed C?H Functionalization and Spiroannulation

Chiral cyclopentadienyl rhodium complexes promote highly enantioselective enol‐directed C(sp²)‐H functionalization and oxidative annulation with alkynes to give spiroindenes containing all‐carbon quaternary stereocenters. High selectivity between two possible directing groups, as well as control of the direction of rotation in the isomerization of an O‐bound rhodium enolate into the C‐bound isomer, appear to be critical for high enantiomeric excesses.     

On the Factorial Closure of Certain Monomial Modules

Abstract

Let R = K[y ₁,…,y _t ] be an affine domain over a field K and I be a nonzero proper ideal of R. In Sec. 1 of this note, we characterize when (K + I, R) is a Mori pair. In Sec. 2 of this note, we prove the following theorem: Let A ? B be domains such that C/Q is Mori for each subring C of B containing A and for any prime ideal Q of C. Then dim A ? 1 ≤ dim B ≤ dim A + 1 and if dim A > 1 or dim B > 1 then dim A = dim B.     

A Note on a Generalisation of Eneström–Kakeya Theorem for Quaternionic Polynomials

Mediterranean Journal of Mathematics - In this paper, we introduce the k-generalized Stockwell transform on $${\mathbb {R}}$$ . We investigate for this transform the main theorems of Harmonic...     

Nonlinear closure modeling in reduced order models for turbulent flows: a dynamical system approach

Nonlinear Dynamics - Reduced-order models (ROM) of structurally dominated fluid flows have significant applications in science and engineering, such as design, control, and optimization....