Solving the Segregated Storage Problem with Benders' Partitioning

We investigate the application of Benders' partitioning to a mixed integer programming formulation of the segregated storage problem. The dual subproblem reduces to an efficiently-solvable network flow problem. This approach is compared empirically to Neebe's multiplier adjustment procedure. Benders' procedure is shown to be computationally effective for an important class of practical applications having high demand-to-capacity ratios and fewer products than compartments.     

Controllability of linear systems,differential geometry curves in grassmannians and generalized grassmannians,and riccati equations

We study the linear system =Ax+Bu from a differential geometric point of view. It is well-known that controllability of the system is related to the one-parameter family of operators e^t B. We use this to give a proof of the classical controllability conditions in terms of the differential geometry of certain curves in ⁿ. We then view (t)=Im(e^t B) as a curve in appropriate Grassmannian and see that, in local coordinates, is an integral curve of the flow induced by a matrix Riccati equation. We obtain qualitative geometric conditions on that are equivalent to the controllability of the system. To get quantitiative results, we lift to a curve l' in a splitting space, a generalized Grassmannian, which has the advantage of being a reductive homogeneous space of the general linear group, GL(ⁿ). Explicit and simple expressions concerning the geometry of are computed in terms of the Lie algebra of GL(ⁿ), and these are related to the controllability of the system.James Wolper was a visiting professor in the Department of Mathematics at Texas Tech University while much of this research was conducted. He would like to express appreciation for the hospitality he received during his visit.     

Structural polymorphism of the actin-espin system: a prototypical system of filaments and linkers in stereocilia

We examine the interaction between cytoskeletal F-actin and espin 3A, a prototypical actin bundling protein found in sensory cell microvilli, including ear cell stereocilia. Espin induces twist distortions in F-actin as well as facilitates bundle formation. Mutations in one of the two F-actin binding sites of espin, which have been implicated in deafness, can tune espin-actin interactions and radically transform the system's phase behavior. These results are compared to recent theoretical work on the general phase behavior linker-rod systems.     

Speeding up the FMMR perfect sampling algorithm: A case study revisited

In a previous paper by the second author, two Markov chain Monte Carlo perfect sampling algorithms—one called coupling from the past (CFTP) and the other (FMMR) based on rejection sampling—are compared using as a case study the move‐to‐front (MTF) self‐organizing list chain. Here we revisit that case study and, in particular, exploit the dependence of FMMR on the user‐chosen initial state. We give a stochastic monotonicity result for the running time of FMMR applied to MTF and thus identify the initial state that gives the stochastically smallest running time; by contrast, the initial state used in the previous study gives the stochastically largest running time. By changing from worst choice to best choice of initial state we achieve remarkable speedup of FMMR for MTF; for example, we reduce the running time (as measured in Markov chain steps) from exponential in the length n of the list nearly down to n when the items in the list are requested according to a geometric distribution. For this same example, the running time for CFTP grows exponentially in n. © 2003 Wiley Periodicals, Inc. Random Struct. Alg., 2003     

Design and performance of BOREAS,the beamline for resonant X‐ray absorption and scattering experiments at the ALBA synchrotron light source

The optical design of the BOREAS beamline operating at the ALBA synchrotron radiation facility is described. BOREAS is dedicated to resonant X‐ray absorption and scattering experiments using soft X‐rays, in an unusually extended photon energy range from 80 to above 4000 eV, and with full polarization control. Its optical scheme includes a fixed‐included‐angle, variable‐line‐spacing grating monochromator and a pair of refocusing mirrors, equipped with benders, in a Kirkpatrick–Baez arrangement. It is equipped with two end‐stations, one for X‐ray magnetic circular dichroism and the other for resonant magnetic scattering. The commissioning results show that the expected beamline performance is achieved both in terms of energy resolution and of photon flux at the sample position.     

