Dimensional reduction for Helmholtz's equation on a bounded domain

Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results. Received April 2, 1996 / Revised version received July 30, 1990     

Synthesis of 3‐(substituted)‐2,4,8,15‐tetroxa‐3‐phosphadispiro[5.2.5]hexadecane‐3‐oxides

Novel 3‐(substituted)‐2,4,8,15‐tetroxa‐3‐phosphadispiro[5.2.5]hexadecane‐3‐oxides (3‐12) have been synthesized by cyclization of 1,5‐dioxaspiro[5.5]undecande‐3,3‐dimethanol (1) with various substituted aryl phosphorus dichloridates (2) in dry toluene‐THF in the presence of triethylamine at 40‐60 ^oC. Their molecular structures were determined by ir, nmr and mass spectral studies and were screened for antifungal activity against Curvularia lunata and Aspergillus niger, and antibacterial activity on Staphylococcus aureus and Escherichia coli. Most of them possess significant activity.     

Tailoring approach for exploring electron densities and electrostatic potentials of molecular crystals

Experimental and theoretical studies of electron densities and the corresponding derived entities such as electrostatic potentials have been the primary means of understanding the chemical nature and electronic properties of crystalline substances. Conventional crystal calculation methods such as the embedded cluster models are capable of performing calculations on small and medium-sized molecules, while periodic ab initio methods can treat crystals with up to 200 atoms per unit cell. A linear scaling method, viz. the molecular tailoring approach, has recently been developed for obtaining ab initio quality one-electron properties. In the present study, the molecular tailoring approach is employed to generate electron density, electrostatic potential and interaction density maps with the ibuprofen crystal as a test case. The interaction density and electrostatic potential maps produced in the present work succinctly bring out the actual crystalline environment around a given reference molecule by including the interactions with atoms in its neighborhood. The results obtained from the molecular tailoring approach may thus be expected to enhance our understanding of the environment in the crystalline material with reasonably small computational effort.Contribution to the Jacopo Tomasi Honorary Issue     

Asymmetric synthesis of 2,3-dihydrofurans and of unsaturated bicyclic tetrahydrofurans through alpha-elimination and migratory cyclization of silyloxy alkenyl aminosulfoxonium salts. Generation and intramolecular O,Si-bond insertion of chiral disubstituted beta-silyloxy alkylidene carbenes

Treatment of the bis(allylsulfoximine)titanium complexes derived from the beta-methyl-substituted acyclic allylic sulfoximines 13a and 13b with aldehydes gave with high selectivities the corresponding sulfoximine-substituted homoallylic alcohols which were isolated as the silyl ethers 15a-h. Methylation of sulfoximines 15a-h afforded the aminosulfoxonium salts 5a-h which upon treatment with LiN(H)tBu gave in high yields the enantio- and diastereomerically pure silyl-substituted 2,3-dihydrofurans 4a-h. Treatment of the titanium complexes derived from the cyclic allylic sulfoximines 17a, 17b, and ent-17c with p-MeOC(6)H(4)CHO delivered with high selectivities the corresponding sulfoximine-substituted cyclic homoallylic alcohols which were isolated as the silyl ethers 18a, 18b, and ent-18c, respectively. Methylation of sulfoximines 18a, 18b, and ent-18c furnished the aminosulfoxonium salts 8a, 8b, and ent-8c, respectively, whose treatment with LiN(H)t-Bu gave the enantio- and diastereomerically pure fused bicyclic 2,3-dihydrofurans 6a, 6b, and ent-6c, respectively, in good yields. It is proposed that the 1-alkenyl aminosulfoxonium salts 5a-h, 8a, 8b, and ent-8c react with the base under alpha-elimination and formation of the acyclic and cyclic beta-silyloxy alkylidene carbenes 2a-h, 7a, 7b, and ent-7c, respectively, which then undergo a 1,5-O,Si-bond insertion and 1,2-silyl migration. The cyclic aminosulfoxonium salts 8a, 8b, and ent-8c upon treatment with 1,8-diazabicyclo[5.4.0]-7-undecene did not undergo an alpha-elimination but suffered a novel migratory cyclization with formation of the enantio- and diastereomerically pure bicyclic tetrahydrofurans 9a, 9b, and ent-9c, respectively. It is proposed that the 1-alkenyl sulfoxonium salts 8a, 8b, and ent-8c are isomerized to the allylic aminosulfoxonium salts 10a, 10b, and ent-10c, respectively, which then suffer an intramolecular substitution of the (dimethylamino)sulfoxonium group by the silyloxy group followed by a desilylation. The syntheses of the 2,3-dihydrofurans 4a-h, 6a, and 6b and of the tetrahydrofurans 9a and 9b are accompanied by the formation of sulfinamide 16 of >or=98% ee, which can be converted via sulfoxide 28 of >or=98% to the starting sulfoximine 11 of >or=98% ee.     

Synthesis of fused imidazo-pyridine and -azepine derivatives by sequential van Leusen/Heck reactions

Fused imidazo-pyridine and -azepine derivatives were synthesized using a sequential van Leusen/intramolecular Heck protocol. The combination of a multicomponent reaction followed by an intramolecular carbon-carbon bond forming reaction generates heterocycles of significant molecular complexity from readily available starting materials in just two steps.     

Interactive effects of ultraviolet-B radiation and temperature on cotton physiology, growth, development and hyperspectral reflectance

Current conditions of 2-11 kJ m(-2) day(-1) of UV-B radiation and temperatures of >30 degrees C during flowering in cotton cultivated regions are projected to increase in the future. A controlled environment study was conducted in sunlit growth chambers to determine the effects of UV-B radiation and temperature on physiology, growth, development and leaf hyperspectral reflectance of cotton. Plants were grown in the growth chambers at three day/night temperatures (24/16 degrees C, 30/22 degrees C and 36/28 degrees C) and three levels of UV-B radiation (0, 7 and 14 kJ m(-2) day(-1)) at each temperature from emergence to 79 days under optimum nutrient and water conditions. Increases in main stem node number and the node of first fruiting branch and decrease in duration to first flower bud (square) and flower were recorded with increase in temperature. Main effects of temperature and UV-B radiation were significant for net photosynthetic rates, stomatal conductance, total chlorophyll and carotenoid concentrations of uppermost, fully expanded leaves during squaring and flowering. A significant interaction between temperature and UV-B radiation was detected for total biomass and its components. The UV-B radiation of 7 kJ m(-2) day(-1) reduced boll yield by 68% and 97% at 30/22 degrees C and 36/28 degrees C, respectively, compared with yield at 0 kJ m(-2) day(-1) and 30/22 degrees C. No bolls were produced in the three temperature treatments under 14 kJ m(-2) day(-1) UV-B radiation. The first-order interactions between temperature, UV-B radiation and leaf age were significant for leaf reflectance. This study suggests a growth- and process-related temperature dependence of sensitivity to UV-B radiation.     

Synthesis and binding studies of new bis-calix[4]arenes containing aromatic and heteroaromatic units

A series of new bis-calix[4]arenes containing different aromatic and heteroaromatic moieties have been synthesized. The complexing behavior of these bis-calix[4]arenes have been studied towards different metal ions and it has been found that these bis-calix[4]arenes bind silver ions selectively over other metal ions. The complexation has been studied by liquid-liquid extraction and by NMR and IR spectroscopy.