具有(F,α,ε)-G凸的分式半无限规划问题的ε-最优性

首次引入了（F,α,ε）-G凸函数,（F,α,ε）-G拟凸函数和（F,α,ε）-G伪凸函数等概念,对已有的凸函数进行了推广,研究了涉及这类函数的一类分式半无限规划的ε-最优性条件,得到了一些有意义的结果．这些结果不仅是现有某些结果的推广,而且为诸如资源分配,投资组合等问题的研究提供了依据,也为理论上研究分式规划提供了参考．     

A decomposition theorem for Herman maps

In 1980s, Thurston established a topological characterization theorem for postcritically finite rational maps. In this paper, a decomposition theorem for a class of postcritically infinite branched covering termed Herman map is developed. It's shown that every Herman map can be decomposed along a stable multicurve into finitely many Siegel maps and Thurston maps, such that the combinations and rational realizations of these resulting maps essentially dominate the original one. This result is motivated by a non-expanding version of McMullen's problem, and Thurston's theory on characterization of rational maps. It enables us to prove a Thurston-type theorem for rational maps with Herman rings.     

Computing projections with LSQR

LSQR uses the Golub-Kahan bidiagonalization process to solve sparse least-squares problems with and without regularization. In some cases, projections of the right-hand side vector are required, rather than the least-squares solution itself. We show that projections may be obtained from the bidiagonalization as linear combinations of (the-oretically) orthogonal vectors. Even the least-squares solution may be obtained from orthogonal vectors, perhaps more accurately than the usual LSQR solution. (However, LSQR has proved equally good in all examples so far.) Presented at the Cornelius Lanczos International Centenary Conference, North Carolina State University, Raleigh, NC, December 1993. Partially supported by Department of Energy grant DE-FG03-92ER25117, National Science Foundation grants DMI-9204208 and DMI-9500668, and Office of Naval Research grants N00014-90-J-1242 and N00014-96-1-0274.     

The eskolemization of universal quantifiers

This paper is a sequel to the papers Baaz and Iemhoff (2006, 2009) [4] and [6] in which an alternative skolemization method called eskolemization was introduced that, when restricted to strong existential quantifiers, is sound and complete for constructive theories. In this paper we extend the method to universal quantifiers and show that for theories satisfying the witness property it is sound and complete for all formulas. We obtain a Herbrand theorem from this, and apply the method to the intuitionistic theory of equality and the intuitionistic theory of monadic predicates.     

Dual divergence estimators and tests: Robustness results

The class of dual ?-divergence estimators (introduced in Broniatowski and Keziou (2009) [5]) is explored with respect to robustness through the influence function approach. For scale and location models, this class is investigated in terms of robustness and asymptotic relative efficiency. Some hypothesis tests based on dual divergence criteria are proposed and their robustness properties are studied. The empirical performances of these estimators and tests are illustrated by Monte Carlo simulation for both non-contaminated and contaminated data.     

Almost arcwise connected continua without dense arc components

A continuum M is almost arcwise connected if each pair of nonempty open subsets of M can be joined by an arc in M. An almost arcwise connected plane continuum without a dense arc component can be defined by identifying pairs of endpoints of three copies of the Knaster indecomposable continuum that has two endpoints. In [7] K.R. Kellum gave this example and asked if every almost arcwise connected continuum without a dense arc component has uncountably many arc components. We answer Kellum's question by defining an almost arcwise connected plane continuum with only three arc components none of which are dense. A continuum M is almost Peano if for each finite collection $\text{C}$ of nonempty open subsets of M there is a Peano continuum in M that intersects each element of $\text{C}$. We define a hereditarily unicoherent almost Peano plane continuum that does not have a dense arc component. We prove that every almost arcwise connected planar λ-dendroid has exactly one dense arc component. It follows that every hereditarily unicoherent almost arcwise connected plane continuum without a dense arc component has uncountably many arc components. Using an example of J. Krasinkiewicz and P Minc [8], we define an almost Peano λ-dendroid that do not have a dense arc component. Using a theorem of J.B. Fugate and L. Mohler [3], we prove that every almost arcwise connected λ-dendroid without a dense arc component has uncountably many arc components. In Euclidean 3-space we define an almost Peano continuum with only countably many arc components no one of which is dense. It is not known if the plane contains a continuum with these properties.     

Fundamental groups of asymptotic cones

We show that for any metric space M satisfying certain natural conditions, there is a finitely generated group G, an ultrafilter ω, and an isometric embedding ι of M to the asymptotic cone Cone_ω(G) such that the induced homomorphism ι^*:π₁(M)→π₁(Cone_ω(G)) is injective. In particular, we prove that any countable group can be embedded into a fundamental group of an asymptotic cone of a finitely generated group.     

Construction of entire modular forms of weights 5 and 6 for the congruence group Γ0(4N)

Two classes of entire modular forms of weight 5 and two of weight 6 are constructed for the congruence subgroup ₀(4N). The constructed modular forms as well as the modular forms from [1] will be helpful in the theory of representation of numbers by the quadratic forms in 10 and 12 variables.     

A note on best conditioned preconditioners

We discuss the solution of Hermitian positive definite systemsAx=b by the preconditioned conjugate gradient method with a preconditionerM. In general, the smaller the condition number(M ^–1/2 AM ^–1/2 ) is, the faster the convergence rate will be. For a given unitary matrixQ, letM _Q = {Q* _N Q | _n is ann-by-n complex diagonal matrix} andM _Q ⁺ ={Q* _n Q | _n is ann-by-n positive definite diagonal matrix}. The preconditionerM _b that minimizes(M ^–1/2 AM ^–1/2 ) overM _Q ⁺ is called the best conditioned preconditioner for the matrixA overM _Q ⁺ . We prove that ifQAQ* has Young's Property A, thenM _b is nothing new but the minimizer of M –A _F overM _Q . Here · _F denotes the Frobenius norm. Some applications are also given here.     

