Scheduling crackdowns on illicit drug markets

This paper presents an analytical approach for scheduling crackdowns on street-corner drug markets. The crackdown scheduling problem is shown to be NP-complete. We then provide efficient optimal algorithms for several special cases and approximation algorithms for the general case. These results show that the optimal strategy is to give priority to markets that take longer to bring down and which require low levels of post-crackdown maintenance. The results are then extended to incorporate dealer displacement between drug markets.     

A note on random coin tossing

Harris and Keane [Probab. Theory Related Fields 109 (1997) 27-37] studied absolute continuity/singularity of two probabilities on the coin-tossing space, one representing independent tosses of a fair coin, while in the other a biased coin is tossed at renewal times of an independent renewal process and a fair coin is tossed at all other times. We extend their results by allowing possibly different biases at the different renewal times. We also investigate the contiguity and asymptotic separation properties in this kind of set-up and obtain some sufficient conditions.Keywords:renewal process, absolute continuity, singularity, contiguity, asymptotic separation, martingale convergence theorem     

Capacity and entry issues in online exchanges

With the advent of open standards and Internet technologies, the number of sellers who can participate in online exchanges is greatly increased. We model the competition between identical sellers vying for the same business, and find that there exists a mixed-strategy equilibrium in prices. The results help us understand the dynamics between a seller’s capacity and his motivation to participate in an auction.     

Carbon-13 NMR signals of some natural coumarins and their derivatives

The ¹³C NMR spectra of the natural coumarins ostruthin, osthol, aegelinol (enantiomer of decursinol), luvangetin, seselin, anomalin, oxypeucedanin (and its enantiomer prangolarin) and oxypeucedanin hydrate and some of their derivatives have been studied. Self-consistent resonance assignments have been made following chemical shift theory and using simple models. Carbon-hydrogen coupling constants of some compounds are also reported. The alkoxy group/s at C-5 and/or C-8 in linear furocoumarins, as well as in linear pyranocoumarins, have unusually small shielding effects on the ortho- and para-carbons. This study also indicates that the C-4a and C-8 resonance assignments of osthol, made earlier, should be reversed.     

4‐Methyl‐N‐[2‐(p‐tolylsulfanyl)phenyl]benzene­sulfonamide

The title compound, C₂₀H₁₉NO₂S₂, is formed by a palladium–copper‐catalyzed reaction between 4‐methyl‐N‐[2‐(prop‐2‐ynyl­sul­fanyl)­phenyl]­benzene­sul­fon­amide and p‐iodo­toluene. The mol­ecules contain three essentially planar parts, namely an amino­thio­phenol moiety (A), a toluene­sulfone moiety excluding the oxo ligands (B) and a tolyl group (C), approximately orthogonal to each other; the dihedral angles A/B, A/C and B/C are 111.6 (1), 89.3 (1) and 101.4 (1)°, respectively. Intermolecular N—H?O hydrogen bonds link the mol­ecules into infinite one‐dimensional chains.     

Bis­[3‐(o‐methoxy­phenyl)‐1‐methyl­triazene 1‐oxidato‐O,N3,O′]­zinc(II)

In the title compound, [Zn(C₈H₁₀N₃O₂)₂], the Zn atom displays a highly distorted octahedral coordination involving O and N atoms of two bidentate planar ligands approximately orthogonal to each other; the dihedral angle between the ligand planes is 84.95 (4)°. The ligand mol­ecules show great asymmetry in their bonding to the Zn²⁺ ion, with Zn—O bond distances ranging between 2.056 (2) and 2.534 (2) Å. The planar phenyl ring and the trigonal–planar geometry about the triazene N atom bonded to the phenyl ring suggest a resonance interaction extending over adjacent atoms.     

Unit cell dependence of optical matrix elements in tight-binding theory: The case of zigzag graphene nanoribbons

In the tight-binding theory, momentum matrix elements (MMEs) needed to calculate the optical properties are normally computed using a formulation based on the gradient of the Hamiltonian in the k space. We demonstrate the inadequacy of this formulation by considering the case of zigzag graphene nanoribbons. We show that one obtains wrong values of MMEs, in violation of the well-known selection rules, if the unit cell chosen in the calculations does not incorporate the symmetries of the bulk. This is in spite of the fact that the band structure is insensitive to the choice of the unit cell. We substantiate our results based on group-theoretic arguments. Our observations will open an avenue for proper formulation of MMEs.     

The influence of linking group in exterior point on mesogenic properties of the basket moulded molecules: calix[4]arene

Novel basket-shaped molecules having calix[4]arene as central rigid core possessing azomaterial in outer space unit in the lengthening arm were synthesised and characterised by elemental analysis and different spectroscopic methods such as Fourier Transform Infrared (FT-IR), electron spin ionization (ESI)-MASS, ¹H nuclear magnetic resonance (NMR) and ¹³C NMR. Mesomorphism behaviour of novel materials was studied using optical polarising microscopy, differential scanning calorimetry and higher-temperature powder X-ray diffraction method to confirm smectic C phase. In most of the compounds, we found rod-like mosaic texture and focal conic textures of smectic C phases. Nematic phases were also quite often found in materials during cooling and heating stage from isotropic phases. The dielectric measurements have been carried out for the determination of real and imaginary parts of the permittivity of the newly designed scaffolds. These studies will give adequate prospects in the field of supramolecular system, especially in calixarene organisation to explore new epoch of calixarene-based liquid crystals with different linking groups.     

Unperturbed Random Coil Dimensions of Two Tricopolypeptides Containing Glycine,Glutamic Acid,and Lysine

Two tricopolypetides with varying amounts of glycyl, ε-carbobenzoxy-L-lysyl, and γ-benzyl-L-glutamyl residues were synthesized and characterized by determining their intrinsic viscosity, refractive index increment, molecular weight, and second virial coefficient in the random coil solvent dichloraoacetic acid. The characteristic ratio (C∞) of the two polypetides was determined using the Brant-Flory equation. C∞ decreased from 8.1 to 4.8 on changing the content of glycine from 27.3 to 46.0 mole %. These values of C∞ are markedly higher than those expected from a consideration of the effect of glycine on random coil dimensions of copolypeptides.