The effect of bond functions on molecular dissociation energies

Multi-reference Cl calculations are reported for the ground states of HCl and N₂ at their equilibrium distances, and for their separated atoms. Basis sets of double-zeta and double-zeta plus polarization quality are systematically augmented by additional sets of functions located at the bond centers. It is shown that use of bond functions can lead to either an underestimate or an overestimate of the the bond energy. Optimum basis sets for each molecule were obtained, giving D_e values of 4.59 eV for HCl (expt. 4.62 eV) and 9.96 eV for N₂ (expt. 9.905 eV) at the estimated full Cl level. The quality of the potential curves obtained with these basis sets is discussed.     

A novel ethylene-bridged spiro[3.2]Hexane

3,3-Dichlorotricyclo[5.1.0.0^1,4]oct-5-en-2-one ($\text{1}$) was prepared by addition of dichloroketene to 1,3-cyclohexadiene followed by allylic bromination and dehydrobromination.     

Synthesis, characterization and dioxygen reactivity of copper(I) complexes with glycoligands

A new family of copper(I) complexes with "glycoligands" containing a central saccharide scaffold, with 2-picolyl ether groups or 2-picolylamine or N-imidazolylamine groups, has been prepared and characterized. For this purpose, the following tetradentate ligands have been synthesized: methyl 2,3-di-O-(2-picolyl)-alpha-D-lyxofuranoside (L1), 1,5-anhydro-2-deoxy-3,4-di-O-(2-picolyl)-d-galactitol (L2), 5-(amino-N-(2-salicyl))-5-deoxy-1,2-O-isopropylidene-3-O-(2-picolyl)-alpha-D-xylofuranose (L3), and 5-(amino-N-(2-salicyl))-5-deoxy-1,2-O-isopropylidene-3-O-(methylimidazol-2-yl)-alpha-D-xylofuranose (L4). The ligands and the complexes were characterized by elemental analysis, IR, 1H and 13C NMR spectroscopies, ESI mass spectrometry, and cyclic voltammetry. Collaterally with the experimental work, HF-DFT(B3LYP/6-31G*) computations were performed to obtain additional structural information. The Cu(I) complexes are found to be pentacoordinated. The redox properties and the O2-reactivity of the Cu(I)Ln complexes have been studied. Reactions of Cu(I) complexes with dioxygen in ethanol yield stable Cu(II) complexes as confirmed by UV-visible spectrophotometry and EPR spectroscopy.     

Synthesis and characterization of copper(II) complexes incorporating pyrazolyl-derived N,S-donor bidentate ligands

The novel bidentate N,S-donor anionic ligands [PhNCSIndz]^?, [PhNCSImz]^?, [PhNCSPz^Me3]^?, and [EtNCSPz]^?, where Indz?=?indazole, Imz?=?imidazole, Pz^Me3?=?3,4,5-trimethylpyrazole, and Pz?=?pyrazole, were synthesized and used to prepare Cu(II) complexes of general formula [Cu(N^S)₂]. The ligands were synthesized via direct addition of phenylisothiocyanate or ethylisothiocyanate into THF suspensions of the corresponding sodium-pyrazolate salts. All of the synthesized compounds, including the ligands and the complexes, were characterized by physico-chemical and spectroscopic methods, and crystal structures of [Cu(EtNCSPz)₂] and [Cu(PhNCSPz^Me2)₂] were determined by X-ray diffraction analysis, showing a trans-square planar geometry for [Cu(EtNCSPz)₂] and a distorted tetrahedral geometry for [Cu(PhNCSPz^Me2)₂].     

Minimality and other properties of the width- nonadjacent form

Let be an integer and let be the set of integers that includes zero and the odd integers with absolute value less than . Every integer can be represented as a finite sum of the form , with , such that of any consecutive 's at most one is nonzero. Such representations are called width- nonadjacent forms (-NAFs). When these representations use the digits and coincide with the well-known nonadjacent forms. Width- nonadjacent forms are useful in efficiently implementing elliptic curve arithmetic for cryptographic applications. We provide some new results on the -NAF. We show that -NAFs have a minimal number of nonzero digits and we also give a new characterization of the -NAF in terms of a (right-to-left) lexicographical ordering. We also generalize a result on -NAFs and show that any base 2 representation of an integer, with digits in , that has a minimal number of nonzero digits is at most one digit longer than its binary representation.