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We consider the smoothed version of sliced average variance estimation (SAVE) dimension reduction method for dealing with spatially dependent data that are observations of a strongly mixing random field. We propose kernel estimators for the interest matrix and the effective dimension reduction (EDR) space, and show their consistency.

In this work, we present existence of mild solutions for partial integro-differential equations with state-dependent nonlocal local conditions. We assume that the linear part has a resolvent operator in the sense given by Grimmer. The existence of mild solutions is proved by means of Kuratowski’s measure of non-compactness and a generalized Darbo fixed point theorem in Fréchet space. Finally, an example is given for demonstration.

We propose an estimation method, named functional average variance estimation (FAVE), for estimating the EDR space in functional semiparametric regression model, based on kernel estimates of density and regression. Consistency results are then established for the estimator of the interest operator, and for the directions of EDR space. A simulation study that shows that the proposed approach performs better than traditional ones is presented. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of testing for the equality of k probability distributions defined on (X , B) , where X is a metric space and B is the corresponding Borel σ-field. We introduce a test statistic based on reproducing kernel Hilbert space embeddings and derive its asymptotic distribution under the null hypothesis. Simulations show that the introduced procedure outperforms a known method. [ABSTRACT FROM AUTHOR]

Let Σ be a submanifold of a Riemannian manifold M. The evolution equations of some extrinsic geometric quantities such as the norm of the second fundamental form, the norm of the mean curvature, etc., have been computed along the mean curvature flow and then used to investigate either the long-time existence of the flow or some extrinsic geometrical properties (minimality, totally geodesic, umbilicity, etc.) of the limiting submanifold (see e.g. [1, 2, 4, 5]). But few results are known about the intrinsic geometry of the evolving submanifold along the flow [3]. In the present work, assuming that the mean curvature flow exists, we compute for a submanifold of a Riemannian manifold, the evolution equations of the Riemannian curvature, the Ricci curvature and the scalar curvature which are intrinsic geometrical invariants of the submanifold. From the evolution equation of the scalar curvature, we derived that the graphical mean curvature flow favours positive scalar curvature; a well known result in this area. [ABSTRACT FROM AUTHOR]

This paper discusses choice procedures that select the set of best alternatives taking into account reflexive binary relations (called pseudo-tournaments in the paper), such as those that can be obtained when constructing an outranking relation à la Electre. The paper contains interesting results which link together the second "exploitation" step in the Electre I outranking method with two choice procedures (Gocha and Getcha choice procedures also known in the literature as Schwartz set and Smith set respectively). A set of results that characterize some properties of the two outranking methods (ElectI and ElectIP choice procedures) is also presented. [ABSTRACT FROM AUTHOR]

A Wasserstein Riemannian Gamma manifold is a space of Gamma probability density functions endowed with the Riemannian Otto met- ric which is related to the Wasserstein distance. In this paper, we study some geometric properties of such Riemanian manifold. In par- ticular we compute the coefficients of -connections and the sectional curvature of those manifolds. [ABSTRACT FROM AUTHOR]

In this paper, we propose a Hilbert bundle of generalized statistical manifold with the introduction of a family of α-connections. The expressions of parallel transport for the exponential and mixture connections are derived, and we prove that those two connections are dual and curvature-free. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of so- lution for a class of stochastic functional differential equations with delay on compact manifolds. The results are established under non-Lipschitz conditions on the coefficients. As an application, a geometrical example is provided to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

The existence and uniqueness of mild solution of an impulsive stochastic system driven by a Rosenblatt process is analyzed in this work by using the Banach fixed point theorem and the theory of resolvent operator developed by R. Grimmer in [12]. Furthermore, the exponential stability in mean square for the mild solution to neutral stochastic integro–differential equations with Rosenblatt process is obtained by establishing an integral inequality. Finally, an example is exhibited to illustrate the abstract theory. [ABSTRACT FROM AUTHOR]

This work is focused on the existence and attractivity of mild solutions for an integrodifferential system with statedependent delay. The results presented here were established by means of a fixed point theorem due to [T. A. Burton, C. Kirk, Math. Nachr., 189 (1998), 23-31]. At the end, the obtained results are illustrated by an example. [ABSTRACT FROM AUTHOR]

This paper is devoted to the existence and asymptotic behavior in p-th moment of the mild solution to a class of impulsive neutral stochastic functional integrodifferential equations with infinite delay in Hilbert spaces. A new and sufficient set of conditions are formulated concerning the existence of solutions and the stability of the nonlinear stochastic system. To obtain the desired result, the theory of the resolvent operator in the sense of Grimmer, the stochastic analysis theory, the fixed point theorem and the Hausdorff measure of non-compactness are used. However, it is very important to specify that in this paper, we have left the classical framework in which the nonlinear terms are assumed to be Lipschitz continuous. At the end of this paper, an illustration is also given to show the application of our results. [ABSTRACT FROM AUTHOR]