Asymptotics for estimation and testing procedures under loss of identifiability

Statistical analyses commonly make use of models that suffer from loss of identifiability. In this paper, we address important issues related to the parameter estimation and hypothesis testing in models with loss of identifiability. That is, there are multiple parameter points corresponding to the same true model. We refer the set of these parameter points to as the set of true parameter values. We consider the case where the set of true parameter values is allowed to be very large or even infinite, some parameter values may lie on the boundary of the parameter space, and the data are not necessarily independently and identically distributed. Our results are applicable to a large class of estimators and their related testing statistics derived from optimizing an objective function such as a likelihood. We examine three specific examples: (i) a finite mixture logistic regression model; (ii) stationary ARMA processes; (iii) general quadratic approximation using Hellinger distance. The applications to these examples demonstrate the applicability of our results in a broad range of difficult statistical problems.     

Remarks on Martin-Löf's partial type theory

In this paper we discuss Martin-Löf's partial type theory, that is type theory with general recursion, and in particular the consequences of the presence of a fixed point operator. We model Martin-Löf's logical framework domain-theoretically in the category of conditional upper semi lattices and parametrizations thereof. An interpretation of a type of sets in the logical framework, which defines partial type theory with one universe, is finally described.During the preparation of this paper, the first author was supported by the Swedish Natural Science Research Council as a PhD-student in mathematical logic.     

On the modification of an eigenvalue problem that preserves an eigenspace

Eigenvalue problems arise in many application areas ranging from computational fluid dynamics to information retrieval. In these fields we are often interested in only a few eigenvalues and corresponding eigenvectors of a sparse matrix. In this paper, we comment on the modifications of the eigenvalue problem that can simplify the computation of those eigenpairs. These transformations allow us to avoid difficulties associated with non-Hermitian eigenvalue problems, such as the lack of reliable non-Hermitian eigenvalue solvers, by mapping them into generalized Hermitian eigenvalue problems. Also, they allow us to expose and explore parallelism. They require knowledge of a selected eigenvalue and preserve its eigenspace. The positive definiteness of the Hermitian part is inherited by the matrices in the generalized Hermitian eigenvalue problem. The position of the selected eigenspace in the ordering of the eigenvalues is also preserved under certain conditions. The effect of using approximate eigenvalues in the transformation is analyzed and numerical experiments are presented.     

Universal extension crystals of 1-motives and applications

We use the crystalline nature of the universal extension of a 1-motive M to define a canonical Gauss-Manin connection on the de Rham realization of M. As an application we provide a construction of the so-called Manin map from a motivic point of view.     

Independence results in formal topology

We analyze a family of games by using formal topology as a tool. In order to win any game in the family one has to find a sequence of moves leading to one of the final states for that game. Thus, two results are relevant to the topic: to find terminating strategies and/or to show that every strategy is terminating. We will show that the language of formal topology can be useful to represent in a topological framework both of the problems, and in particular that the property of termination of all the strategies for a game is equivalent to the discreteness of a suitable formal space. Finally, we will provide some examples of games which are terminating according to any strategy, that is, such that the associated formal spaces are discrete, but the first order formulas expressing such a discreteness cannot be proved in Peano Arithmetic.     

Stability of orbit spaces of endomorphisms

In this paper it is first proved that, for a hyperbolic set of aC ¹ (non-invertible) endomorphism of a compact manifold, the dynamical structure of its orbit space (inverse limit space) is stable underC ¹-small perturbations and is semi-stable underC ⁰-small perturbations. It is then proved that if an Axiom A endomorphism satisfies no-cycle condition then its orbit space is Θ-stable andR-stable underC ¹-small perturbations and is semi-Θ-stable and semi-R-stable underC ⁰-small perturbations. This research is supported by the National Natural Science Foundation of China     

Reduction and Equivariant Branching Lemma: Dynamical systems,evolution PDEs,and gauge theories

We review and recast the Equivariant Branching Lemma-which has proved a remarkable tool in linearly equivariant bifurcation theory-and consider its extension to the case of nonlinear (Lie-point) symmetries. This is then applied to gauge theories and gauge theoretic problems, and to nonlinear evolution PDE's; the paper also contains an original setting of Lie-point symmetries for evolution PDEs, modelled on the dynamical systems setting.     

On some entire modular forms of weights 5 and 6 for the congruence group Г(in0)(4N)

Two entire modular forms of weight 5 and two of weight 6 for the congruence subgroup Γ₀ (4N)are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 10 and 12 variables.     

Epsilon substitution for transfinite induction

We apply Mints technique for proving the termination of the epsilon substitution method via cut-elimination to the system of Peano Arithmetic with Transfinite Induction given by Arai.     

On the oscillatory behavior of certain arithmetic functions associated with automorphic forms

We establish the oscillatory behavior of several significant classes of arithmetic functions that arise (at least presumably) in the study of automorphic forms. Specifically, we examine general L-functions conjectured to satisfy the Grand Riemann Hypothesis, Dirichlet series associated with classical entire forms of real weight and multiplier system, Rankin-Selberg convolutions (both “naive” and “modified”), and spinor zeta-functions of Hecke eigenforms on the Siegel modular group of genus two. For the second class we extend results obtained previously and jointly by M. Knopp, W. Kohnen, and the author, whereas for the fourth class we provide a new proof of a relatively recent result of W. Kohnen.