Directed triangles in directed graphs

We show that each directed graph (with no parallel arcs) on n vertices, each with indegree and outdegree at least n/twhere t=2.888997… contains a directed circuit of length at most 3.     

Novel scaling behavior of directed polymers: Disorder distribution with long tails

We study the problem of directed polymers (DP) on a square lattice. The distribution of disorder is assumed to be independent but non-Gaussian. We show that for distributions with a power-law tailP() 1/||¹⁺ , where>2, so that the mean and variance are well defined, the scaling exponentv of the DP model depends on in a continuous fashion.     

Directed polymers in Hartree-Fock approximation

A replica trick is used to map the problem of directed polymers into a quantum mechanics problem ofn-body bound states. This bound-state problem is then treated using a self-consistent method of Hartree-Fock. Ford=2, the exact result of the DP exponents is reproduced; and for complex DP, the ground-state energyE _n n² is found, confirming previous numerical results.     

Nonuniversality and analytical continuation in moments of directed polymers on hierarchical lattices

We prove the moments of the directed polymer partition function GZ, using an exact position space renormalization group scheme on a hierarchical lattice. After sufficient iteration the characteristic functionf(n)=lnGZⁿ of the probability (Z) converges to a stable limitf ^*(n). For smalln the limiting behavior is independent of the initial distribution, while for largen,f ^*(n) is completely determined by it and is thus nonuniversal. There is a smooth crossover between the two regimes for small effective dimensions, and the nonlinear behavior of the small moments can be used to extract information on the universal scaling properties of the distribution. For large effective dimensions there is a sharp transition between the two regimes, and analytical continuation from integer moments ton0 is not possible. Replica arguments can account for most features of the observed results.     

Application of directed metalation in synthesis. Part 7: Synthesis of suitably functionalised benzo[b]thiophenes as key intermediates in the synthesis of benzothienopyranones

One-pot syntheses of (3-hydroxybenzo[b]thiophen-2-yl) aryl methanones from ortho-methylsulfanylaryl N,N-diethyl amides and of 1-(3-hydroxybenzo[b]thiophen-2-yl)ethanone and 1-(3-hydroxybenzo[b]thiophen-2-yl)propan-1-one via an anionic ortho-Fries rearrangement are described. The hydroxy ketones were used as key intermediates in the synthesis of benzothienopyranones.     

Two improved formulations for the minimum latency problem

In network problems, latency is associated with the metric used to evaluate the length of the path from a root vertex to each vertex in the network. In this work we are dealing with two applications or variations of the minimum latency problem known as the repairman problem and the deliveryman problem. We have developed two integer formulations for the minimum latency problem and compared them with other two formulations from the literature for the time-dependent traveling salesman problem. The present work highlights the similarities and differences between the different formulations. In addition, we discuss the convenience of including a set of constraints in order to reduce the computation time needed to reach the optimal solution. We have carried out extensive computational experimentation on asymmetrical instances, since they provide the characteristics of the deliveryman and repairman problems in a better way.     

Complete Photochromic Structural Changes in Ruthenium(II)?Diimine Complexes,Based on Control of the Excited States by Metalation

The thermal and photochemical reactions of a newly synthesized complex, [Ru^II(TPA)(tpphz)]²⁺ ( 1 ; TPA=tris(2‐pyridylmethyl)amine, tpphz=tetrapyrido[3,2‐a:2′,3′‐c:3′′,2′′‐h: 2′′′,3′′′‐j]phenazine), and its derivatives have been investigated. Heating a solution of complex 1 (closed form) and its derivatives in MeCN caused the partial dissociation of one pyridylmethyl moiety of the TPA ligand and the resulting vacant site on the Ru^II center was occupied by a molecule of MeCN from the solvent to give a dissociated complex, [Ru^II(η³‐TPA)(tpphz)(MeCN)]²⁺ ( 1′ , open form), and its derivatives, respectively, in quantitative yields. The thermal dissociation reactions were investigated on the basis of kinetics analysis, which indicated that the reactions proceeded through a seven‐coordinate transition state. Although the backwards reaction was induced by photoirradiation of the MLCT absorption bands, the photoreaction of complex 1′ reached a photostationary state between complexes 1 and 1′ and, hence, the recovery of complex 1 from complex 1′ was 67 %. Upon protonation of complex 1 at the vacant site of the tpphz ligand, the efficiency of the photoinduced recovery of complex 1 +H⁺ from complex 1′ +H⁺ improved to 83 %. In contrast, dinuclear μ‐tpphz complexes 2 and 3 , which contained the Ru^II(TPA)(tpphz) unit and either a Ru^II(bpy)₂ or Pd^IICl₂ moiety on the other coordination edge of the tpphz ligand, exhibited 100 % photoconversion from their open forms into their closed forms ( 2′ → 2 and 3′ → 3 ). These results are the first examples of the complete photochromic structural change of a transition‐metal complex, as represented by complete interconversion between its open and closed forms. Scrutinization by performing optical and electrochemical measurements allowed us to propose a rationale for how metal coordination at the vacant site of the tpphz ligand improves the efficiency of photoconversion from the open form into the closed form. It is essential to lower the energy level of the triplet metal‐to‐ligand charge‐transfer excited state (³MLCT*) of the closed form relative to that of the triplet metal‐centered excited state (³MC*) by metal coordination. This energy‐level manipulation hinders the transition from the ³MLCT* state into the ³MC* state in the closed form to block the partial photodissociation of the TPA ligand.