The image of the transfer map

Archiv der Mathematik -     

\mathcal{A}(p) generators for H^*V and Singer's homological transfer

We list explicitly a minimal set of generators for the cohomology of an elementary abelian p-group, V, of rank 1 or 2, as a module over the mod p Steenrod algebra, for an odd prime p. Following Singer, we then construct a transfer map to the vector space spanned by such generators, where V now has arbitrary rank, from the homology of the Steenrod algebra. We show that this map takes images in the subspace of GL(V)-invariants and that it is an isomorphism for V having rank 1 or 2. Received June 11, 1996; in final form June 9, 1997     

Well-posedness for a class of fourth order diffusions for image processing

A number of image denoising models based on higher order parabolic partial differential equations (PDEs) have been proposed in an effort to overcome some of the problems attendant to second order methods such as the famous Perona–Malik model. However, there is little analysis of these equations to be found in the literature. In this paper, methods of maximal regularity are used to prove the existence of unique local solutions to a class of fourth order PDEs for noise removal. The proof is laid out explicitly for two newly proposed fourth order models, and an outline is given for how to apply the techniques to other proposed models.     

A simple proof of Singer's representation theorem

Let be a compact Hausdorff space and a Banach space. Singer's theorem states that under the dual pairing , the dual space of is isometric to . Using the Hahn-Banach theorem and the (scalar) Riesz representation theorem, a proof of Singer's theorem is given which appears to be simpler than the proofs supplied earlier by Singer (1957, 1959) and Dinculeanu (1959, 1967).

     

Well-posedness for a fourth order nonlinear equation related to image processing

Using the entropy estimates in Min et al. (2013), we establish the global existence and uniqueness of solutions to a fourth order equation related to image processing. Some numerical results on the Lena image are also presented to show the effectiveness of the equation for noise removal.     

The influence of Hall current and heat transfer on the flow of a fourth grade fluid

In this article, a mathematical model is analyzed to investigate the effects of Hall current and heat transfer on the flow of a fourth grade fluid between two heated and rotating disks. The corresponding problem of velocity and temperature are solved analytically by homotopy analysis method. Comparison is given between the results of velocity in fourth grade, third grade, second grade, and viscous fluids. The variation of pertinent parameters are graphed and discussed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Affine Versions of Singer's Theorem on Locally Homogeneous Spaces

A theorem of Singer says that an infinitesimaly homogeneous Riemannian manifold is locally homogeneous. We propose two result on affine connections similar to the theorem of Singer. As an application we prove a theorem giving a sufficient condition for local homogeneity in case of affine connections on 2-dimensional manifolds.     

Counter-example to the “Second Singer's theorem”

We give an explicit example showing that a theorem by I. M. Singer announced in [3] (about the existence of a Riemannian homogeneous space with the prescribed curvature tensor and some of its covariant derivatives) cannot hold without an additional topological condition of closeness.All references in this short note concern Chapter 3 of the paper by L. Nicolodi and F. Tricerri [2] published in the same volume. We shall use freely the concepts and formulas from there.Consider the infinitesimal model (V,T,K) given as follows: LetV be a 5-dimensional     

Strengthening of Singer's result on absence of global gauge fixing

P. N. Lebedev Physics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 78, No. 2, pp. 163–176, February, 1989.     

The fourth power of the Fermat quotient

Let p be an odd prime and qp(a)=(ap−1−1)/p be the Fermat quotient with base a, p?a. The main purpose of this paper is to investigate the fourth power problem of qp(2) and deduce an explicit formula represented by a linear combination of Mirimanoff polynomial values.     

The long time behavior of fourth order curvature flows

We show precompactness results for solutions to parabolic fourth order geometric evolution equations. As part of the proof we obtain smoothing estimates for these flows in the presence of a curvature bound, an improvement on prior results which also require a Sobolev constant bound. As consequences of these results we show that for any solution with a finite time singularity, the L ^∞ norm of the curvature must go to infinity. Furthermore, we characterize the behavior at infinity of solutions with bounded curvature.     

The Bernstein theorem for a class of fourth order equations

In this paper, we prove the 2-dimensional Bernstein theorem for a class of fourth order equations including Abreu’s equation. The main ingredients of the paper are the a priori estimates and the proof of the strict convexity.     

The determinants of fourth order dissipative operators with transmission conditions

In this paper, discontinuous non-self-adjoint differential operators in Weyl?s limit circle are studied. We give the determinant of perturbation connected with the dissipative operator L   generated by fourth order differential expression in L²(I)$L^2(I)$, where discontinuity of operator is dealt with transmission conditions. We obtain the Green?s function, then, using characteristic determinant, we prove the completeness of the system of eigenfunctions and associated functions of this dissipative operator.     

Efficient fourth orderP-stable formulae

In this paper, a family of fourth orderP-stable methods for solving second order initial value problems is considered. When applied to a nonlinear differential system, all the methods in the family give rise to a nonlinear system which may be solved using a modified Newton method. The classical methods of this type involve at least three (new) function evaluations per iteration (that is, they are 3-stage methods) and most involve using complex arithmetic in factorising their iteration matrix. We derive methods which require only two (new) function evaluations per iteration and for which the iteration matrix is a true real perfect square. This implies that real arithmetic will be used and that at most one real matrix must be factorised at each step. Also we consider various computational aspects such as local error estimation and a strategy for changing the step size.