Association equlibria in acetonitrile solution of tetracyanoquinodimethanides

Trimetric ion (TCNQ)^2?₃ has been discovered in mixed solutions of TCNQ and LiTCNQ in acetonitrile. The estimated association constant isK_T = 5.6 × 10¹⁰ øl² mol^?2.     

Proton transfer reactions from N-H acid [5,10,15,20-tetrakis(pentafluorophenyl)-21-H, 23-H-porphyrin] to strong bases in acetonitrile

Deprotonation of 5,10,15,20-tetrakis(pentafluorophenyl)-21-H, 23-H-porphyrin (PhF₅PorH₂) by various bases has been studied by ¹H NMR and kinetic methods. The kinetic parameters in acetonitrile were defined for proton transfer reactions yielding [NH]⁺ protonated bases and [NHN]⁻ anions with intramolecular hydrogen-bonded chains.     

On the Ehrenfeucht–Mycielski sequence

We introduce the inverted prefix tries (a variation of suffix tries) as a convenient formalism for stating and proving properties of the Ehrenfeucht–Mycielski sequence [A. Ehrenfeucht, J. Mycielski, A pseudorandom sequence—how random is it? American Mathematical Monthly 99 (1992) 373-375]. We also prove an upper bound on the position in the sequence by which all strings of a given length will have appeared; our bound is given by the Ackermann function, which, in light of experimental data, may be a gross over-estimate. Still, it is the best explicitly known upper bound at the moment. Finally, we show how to compute the next bit in the sequence in a constant number of operations.     

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.     

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 .

     

Silicon polypodands: powerful metal cation complexing agents and solid-liquid phase-transfer catalysts of new generation

Silicon polypodands 5-7 are found to be powerful complexing agents of alkali metal salts in low polarity solvents and very efficient catalysts in anion-promoted reactions under solid-liquid PTC conditions. The catalytic activity is comparable with that of the cyclic polyether PHDB18C6 8.