Matrix pencils and existence conditions for quadratic programming with a sign-indefinite quadratic equality constraint

We consider minimization of a quadratic objective function subject to a sign-indefinite quadratic equality constraint. We derive necessary and sufficient conditions for the existence of solutions to the constrained minimization problem. These conditions involve a generalized eigenvalue of the matrix pencil consisting of a symmetric positive-semidefinite matrix and a symmetric indefinite matrix. A complete characterization of the solution set to the constrained minimization problem in terms of the eigenspace of the matrix pencil is provided.     

A review of silicon and silicone determination in tissue and body fluids – a need for standard reference materials

The role of Si in nature is briefly described, especially the toxic properties of inorganic and organic Si for humans. The use of different forms of silicones in medicine and food industry is noted and potential consequences of their use are discussed. Since Si is an essential trace element there is need for establishment of the “normal” level of Si in blood, other body fluids and tissues and development of speciation of Si forms in biological samples. Numerous difficulties in the determination of Si are described and the need for SRM is stressed. The results of the determination of Si in blood of patients with Si breast implants and controls, Si in milk and blood of nursing mothers – with and without Si breast implants and extractable Si in capsules – are summarized. The obtained data reinforce the need for a reliable SRM.     

Spectral density analysis of the chiral transition in nf=4 finite temperature QCD

We apply the spectral density reweighting technique to the analysis of the chiral phase transition in finite-temperature lattice quantum chromodynamics (QCD) with four flavors of dynamical staggered fermions and m_qa=0.025. Our simulations were performed using the hybrid Monte Carlo method for L_tL³ lattices with L_t=4 and L=6, 8 and 10. We calculate partition function zeros, as well as the maxima of the specific heat and of the susceptibilities for the Polyakov loop and for the chiral condensate. A finite size scaling analysis of these data leads to preliminary results for the critical coupling β_c, for the critical exponent ν, for the latent heat, and for the jumps in the Polyakov loop and in the chiral condensate.     

Some uses of Green's theorem in solving the Navier–Stokes equations

This paper gives a review of methods where Green's theorem may be employed in solving numerically the Navier–Stokes equations for incompressible fluid motion. They are based on the concept of using the theorem to transform local boundary conditions given on the boundary of a closed region in the solution domain into global, or integral, conditions taken over it. Two formulations of the Navier–Stokes equations are considered: that in terms of the streamfunction and vorticity for two-dimensional motion and that in terms of the primitive variables of the velocity components and the pressure. In the first formulation overspecification of conditions for the streamfunction is utilized to obtain conditions of integral type for the vorticity and in the second formulation integral conditions for the pressure are found. Some illustrations of the principle of the method are given in one space dimension, including some derived from two-dimensional flows using the series truncation method. In particular, an illustration is given of the calculation of surface vorticity for two-dimensional flow normal to a flat plate. An account is also given of the implementation of these methods for general two-dimensional flows in both of the mentioned formulations and a numerical illustration is given.     

Book review

The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions , Bruce Sagan, Chapman & Hall, London, 1991, xv+197 pages. ISBN 0-534-15540-5(59.95 US)     

Some Consequences of the Nature of the Distance Function on the Cut Locus in a Riemannian Manifold

We render the cut locus more accessible to analysis by showingthat each non-conjugate cut point has a neighbourhood on whichthe distance function is the minimum of finitely many smooth‘radial functions’. This enables us to generaliseto an arbitrary complete manifold a number of recent results,mainly from stochastic analysis, which were either limited ornot valid on the cut locus because of the lack of differentiabilitythere of the distance function.     

Biopolymer mimicry with polymeric wormlike micelles: Molecular weight scaled flexibility,locked-in curvature,and coexisting microphases

Giant and stable wormlike micelles formed in water from a series of poly(ethylene oxide) (PEO)-based diblock copolymer amphiphiles mimicked the flexibility of various cytoskeletal filaments. The worm diameter (d) was found by cryo-transmission electron microscopy to scale with the length of the hydrophobic chain (N_h) of the copolymer as d ∼ N_h^0.61. By fluorescence video imaging of worm dynamics, we also showed that the persistence length (l_P) of wormlike micelles scaled as l_P ∼ d^2.8, consistent with a fluid aggregate (∼d³) rather than a solid rod (∼d⁴). By polymerizing the unsaturated bonds of assembled copolymers, fluid worms were converted to solid-core worms, extending the bending rigidity from that of intermediate filament biopolymers to actin filaments and, in principle, microtubules. Through partial crosslinking, polymerized worms further locked in spontaneous curvature at a novel fluid-to-solid percolation point. The dynamics of distinct, branched conformations were also imaged for recently discovered Y-junctioned wormlike micelles composed of diblocks of high molecular weight (>10–15 kg/mol). Finally, block copolymers of hydrophilic weight fraction close to the transition between a vesicle- and worm-former assembled into both structures, allowing encapsulation of wormlike micelles in giant vesicles reminiscent of cytoskeletal filaments enclosed within cells. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 168–176, 2004