Optimal decompositions for theK-functional for a couple of Banach lattices

Letf=g _t+h _t be the optimal decomposition for calculating the exact value of theK-functionalK(t, f; ) of an elementf with respect to a couple =(X ₀ ,X ₁) of Banach lattices of measurable functions. It is shown that this decomposition has a rather simple form in many cases where one of the spacesX ₀ andX ₁ is eitherL ^∞ orL ¹. Many examples are given of couples of lattices for which |g _t| increases monotonically a.e. with respect tot. It is shown that this property implies a sharpened estimate from above for the Brudnyi-KrugljakK-divisibility constant γ( ) for the couple. But it is also shown that certain couples do not have this property. These also provide examples of couples of lattices for which γ( ). Research supported by the Technion V. P. R. Fund.     

On a superatomic Boolean algebra which is not generated by a well-founded sublattice

Let b denote the unboundedness number of ω^ω. That is, b is the smallest cardinality of a subset such that for everyg∈ω^ω there isf ∈ F such that {n: g(n) ≤ f(n)}is infinite. A Boolean algebraB is wellgenerated, if it has a well-founded sublatticeL such thatL generatesB. We show that it is consistent with ZFC that , and there is a Boolean algebraB such thatB is not well-generated, andB is superatomic with cardinal sequence 〈ℵ₀, ℵ₁, ℵ₁, 1〉. This result is motivated by the fact that if the cardinal sequence of a Boolean algebraB is 〈ℵ₀, ℵ₀, λ, 1〉, andB is not well-generated, then λ≥b.     

Bounds for solutions of a differential inequality

This work compares the solutions of an th order differential inequality plus boundary conditions with the solution of the related differential equation with boundary conditions. The differential operator is assumed to be disconjugate. It is proved that under suitable conditions the ratio of these solutions is monotone. The solution of the inequality can be replaced by the corresponding Green's function.

     

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.     

Site-directed electronic tunneling through a vibrating molecular network

The effect of electronic-nuclear coupling on electronic transport through a complex molecular network is studied. Electronic tunneling dynamics in a network of N donor/acceptor sites, connected by molecular bridges, is shown to be controlled by electronic-nuclear coupling at the bridges. Particularly, electronic coupling to an accepting nuclear mode at the contact site between the donor and the rest of the network is shown to affect the tunneling path selection to specific acceptors. In the "deep" tunneling regime, the network is mapped onto an N-level system using a recursive perturbation expansion, enabling analytical treatment of the electronic dynamics. The analytic formulation is applied for two model systems, demonstrating site-directed tunneling by electronic-nuclear coupling. Numerical simulations suggest that this phenomenon is not limited to the deep tunneling regime.     

Photoinitiated free radical polymerization of vinyl compounds in aqueous solution

A new method for the photochemical initiation of polymerization of vinyl compounds in aqueous solution is described. The photochemically active species is an ion pair complex of the formula Fe³⁺X⁻(X⁻ = OH⁻, CI⁻, N⁻₃, etc.). The light absorption by the ion pair leads to an electron transfer causing reduction of the cation and oxidation of the anion to an atom or free radical X. The latter leads to the initiation of polymerization in accordance with X + CH₂CHR→XCH₂ CHR . The kinetics of the reaction were studied by the measurement of: (a) ferrous ion formed (colorimetrically), (b) monomer disappearance (by titration and by weighting the polymer), (c) the chain length of the polymer (in the case of methyl methacrylate). The dependence of the quantum yield on the light intensity, light absorption fraction, and the concentration of vinyl monomer and ferrous ion added initially was investigated. A complete mechanism, both with regard to the formation of free radicals and the polymerization reaction, was put forward involving: (1) light absorption, (2) a primary dark back reaction, (3) dissociation of the primary product, (4) a secondary dark back reaction, (5) initiation of polymerization by free radicals, (6) propagation of polymerization, and (7) termination by recombination of active polymer endings. The mechanism was verified by the experimental results and some constant ratios were estimated quantitatively.     

Surface properties of plasma membrane vesicles isolated from melon (Cucumus melo L.) root cells differing in salinity tolerance

The hypotheses that genotypic differences in salinity tolerance may result from (i) differences in global surface charge density or (ii) from differences in global Ca²⁺ binding were tested. An attempt was made to correlate the differing salinity tolerance of four melon cultivars with surface properties of vesicles extracted from the plasma membrane (PM) of their root cells. Surface characterization involved measurements of electrophoretic mobility and sorption of ⁴⁵Ca²⁺ to the vesicles in the presence of varying concentrations of Ca²⁺, Na⁺ and Mg²⁺. Irrespective of salinity tolerance, vesicles from the four cultivars yielded similar ζ potentials under similar conditions, indicating similar global surface charge densities. Sorption studies with vesicles from two cultivars differing in salinity tolerance predicted independently this result of equal surface charge density. The estimated global binding affinities of Ca²⁺, Na⁺ and Mg²⁺ to the PM of both cultivars were the same with binding coefficients of 50, 0.8 and 9 M⁻¹, respectively. Consequently, the hypotheses enumerated above to interpret genotypic differences in salinity toxicity are rejected. However, vesicles from the salt-resistant strain sorbed 19% more Ca²⁺ per given amount of protein in the membrane, indicating the existence of a larger number of negatively charged surface sites per given amount of protein and a smaller amount of protein per given area of membrane. Genotypic differences in site-specific Ca²⁺-binding affinity (e.g. at ion channels) remain a viable hypothesis for genotypic differences in salinity tolerance.     

Fluid polling systems

We study N-queues single-server fluid polling systems, where a fluid is continuously flowing into the queues at queue-dependent rates. When visiting and serving a queue, the server reduces the amount of fluid in the queue at a queue-dependent rate. Switching from queue i to queue j requires two random-duration steps: (i) departing queue i, and (ii) reaching queue j. The length of time the server resides in a queue depends on the service regime. We consider three main regimes: Exhaustive, Gated, and Globally-Gated. Two polling procedures are analyzed: (i) cyclic and (ii) probabilistic. Under steady-state, we derive the Laplace–Stieltjes transform (LST), mean, and second moment of the amount of flow at each queue at polling instants, as well as at an arbitrary moment. We further calculate the LST and mean of the “waiting time” of a drop at each queue and derive expressions for the mean total load in the system for the various service regimes. Finally, we explore optimal switching procedures.