A tabu search procedure for multicommodity location/allocation with balancing requirements

We propose a tabu search heuristic for the location/allocation problem with balancing requirements. This problem typically arises in the context of the medium term management of a fleet of containers of multiple types, where container depots have to be selected, the assignment of customers to depots has to be established for each type of container, and the interdepot container traffic has to be planned to account for differences in supplies and demands in various zones of the geographical territory served by a container shipping company. It is modeled as a mixed integer program, which combines zero-one location variables and a multicommodity network flow structure. Extensive computational results on a set of benchmark problems and comparisons with an efficient dual ascent procedure are reported. These show that tabu search is a competitive approach for this class of problems.     

Measurement of coupling constants in symmetrical spin systems using a full multiple-step cross-polarization-driven NMR pulse scheme

New NMR pulse schemes completely driven under homonuclear and heteronuclear cross-polarization conditions are proposed for the study and the measurement of coupling constants in symmetrical molecules in solution. The appropriate superimposition of independent magnetization components can afford several spin-selective multiplet patterns that are suitable for the determination of the magnitude and the sign of proton-proton and proton-carbon coupling constants with optimum sensitivity levels. A detailed product operator formalism analysis for the proposed doubly selective 1D and nonselective 2D HCP-TOCSY versions is provided and experimental verification for the configurational analysis of symmetric olefinic systems having chemical equivalence is demonstrated.     

Structural characterization of artificial self-assembling porphyrins that mimic the natural chlorosomal bacteriochlorophylls c, d, and e

We report two crystal structures of a synthetic porphyrin molecule which was programmed for self-assembly. The same groups which ensure that bacteriochlorophylls c, d, and e can self-assemble into the chlorosomal nanorods, the photosynthetic antenna system of some green bacteria, have been engineered into desired positions of the tetrapyrrolic macrocycle. In the case of the 5,15-meso-substituted anchoring groups, depending upon the concentration, by using the same crystallization solvents, either a tetragonal or a layered structure of porphyrin stacks were encountered. Surprisingly, pi-pi interactions combined with extensive dispersive interactions, which also encompass cyclohexane, one of the crystallization solvents, win over putative hydrogen bonding. We are aware that our compounds differ considerably from the natural bacteriochlorophylls, but based upon our findings, we now question the hydrogen-bonding network, previously proposed to organize stacks of bacteriochlorophylls. Transmission electron microscopy (TEM), atomic force microscopy (AFM), and small-angle X-ray scattering (SAXS) on various isomeric compounds support our challenge of current models for the chlorosomal antenna as these show structures, astonishingly similar to those of chlorosomes.     

On a model of viscoelastic rod in unilateral contact with a rigid wall

^** Corresponding author. Email: atanackovic{at}uns.ns.ac.yu We study translatory motion of a body to which a viscoelasticrod with the constitutive equation with fractional derivativesis attached. The body with a rod impacts against a rigid wall.It is shown that the problem is described with a coupled systemof differential equations having integer and fractional derivativeshaving the form x⁽²⁾ = –f; f + af⁽⁾ = x + bx⁽⁾, x(0) =0, x⁽¹⁾(0) = 1. The unique solvability in S'₊ is proved andinterpretation of solutions is given. Also, some a priori estimatesof the solution are given. In particular, we showed that restrictionson coefficients that follow from the second law of thermodynamicsimply that the velocity after the impact is smaller than thevelocity before the impact.     

The Orthogonal Weingarten Formula in Compact Form

We present a compact formulation of the orthogonal Weingarten formula, with the traditional quantity \({I(i_1,\ldots,i_{2k}:j_1,\ldots,j_{2k})=\int_{O_n}u_{i_1j_1}\cdots u_{i_{2k}j_{2k}}\,{\rm d}u}\) replaced by the more advanced quantity \({I(a)=\int_{O_n}\Pi u_{ij}^{a_{ij}}\,{\rm d}u}\), depending on a matrix of exponents \({a\in M_n(\mathbb{N})}\). Among consequences, we establish a number of basic facts regarding the integrals I(a): vanishing conditions, possible poles, asymptotic behavior.     

Semilinear ordinary differential equation coupled with distributed order fractional differential equation

The system , where D^γ,γ∈[0,2] are operators of fractional differentiation, is investigated and the existence of a mild and classical solution is proven. Also, a necessary and sufficient condition for the existence and uniqueness of a solution to a general linear fractional differential equation , in is given.     

How to measure long-range proton-carbon coupling constants from 1H-selective HSQMBC experiments

Heteronuclear long-range scalar coupling constants (ⁿJ_CH) are a valuable tool for solving problems in organic chemistry and are especially suited for stereochemical and configurational analyses of small molecules and natural products. This tutorial will focus on the step-by-step implementation of several 2D ¹H frequency selective HSQMBC experiments for the easy and accurate measurement of either the magnitude or both the magnitude and the sign of long-range ⁿJ_CH couplings. The performance of these experiments will be showcased with several scenarios in a range of different experimental conditions.     

LR-selHSQMBC: Simultaneous Detection and Quantification of Very Weak Long-Range Heteronuclear NMR Correlations

The optimum detection and accurate measurement of longer-range (⁴J and higher) heteronuclear NMR correlations is described. The magnitude and/or the sign of a wide range of large and small long-range couplings can be simultaneously determined for protonated and non-protonated ¹³C and ¹⁵N nuclei using the LR-selHSQMBC experiment.