On the asymptotic behavior of solutions of weakly nonlinear stochastic systems

We study problems of the asymptotic correspondence with probability one and in mean square between solutions of a stochastic system and the corresponding linear deterministic system.     

Azlactone Synthesis. 2-Phenyl-2-Oxazolin-5-One

Abstract

2-Phenyl-2-oxazolin-5-one (3) has been used as an intermediate in the synthesis of α-amino acids¹, derivatives of α-amino acids,² and peptides.³ Procedures for the dehydration/cyclization of hippuric acid (1) leading to the isolation of azlactone 3, have been reported using acetic anhydride,⁴ phosphorus trihalides⁵, and N, N′-dicyclohexylcarbodiimide.⁶ We report herein an alternative, high yield procedure utilizing a water soluble carbodiimide.     

Crystal and molecular structure of [Cu(pyrimidine)4]2BF4

The crystal structure of [Cu(pyrimidine)₄]2BF₄ was determined using single crystal X-ray diffraction. The compound crystallizes in the monoclinic space groupP2₁/n, with lattice parametersa=9.9736(8),b=13.872(1),c=16.568(1) Å. β=98.002(1), andZ=8, yielding a calculated density of 1.857 g/cm³. The Jahn-Teller distorted copper coordination sphere is composed of the four pyrimidine ligands in the equatorial positions (ave. Cu?N=2.02 Å) and the longer axial bonds from the copper to one fluorine (ave Cu?F=2.39 Å) on each of the BF ₄ ^? anions. The crystal structure features layers of molecules having interleaved pyrimidine rings: the layers are connected through intermolecular H … F hydrogen bonds.     

Phase transitions in 3,5-dichloropyridine

Abstract

Structural phase transitions in 3,5-dichloropyridine crystal have been studied by calorimetry (150–300 K), X-ray diffraction (300 K), ³⁵Cland ¹⁴N nuclear quadrupole resonance (75–300 K) and vibrational spectroscopy (20–300K). Three phases have been shown to exist: phase I, between 338 and 287.5 K, phase 11, between 287.5 and 167.5 K, and phase 111, below 167.5 K. Phase I is characterised by the space group P 2,/m and Z = 2 whereas phases I1 and 111 remain centrosymmetric but double the unit cell. All the phases are ordered and contain crystallo- graphically equivalent molecules. The I ? I1 transition is of first order and probably of the reconstructive type while the II ? III transition is believed to be displacive. Both transitions are monitored by predominantly R′_x and R′_z librational motions.     

ENVIRONMENTAL AND FINANCIAL SUSTAINABILITY OF FOREST MANAGEMENT PRACTICES

One of the guiding themes for forest management policy throughout much of North America is sustained yield. The basic premise behind this theme is that a constant or nondeclining flow of services from the forest is socially desirable. Unfortunately, the act of capturing the benefits of this service (timber harvesting) often has detrimental effects on the timber-productive capacity of a forest site. This paper presents a dynamic program that is used to determine the optimal harvest system choice for a timber stand described by average piece size, stand density, a measure of site quality, and stumpage value. The harvest systems are defined by logging costs, reforestation and rehabilitation costs, and the impact of the system on the productivity of the site. An application of the model is presented for lodgepole pine in Alberta. We conclude that, at high discount rates, soil conservation is not economically rational. At lower discount rates, some degree of soil conservation is desirable on the more productive sites. At lower discount rates, there also appears to be an incentive for more intensive forest management. Limitations on acceptable harvest practices can have a large impact on optimal rotation age and the volume harvested. There is a large opportunity cost resulting from a requirement for sustainable volume production because of the impact of harvesting on soil productivity.     

Computational study of lithioprismanes

The molecular structure and thermochemical stability of mono to hexalithiated [3]-prismanes has been investigated by DFT and G3 methods, respectively. Relative isomer stabilities, standard enthalpies of formation and strain energies are discussed and compared. Our results suggest that in lithioprismanes (as in the isomeric lithiobenzenes), Li atom prefers to be in a bridging position along the CC edge rather than to occupy a vertex substitution site. We have estimated the energy stabilization due to bridging and have also studied singlet–triplet energy gaps for the title molecules in order to establish the nature of the ground electronic state.     

Comparison of Optical Transport Schemes for LMDS with Optical Fiber Backbone

We investigate and compare the performance of four optical transport schemes for distributing Local Multipoint Distribution Service (LMDS) signals using an optical fiber backbone.