Convex surfaces whose geodesics are planar

It is shown that ifC is a convex surface, in euclidean space of dimension at least 3, having the property that all shortest paths onC between pairs of its points are planar, thenC is a sphere, a hyperplane or the boundary of an intersection of two half-spaces. No smoothness assumptions are made.     

19F spectra—structure correlations of fluorinated quaternary phosphonium salts

The ¹⁹F NMR chemical shifts and geminal FCP and FCH coupling constants are reported for a number of fluorinated quaternary phosphonium salts of the type \documentclass{article}\pagestyle{empty}\begin{document}$ [{\rm R}_3 \mathop {\rm P}\limits^ \oplus {\rm CFXY}]{\rm Z}^ \ominus $\end{document}, where generally R = alkyl or aryl; X, Y = hydrogen or halogen and Z = halogen. Spectral parameters remain relatively unaffected upon variance of R, Z^?, and/or solvent, except when R is a bulky alkyl group. Linear relationships accurately describe the correlation between the summation of the electronegativities of X and Y, or simply of Y if X = F, and the ¹⁹F NMR chemical shift and geminal FCP coupling constant; geminal FCH coupling constants show no such dependence. These relationships are of demonstrated analytical value, particularly for the purpose of spectral prediction.     

Potential causal prophylactic antimalarial agents. Synthesis of quinoxaline,benzimidazole, and alkoxybenzene derivatives containing a novoldiamine moiety

Several quinoxaline, benzimidazole, and alkoxybenzene derivatives containing the novoldiamine function, either as a side chain or incorporated as a ring constituent, were synthesized as potential causal prophylactic antimalarial agents. 1-(5-Dimethylamino-2-pentyl)-5-methoxy-benzimidazole ( 2a ) was shown to have the desired prophylactic activity in the preliminary sporozoitc-indueed Plasmodium gallinaceum test.     

A convenient preparation of deuterated fluoroolefins

The reduction of iodo-containing fluoroolefins with NaAlH₄ in diglyme followed by hydrolysis with D₂O provides a convenient preparative procedure to the corresponding deuterated fluoroolefin.     

Site-specific preparation of 2-carboalkoxy-4-substituted naphthalenes and 9-alkylphenanthrenes and evidence for an allene intermediate in the novel base-catalyzed cyclization of 2-alkynylbiphenyls

[Structure: see text] A site-specific preparation of 2-carboalkoxy-4-substituted naphthalenes and 9-alkylphenanthrenes is described. The successful cyclization of an allene intermediate provides supportive evidence for the previously proposed mechanism.     

A Liapunov functional for a singular integral equation

We consider a scalar integral equation where a∈L²[0,∞), while C(t,s) has a significant singularity, but is convex when t−s>0. We construct a Liapunov functional and show that g(t,x(t))−a(t)∈L²[0,∞) and that x(t)−a(t)→0 pointwise as t→∞. Small perturbations are also added to the kernel. In addition, we consider both infinite and finite delay problems. This paper offers a first step toward treating discontinuous kernels with Liapunov functionals.     

Justification shift and uncertainty: why are low-probability near misses underrated against organizational routines?

Knowledge of near misses is helpful in preventing accidents, but it does not always lead to changes in organizational routines or contribute to accident prevention. In this article, the authors argue that low-probability near misses reinforce beliefs of experts and professionals in existing routines, proposing a concept of justification shift. Justification shift is underestimation of risks of known near misses vis-à-vis overestimation of reliabilities of existing routines. Consequently, signals of “close calls” tend to be disregarded, and accidents become more likely. When justification shift occurs, experts and professionals who want changes in routines face burden of proof about risks of those routines. Uncertainty in requirements and data may increase the burden and make justification shift more likely. To explore how justification shift occurs and how uncertainty influences the shift, the authors have developed an agent-based model based on theories in organizational studies and the case of the space shuttle Challenger accident in 1986. From the simulation using the model, it becomes clear that uncertainty does not make a difference in frequencies and degrees of justification shift. The authors also discuss implications of this finding to efforts to utilize knowledge of near misses and to further research on the efforts and organizational decisions.     

A constrained variational problem for steady vortices in a shear flow

We prove existence of maximisers for a variational problem for a steady vortex anomaly of bounded extent in a uniform shear flow in IR². Kinetic energy is maximised subject to the vorticity being a rearrangement of a prescribled function, and subject to a linear pseudo impulse constrint     

Divisible groups that are brauer groups ∗

Throughour this paper G denotes an abelian divisible torsion group. It is not unreasonable to conjecture that such a G must occur as the Brauer group B(K) of some field K. Some evidence to support this conjecture is provided in [3]; it is proved there that if G is countable then G ? B(K) for some K algebraic over the rational field Q [3, Theorem 2]. In this note we provide still more evidence in support of htis conjecture.