On copowers of an ordered skew field

It is shown that the 16.gif" alt="lsquo" align="BASELINE" BORDER="0">double of an ordered skew fieldE over a subfieldK, which is its own bicentralizer, can again be ordered, and a corresponding result for groups is deduced.     

Characterization of SiO2-P2O5-ZrO2 Sol-Gel/NAFION™ Composite Membranes

Composite membranes were prepared by (a) infiltrating NAFION16m8vq47r0670g1/xxlarge8482.gif" alt="trade" align="BASELINE" BORDER="0"> with SiO₂-P₂O₅-ZrO₂ sol, and (b) recasting a film using NAFION16m8vq47r0670g1/xxlarge8482.gif" alt="trade" align="BASELINE" BORDER="0"> solution containing SiO₂-P₂O₅-ZrO₂ sol. The membranes were characterized by Differential Thermal Analysis and ac-impedance spectroscopy as a function of relative humidity. The influences of the heat treatment (80°C–150°C) and cleaning on the electrical properties were investigated. The incorporation of SiO₂-P₂O₅-ZrO₂ gels into NAFION16m8vq47r0670g1/xxlarge8482.gif" alt="trade" align="BASELINE" BORDER="0"> lead to improvements in its thermal stability and proton conductivity.     

Flow injection system with in-line Winkler's procedure using 16-way valve and spectrofluorimetric determination of dissolved oxygen in environmental waters

Flow injection spectrofluorimetry with in-line Winklers procedure was developed for the dissolved oxygen (DO) determination. 2-Thionaphthol reacted with iodine produced by Winkler’s method to form fluorescence inactive disulfide compound. To automate the process completely, a 5-channel flow system with a newly designed 16-way valve was assembled. The system consisted of a dispersion coil (DC), a precipitate formation coil (PFC), a precipitate dissolving coil (PDC), and extraction coil (EC). A calibration can be constructed by using a standard iodine solution for dissolved oxygen. The calibration graph was linear over the range 1.2×10⁻⁴∼6.0×10⁻⁴ mol l⁻¹ iodine (1.96∼9.80 mg O l⁻¹)). The relative standard deviation (n=6) was below 0.3% for the 4×10⁻⁴ mol l⁻¹ iodine (6.27 mg O l⁻¹) determination. The sample throughput was 12/h.     

Rearrangements of the carbanions derived from allyl benzyl thioether

The metalation of allyl benzyl thioether involves the benzylic or the allylic hydrogens. The benzylic carbanion undergoes a rapid[2,3] sigmatropic shift whereas the allylic carbanion gives rise to various rearrangements, among them migration of the allylic unit to the para position with allylic inversion. The temperature dependence of the ratio of products arising from the benzylic carbanion vs those from the allylic carbanion shows that the allylic-to-benzylic carbanion transformation occurs only under special conditions: (a) with slow addition of the base; (b) with thioether in excess relative to the base, and (c) on raising the temperature of the reaction medium from ?78° to ?15°. In the last instance, the proton transfer is intramolecular as shown with labeled thioethers. The extent of the different rearrangements depends on the temperature and solvent. A choice of mechanism cannot be made at this time for the para migration 5→9a. A leaving group effect on the reaction regioselectivity of the carbanion from allyl methyl thioether with benzyl halides has been noticed. The presence of dibenzyl indicates that, in addition to S_N2 reactions, some electron transfer process is occurring.     

Synthese und thermische Eigenschaften von molekularen Clusterverbindungen zusammengesetzt aus Elementen der Gruppen 11‐13‐16

Syntheses and Thermal Properties of Cluster Molecules, formed from Groups 11‐13‐16 Elements In the presence of PPh₃, CuX (X = Cl, CH₃COO) or AgOC(O)C₆H₅ and GaCl₃ react in THF with S(SiMe₃)₂ or Se(SiMe₃)₂ to yield [Cu₆Ga₈Cl₄S₁₃(PPh₃)₆] ( 1 ), [Cu₆Ga₈Cl₄Se₁₃(PPh₃)₆] ( 2 ), [Ag₆Ga₈Cl₄S₁₃(PPh₃)₆] ( 4 ) and [Ag₆Ga₈Cl₄Se₁₃(PPh₃)₆] ( 5 ). The use of PⁿPr₂Ph instead of PPh₃ and subsequent layering with n‐hexane leads to the formation of the cluster [Cu₆Ga₈Cl₄Se₁₃(PⁿPr₂Ph)₁₂] ( 3a , 3b ). Reaction of CuCl, GaCl₃ and PⁿPr₃ with Se(SiMe₃)₂ in THF results in the crystallisation of the ionic cluster (HPⁿPr₃)₂[Cu₂Ga₄Cl₄Se₆(PⁿPr₃)₄] ( 6 ). The structures of 1 — 6 were determined by X‐ray single crystal structure analysis. Thermogravimetric measurements of the cluster molecules and powder diffraction patterns of the remaining powders reveal the potential use of them as single source precursor compounds for the synthesis of the related ternary solid state materials.     

