NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE

The nonlocal initial problem for nonlinear nonautonomous evolution equati-ons in a Banach space is considered. It is assumed that the nonlinearities havethe local Lipschitz properties. The existence and uniqueness of mild solutionsare proved. Applications to integro-differential equations are discussed.The main tool in the paper is the normalizing mapping (the generalizednorm).     

A better step-off algorithm for the knapsack problem

The knapsack problem, maximize Σ^m_{i = 1}c_ix_i when Σ^m_{i = 1}a_ix_i?b for integers x_i?0, can be solved by the classical step-off algorithm. The algorithm develops a series of feasible solutions with ever-increasing objective values. We make a change in the problem so that the step-off algorithm produces a series of solutions of not necessarily increasing objective values. A point is reached when no better solutions can be found and the calculation is stopped.     

Analysis of a statistical multiplexer with generalized periodic sources

We provide solution techniques for the analysis of multiplexers with periodic arrival streams, which accurately account for the effects of active and idle periods and of gradual arrival. In the models considered in this paper, it is assumed that each source alternates (periodically) between active and idle periods of fixed durations. Incoming packets are transmitted on the network link and excess information is stored in the multiplexing buffer when the aggregate input rate exceeds the capacity of the link. We are interested in the probability distribution of the buffer content for a given network link speed as a function of the number of sources and their characteristics, i.e., rate and duration of idle and active periods. We derive this distribution from two models: discrete time and continuous time systems. Discrete time systems operate in a slotted fashion, with a slot defining the base unit for data generation and transmission. In particular, in each slot the link is capable of transmitting one data unit and conversely an active source generates one data unit in that time. The continuous time model of the paper falls in the category of fluid models. Compared to previous works we allow a more general model for the periodic packet arrival process of each source. In discrete time, this means that the active period of a source can now extend over several consecutive slots instead of a single slot as in previous models. In continuous time, packet arrivals are not required to be instantaneous, but rather the data generation process can now take place over the entire duration of the active period. In both cases, these generalizations allow us to account for the progressive arrival of source data as a function of both the source speed and the amount of data it generates in an active period.This work was done while at the IBM T.J. Watson Research Center.This work was done while at the IBM T.J. Watson Research Center.Part of the work was done while visiting the IBM T.J. Watson Research Center.     

Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field

We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantized electromagnetic field are described by minimal coupling, p→p−e A (x), where A(x) is the electromagnetic vector potential with an ultraviolet cutoff. If the interactions between the electrons and the quantized radiation field are turned off, the atom or molecule is assumed to have at least one bound state. We prove that, for sufficiently small values of the fine structure constant α, the interacting system has a ground state corresponding to the bottom of its energy spectrum. For an atom, we prove that its excited states above the ground state turn into metastable states whose life-times we estimate. Furthermore the energy spectrum is absolutely continuous, except, perhaps, in a small interval above the ground state energy and around the threshold energies of the atom or molecule. Received: 3 September 1998 / Accepted: 17 March 1999     

Routes to new hafnium(IV) tetraaryl porphyrins and crystal structures of unusual phosphate-, sulfate-, and peroxide-bridged dimers

