Optimal stopping-time problem for stochastic Navier–Stokes equations and infinite-dimensional variational inequalities

We prove the existence of a solution for the obstacle problem associated with the Kolmogorov operator corresponding to the stopping-time problem for stochastic Navier–Stokes equations in 2-D.     

Bellman equations associated to the optimal feedback control of stochastic Navier‐Stokes equations

In this paper we study infinite‐dimensional, second‐order Hamilton‐Jacobi‐Bell‐man equations associated to the feedback synthesis of stochastic Navier‐Stokes equations forced by space‐time white noise. Uniqueness and existence of viscosity solutions are proven for these infinite‐dimensional partial differential equations. © 2005 Wiley Periodicals, Inc.     

Synthesis, characterisation and antitubercular activities of a series of pyruvate-containing aroylhydrazones and their Cu-complexes

A series of eight pyruvate-based aroylhydrazones was synthesised and characterised. The reaction of the sodium salts of the aroylhydrazones with one equivalent of copper(II) chloride allowed the isolation of neutral 1:1 complexes in which the hydrazones occupy three basal coordination sites of a square pyramidal Cu(II)-centre, with two solvent molecules completing the coordination sphere. Structural details were obtained through the determination of the crystal structures of two representative pyruvate-based aroylhydrazones and three Cu(II) complexes. The evaluation of the antimycobacterial activity of the sodium salts of the eight pryruvate hydrazones showed that the compounds are essentially inactive in their anionic form. The corresponding neutral Cu(II) complexes, however, exhibit promising antimycobacterial activities if tested under high iron (8 μg Fe per mL) conditions. As observed for the related antimycobacterial agent isoniazid, the activity of the complexes decreases if the M. tuberculosis cells are grown under low iron (0.02 μg Fe per mL) conditions. The Cu(II) complexes may thus have a similar mode of action and may require an iron-containing heme-dependent peroxidase for activation.     

Finding a Sun in Building-Free Graphs

Deciding whether an arbitrary graph contains a sun was recently shown to be NP-complete (Hoàng in SIAM J Discret Math 23:2156–2162, 2010). We show that whether a building-free graph contains a sun can be decided in O(min{mn ³, m ^1.5 n ²}) time and, if a sun exists, it can be found in the same time bound. The class of building-free graphs contains many interesting classes of perfect graphs such as Meyniel graphs which, in turn, contains classes such as hhd-free graphs, i-triangulated graphs, and parity graphs. Moreover, there are imperfect graphs that are building-free. The class of building-free graphs generalizes several classes of graphs for which an efficient test for the presence of a sun is known. We also present a vertex elimination scheme for the class of (building, gem)-free graphs. The class of (building, gem)-free graphs is a generalization of the class of distance hereditary graphs and a restriction of the class of (building, sun)-free graphs.     

Maximum induced matching problem on hhd-free graphs

We show that the maximum induced matching problem can be solved on hhd-free graphs in O(m²) time; hhd-free graphs generalize chordal graphs and the previous best bound was O(m³). Then, we consider a technique used by Brandstädt and Hoàng (2008) [4] to solve the problem on chordal graphs. Extending this, we show that for a subclass of hhd-free graphs that is more general than chordal graphs the problem can be solved in linear time. We also present examples to demonstrate the tightness of our results.     

Disjoint clique cutsets in graphs without long holes

A biclique cutset is a cutset that induces the disjoint union of two cliques. A hole is an induced cycle with at least five vertices. A graph is biclique separable if it has no holes and each induced subgraph that is not a clique contains a clique cutset or a biclique cutset. The class of biclique separable graphs contains several well‐studied graph classes, including triangulated graphs. We prove that for the class of biclique separable graphs, the recognition problem, the vertex coloring problem, and the clique problem can be solved efficiently. Our algorithms also yield a proof that biclique separable graphs are perfect. Our coloring algorithm is actually more general and can be applied to graphs that can be decomposed via a special type of biclique cutset. Our algorithms are based on structural results on biclique separable graphs developed in this paper. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 277–298, 2005     

Ergodicity for the 3D stochastic Navier–Stokes equations perturbed by Lévy noise

In this work we construct a Markov family of martingale solutions for 3D stochastic Navier–Stokes equations (SNSE) perturbed by Lévy noise with periodic boundary conditions. Using the Kolmogorov equations of integrodifferential type associated with the SNSE perturbed by Lévy noise, we construct a transition semigroup and establish the existence of a unique invariant measure. We also show that it is ergodic and strongly mixing.     

Viscosity Solutions of Dynamic-Programming Equations for the Optimal Control of the Two-Dimensional Navier-Stokes Equations

In this paper we study the infinite-dimensional Hamilton-Jacobi equation associated with the optimal feedback control of viscous hydrodynamics. We resolve the global unique solvability problem of this equation by showing that the value function is the unique viscosity solution.     

Nonlinear finite element analyses of concrete bridge joint systems subjected to seismic actions

Following widespread damage to bridge joints in the San Francisco region from the 1989 Loma Prieta earthquake, the necessity for establishing an alternative method for seismic design of bridge joints was identified. Recognizing that conventional joint design practice based directly on shear forces results in congested reinforcement details, which are difficult to implement in practice, a rational design procedure was sought through large-scale testing of bridge joint systems and subsequent finite element and strut-and-tie analyses. The finite element part of the study is presented in this paper, which focuses on (a) identification of compression force flow and thus the load path across the joint, (b) examination of an efficient joint force transfer model, and (c) influence of cap beam prestressing. Combining the experimental and analytical results, a joint design method has been established in which reduction of joint reinforcement was achieved by treating joint shear as part of the complete force transfer across the joint, rather than as an independent action. The proposed design approach has been validated in a laboratory test on a full-scale multiple-column bridge bent.