Controlling an oscillating Jackson-type network having state-dependent service rates

We consider a Jackson-type network comprised of two queues having state-dependent service rates, in which the queue lengths evolve periodically, exhibiting noisy cycles. To reduce this noise a certain heuristic, utilizing regions in the phase space in which the system behaves almost deterministically, is applied. Using this heuristic, we show that in order to decrease the probability of a customers overflow in one of the queues in the network, the server in that same queue – contrary to intuition – should be shut down for a short period of time. Further noise reduction is obtained if the server in the second queue is briefly shut down as well, when certain conditions hold.     

Property (<Emphasis Type="Italic">T</Emphasis>) and rigidity for actions on Banach spaces

We study property (T) and the fixed-point property for actions on L ^p and other Banach spaces. We show that property (T) holds when L ² is replaced by L ^p (and even a subspace/quotient of L ^p ), and that in fact it is independent of 1≤p<∞. We show that the fixed-point property for L ^p follows from property (T) when 1<p< 2+ε. For simple Lie groups and their lattices, we prove that the fixed-point property for L ^p holds for any 1< p<∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive spaces. Bader partially supported by ISF grant 100146; Furman partially supported by NSF grants DMS-0094245 and DMS-0604611; Gelander partially supported by NSF grant DMS-0404557 and BSF grant 2004010; Monod partially supported by FNS (CH) and NSF (US).     

Considerations on modelling the market for softwood lumber in the United States

The analysis in this paper looks at two important elements in modelling the market for timber in the United States. First, the issue of directional causality between price and quantity and its implications in a modelling effort is investigated. Second, the extent of the geographic market for timber is discussed and a method of detecting it is suggested. The method for detecting the extent of the geographical market is tractable and can be applied in a straightforward way. Both considerations are applied to the softwood lumber market in the United States.     

Positive value of information in games

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments à la Blackwell. AMS 2000 Subject Classification:Primary 91A35.The work of Bruno Bassan and Marco Scarsini was partially supported by MIUR-COFIN. The authors express their thanks to Sylvain Sorin for enlightening comments.     

An investigation of tautomeric equilibria by means of mass spectrometry

Changes in the mass spectra with inlet temperature were used in this work to demonstrate the dependence of keto-enol tautomerism of acetylacetone, 3-methyl acetylacetone and 3-allyl acetylacetone on temperature. The largest dependence of temperature were shown by the ion [M ? 42]^+. arising from a McLafferty type rearrangement and by the ion [M ? Me]⁺ resulting from simple α-cleavage. The ion [M ? 42]^+. peak increases with the temperature of the inlet system while the ion [M ? Me]⁺ peak decreases. By assuming that the ion [M ? 42]^+. represents the keto form and that the ion [M ? Me]⁺ represents the cis-enol form (stabilized by the hydrogen bond) one sees that the direction of the intensity variation of these peaks with temperature is in accord with the expected change of keto-enol tautomerism with temperature. A quantitative correlation on the basis of the above assumptions is also approached. Recording of the mass spectra of these three β-diketones at different energies of the incident electrons enables us to estimate whether or not the particular ions present in the mass spectra result from energetically favourable processes. The variation of the intensities of the peaks with the temperature of the inlet at different electron energies is also discussed.     

The synthesis of malonimide derivatives as potential penicillin analogs

Malonimidoacetic acid derivatives (VIII, XIII) were synthesized as a potential penicillin analogs, hut they failed to inhibit the growth of bacteria when tested in vitro against a range of Gram-positive and Gram-negative microorganisms.     

Finding the αn-th largest element

We describe an algorithm for selecting the n-th largest element (where 0<<1), from a totally ordered set ofn elements, using at most (1+(1+o(1))H())·n comparisons whereH() is the binary entropy function and theo(1) stands for a function that tends to 0 as tends to 0. For small values of this is almost the best possible as there is a lower bound of about (1+H())·n comparisons. The algorithm obtained beats the global 3n upper bound of Schönhage, Paterson and Pippenger for <1/3.     

RMS dipole moments of the valence excited states of linear polyenes

Asymmetrical vibrations induce small oscillating dipole moments in the ground states of linear all-trans polyenes. Upon vertical excitation into one of the two low-lying valence excited states the induced in-plane dipole moments are increased 3 times and more. The rms dipole moments increase with the chain length. The inducing modes are the CCC skeletal bending and the CC stretching vibrations. CH stretching vibrations are also found to contribute non-negligible polarization.