New routes for the synthesis of mono tetraaryl porphyrinato hafnium(IV) complexes, Hf(IV)Por(L)(2), are reported, where the secondary ligands, L, are determined by the method of purification. These synthetic routes cater to the solubility of the macrocycles and provide access to Hf(IV) complexes of meso tetraaryl porphyrins bearing diverse functional groups such as phenyl, tolyl, pyridyl, pentafluorophenyl, and carboxyphenyl. The latter three derivatives significantly expand the repertoire of hafnium porphyrinates. One route refluxes the porphyrin with HfCl(4) in 1-chloronaphthalene or in a mixed solvent of 1-chloronaphthalene and o-cresol. A second, solventless method is also reported wherein the porphyrin is mixed with Hf(cp)(2)Cl(2) and heated to give the metalated porphyrin in good yields. Simultaneous purification and formation of stable porphyrinato hafnium(IV) diacetate complexes, Hf(Por)OAc(2), is accomplished by elution over silica gel using 3-5% acetic acid in the eluent. Exchange of the acetate ligands for other oxo-bearing ligands can be nearly quantitative, such as p-aminobenzoate (PABA), pentanoate (pent), or octanoate (oct). Notably, we find that two to three of a variety of small multitopic dianions such as peroxo (O(2)(-2)), SO(4)(-2), and HPO(4)(-2) serve to bridge between two Hf(Por) moieties to form stable dimers. The crystal structures of this library of Hf(Por) complexes are reported, and we note that careful analysis of crystallography data reveals (Por)Hf(micro-eta(2)-O(2))(2)Hf(Por) rather than four bridging oxo or hydroxy ions.     

The Adsorption of Polyvinylpyrrolidone on Kaolinite Saturated with Sodium Chloride

The adsorption of two different molecular weights of polyvinylpyrrolidone (PVP) (M(w)=44,000 and M(w)=360,000 g mol(-1)) from water on kaolinite saturated with sodium chloride has been studied. The adsorption of PVP increases slowly as temperature increases. The adsorption of PVP on the kaolinite was studied by considering Fourier transform infrared (FTIR) spectra, X-ray diffraction patterns, and dielectric constants. During the adsorption process, PVP interacts with saturating sodium cations and possibly forces some of them onto the edges of the kaolinite; thus, the dielectric constant of saturated kaolinite is reduced after PVP adsorption. Copyright 2001 Academic Press.     

Why Do Cycloaddition Reactions Involving C60 Prefer [6,6] over [5,6] Bonds?

The origin of the experimentally known preference for [6,6] over [5,6] bonds in cycloaddition reactions involving C₆₀ has been computationally explored. To this end, the Diels–Alder reaction between cyclopentadiene and C₆₀ has been analysed by means of the recently introduced activation strain model of reactivity in combination with the energy decomposition analysis method. Other issues, such as the aromaticity of the corresponding transition states, have also been considered. These results indicate that the major factor controlling the observed regioselectivity is the more stabilising interaction between the deformed reactants in the [6,6] reaction pathway along the entire reaction coordinate.     

Supra­molecular assembly of (methanol)[10,15,20‐tris­(4‐cyano­phenyl)‐5‐(4‐pyridyl)­porphyrin­ato]­zinc(II) by inter­molecular hydrogen bonding and weak coordination

The crystal structure of the title compound, [Zn(C₄₆H₂₄N₈)(CH₄O)], consists of two‐dimensional supra­molecular arrays sustained by O—H⋯N(pyrid­yl) hydrogen bonding and weak Zn⋯NC coordination. The inter­layer organization in the crystal structure is characterized by tight stacking of the corrugated layers.     

How Strain Affects the Reactivity of Surface Metal Oxide Catalysts

Highly dispersed molybdenum oxide supported on mesoporous silica SBA‐15 has been prepared by anion exchange resulting in a series of catalysts with changing Mo densities (0.2–2.5 Mo atoms nm^?2). X‐ray absorption, UV/Vis, Raman, and IR spectroscopy indicate that doubly anchored tetrahedral dioxo MoO₄ units are the major surface species at all loadings. Higher reducibility at loadings close to the monolayer measured by temperature‐programmed reduction and a steep increase in the catalytic activity observed in metathesis of propene and oxidative dehydrogenation of propane at 8 % of Mo loading are attributed to frustration of Mo oxide surface species and lateral interactions. Based on DFT calculations, NEXAFS spectra at the O‐K‐edge at high Mo loadings are explained by distorted MoO₄ complexes. Limited availability of anchor silanol groups at high loadings forces the MoO₄ groups to form more strained configurations. The occurrence of strain is linked to the increase in reactivity.