Uncertainty and stepwise investment

We analyze the optimal investment strategy of a firm that can complete a project either in one stage at a single freely chosen time point or in incremental steps at distinct time points. The presence of economies of scale gives rise to the following trade-off: lumpy investment has a lower total cost, but stepwise investment gives more flexibility by letting the firm choose the timing individually for each stage. Our main question is how uncertainty in market development affects this trade-off. The answer is unambiguous and in contrast with a conventional real-options intuition: higher uncertainty makes the single-stage investment more attractive relative to the more flexible stepwise investment strategy.     

Highly sulfurated heterocycles via dithiiranes and trithietanes as key intermediates

2,2,4,4-Tetramethyl-3-thioxocyclobutanone (8b) easily reacts with gaseous chlorine to yield the stable alpha-chloro sulfenyl chloride 10. The same product was obtained when 8b was treated either with phosphorus pentachloride (PCl(5)) or sulfuryl chloride (SO(2)Cl(2)) in CCl(4) solution. Sulfur dichloride (SCl(2)) reacts with 8b to give the alpha-chloro thiosulfenyl chloride 12 along with an almost equimolar amount of the trisulfide 13b. The less reactive disulfur dichloride (S(2)Cl(2)) was shown to react slowly with 8b and the symmetrical tetrasulfide 15 was found as the exclusive product. The pure thiosulfenyl chloride 12 added to adamantanethione (8c) yielded the unsymmetrical trisulfide 13c. When 12 was treated with thioacetic acid, the acetylated trisulfide 17 was formed in high yield. "Unzipping" reactions with the acetylated disulfide 16 and trisulfide 17 with morpholine in THF at -40 degrees C led to the formation of mixtures of two sulfur-rich heterocycles identified as the pentathiepane 6b and the hexathiepane 7b. A mixture of analogous products was obtained when alpha-chloro sulfenyl chloride 10 was treated with sodium sulfide in anhydrous THF at -40 degrees C. The formation of 6b and 7b is believed to occur via the intermediate dithiirane 1b and/or the isomeric thiosulfine 2b. In the case of 17 the reaction starts probably with the formation of a nonisolable tetrathiane 18b as presented in Scheme 5.     

Minimal Extensions in Tensor Product Spaces

LetX,Ybe two separable Banach spaces and letVXandWYbe finite dimensional subspaces. Suppose thatVSX,WZYand letM (S, V),N (Z, W). We will prove that ifαis a reasonable, uniform crossnorm onXYthenλ_MN(V_αW,X_αY)=λ_M(V, X) λ_N(W, Y).Here for any Banach spaceX,VSXandM (S, V)

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Also some applications of the above mentioned result will be presented.     

The magnetic field-induced deformations in nematic layers with non-zero splay-bend elastic constant

The magnetic field-induced deformations of weakly anchored nematic layers in the presence of the non-zero splay-bend elastic constant K₁₃ are analysed by use of the Pergamenshchik approach. Most of the anomalous phenomena reported by other authors, that do not occur if k₁₃ = 0, have been confirmed. New effects suitable for experimental verification are predicted: the discontinuous transition with hysteresis between the uniform undistorted state and the state uniformly aligned along the field, and the rotation of the director in the tilted layer during continuous increase and decrease of the perpendicular field.     

Collisional effects upon optical coherences: Experimental study in a xenon three-level system

Laser induced nonlinear absorption profiles in a three-level system have been recorded to study the effect of elastic collisions upon optical coherences. In our particular system, the signal is due to a pure double-quantum term, where we have separated the effect of phase-interrupting collisions from the effect of velocity-changing collisions. Experimental results show that the effect of velocity-changing collisions is very small, and that broadening of the signal is due to phase-interrupting collisions mainly. We are able to determine the increase of the decay rate of the coherent superposition (the “coherence”) of two levels of same parity [Dγ ₁₃/dp=(6.5±1) MHz/Torr] and an upper limit for the mean velocity change (ũ≲5m/s).     

Order-parameter and the discontinuous antiferro-paramagnetic transition in manganese oxide

Studies of monodomain manganese oxide by neutron diffraction and strain gauge measurements show that the antiferro-paramagnetic transition is clearly discontinuous. At the transition the order-parameter drops by about 60 percent of the T = 0 K value.     

Eine Synthese vondl-4-Dimethylamino-isoxazolidon-(3) (N,N-Dimethylcycloserin) und Versuche zur Synthese am Ring alkylierter 4-Amino-isoxazolidone

Zusammenfassung Aus -Diphenylmethylenaminoxy--oxy-propionitril², einem Zwischenprodukt der von uns veröffentlichten Cycloserinsynthese², wurde in 4stufiger Synthese über -Aminoxy--aminopropionsäuremethylester N,N-Dimethylcycloserin dargestellt. Versuche, nach gleichem Syntheseprinzip an C₄bzw. C₅ alkylierte bzw. arylierte Cycloserinanaloga zu gewinnen, blieben erfolglos. H. Bretschneider, W. Vetter undE. Semenitz, Kurze Mitt.: Synthese und antibakterielle Eigenschaften desd,l-N,N-Dimethylcycloserins, Mh. Chem.89, 627 (1958).     

Global regular and singular solutions for a model of gravitating particles

The existence of solutions of a nonlinear parabolic equation describing the gravitational interaction of particles is studied for the initial data in spaces of (generalized) pseudomeasures. This approach permits us to relax regularity assumptions on the initial conditions and to prove asymptotic stability results for the above problem.Mathematics Subject Classification (2000):35B40, 35K15, 82C21     

On tractability of weighted integration over bounded and unbounded regions in

We prove that for the space of functions with mixed first derivatives bounded in norm, the weighted integration problem over bounded or unbounded regions is equivalent to the corresponding classical integration problem over the unit cube, provided that the integration domain and weight have product forms. This correspondence yields tractability of the general weighted integration problem.

     

On strong tractability of weighted multivariate integration

We prove that for every dimension and every number of points, there exists a point-set whose -weighted unanchored discrepancy is bounded from above by independently of provided that the sequence has for some (even arbitrarily large) . Here is a positive number that could be chosen arbitrarily close to zero and depends on but not on or . This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals over unbounded domains such as . It also supplements the results that provide an upper bound of the form when .