A variational problem in Hilbert space

Let? be a Hilbert space over the field of complex numbers, with inner product (g,h). Letf be a fixed element in?, and letH be a compact, self-adjoint linear operator on?. We find the maximum value ofQ _f (u)=|(f,u)|² in the classU of elementsu in? for which (u,u)=1, (u, Hu)=0.     

The Reaction of 4-Hydroperoxy-2,4,6-trimethylcyclohexa-2,5-dienone with Acetaldehyde. Formatino of the Bis(peroxyacetal)

The reaction of 4-hydroperoxy-2,4,6-trimethylcyclohexa-2,5-dienone with acetaldehyde using trimethylsilyl trifluoromethanesulfonate as catalyst gives 1,1′-bis[(1,3,5-trimethyl-4-oxo-2,5-cyclohexadienyl) peroxy]diethyl ether ( 7 ) in 70% yield. The structure of this unusual acetal was determined by X-ray analysis.     

Determination of arsenic and gallium in standard materials by instrumental epithermal neutron activation analysis

Epithennal neutron activation analysis has been applied to the determination of arsenic and gallium in standard materials at trace concentrations. The reduction of ²⁴Na activity compared to thermal neutron activation is advantageous. Arsenic detection limits (1σ) are 0.04 and 0.015 μg for inorganic and organic materials, respectively. The corresponding gallium detection limits, for the best cases, are 0.13 and 0.29 μg. Gallium determinations with the 834-keV photopeak of ⁷²Ga suffered interferences attributed to the threshold reaction ⁵⁴Fe(n,p) ⁵⁴Mn; the less intense ⁷²Ga peaks at 629 and 2200 keV provided quantitative results for all samples tested. Gallium detection limits with the less intense, but more reliable 629-keV peak were 0.9 and 0.1 μg for inorganic and organic materials, respectively. Arsenic determinations are best performed with the more intense ⁷⁶As 559-keV line, as the 657-keV line has an unknown interference.     

Large concentration effects on conformational equilibria

The conformational equilibrium in $\text{cis}$-3-Hydroxythiane S-oxide (Scheme 1) is strongly concentration dependent, being affected by intermolecular hydrogen bonding at high concentration.     

Sequential W and Z bosons

We present and discuss a class of electroweak gauge models where the low-energy phenomenology is naturally identical to that of the standard model, but which allows for the existence of an arbitrary number of weak gauge bosons which have nontrivial couplings to the known fermions. The lightest W and Z in these models must be lighter than the W and Z of the standard model.     

New photosensitive materials

The emergence and growth of some far reaching applications have triggered quite a few new developments in the field of photosensitive materials.Among those applications of growing technical and economical interest, we concentrate on both the “solar photovoltaic conversion” and the “xerographic” type applications (e.g. laser printing and recording).     

Associative monotonic operations in fuzzy set theory

The properties of binary operations in a real interval are considered and used in the discussion of generalized operations on fuzzy sets, on fuzzy numbers and on fuzzy probabilistic sets.     

Twenty Five Years of Cyclic Queues and Closed Queue Networks: A Review

The first paper to introduce the concept of a cyclic queue appeared in the Operational Research Quarterly in 1954. The paper dealt with the 'flow' of aircraft engines from operation to maintenance to available for operation. In 1958, the first paper analyzing the cyclic queue model appeared in the same journal. This paper was application of queue theory to underground coal mining. In 1965 it was shown that stochastic queue networks can be treated analytically in the same manner as cyclic queues with a small adjustment in the auxiliary parameters. Since then cyclic queue models have been applied not only to the problems mentioned above but also to many other production and service industry problems: computer design and control, ship operations, production processes, communications flow, ingot movements in a steel mill, to name but a few. In order for this to be possible, extension and advances in theory have been required and these have come from many nations and many fields of endeavour. This paper traces the development of the theory of cyclic queues and queue networks from 1954 to the present.