Scattering of regularized-long-wave solitary waves

The Lagrangian density for the regularized-long-wave equation (also known as the BBM equation) is presented. Using the trial function technique, ordinary differential equations that describe the time dependence of the position of the peaks, amplitudes, and widths for the collision of two solitary waves are obtained. These equations are analyzed in the Born and “equal-width” approximations and compared with numerical results obtained by direct integration utilizing the split-step fast Fourier-transform method. The computations show that collisions are inelastic and that production of solitary waves may occur.     

Semi-synthesis of bioactive fluorescent analogues of the cytotoxic marine alkaloid discorhabdin C

Semi-synthetic N-13 alkylated analogues of the cytotoxic marine alkaloid discorhabdin C have been found to exhibit cytotoxicity towards tumour cell lines at comparable levels to that of the natural product. Incorporation of an ethylenediamine linker facilitated the synthesis of a variety of fluorophore-labelled probes, of which dansyl analogue 20 exhibited biological activity, providing a tool for mechanism of action and cellular localization studies. An alternative probe design was also exemplified, whereby a bioactive alkyne-terminated analogue (24) was found to undergo Huisgen 1,3-dipolar cycloaddition ‘click’ reactions with fluorescent azides, enabling studies directed towards activity-based protein profiling.     

Algebraic decay in self-similar Markov chains

A continuous-time Markov chain is used to model motion in the neighborhood of a critical invariant circle for a Hamiltonian map. States in the infinite chain represent successive rational approximants to the frequency of the invariant circle. For the case of a noble frequency, the chain is self-similar and the nonlinear integral equation for the first passage time distribution is solved exactly. The asymptotic distribution is a power law times a function periodic in the logarithm of the time. For parameters relevant to the critical noble circle, the decay proceeds ast ^–4.05.     

Invariants and constructions of mendelsohn designs

In this paper we examine Mendelsohn designs and some connections to topology which lead to an easily described algorithm for computing invariants of these designs. The results are applied to designs which have natural group actions. We also use the topology to describe when ordinary two-fold triple systems with a group action lead to Mendelsohn designs with the same group action. Procedures for constructing Mendelsohn designs are also given. In particular, we give necessary and sufficient conditions for constructing 2-(v, 4, 1) Mendelsohn designs.     

A note on column generation in Dantzig—Wolfe decomposition algorithms

A modification of the column generation operation in Dantzig—Wolfe decomposition is suggested. Instead of the usual procedure of solving one or more subproblems at each major iteration, it is shown how the subproblems may be solved parametrically in such a way as to maximize the immediate improvement in the value of objective in the master problem, rather than to maximize the reduced profit of the entering column. The parametric problem is shown to involve the maximization of a piece-wise linear concave function of a single variable. It is hoped that in some cases the use of the suggested procedure may improve the slow rates of convergence common in decomposition algorithms.     

Structures of 355-1355-1355-1tricarbonyl: structural evidence for the near-electroneutrality of the dialkylacetal substituent

The structures of the (benzene dialkylacetal)tricarbonyl chromium complexes [⁶-C₆H₅-CH(OR)₂]Cr(CO)₆ (R=Me,1; Et,2), are reported. The compounds were examined as part of a study of the conformations of the tripodal tricarbonylchromium group. For [⁶-C₆H₅-CH(OMe)₂]Cr(CO)₃,1, monoclinic,P2₁/c (# 14),a=15.235(1) Å,b=6.5304(5) Å,c=12.702 Å, =103.197(1)^o,Z=4. For [⁶-C₆H₅-CH(OEt)₂]Cr(CO)₃,2, monoclinic,P2₁/c (# 14),a=9.859(3) Å,b=10.547(3) Å,c=15.138(3) Å, =108.42(2)^o,Z=4. The data show that the molecules adopt the expected three-legged piano stool structure. The carbonyl ligands in1 adopt an eclipsed arrangement with respect to the arene ring and its substituent, while those in2 are staggered. These conformations are consistent with the notion that the acetal substituent behaves largely as an electroneutral group, or at most as a weak electronic acceptor.     

Transition Metal Complexes of p-Sulfonatocalix[5]arene

The X-ray crystal structure of the p-sulfonatocalix[5]arene(5)(-) anion (1b) in the form of the dimeric hydrate Na(10)[p-sulfonatocalix[5]arene](2).33.5H(2)O (2) is reported. The reactions of 1b with a number of transition metal salts to form transition metal bridged bis(calixarene) inclusion complexes have also been investigated. The X-ray crystal structure of the "Co(H(2)O)(4)(2+)" bridged species Na(8)[Co(H(2)O)(4)(p-sulfonatocalix[5]arene)(2)].2CH(3)C(O)N(CH(3))(2).37H(2)O (3) which incorporates a "supercavity" large enough to encompass 2 N,N-dimethylacetamide (dma) guest molecules as well as ca. 15 water molecules and Na(+) ions is reported. Crystal data are as follows: for 2, monoclinic space group P2(1)/c, Z = 4, a = 22.0644(4), b = 19.1180(3), c = 27.7834(4) ?, beta = 91.780(1), V = 11714.1(5) ?(3); complex 3, orthorhombic space group Pnma, Z = 4, a = 22.2271(5), b = 30.1693(6), c = 18.8503(4) ?, V = 12640.6(5) ?(3).