Lower Bounds from State Space Relaxations for Concave Cost Network Flow Problems

In this paper we obtain Lower Bounds (LBs) to concave cost network flow problems. The LBs are derived from state space relaxations of a dynamic programming formulation, which involve the use of non-injective mapping functions guaranteing a reduction on the cardinality of the state space. The general state space relaxation procedure is extended to address problems involving transitions that go across several stages, as is the case of network flow problems. Applications for these LBs include: estimation of the quality of heuristic solutions; local search methods that use information of the LB solution structure to find initial solutions to restart the search (Fontes et al., 2003, Networks, 41, 221–228); and branch-and-bound (BB) methods having as a bounding procedure a modified version of the LB algorithm developed here, (see Fontes et al., 2005a). These LBs are iteratively improved by penalizing, in a Lagrangian fashion, customers not exactly satisfied or by performing state space modifications. Both the penalties and the state space are updated by using the subgradient method. Additional constraints are developed to improve further the LBs by reducing the searchable space. The computational results provided show that very good bounds can be obtained for concave cost network flow problems, particularly for fixed-charge problems.     

Reactions of dimethyldivinylsilane,dimethyldivinyltin and allyltrimethyltin with diethylene (tertiary) phosphine)platinum complexes

The compounds [Pt(C₂H₄)₂(PR₃)] [PR₃ = P-tBu₂Me, P(C₆H₁₁)₃, PPh₃] react dimethyldivinylsilane or dimethyldivinyltin to give chelate complexes [Pt{(CH₂CH)₂MMe₂} (PR₃)] (M = Si or Sn). allyltrimethyltin reacts with various diethylene (tertiary phosphine)platinum compounds with cleavage of the allyl group to afford complexes [Pt(SnMe₃)(η³-C₃H₅)(PR₂)]. The NMR spectra (¹³C, ¹H and ³¹P) of the new compounds have been recorded, and the data are discussed in terms of the structures proposed.     

The dipole moments of the excited states of FeC

With the purpose of comparing expectation dipole moment values mu with finite-field obtained dipole moments mu(FF), we recalculated by the finite-field method previously reported mu values of 38 excited states of FeC. In most of the cases mu(FF) is significantly larger than mu.     

The electronic structure of vanadium carbide, VC

Within an energy range of 2.4 eV, we have explored 29 of the 36 states of the diatomic molecule VC that arise from the atoms in their ground state, V(4s23d3;4F)+C(2s2 2p2;3P). We use multireference methods with large atomic natural orbital basis sets. The ground state is of 2Delta symmetry with the first two excited states, 4Delta and 2Sigma+, located 4.2 and 7.0 kcal/mol above the X state. All the states examined in this work are relatively strongly bound and show significant charge transfer from V to C. The binding energy of the X 2Delta state is estimated to be 95.3 kcal/mol in good agreement with the experimental value.     

A multireference coupled-cluster potential energy surface of diazomethane, CH(2)N(2)

The intrinsically multireference dissociation of the C-N bond in ground-state diazomethane (CH(2)N(2)) at different angles has been studied with the multireference Brillouin-Wigner coupled-cluster singles and doubles (MRBWCCSD) method. The morphology of the calculated potential energy surface (PES) in C(s)() symmetry is similar to a multireference perturbational (CASPT3) PES. The MRBWCCSD/cc-pVTZ H(2)C-N(2) dissociation energy with respect to the asymptotic CH(2)(?(1)A(1)) + N(2)(X(1)Sigma(g)(+)) products is D(e) = 35.9 kcal/mol, or a zero-point corrected D(0) = 21.4 kcal/mol with respect to the ground-state CH(2)(X(3)B(1)) + N(2)(X(1)Sigma(g)(+)) fragments.     

Thermal wave photopyroelectric characterization of advanced materials: State of the art

This article reviews the history, background, theoretical basis, development, attempts to optimize, and experimental performance of the photopyroelectric technique for the optothermal characterization of advanced materials such as semiconductors, superconductors, pure metals and alloys, quantum wells, liquid crystals, paramagnetic and ferromagnetic materials, as well as solar cells. The state of the art in the experimental processes in this field is also reviewed. This new photothermal technique can be used after a careful optimization, as a highly sensitive method for photopyroelectric spectroscopy and general thermal wave measurements. It has been shown to be a highly sensitive spectroscopic method for the nondestructive evaluation of advanced materials. This review presents the main photopyroelectric theoretical models that have been used for the extraction of some important optoelectronic properties such as the optical absorption coefficient and the nonradiative quantum efficiency spectra, as well as some thermal properties such as the thermal diffusivity, thermal conductivity, and specific heat. The applicability of the general basic theoretical model with its many special cases is also described in detail. This review demonstrates how photopyroelectric spectroscopy can be complementary to the conventional spectroscopic methods. The different experimental modes of the technique are also discussed. Moreover, some ideas concerning future perspectives of applying the technique to other scientific fields are outlined. This article does not aspire to an in-depth analysis of the experimental results in the field; rather, it focuses on the technique itself.     

Molecular Mixing and Flowfield Measurements in a Recirculating Shear Flow. Part I: Subsonic Flow

The mixing and flowfield of a complex geometry, similar to a rearward-facing step flow but with injection, is studied. A subsonic top-stream is expanded over a perforated ramp at an angle of 30°, through which a secondary stream is injected. The mass flux of the second stream is chosen to be insufficient to provide the entrainment requirements of the shear layer, which, as a consequence, attaches to the lower guidewall. Part of the flow is directed upstream forming a re-entrant jet within the recirculation zone that enhances mixing and flameholding. A control-volume model of the flow is found to be in good agreement with the variation of the overall pressure coefficient of the device with variable mass injection. The flowfield response to changing levels of heat release is also quantified. While increased heat release acts somewhat analogously to increased mass injection, fundamental differences in the flow behaviour are observed. The hypergolic hydrogen-fluorine chemical reaction employed allows the level of molecular mixing in the flow to be inferred. The amount of mixing is found to be higher in the expansion-ramp geometry than in classical free-shear layers. As in free-shear layers, the level of mixing is found to decrease with increasing top-stream velocity. Results for a similar configuration with supersonic flow in the top stream are reported in Part II of this two-part series.     

The thresholds for diameter 2 in random Cayley graphs

Given a group G, the model denotes the probability space of all Cayley graphs of G where each element of the generating set is chosen independently at random with probability p. In this article we show that for any and any family of groups G_k of order n_k for which , a graph with high probability has diameter at most 2 if and with high probability has diameter greater than 2 if . We also provide examples of families of graphs which show that both of these results are best possible. Of particular interest is that for some families of groups, the corresponding random Cayley graphs achieve Diameter 2 significantly faster than the Erd?s‐Renyi random graphs. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 45, 218–235, 2014     

What is your “birthday elliptic curve”?

In this article, Ramanujan–Weber class invariants and its analogue are used to derive birthday elliptic curves.     

Nanoparticle Patterns

Journal of Nanoparticle Research -