Heteroaryl substituted ansa‐titanocene anti‐cancer drugs derived from fulvenes and titanium dichloride

Starting from 2‐furylfulvene (1a) , 2‐thiophenylfulvene (1b) , and 1‐methyl‐2‐pyrrolylfulvene (1c), [1,2‐di(cyclopentadienyl)‐1,2‐di‐(2‐furyl)ethanediyl] titanium dichloride (2a) , [1,2‐di(cyclopentadienyl)‐1,2‐di‐(2‐thiophenyl)ethanediyl] titanium dichloride (2b) , and [1,2‐di(cyclopentadienyl)‐1,2‐bis‐(1‐methyl‐2‐pyrrolyl)ethanediyl] titanium dichloride (2c) were synthesized. When titanocenes (2a–c) were tested against pig kidney carcinoma cells (LLC‐PK), inhibitory concentrations (50%) of 4.5 × 10^?4 M , 2.9 × 10^?4 M and 2.0 × 10^?4 M respectively were observed. Copyright © 2005 John Wiley & Sons, Ltd.     

On the Floer homology of cotangent bundles

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T* M of a compact orientable manifold M. The first result is a new L^∞ estimate for the solutions of the Floer equation, which allows us to deal with a larger—and more natural—class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Floer homology and the singular homology of the free loop space of M in the periodic case, or of the based loop space of M in the Lagrangian intersection problem. The idea for the construction of such an isomorphism is to consider a Hamiltonian that is the Legendre transform of a Lagrangian on T M and to construct an isomorphism between the Floer complex and the Morse complex of the classical Lagrangian action functional on the space of W^1,2 free or based loops on M. © 2005 Wiley Periodicals, Inc.     

The Galois representations associated to a Drinfeld module in special characteristic—III: Image of the group ring

Let K be a finitely generated field of transcendence degree 1 over a finite field, and set G_K?Gal(K^sep/K). Let φ be a Drinfeld A-module over K in special characteristic. Set E?End_K(φ) and let Z be its center. We show that for almost all primes p of A, the image of the group ring A_p[G_K] in End_A(T_p(φ)) is the commutant of E. Thus, for almost all p it is a full matrix ring over Z⊗_AA_p. In the special case E=A it follows that the representation of G_K on the p-torsion points φ[p] is absolutely irreducible for almost all p.     

On the complexity of recognizing perfectly orderable graphs

The question whether a polynomial time recognition algorithm for the class of perfectly orderable graphs exists was posed by Chvátal in 1981 when he introduced the notion of perfect orders. Since then several classes of perfectly orderable graphs have been identified. In this note we prove that recognizing perfectly orderable graphs is NP-complete.     

Protein side chains facilitate Mg/Al exchange in model protein binding sites.

Among the most frequent protein binding sites served by Mg(II), we identify those which have higher affinity towards Al(III). We also estimate the free energies of metal exchange for all these binding sites taking into account solvent effects explicitly. The obtained results show that thermodynamically favored Mg(II)/Al(III) exchange reactions take place at a number of these metal binding sites, which could possibly be related to some dysfunctions of Mg(II)-dependent biological processes. Additionally, they shed light on the molecular basis of the toxicity of Al(III) in living organisms.     

On the cardinality of the Pareto set in bicriteria shortest path problems

Computing shortest paths with two or more conflicting optimization criteria is a fundamental problem in transportation and logistics. We study the problem of finding all Pareto-optimal solutions for the multi-criteria single-source shortest-path problem with nonnegative edge lengths. The standard approaches are generalizations of label-setting (Dijkstra) and label-correcting algorithms, in which the distance labels are multi-dimensional and more than one distance label is maintained for each node. The crucial parameter for the run time and space consumption is the total number of Pareto optima. In general, this value can be exponentially large in the input size. However, in various practical applications one can observe that the input data has certain characteristics, which may lead to a much smaller number—small enough to make the problem efficiently tractable from a practical viewpoint. For typical characteristics which occur in various applications we study in this paper whether we can bound the size of the Pareto set to a polynomial size or not. These characteristics are also evaluated (1) on a concrete application scenario (computing the set of best train connections in view of travel time, fare, and number of train changes) and (2) on a simplified randomized model. It will turn out that the number of Pareto optima on each visited node is restricted by a small constant in our concrete application, and that the size of the Pareto set is much smaller than our worst case bounds in the randomized model. A preliminary short version of this paper appeared in the Proceedings of the 5th Workshop on Algorithm Engineering (WAE 2001), LNCS 2141, Springer Verlag, pp. 185–197 (2001) under the title “Pareto shortest paths is often feasible in practice.”