Superized Troesch complexes and cohomology for strict polynomial superfunctors

We adapt a construction due to Troesch to the category of strict polynomial superfunctors in order to construct complexes of injective objects whose cohomology is isomorphic to Frobenius twists of the (super)symmetric power functors. We apply these complexes to construct injective resolutions of the even and odd Frobenius twist functors, to investigate the structure of the Yoneda algebra of the Frobenius twist functor, and to compute other extension groups between strict polynomial superfunctors. By an equivalence of categories, this also provides cohomology calculations in the category of left modules over Schur superalgebras.     

Bilimits are bifinal objects

We prove that a (lax) bilimit of a 2-functor is characterized by the existence of a limiting contraction in the 2-category of (lax) cones over the diagram. We also investigate the notion of bifinal object and prove that a (lax) bilimit is a limiting bifinal object in the 2-category of (lax) cones. Everything is developed in the context of marked 2-categories, so that the machinery can be applied to different levels of laxity, including pseudo-limits.     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

Frobenius distributions of elliptic curves in short intervals on average

The Ramanujan Journal - For an elliptic curve $$E/{\mathbb {Q}}$$ , let $$a_p$$ denote the trace of its Frobenius endomorphism over $${\mathbb {F}}_p$$ , where p is a prime of good reduction for E....     

Generalized motion by mean curvature as a macroscopic limit of stochastic ising models with long range interactions and Glauber dynamics

We study themacroscopic limit of an appropriately rescaledstochastic Ising model withlong range interactions evolving withGlauber dynamics as well as the correspondingmean field equation, which is nonlinear and nonlocal. In the limit we obtain an interface evolving with normal velocity k, wherek isthe mean curvature and thetransport coefficient is identified by aneffective Green-Kubo type formula. The above assertions are valid for all positive times, the motion of the interface being interpreted in theviscosity sense after the onset of the geometric singularities.Supported by ONRPartially supported by NSF, ARO, ONR and the Alfred P. Sloan Foundation     

Best interpolation in seminorm with convex constraints

Implicit and explicit characterizations of the solutions to the following constrained best interpolation problem $$\min \left\{ {\left\| {Tx - z} \right\|:x \in C \cap A^{ - 1} d} \right\}$$ are presented. Here,T is a densely-defined, closed, linear mapping from a Hilbert spaceX to a Hilbert spaceY, A: X→Z is a continuous, linear mapping withZ a locally, convex linear topological space,C is a closed, convex set in the domain domT ofT, andd∈AC. For the case in whichC is a closed, convex cone, it is shown that the constrained best interpolation problem can generally be solved by finding the saddle points of a saddle function on the whole space, and, if the explicit characterization is applicable, then solving this problem is equivalent to solving an unconstrained minimization problem for a convex function.     

Metastable fluid flow described via a discrete-velocity coagulation-fragmentation model

A discrete-velocity Boltzmann model is introduced. It is based on two principles: (i) clusters of particles move in ³ with seven fixed momenta; (ii) clusters may gain or lose particles according to the rules of Becker-Döring cluster equations. The model provides a kinetic representation of evaporation and condensation. The model is used to obtain macroscopic fluid equations which are valid into the metastable fluid regime, , where is any positive number, is the inelastic Knudsen number, and _s is the saturation density.     

Variable-Energy Photoelectron Spectroscopy of (eta(5)-C(5)H(5))NiNO: Molecular Orbital Assignment and Xalpha-SW Calculations

Variable-energy valence and inner-valence photoelectron spectra have been recorded for the CpNiNO complex (Cp = eta(5)-C(5)H(5)) between 21.2 and 100 eV, using He I radiation and synchrotron radiation. The ground state electronic structure has been calculated by using the Xalpha-SW method. Photoionization cross sections (sigma) have also been calculated for the valence ionizations using the Xalpha-SW method. The theoretical branching ratios (sigma(i)/ summation operatorsigma) have been compared with the observed branching ratios (A(i)()/ summation operatorA) between 21.2 and 100 eV. The assignment of the photoelectron spectrum based on the analysis of intensity variations and width of vibrational peaks is consistent with the ion state orbital ordering 5e(1)(1) < 7a(1)(2) < 3e(2)(3) < 4e(1)(4) (band numbers are in parentheses) and is inconsistent with another recently proposed ordering 5e(1)(1), 5e(1)(2) < 7a(1), 3e(2)(3) < 4e(1)(4), which takes the 5e(1) vibronic effects into consideration. The experimental branching ratio results indicate a Ni 3p resonance effect around 75 eV in the photoionization process. The inner-valence spectrum has also been assigned with the aid of the Xalpha-SW calculations.     

Synthetic surfaces for ribonuclease adsorption

Intact RNA and DNA are of central importance to biochemical research and biotechnology. The preservation of these nucleic acids requires the absence of nuclease activity. Here, radical-mediated polymerization of vinylsulfonate on resin and glass surfaces is shown to produce a high-density poly(vinylsulfonate) coating that sequesters ribonucleases from aqueous solutions quickly and completely. The adsorptive efficacy of this coating exceeds that of other known coatings by > or =10(7)-fold. Surfaces coated with poly(vinylsulfonate) could be used to maintain the integrity of ribonucleic acids in a variety of contexts.