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991.
We show that there exists a family of Riemannian metrics on the tangent bundle of a two-sphere, which induces metrics of constant curvature on its unit tangent bundle. In other words, given such a metric on the tangent bundle of a two-sphere, the Hopf map is identified with a Riemannian submersion from the universal covering space of the unit tangent bundle, equipped with the induced metric, onto the two-sphere. A hyperbolic counterpart dealing with the tangent bundle of a hyperbolic plane is also presented. 相似文献
992.
Classification of a screened data into one of two normal populations perturbed by a screening scheme
Hea-Jung Kim 《Journal of multivariate analysis》2011,102(10):1361-1373
In normal classification analysis, there may be cases where the population distributions are perturbed by a screening scheme. This paper considers a new classification method for screened data that is obtained from the perturbed normal distributions. Properties of each population distribution is considered and the best region for classifying the screened data is obtained. These developments yield yet another optimal rule for the classification. The rule is studied from several aspects such as a linear approximation, error rates, and estimation of the rule using the EM algorithm. Relationships among these aspects as well as investigation of the rule’s performance are also considered. The screened classification ideas are illustrated in detail using numerical examples. 相似文献
993.
J.S. Manhas 《Applied mathematics and computation》2011,218(3):929-934
Let B(E, F) be the Banach Space of all continuous linear operators from a Banach Space E into a Banach space F. Let UX and UY be balanced open subsets of Banach spaces X and Y, respectively. Let V and W be two Nachbin families of continuous weights on UX and UY, respectively. Let HV(UX, E) (or HV0(UX, E)) and HW(UY, F) (or HW0(UY, F)) be the weighted spaces of vector-valued holomorphic functions. In this paper, we investigate the holomorphic mappings ? : UY → UX and ψ : UY → B(E, F) which generate weighted composition operators between these weighted spaces. 相似文献
994.
Kunal Chakraborty Milon ChakrabortyT.K. Kar 《Applied mathematics and computation》2011,217(21):8778-8792
This paper describes a prey-predator model with stage structure for prey. The adult prey and predator populations are harvested in the proposed system. The dynamic behavior of the model system is discussed. It is observed that singularity induced bifurcation phenomenon is appeared when variation of the economic interest of harvesting is taken into account. State feedback controller is incorporated to stabilize the model system in case of positive economic interest. Harvesting of prey and predator population are used as controls to develop a dynamic framework to investigate the optimal utilization of the resource, sustainability properties of the stock and the resource rent earned from the resource. The Pontryagin’s maximum principle is used to characterize the optimal controls. The optimality system is derived and then solved numerically using an iterative method with Runge-Kutta fourth order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem. 相似文献
995.
Jonathan D. Hauenstein Andrew J. Sommese Charles W. Wampler 《Applied mathematics and computation》2011,218(4):1240-1246
A key step in the numerical computation of the irreducible decomposition of a polynomial system is the computation of a witness superset of the solution set. In many problems involving a solution set of a polynomial system, the witness superset contains all the needed information. Sommese and Wampler gave the first numerical method to compute witness supersets, based on dimension-by-dimension slicing of the solution set by generic linear spaces, followed later by the cascade homotopy of Sommese and Verschelde. Recently, the authors of this article introduced a new method, regeneration, to compute solution sets of polynomial systems. Tests showed that combining regeneration with the dimension-by-dimension algorithm was significantly faster than naively combining it with the cascade homotopy. However, in this article, we combine an appropriate randomization of the polynomial system with the regeneration technique to construct a new cascade of homotopies for computing witness supersets. Computational tests give strong evidence that regenerative cascade is superior in practice to previous methods. 相似文献
996.
We build on Gruenhage, Natkaniec, and Piotrowski?s study of thin, very thin, and slim dense sets in products, and the related notions of (NC) and (GC) which they introduced. We find examples of separable spaces X such that X2 has a thin or slim dense set but no countable one. We characterize ordered spaces that satisfy (GC) and (NC), and we give an example of a separable space which satisfies (GC) but not witnessed by a collection of finite sets. We show that the question of when the topological sum of two countable strongly irresolvable spaces satisfies (NC) is related to the Rudin-Keisler order on βω. We also introduce and study the concepts of <κ-thin and superslim dense sets. 相似文献
997.
We study three types of quotient maps of frames which are closely related to C- and C?-quotient maps. We call them C1-, strong C1-, and uplifting quotient maps. C1-quotient maps are precisely those whose induced ring homomorphisms contract maximal ideals to maximal ideals. We show that every homomorphism onto a frame is a C1-, a strong C1-, or an uplifting quotient map iff the frame is pseudocompact, compact, or almost compact and normal, respectively. These quotient maps are used to characterize normality and also certain weaker forms of normality in a manner akin to the characterization of normal frames as those for which every closed quotient map is a C-quotient map. Under certain conditions, we show that the Stone extension of a quotient map is C1-, strongly C1- or uplifting if the map has the corresponding property. 相似文献
998.
We show that every nonempty compact and convex space M of probability Radon measures either contains a measure which has ‘small’ local character in M or else M contains a measure of ‘large’ Maharam type. Such a dichotomy is related to several results on Radon measures on compact spaces and to some properties of Banach spaces of continuous functions. 相似文献
999.
In this article, we investigate the tail probability of the product of finitely many non-negative dependent random variables. They follow distributions from max-domains of attraction of extreme value distributions and their dependence is modeled via a multivariate Farlie–Gumbel–Morgenstern distribution. For each of the Fréchet, Gumbel and Weibull cases, we obtain an explicit asymptotic formula for the tail probability of the product. Our study extends a few known results in the literature. 相似文献
1000.
The problem of fitting a parametric model in Tobit errors-in-variables regression models is discussed in this paper. The proposed test is based on the supremum of the Khmaladze type transformation of a certain partial sum process of calibrated residuals. This framework covers the usual error-free Tobit model as a special case. The asymptotic null distribution of this transformed process is shown to be the same as that of a time transformed standard Brownian motion. Consistency against some fixed alternatives and asymptotic power under some local nonparametric alternatives of this test are also discussed. Simulation studies are conducted to assess the finite sample performance of the proposed test. 相似文献