Isolation and characterization of thermophilic benzothiophene-degrading Mycobacterium sp.

A bacterial strain, SWU-4, capable of using benzothiophene (BT) as a sole carbon and energy source was isolated from a petroleum-contaminated site in Thailand and identified by 16S rRNA gene sequence analysis to be in the genus of Mycobacterium. The strain was Gram-positive, nonspore former, and grew at 50° C. Colonies of the strain on nutrient agar were rod-shaped, smooth with a convex surface, slightly mucoid, and yellow pigmented. The thermophilic Mycobacterium sp. strain SWU-4 rapidly degraded 2% (w/v) BT at 50°C. Interestingly, this strain was able to degrade a wide variety of organosulfur compounds including thiophene, bromo(α)thiophene, and 3-methylthiophene in liquid minimum medium at 50°C, which will be beneficial for industrial applications.     

烷基磷脂-一类抗癌药物的合成

曾报道烷基磷脂类化合物能抑制小鼠体内移植肿瘤的生长并能选择破坏白血病细胞。在Andreesen等所试的九种溶血磷脂化合物中,1-O-十八烷基-2-O-甲基甘油-3-磷脂胆碱(ET-18-OCH_3,1)具有杀死白血病癌细胞的最高能力。其作用机制可能是抑制后者的新陈代谢或活化巨噬细胞。     

Relationship between tetrahedron shape measures

Tetrahedron shape measures are used for evaluating the quality of tetrahedra in finite element meshes. Three shape measures, theminimum solid angle _min theradius ratio , and themean ratio , are discussed in this paper. A new formula for the computation of a solid angle of tetrahedron is derived. For different shape measures andv (with values 1), we establish a relationship between andv of the form wherec ₀,c ₁,e ₀, ande ₁ are positive constants. This means that if one measure approaches zero for a poorly-shaped tetrahedron, so does the other. Combined with the property that each measure attains a maximum value only for the regular tetrahedron, this means that the shape measures are equivalent.This work was partially supported by a grant from the Natural Sciences and Engineering Research Council of Canada.     

On stable geometries

Within the concept of projective lattice geometry we are considering the class of stable geometries which have also been introduced in [14]. The investigation of their basic properties will result in fundamental structure theorems which especially give a lattice-geometric characterization of free left modules of rank 6 over proper right Bezout rings of stable rank 2. This yields a proper generalization of previous results of ours.     

Inclusion-exclusion: Exact and approximate

It is often required to find the probability of the union of givenn eventsA ₁ ,...,A _n . The answer is provided, of course, by the inclusion-exclusion formula: Pr(A _i )= _i – _i<j Pr(A _i A _j )±.... Unfortunately, this formula has exponentially many terms, and only rarely does one manage to carry out the exact calculation. From a computational point of view, finding the probability of the union is an intractable, #P-hard problem, even in very restricted cases. This state of affairs makes it reasonable to seek approximate solutions that are computationally feasible. Attempts to find such approximate solutions have a long history starting already with Boole [1]. A recent step in this direction was taken by Linial and Nisan [4] who sought approximations to the probability of the union, given the probabilities of allj-wise intersections of the events forj=1,...k. The developed a method to approximate Pr(A _i ), from the above data with an additive error of exp . In the present article we develop an expression that can be computed in polynomial time, that, given the sums _|S|=j Pr( _iS A _i ) forj=1,...k, approximates Pr(A _i ) with an additive error of exp . This error is optimal, up to the logarithmic factor implicit in the notation.The problem of enumerating satisfying assignments of a boolean formula in DNF formF=v _l ^m C _i is an instance of the general problem that had been extensively studied [7]. HereA _i is the set of assignments that satisfyC _i , and Pr( _iS A _i )=a _S /2ⁿ where _iS C _i is satisfied bya _S assignments. Judging from the general results, it is hard to expect a decent approximation ofF's number of satisfying assignments, without knowledge of the numbersa _S for, say, all cardinalities . Quite surprisingly, already the numbersa _S over |S|log(n+1)uniquely determine the number of satisfying assignments for F.We point out a connection between our work and the edge-reconstruction conjecture. Finally we discuss other special instances of the problem, e.g., computing permanents of 0,1 matrices, evaluating chromatic polynomials of graphs and for families of events whose VC dimension is bounded.Work supported in part by a grant of the Binational Israel-US Science Foundation.Work supported in part by a grant of the Binational Israel-US Science Foundation and by the Israel Science Foundation.