Spectrophotometric flow-injection determination of cellobiose dehydrogenase activity in fermentation samples with 2,6-dichlorophenolindophenol

Cellobiose dehydrogenase activity (0.25–1 U Ml^?1) is monitored by oxidation of cellobiose to cellobionolactone, thus reducing 2,6-dichlorophenolindophenol to a colourless compound. To prevent any β-glucosidase from reacting, gluconolactone is added as inhibitor. The sample throughput is 120 h^?1.     

Time-reversal multiple signal classification in case of noise: a phase-coherent approach

The problem of locating point-like targets beyond the classical resolution limit is revisited. Although time-reversal MUltiple SIgnal Classification (MUSIC) is known for its super-resolution ability in localization of point scatterers, in the presence of noise this super-resolution property will easily break down. In this paper a phase-coherent version of time-reversal MUSIC is proposed, which can overcome this fundamental limit. The algorithm has been tested employing synthetic multiple scattering data based on the Foldy-Lax model, as well as experimental ultrasound data acquired in a water tank. Using a limited frequency band, it was demonstrated that the phase-coherent MUSIC algorithm has the potential of giving significantly better resolved scatterer locations than standard time-reversal MUSIC.     

G-Strands

A G-strand is a map g(t,s):?×?→G for a Lie group G that follows from Hamilton’s principle for a certain class of G-invariant Lagrangians. The SO(3)-strand is the G-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, SO(3) _K -strand dynamics for ellipsoidal rotations is derived as an Euler–Poincaré system for a certain class of variations and recast as a Lie–Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the SO(3) _K -strand is mapped into a completely integrable generalization of the classical chiral model for the SO(3)-strand. Analogous results are obtained for the Sp(2)-strand. The Sp(2)-strand is the G-strand version of the Sp(2) Bloch–Iserles ordinary differential equation, whose solutions exhibit dynamical sorting. Numerical solutions show nonlinear interactions of coherent wave-like solutions in both cases. Diff(?)-strand equations on the diffeomorphism group G=Diff(?) are also introduced and shown to admit solutions with singular support (e.g., peakons).     

Cotorsion pairs associated with Auslander categories

Let N ≥ n + 1, and denote by K the convex hull of N independent standard gaussian random vectors in ℝⁿ. We prove that with high probability, the isotropic constant of K is bounded by a universal constant. Thus we verify the hyperplane conjecture for the class of gaussian random polytopes. Supported by the Clay Mathematics Institute and by NSF grant #DMS-0456590     

Torsion in the full orbifold <Emphasis Type="Italic">K</Emphasis>-theory of abelian symplectic quotients

Let (M, ω, Φ) be a Hamiltonian T-space and let H í T{H\subseteq T} be a closed Lie subtorus. Under some technical hypotheses on the moment map Φ, we prove that there is no additive torsion in the integral full orbifold K-theory of the orbifold symplectic quotient [M//H]. Our main technical tool is an extension to the case of moment map level sets the well-known result that components of the moment map of a Hamiltonian T-space M are Morse-Bott functions on M. As first applications, we conclude that a large class of symplectic toric orbifolds, as well as certain S ¹-quotients of GKM spaces, have integral full orbifold K-theory that is free of additive torsion. Finally, we introduce the notion of semilocally Delzant which allows us to formulate sufficient conditions under which the hypotheses of the main theorem hold. We illustrate our results using low-rank coadjoint orbits of type A and B.     

The Momentum Map Representation of Images

This paper discusses the mathematical framework for designing methods of Large Deformation Diffeomorphic Matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, we prove a theorem showing that these methods may be designed by using the actions of diffeomorphisms on the image data structure to define their associated momentum representations as (cotangent-lift) momentum maps. To illustrate its use, the momentum map theorem is shown to recover the known algorithms for matching landmarks, scalar images, and vector fields. After briefly discussing the use of this approach for diffusion tensor (DT) images, we explain how to use momentum maps in the design of registration algorithms for more general data structures. For example, we extend our methods to determine the corresponding momentum map for registration using semidirect product groups, for the purpose of matching images at two different length scales. Finally, we discuss the use of momentum maps in the design of image registration algorithms when the image data is defined on manifolds instead of vector spaces.     

Optimal control problems with applications to the elimination of substrate diffusing and convecting through immobilized enzyme

Some optimization problems concerning a substrate in a fluid are considered. The concentration of the substrate is affected by diffusion, convection, and elimination by enzymes, and the problem is to find the optimal distribution of enzymes. In this paper, the rate of elimination and the transmission coefficient are optimized. Mathematically, these problems are optimal control problems, and they are analyzed by means of Pontryagin's maximum principle.     

Torsion and Abelianization in Equivariant Cohomology

Let X be a topological space upon which a compact connected Lie group G acts. It is well known that the equivariant cohomology H ^* _G (X; Q) is isomorphic to the subalgebra of Weyl group invariants of the equivariant cohomology H ^* _T (X; Q), where T is a maximal torus of G. This relationship breaks down for coefficient rings k other than Q. Instead, we prove that under a mild condition on k the algebra H ^* _G (X; k) is isomorphic to the subalgebra of H ^* _T (X; k) annihilated by the divided difference operators.     

The representation dimension of domestic weakly symmetric algebras

Auslander’s representation dimension measures how far a finite dimensional algebra is away from being of finite representation type. In [1], M. Auslander proved that a finite dimensional algebra A is of finite representation type if and only if the representation dimension of A is at most 2. Recently, R. Rouquier proved that there are finite dimensional algebras of an arbitrarily large finite representation dimension. One of the exciting open problems is to show that all finite dimensional algebras of tame representation type have representation dimension at most 3. We prove that this is true for all domestic weakly symmetric algebras over algebraically closed fields having simply connected Galois coverings.     

Multiple lie-poisson structures,reductions, and geometric phases for the Maxwell-Bloch travelling wave equations

Summary The real-valued Maxwell-Bloch equations on ℝ³ are investigated as a Hamiltonian dynamical system obtained by applying an S¹ reduction to an invariant subsystem of a dynamical system on ℂ³. These equations on ℝ³ are bi-Hamiltonian and possess several inequivalent Lie-Poisson structures parametrized by classes of orbits in the group SL(2, ℝ). Each Lie-Poisson structure possesses an associated Casimir function. When reduced to level sets of these functions, the motion takes various symplectic forms, from that of the pendulum to that of the Duffing oscillator. The values of the geometric (Hannay-Berry) phases obtained in reconstructing the solutions are found to depend upon the choice of Casimir function, that is, upon the parametrization of the reduced symplectic space.