Pairs of shift invariant subspaces of matrices and noncanonical factorization

This paper contains a generalization of results from [BG1]. Here we classify the set of pairs of shift invariant subspaces, find the invariants and simplest representative of each class. The results are applied to analyse different types of LU factorizations with a middle factor.     

On queueing delays of dispersed messages

We study the message queueing delays in a node of a communication system, where a message consists of a block of consecutive packets. The message delay is defined as the time elapsing between the arrival epoch of the first packet of the message to the system until after the transmission of the last packet of that message is completed. We distinguish between two types of message generation processes. The message can be generated as abatch or it can bedispersed over time. In this paper we focus on the dispersed generation model. The main difficulty in the analysis is due to the correlation between the system states observed by different packets of the same message. This paper introduces a new technique to analyze the message delay in such systems for different arrival models and different number of sessions. For anM/M/1 system with variable size messages and for the bursty traffic model, we obtain an explicit expression for the Laplace-Stieltjes transform (LST) of the message delay. Derivations are also provided for anM/G/1 system, for multiple session systems and for fixed message sizes. We show that the correlation has a strong effect on the performance of the system, and that the commonly usedindependence assumption, i.e., the assumption that the delays of packets are independent from packet to packet, can lead to wrong conclusions.     

The chern classes of the eigenbundles of an automorphism of a curve

LetX be smooth complex projective curve. Leth be an automorphism ofX of orderp. We improve a formula to compute the characteristic classes of the normal bundles of certain components of the fixed point set ofh acting on the symmetric products ofX. The author was supported by the Emmy Noether Research Institute for Mathematics.     

Linear complexity algorithm for semiseparable matrices

A new linear complexity algorithm for general nonsingular semiseparable matrices is presented. For symmetric matrices whose semiseparability rank equals to 1 this algorithm leads to an explicit formula for the inverse matrix.Supported in part by the NSF Grant DMS 9306357     

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.     

Twisted cubics, bis

We consider the smooth compactification constructed in [12] for a space of varieties like twisted cubics. We show this compactification embeds naturally in a product of flag varieties.Partially supported by CNPq, Pronex (ALGA)     

Mechanistic Insight into the Stereochemical Control of Lactide Polymerization by Salan–Aluminum Catalysts

Alkyl aluminum complexes of chiral salan ligands assembled around the 2,2′‐bipyrrolidine core form as single diastereomers that have identical configurations of the N donors. Active catalysts for the polymerization of lactide were formed upon the addition of benzyl alcohol. Polymeryl exchange between enantiomorphous aluminum species had a dramatic effect on the tacticity of the poly(lactic acid) (PLA) in the polymerization of racemic lactide (rac‐LA): The enantiomerically pure catalyst of the nonsubstituted salan ligand led to isotactic PLA, and the racemic catalyst exhibited lower stereocontrol. The enantiomerically pure catalyst of the chloro‐substituted salan ligand led to PLA with a slight tendency toward heterotacticity, whereas the racemic catalyst led to PLA of almost perfect heterotacticity following an insertion/auto‐inhibition/exchange mechanism.     

Coating Platinum Nanoparticles with Methyl Radicals: Effects on Properties and Catalytic Implications

It was recently reported that the reaction of methyl radicals with Pt⁰ nanoparticles (NPs), prepared by the reduction of Pt(SO₄)₂ with NaBH₄, is fast and yields as the major product stable (Pt⁰‐NPs)?(CH₃)_n and as side products, in low yields, C₂H₆, C₂H₄, and some oligomers. We decided to study the effect of this coating on the properties of the Pt⁰‐NPs. The results show that the coating can cover up to 75 % of the surface Pt⁰ atoms. The rate constant of the reaction, k( ^. CH₃+Pt⁰‐NPs), decreases with the increase in the surface coverage, leading to competing reaction paths in the solution, which gradually become dominant, affecting the composition of the products. The methyl coating also affects the zeta potential, the UV spectra, and the electrocatalytic reduction of water in the presence of the NPs. Thus, the results suggest that binding alkyl radicals to Pt⁰ surfaces might poison the NPs catalytic activity. When the Pt⁰‐NPs are prepared by the reduction of a different precursor salt, PtCl₆^2?, nearly no C₂H₄ and oligomers are formed and the methyl coating covers a larger percentage of the surface Pt⁰ atoms. The difference is attributed to the morphology of the Pt⁰‐NPs: those prepared from Pt(SO₄)₂ are twinned nanocrystals, whereas those prepared from PtCl₆^2? consist mostly of single crystals. Thus, the results indicate that the side products, or most of them at least, are formed on the twinned Pt⁰ nanocrystal edges created between (111) facets. In addition, the results show that Pt⁰‐NPs react very differently compared with other noble metals, for example, Au⁰ and Ag⁰; this difference is attributed in part to the difference in the bond strength, (M⁰‐NP)?CH₃, and should be considered in heterogeneous catalytic processes involving alkyl radicals as intermediates.     

Aromaticity in Group 14 homologues of the cyclopropenylium cation

The nature of the bonding and the aromaticity of the heavy Group 14 homologues of cyclopropenylium cations E₃H₃⁺ and E₂H₂E′H⁺ (E, E′=C–Pb) have been investigated systematically at the BP86/TZ2P DFT level by using several methods. Aromatic stabilization energies (ASE) were evaluated from the values obtained from energy decomposition analysis (EDA) of charged acyclic reference molecules. The EDA‐ASE results compare well with the extra cyclic resonance energy (ECRE) values given by the block localized wavefunction (BLW) method. Although all compounds investigated are Hückel 4n+2 π electron species, their ASEs indicate that the inclusion of Group 14 elements heavier than carbon reduces the aromaticity; the parent C₃H₃⁺ ion and Si₂H₂CH⁺ are the most aromatic, and Pb₃H₃⁺ is the least so. The higher energies for the cyclopropenium analogues reported in 1995 employed an isodesmic scheme, and are reinterpreted by using the BLW method. The decrease in the strength of both the π cyclic conjugation and the aromaticity in the order C?Si>Ge>Sn>Pb agrees reasonably well with the trends given by the refined nucleus‐independent chemical shift NICS(0)_πzz index.