Solution to torsion relations in finsler-spacetime tangent bundle

In the Finsler-spacetime tangent bundle, a simple solution is determined to the torsion relations that were obtained previously to maintain (1) compatibility with Cartan's theory of Finsler space, (2) the almost complex structure, and (3) the vanishing of the covariant derivative of the almost complex structure.     

Macrocyclic bipyridines for alkyltin trichloride deactivation

The synthesis of two macrocyclic bipyridines whose frameworksare suitable for alkyltin trichloride encapsulation is described.     

The rhodophytin and chondriol natural products; structures of several new acetylenes from laurencia, and a reassignment of structure for cis-rhodophytin

The structures of five new halogenated vinyl acetylenes are described which are natural products from various species of the red seaweed Laurencia. The structure of epoxyrhodophytin (1) was determined by spectral, chemical, and X-ray diffraction analyses. The structures of trans-rhodophytin (5) and trans-chondriol (8) are based on chemical and spectral comparisons with the previously reported compounds cis-rhodophytin (4) and cis-chondriol (7). The structures of cis-chondrin (14) and trans-chondrin (15) were secured by synthesis from cis- and trans-chondriol, respectively. The reactivity of these enol-ethers to various conditions of catalytic hydrogenation has been examined in detail. Hydrogenation yields an unexpected and facile incorporation of oxygen into the reaction products. Based upon these studies, and upon combustion analysis, the structure of rhodophytin has been revised as the vinyl ether rather than the vinyl peroxide originally proposed.     

The accuracy and stability of time domain finite element solutions

The use of finite elements in the time domain provides a means of determining the response of a mechanical system to any forcing function. Two types of elements are used; a cubic element which maintains continuity of displacement and velocity between adjacent elements, and a quintic element which also ensures continuity of acceleration. The accuracy of solutions depends on the number of elements per unit time, errors being inversely proportional to the square of the number of elements for the cubic and inversely proportional to the fourth power of the number of elements for the quintic element. A condition for the stability of a solution is also established.     

Azole chemistry VII. The effect of metal complexation on a ring—chain tautomeric equilibrium

The chromium tricarbonyl group significantly affects the position of an oxazolidine-imino alcohol tautomeric equilibrium.     

Convergence in law of random sums with non-random centering

We extend results obtained in Kruglov,⁽⁷⁾ and Finkelstein and Tucker⁽³⁾ to obtain necessary and sufficient conditions for convergence in law of random sums of non-identically distributed independent random variables under non-random centering. Thei.i.d. case is also considered for random variables attracted to a stable law. Necessary and sufficient conditions for convergence in law of these random variables under non-random centering, and in some cases, under non-random norming, are also obtained. The distribution functions for the limit laws are determined as well, generalizing results of Robbins.⁽¹⁰⁾ Supported in part by The State University of New York and United States Information Agency Grant No. IA AEMP69193692.     

The discovery of hidden arsenic species in coastal waters

The analysis of ultraviolet (UV)-irradiated and untreated seawater samples has shown that the dissolved arsenic content of marine waters cannot be completely determined by hydride generation–atomic absorption spectrophotometry without sample pretreatment. Irradiation of water samples obtained during a survey of arsenic species in coastal waters during the summer of 1988 gave large increases in the measured speciation. Average increases in the measured speciation. Average increases in total arsenic, monomethylarsenic and dimethylarsenic were 0.29 μg As dm^?3 (25%), 0.03 μg As dm^?3 (47%) and 0.12 μg As dm^?3 (79%), respectively. Overall, an average 25% increase in the concentration of dissolved arsenic was observed following irradiation. This additional arsenic may be derived from compounds related to algal arsenosugars or to their breakdown products. These do not readily yield volatile hydrides when treated with borohydride and are not therefore detected by the normal hydride generation technique. This has important repercussions as for many years this procedure, and other analytical procedures which are equally unlikely to respond to such compounds, have been accepted as giving a true representation of the dissolved arsenic speciation in estuarine and coastal waters. A gross underestimate may therefore have been made of biological involvement in arsenic cycling in the aquatic environment.