A projection method of estimation for a subfamily of exponential families

Summary This paper is concerned with estimation for a subfamily of exponential-type, which is a parametric model with sufficient statistics. The family is associated with a surface in the domain of a sufficient statistic. A new estimator, termed a projection estimator, is introduced. The key idea of its derivation is to look for a one-to-one transformation of the sufficient statistic so that the subfamily can be associated with a flat subset in the transformed domain. The estimator is defined by the orthogonal projection of the transformed statistic onto the flat surface. Here the orthogonality is introduced by the inverse of the estimated variance matrix of the statistic on the analogy of Mahalanobis's notion (1936,Proc. Nat. Inst. Sci. Ind.,2, 49–55). Thus the projection estimator has an explicit representation with no iterations. On the other hand, the MLE and classical estimators have to be sought as numerical solutions by some algorithm with a choice of an initial value and a stopping rule. It is shown that the projection estimator is first-order efficient. The second-order property is also discussed. Some examples are presented to show the utility of the estimator.     

Hilbert空间中非扩张映象的最近的公共不动点的逼近问题

本文在Hilbert空间的框架下,研究无限族非扩张映象T_1,T_2,…的迭代程序x_n+1=λ_(n+1)y+(1-λ_(n+1))T_(n+1)x_n的收敛性问题．在适当的条件下,证明了该迭代序列收敛于这一非扩张映象族的最近的公共不动点．其结果改进和推广了引文中相应的结果．     

MAXIMAL ELEMENTS OF A FAMILY OF GB-MAJORIZED MAPPINGS IN PRODUCT FC-SPACES AND APPLICATIONS

A new family of GB-majorized mappings from a topological space into a finite continuous topological spaces （in short, FC-space） involving a better admissible set-valued mapping is introduced. Some existence theorems of maximal elements for the family of GB-majorized mappings are proved under noncompact setting of product FCspaces. Some applications to fixed point and system of minimax inequalities are given in product FC-spaces. These theorems improve, unify and generalize many important results in recent literature.     

Triple Systems are Eulerian

An Euler tour of a hypergraph (also called a rank‐2 universal cycle or 1‐overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, using a graph‐theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour. Horan and Hurlbert have previously shown that for every admissible order >3, there exists a Steiner triple system with an Euler tour, while Dewar and Stevens have proved that every cyclic Steiner triple system of order >3 and every cyclic twofold triple system admits an Euler tour.     

Existence and exact controllability of fractional evolution inclusions with damping

The aim of this paper is to deal with the existence of mild solutions and exact controllability for a class of fractional evolution inclusions with damping (FEID, for short) in Banach spaces. Firstly, we provide the representation of mild solutions for FEID by applying the method of Laplace transform and the theory of (α,κ)‐regularized families of operators. Next, we are concerned with the existence and exact controllability of FEID under some suitable sufficient conditions by using the method of measure of noncompactness and an appropraite fixed point theorem. Finally, an application to nonlinear partial differential equations with temporal fractional derivatives is presented to illustrate the effectiveness of our main results. Copyright © 2017 John Wiley & Sons, Ltd.     

Existence of μ−pseudo almost periodic solutions to some evolution equations

In this article, a new approach for pseudo almost periodic solution under the measure theory, under Acquistpace‐Terreni conditions. We make extensive use of interpolation spaces and exponential dichotomy techniques to obtain the existence of μ‐pseudo almost periodic solutions to some classes of nonautonomous partial evolution equations. For illustration, we propose some application to a nonautonomous heat equation. Copyright © 2017 John Wiley & Sons, Ltd.     

Blow‐up for the b‐family of equations

In this paper, we consider the b‐family of equations on the torus u _t ?u _{t x x} +(b + 1)u u _x =b u _x u _{x x} +u u _{x x x} , which for appropriate values of b reduces to well‐known models, such as the Camassa–Holm equation or the Degasperis–Procesi equation. We establish a local‐in‐space blow‐up criterion. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical investigation of the first transition in the three-dimensional problem of convective flow in a porous medium

The branching off of steady-state regimes from mechanical equilibrium is studied for the problem of filtration convection in a parallelepiped. The conditions for the geometric parameters under which stable continuous families of steady-state regimes develop are found. The stability of equilibria of the family with respect to three-dimensional perturbations is analyzed in a numerical experiment using a finite-difference method.     

Low-temperature structural phase transition in synthetic libethenite Cu2PO4OH

Low-temperature structural properties of the synthetic mineral libethenite Cu₂PO₄OH were investigated by single-crystal X-ray diffraction, synchrotron X-ray powder diffraction, specific heat measurements, and Raman spectroscopy. A second-order structural phase transition from the Pnnm symmetry (a=8.0553(8) Å, b=8.3750(9) Å, c=5.8818(6) Å at 180 K) to the P2₁/n symmetry (a=8.0545(8) Å, b=8.3622(9) Å, c=5.8755(6) Å, β=90.0012(15) at 120 K) was found at 160 K during cooling. At 120 K, the monoclinic angle is 90.0012(15) from single crystal X-ray data vs 90.083(1) from powder X-ray diffraction data. The P2₁/n–to–Pnnm transition may be a general feature of the adamite-type compounds, M₂XO₄OH.