Path-integral solution of the one-dimensional Dirac quantum cellular automaton

Quantum cellular automata, which describe the discrete and exactly causal unitary evolution of a lattice of quantum systems, have been recently considered as a fundamental approach to quantum field theory and a linear automaton for the Dirac equation in one dimension has been derived. In the linear case a quantum cellular automaton is isomorphic to a quantum walk and its evolution is conveniently formulated in terms of transition matrices. The semigroup structure of the matrices leads to a new kind of discrete path-integral, different from the well known Feynman checkerboard one, that is solved analytically in terms of Jacobi polynomials of the arbitrary mass parameter.     

Optical co-ordinates in general relativity 2 — the problem of distance

Summary Let denote the congruence of null geodesics associated with a given optical observer inV ₄. We prove that determines a unique collection of vector fieldsM₍₎ ( =1, 2, 3) and ₍₀₎ overV ₄, satisfying a weak version of Killing's conditions.This allows a natural interpretation of these fields as the infinitesimal generators of spatial rotations and temporal translation relative to the given observer. We prove also that the definition of the fieldsM₍₎ and ₍₀₎ is mathematically equivalent to the choice of a distinguished affine parameter f along the curves of, playing the role of a retarded distance from the observer.The relation between f and other possible definitions of distance is discussed.

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Sommario Sia la congruenza di geodetiche nulle associata ad un osservatore ottico assegnato nello spazio-tempoV ₄. Dimostriamo che determina un'unica collezione di campi vettorialiM₍₎ ( =1, 2, 3) e ₍₀₎ inV ₄ che soddisfano una versione in forma debole delle equazioni di Killing. Ciò suggerisce una naturale interpretazione di questi campi come generatori infinitesimi di rotazioni spaziali e traslazioni temporali relative all'osservatore assegnato. Dimostriamo anche che la definizione dei campiM₍₎, ₍₀₎ è matematicamente equivalente alla scelta di un parametro affine privilegiato f lungo le curve di, che gioca il ruolo di distanza ritardata dall'osservatore. Successivamente si esaminano i legami tra f ed altre possibili definizioni di distanza in grande.

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Work performed in the sphere of activity of: Gruppo Nazionale per la Fisica Matematica del CNR.     

On degenerate multi-row Gomory cuts

Borozan and Cornuéjols show that valid inequalities for an infinite relaxation for MIPs, relative to some vertex f of the linear relaxation, are determined by maximal lattice-free convex sets containing f. We show that cuts for the original MIP are given by such sets with f in the interior.     

Toward the complete prediction of the 1H and 13C NMR spectra of complex organic molecules by DFT methods: application to natural substances

The NMR parameters (1H and 13C chemical shifts and coupling constants) for a series of naturally occurring molecules have been calculated mostly with DFT methods, and their spectra compared with available experimental ones. The comparison includes strychnine as a test case, as well as some examples of recently isolated natural products (corianlactone, daphnipaxinin, boletunone B) featuring unusual and/or crowded structures and, in the case of boletunone B, being the subject of a recent revision. Whenever experimental spectra were obtained in polar solvents, the calculation of NMR parameters was also carried out with the Integral Equation-Formalism Polarizable Continuum Model (IEF-PCM) continuum method. The computed results generally show a good agreement with experiment, as judged not only by statistical parameters but also by visual comparison of line spectra. The origin of the remaining discrepancies is attributed to the incomplete modeling of conformational and specific solvent effects.     

Computing the NMR spectrum of a bulk ionic liquid phase by QM/MM methods

The dependence of (1)H and (13)C NMR chemical shifts of 1-butyl-3-methylimidazolium ([bmim])-based room-temperature ionic liquids on the counteranion ([BF(4)], [MeSO(4)]) is investigated experimentally and computationally. The local structure of the ionic liquids is investigated by means of DFT calculations of the structure of ion pairs and molecular dynamics simulations. Clusters extracted from the simulation runs are used to calculate (1)H and (13)C chemical shifts by means of QM/MM methods with various partition schemes. Proton H2 of the imidazolium ring is the most sensitive to the counteranion; its chemical shift is strongly dependent on subtle details of the arrangement of the two closest anions. It is shown that a correct spacing of signals can be attained by including the two anions closest to C2 and H2 in the QM layer.     

Decomposing Berge Graphs Containing No Proper Wheel, Long Prism Or Their Complements

In this paper we show that, if G is a Berge graph such that neither G nor its complement contains certain induced subgraphs, named proper wheels and long prisms, then either G is a basic perfect graph( a bipartite graph, a line graph of a bipartite graph or the complement of such graphs) or it has a skew partition that cannot occur in a minimally imperfect graph. This structural result implies that G is perfect. This work was supported in part by NSF grant DMI-0352885 and ONR grant N00014-03-1-0188.     

Fast paths in large-scale dynamic road networks

Efficiently computing fast paths in large-scale dynamic road networks (where dynamic traffic information is known over a part of the network) is a practical problem faced by traffic information service providers who wish to offer a realistic fast path computation to GPS terminal enabled vehicles. The heuristic solution method we propose is based on a highway hierarchy-based shortest path algorithm for static large-scale networks; we maintain a static highway hierarchy and perform each query on the dynamically evaluated network, using a simple algorithm to propagate available dynamic traffic information over a larger part of the road network. We provide computational results that show the efficacy of our approach.     

Step by step palladium mediated syntheses of new 2-(pyridin-2-yl)-6-R-nicotinic acids and esters

Taking advantage of palladium peculiar “rollover” C,N cyclometallation, it is possible to promote C(3) functionalization of 6-alkyl-substituted-2,2′-bipyridines. The carbonylation reaction of rollover species [Pd(Lⁿ)Cl]₂, (HL¹ = 6-isopropyl-2,2′-bipy, 1; HL² = 6-neopentyl-2,2′-bipy, 2; HL³ = 6-ethyl-2,2′-bipy, 3; HL⁴ = 6-methyl-2,2′-bipy, 4) allowed the synthesis of 2-(pyridin-2-yl)-6-alkyl-nicotinic acids or esters. These nicotinic derivatives are extremely rare and, as far as we know, quite unreported in the case of the 6-substituted molecules.     

Dichroic properties of bis(benzoxazolyl)stilbene and bis(benzoxazolyl)thiophene dispersed into oriented polyethylene films: a combined experimental and density functional theory approach

In this work, a combination of experimental and quantum mechanical investigations is performed for the study of dichroic absorption properties of melt-processed linear low-density polyethylene (LLDPE) oriented films containing < or =0.5 wt % of either 4,4'-bis(2-benzoxazolyl)stilbene (BBS) or 2,5-bis(5-tert-butyl-2-benzoxazolyl)thiophene (BTBBT). The data acquired reveal that the film optical anisotropy and the performances as linear polarizer are strongly dependent on the molecular structure of the chromophore. In particular, the rodlike structure of BBS favors the alignment of the dye along the drawing direction of the PE film, providing dichroic ratios as high as 100 and optical performances as linear polarizer close to the pseudo-affine deformation scheme. On the contrary BTBBT, although characterized by huge anisotropic potentialities, confers the oriented film very poor dichroism and is unsuitable for linear polarizer applications. This behavior is attributed to the more complex banana-shaped structure of BTBBT dye caused by the thiophene 2,5-functionalization that limits the molecule parallel orientation to the drawing direction.