On the Hartshorne-Speiser-Lyubeznik theorem about Artinian modules with a Frobenius action

Let be a commutative Noetherian local ring of prime characteristic. The purpose of this paper is to provide a short proof of G. Lyubeznik's extension of a result of R. Hartshorne and R. Speiser about a module over the skew polynomial ring (associated to and the Frobenius homomorphism , in the indeterminate ) that is both -torsion and Artinian over .

     

Graded annihilators of modules over the Frobenius skew polynomial ring, and tight closure

This paper is concerned with the tight closure of an ideal in a commutative Noetherian local ring of prime characteristic . Several authors, including R. Fedder, K-i. Watanabe, K. E. Smith, N. Hara and F. Enescu, have used the natural Frobenius action on the top local cohomology module of such an to good effect in the study of tight closure, and this paper uses that device. The main part of the paper develops a theory of what are here called `special annihilator submodules' of a left module over the Frobenius skew polynomial ring associated to ; this theory is then applied in the later sections of the paper to the top local cohomology module of and used to show that, if is Cohen-Macaulay, then it must have a weak parameter test element, even if it is not excellent.

     

Hermite–Birkhoff–Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size

A four-stage Hermite–Birkhoff–Obrechkoff method of order 14 with four quantized variable steps, denoted by HBOQ(14)4, is constructed for solving non-stiff systems of first-order differential equations of the form y^′=f(t,y)$y^{\prime }=f(t,y)$ with initial conditions y(_t0)=_y0$y\left(t_0\right)=y_0$. Its formula uses y^′$y^{\prime }$, y^″$y^{″}$ and y^?$y^{?}$ as in Obrechkoff methods. Forcing a Taylor expansion of the numerical solution to agree with an expansion of the true solution leads to multistep- and Runge–Kutta-type order conditions which are reorganized into linear Vandermonde-type systems. To reduce overhead, simple formulae are derived only once to obtain the values of Hermite–Birkhoff interpolation polynomials in terms of Lagrange basis functions for 16 quantized step size ratios. The step size is controlled by a local error estimator. When programmed in C ++, HBOQ(14)4 is superior to the Dormand–Prince Runge–Kutta pair DP(8,7)13M of order 8 in solving several problems often used to test higher order ODE solvers at stringent tolerances. When programmed in Matlab, it is superior to ode113 in solving costly problems, on the basis of the number of steps, CPU time, and maximum global error. The code is available on the URL www.site.uottawa.ca/~remi.     

Chaos,transport and mesh convergence for fluid mixing

Chaotic mixing of distinct fluids produces a convoluted structure to the interface separating these fluids. For miscible fluids （as considered here）, this interface is defined as a 50% mass concentration isosurface. For shock wave induced （Richtmyer-Meshkov） instabilities, we find the interface to be increasingly complex as the computational mesh is refined. This interfacial chaos is cut off by viscosity, or by the computational mesh if the Kolmogorov scale is small relative to the mesh. In a regime of converged interface statistics, we then examine mixing, i.e. concentration statistics, regularized by mass diffusion. For Schmidt numbers significantly larger than unity, typical of a liquid or dense plasma, additional mesh refinement is normally needed to overcome numerical mass diffusion and to achieve a converged solution of the mixing problem. However, with the benefit of front tracking and with an algorithm that allows limited interface diffusion, we can assure convergence uniformly in the Schmidt number. We show that different solutions result from variation of the Schmidt number. We propose subgrid viscosity and mass diffusion parameterizations which might allow converged solutions at realistic grid levels.     

Asymptotic Expansions for Closed Orbits in Homology Classes

In this paper, we study the behaviour of the counting function associated to the closed geodesics lying in a prescribed homology class on a compact negatively curved manifold. Our main result is an asymptotic expansion. We also obtain results in the wider context of periodic orbits of Anosov flows.     

A conservative formulation for plasticity

In this paper we propose a fully conservative form for the continuum equations governing rate-dependent and rate-independent plastic flow in metals. The conservation laws are valid for discontinuous as well as smooth solutions. In the rate-dependent case, the evolution equations are in divergence form, with the plastic strain being passively convected and augmented by source terms. In the rate-independent case, the conservation laws involve a Lagrange multiplier that is determined by a set of constraints; we show that Riemann problems for this system admit scale-invariant solutions.     

On the photoisomerization of the benzisothiazole portion of ziprasidone

Photostability challenge of ziprasidone in solution shows that the benzisothiazole moiety undergoes isomerization to the corresponding benzthiazole. A model compound, 3-piperazinyl-1,2-benzisothiazole, also undergoes this photoisomerization. Identification of the products has been confirmed by synthesis of the proposed molecules.     

A rapid method for calculating derivatives of solvent accessible surface areas of molecules

A novel method to calculate the derivatives of solvent accessible surface areas is presented. Unlike earlier analytic methods, which require the molecular topology and the use of global Gauss-Bonnet theorem, this method requires only the fractional accessibilities of surface arcs. We developed an efficient numerical algorithm to calculate the surface arcs by creating a uniform set of points on the circles of intersection between surface atoms. A hierarchical point density doubling scheme led to a logarithmic dependence of Central Processing Unit (CPU) time on the number of points used. This algorithm calculated area derivatives for a 1000-atom protein in 1.5 s on an SGI INDIGO² which were within 2% of the analytic area derivatives calculated with the program ANAREA. This algorithm scales linearly with the number of atoms for large molecules and is easily parallelizable. © 1995 by John Wiley & Sons, Inc.