Nonadditive Shortest Paths: Subproblems in Multi-Agent Competitive Network Models

A variety of different multi-agent (competitive) network models have been described in the literature. Computational techniques for solving such models often involve the iterative solution of shortest path subproblems. Unfortunately, the most theoretically interesting models involve nonlinear cost or utility functions and they give rise to nonadditive shortest path subproblems. This paper both describes some basic existence and uniqueness results for these subproblems and develops a heuristic for solving them.     

Maximal transitive sets with singularities for genericC 1 vector fields

A transitive set of a vector fieldX ismaximal transitive if it contains every transitive set ofX intersecting it. We shall prove that ifX isC ¹ generic then every singularity ofX with either only one positive or only one negative eigenvalue belongs to a maximal transitive set ofX. In particular, we characterize maximal transitive sets with singularities for genericC ¹ vector fields on closed 3-manifolds in terms of homoclinic classes associated to a unique singularity. We apply our results to the examples introduced in [3] and [15].This work is partially supported by CNPq 001/2000, FAPERJ and PRONEX/Dynamical Systems, FINEP-CNPq.     

Differentiable structures with zero entropy on simply connected 4-manifolds

We show that a closed 4-dimensional simply connected topological manifoldM admits a differentiable structure with aC Riemannian metric whose geodesic flow has zero topological entropy if and only ifM is homeomorphic toS ⁴, ²,S ²×S ², or ²#².     

Prime Non-Commutative JB*-Algebras

We prove that if A is a prime non-commutative JB*-algebra whichis neither quadratic nor commutative, then there exist a primeC*-algebra B and a real number with < 1 such that A =B as involutive Banach spaces, and the product of A is relatedto that of B (denoted by , say) by means of the equality xy= xy+(1 – )yx. 2000 Mathematics Subject Classification46K70, 46L70.     

Numerical and experimental analysis of the plasma in the synthesis of polyaniline

A numerical and experimental study of the plasma variables in the synthesis of polyaniline in radio‐frequency (RF) glow discharges is presented. The plasma variables were measured on the basis of data collected by electrostatic Langmuir probes placed along the reactor. The results showed the distribution of the electric potential and the electronic energy and density during the polymerization reactions. The region with the lowest energy was the zone adjoining the grounded electrode, whereas the maximum energy was located near the RF electrode. In the second zone, the energy was around twice that of the grounded zone, and both were beyond the typical atomic bonding energy found in most organic polymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1501–1508, 2003     

Surface structure of unreconstructed W(001) from alternative leed techniques

The surface geometry of the high temperature phase W(001) is obtained by comparing relative intensities of diffraction beams at individual energies. The influence of non-structural parameters — Debye temperatures, ion core scattering potential, inner potential and incident beam angle, are examined. The results are contrasted with a comparison using conventional I(E) curve methods and a quantitative r-factor analysis. Uncertainty in the choice of non-structural parameters is shown capable of partly explaining the wide variation of results found in previous studies of this surface. The two methods are shown to give very similar results, and a surface layer contraction 6.7 ± 2% concluded.     

The shifted scheme in the general-model-space diagrammatic perturbation theory

The shifted scheme of many-body perturbation theory is applied to open-shell states within the framework of the general-model-space theory. Rules for shifting the denominators of folded diagrams. which appear in open-shell perturbation expansions, are given. The finite-order energies in the shifted scheme obtained in two equivalent representations may differ. This happens, for instance, in the case of triplet states. For ³Σ_u⁺ states of the He₂, differences up to 0.07 mhartree have been found in third order. A similar phenomenon is the size inconsistency of the shifted scheme observed by Silver in the ground state of He₂. A possible advantage of the shifted scheme is its faster convergence for excited states.     

Direct synthesis of a polyamide by an enol phosphite and imidazole

Direct polycondensation of various dicarboxylic acids and diamines was effected under mild conditions by using an enol phosphite, diethyl 1-methyl-3-oxo-1-butenyl phosphite (I), in the presence of imidazole. To check the activity of the enol phosphite and various organic bases in an amidation reaction, the model reaction of acetic acid and aniline was carried out, and the yield of acetanilide was estimated by means of gas chromatography. Among organic bases, imidazole was the best in terms of yield of acetanilide. Polycondensation performed by varying solvents, temperature, and amount of imidazole resulted in high yields of polyamides with inherent viscosities of 0.1-0.25.