On the Strong Law of Large Numbers for Non-Independent B-Valued Random Variables

This paper investigates some conditions which imply the strong laws of large numbers for Banach space valued random variable sequences. Some generalizations of the Marcinkiewicz-Zygmund theorem and the Hoffmann-J?rgensen and Pisier theorem are obtained. Key words strong law of large numbers - Banach space valued random variable sequence - p-smoothable Banach space CLC number O 211.4 - O 211.6 Foundation item: Supported by the National Natural Science Foundation of China (10071058)Biography: Gan Shi-xin (1939-), male, Professor, research direction: martingale theory, probability limiting theory and Banach space geometry theory.

Ant Colony System for a Fuzzy Adjacent Multiple-Level Warehouse Layout Problem

A warehouse layout problem where the warehouse has more than one level and both the distance from the cell to the receive/exit bay and demand of item types are fuzzy variables is proposed. The problem is to find a layout with the minimum transportation cost subject to adjacency and other constraints. A fuzzy expected value model is given and an ant colony system is designed to solve the problem. Computational results indicate the efficiency and effectiveness of the method.

Three-Dimensional Generalized Inverse Matrix Rational Interpolation

In this paper, a three dimensional matrix valued rational interpolant (TGMRI) is first constructed by making use of the generalized inverse of matrices. The interpolants are of the Thiele type branched continued fraction form, with matrix numerator and scalar denominator. Some properties of TGMRI are given. An efficient recursive algorithm is proposed. The results in the paper can be extend to n variable.

A continuum damage model for piezoelectric materials

In this paper, a constitutive model is proposed for piezoelectric material solids containing distributed cracks. The model is formulated in a framework of continuum damage mechanics using second rank tensors as internal variables. The Helrnhotlz free energy of piezoelectric mate- rials with damage is then expressed as a polynomial including the transformed strains, the electric field vector and the tensorial damage variables by using the integrity bases restricted by the initial orthotropic symmetry of the material. By using the Talreja＇s tensor valued internal state damage variables as well as the Helrnhotlz free energy of the piezoelectric material, the constitutive relations of piezoelectric materials with damage are derived. The model is applied to a special case of piezoelectric plate with transverse matrix cracks. With the Kirchhoff hypothesis of plate, the free vibration equations of the piezoelectric rectangular plate considering damage is established. By using Galerkin method, the equations are solved. Numerical results show the effect of the damage on the free vibration of the piezoelectric plate under the close-circuit condition, and the present results are compared with those of the three-dimensional theory.

Relationship between heart rate variability and posterior circulation cerebral infarction and its value in prognosis prediction

Objective To investigate the characteristic of heart rate variability(HRV)changes in patients with posteriorcirculation cerebral infarction and its value in prognosis prediction.Methods Fifty-four cases continuously diagnosed with acute posterior circulation cerebral infarction from March 2015 to November 2015 in the Department

A Supplement to the Baum-Katz-Spitzer Complete Convergence Theorem

Let {X, Xn; n≥ 1} be a sequence of i.i.d. Banach space valued random variables and let {an; n ≥ 1} be a sequence of positive constants such thatan↑∞ and 1〈 lim inf n→∞ a2n/an≤lim sup n→∞ a2n/an〈∞Set Sn=∑i=1^n Xi,n≥1.In this paper we prove that∑n≥1 1/n P（｜｜Sn｜｜≥εan）〈∞ for all ε〉0if and only if lim n→∞ Sn/an=0 a.s. This result generalizes the Baum-Katz-Spitzer complete convergence theorem. Combining our result and a corollary of Einmahl and Li, we solve a conjecture posed by Gut.