Hardy Spaces on the Plane and Double Fourier Transforms

We provide a direct computational proof of the known inclusion where is the product Hardy space defined for example by R. Fefferman and is the classical Hardy space used, for example, by E.M. Stein. We introduce a third space of Hardy type and analyze the interrelations among these spaces. We give simple sufficient conditions for a given function of two variables to be the double Fourier transform of a function in and respectively. In particular, we obtain a broad class of multipliers on and respectively. We also present analogous sufficient conditions in the case of double trigonometric series and, as a by-product, obtain new multipliers on and respectively.     

Optimal linear estimators of the unknown mean of a random field observed on a cross

Explicit formulas of minimum-variance linear unbiased estimators of the unknown mean are derived for homogeneous random fields with correlation functions observed on the set (a cross).Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 116–121, 1988.     

A sequential multielement separation scheme for determination of As,Mn, Mo,Cu and Zn in human milk by neutron activation analysis

A simple separation scheme for the analysis of As, Mn, Mo, Cu and Zn using neutron activation is described. It has been checked using three standard reference materials, A-11 milk powder (IAEA) and bovine liver and orchard leaves (USNBS) and found to give acceptable results. This scheme was applied for determination of these trace elements in mature human milk samples. The concentrations of As, Mn, Mo, Cu in samples obtained from two socio-economic groups—low and middle incomes—were not significantly different. However, Zn levels in samples obtained from the poor income group were significantly lower than in those obtained from the other group. Work carried out under Research Contract No. 2598/RB of International Atomic Energy, Vienna. Health Physics Division. Analytical Chemistry Division.     

含茂钛低聚物的制备与光谱

文中报道两种新的含茂钛低钛物Cp_2Ti(Cl)-O-[-Ti(Cp)(O_2CCH_4CH-O)-O-]n-H(Ⅰ)与Cp_2Ti(Cl)-O-[-Ti(Cp)(O_2CCH_2CH)-O-]_u-H(Ⅰ)的制备并用元素分析和光谱(IR,1~H NMR,MS)对它们进行了鉴定。     

Dissolution of ionisable groups and lignocellulosic components during low-temperature kraft pulping of pinus radiata

A wide range of kraft pulps from radiata pine produced by low-temperature kraft pulping in flow-through reactors was assessed for carboxyl and hexenuronic acid (HexA) contents using the conductometric titrations and UV spectrophotometer, respectively. The Kappa number of pulps varied from 20.8 to 84.7 when using a cooking liquor of 1 M effective alkali as Na₂O, 25% sulfidity, and cooking time of 100–250 min. The experimental results showed that the carboxyl groups (including HexA) and HexA groups dissolved and their residual values in the pulp samples correlate linearly with Kappa number and pulp yield. The dissolving rate of all carboxyl groups is much faster than the loss of HexA. The HexA/lignin ratio decreased non-linearly with Kappa number.     

Large scale Biginelli reaction via water-based biphasic media: a green chemistry strategy

An important stage in process development is kilo scale preparation of the target compound. For this reason, a procedure involving water-based biphasic reaction media has been developed for conducting some exothermic reactions on a large scale. This protocol is illustrated by the energy-efficient and rapid preparation of dihydropyrimidinones by a solvent-free, green chemistry procedure applied to the Biginelli reaction using p-toluenesulfonic acid as catalyst.     

Asymmetric Reductive Alkylation of Alanylproline by the Ethyl Esters of 4-Substituted 2-Oxobutenoic Acids

A method was developed for the synthesis of N-[1-(S)-(ethoxycarbonyl)-3-phenylpropyl]alanylproline (enalapril) by reductive alkylation of alanylproline with ethyl 2-oxo-4-phenylbutenoate under the conditions of hydrogenation in the presence of palladium black and 1.6% Pd/C. The yield of enalapril amounted to 65%. With the ethyl ester of the -oxo acid the diastereoselectivity of formation of the S,S,S-diastereomer was higher than with the saturated synthon. It is assumed that with ethyl 2-oxo-4-phenylbutenoate as synthon a conformationally restricted surface complex is formed between the unsaturated synthon and the active centers of the catalyst. During reductive alkylation of alanylproline by ethyl 2-oxo-4-(2-thienyl)butenoate poisoning of the catalyst occurs.     

Steps to demarcate the effects of chromophore aggregation and planarization in poly(phenyleneethynylene)s. 2. The photophysics of 1,4-diethynyl-2-fluorobenzene in solution and in crystals

Crystals of 1,4-bis(2-hydroxy-2-methyl-3-butynyl)-2-fluorobenzene 4 have a rich packing structure with four distinct molecules in the unit cell. A complex hydrogen bonding network results in the formation of cofacial trimers, cofacial dimers, and monomers within the same unit cell. Given a remarkable opportunity to investigate the effect of aggregation on the photophysics of 1,4-diethynylbenzenes, we analyzed the absorption, diffuse reflectance, and emission spectra of compound 4 in solutions and in crystals. Diffuse reflectance and fluorescence excitation revealed a red-shifted absorption that is absent in dilute solution but becomes observable at high concentrations and low temperatures. The fluorescence emission in the solid state is dual with components assigned to monomers and aggregates. The excitation and emission assigned to the monomer are nearly identical in crystals and dilute solutions. The absorption and emission bands assigned to aggregates are broad and red-shifted by 60--80 nm. As expected for a sample with absorbers and emitters with different energies and incomplete equilibration, efficient monomer-to-aggregate energy transfer was observed by a proper selection of excitation wavelengths. The fluorescence quantum yield of 4 in solution is relatively low (Phi(F) = 0.15) and the singlet lifetime short (tau(F) = 3.8 ns). A lower limit for the triplet yield of Phi(T) = 0.64 was determined indirectly in solution by (1)O(2) sensitization, and a relatively strong and long-lived phosphorescence was observed in low-temperature glasses and in crystals at 77 K.     

Deoxygenative α-alkylation and α-arylation of 1,2-dicarbonyls

Construction of C–C bonds at the α-carbon is a challenging but synthetically indispensable approach to α-branched carbonyl motifs that are widely represented among drugs, natural products, and synthetic intermediates. Here, we describe a simple approach to generation of boron enolates in the absence of strong bases that allows for introduction of both α-alkyl and α-aryl groups in a reaction of readily accessible 1,2-dicarbonyls and organoboranes. Obviation of unselective, strongly basic and nucleophilic reagents permits carrying out the reaction in the presence of electrophiles that intercept the intermediate boron enolates, resulting in two new α-C–C bonds in a tricomponent process.

α-Branched carboxylic acids and other carbonyls are readily accessed by a metal- and base-free deoxygenative α-alkylation and α-arylation of 1,2-dicarbonyls via boron enolates, resulting in a tricomponent coupling with unconventional electrophiles.