Partial Information Differential Games for Mean-Field SDEs

This paper is concerned with non-zero sum differential games of mean-field stochastic differential equations with partial information and convex control domain. First, applying the classical convex variations, we obtain stochastic maximum principle for Nash equilibrium points. Subsequently, under additional assumptions, verification theorem for Nash equilibrium points is also derived. Finally, as an application, a linear quadratic example is discussed. The unique Nash equilibrium point is represented in a feedback form of not only the optimal filtering but also expected value of the system state, throughout the solutions of the Riccati equations.Comment: 7 page

Trees with the most subtrees -- an algorithmic approach

When considering the number of subtrees of trees, the extremal structures which maximize this number among binary trees and trees with a given maximum degree lead to some interesting facts that correlate to other graphical indices in applications. The number of subtrees in the extremal cases constitute sequences which are of interest to number theorists. The structures which maximize or minimize the number of subtrees among general trees, binary trees and trees with a given maximum degree have been identified previously. Most recently, results of this nature are generalized to trees with a given degree sequence. In this note, we characterize the trees which maximize the number of subtrees among trees of a given order and degree sequence. Instead of using theoretical arguments, we take an algorithmic approach that explicitly describes the process of achieving an extremal tree from any random tree. The result also leads to some interesting questions and provides insight on finding the trees close to extremal and their numbers of subtrees.Comment: 12 pages, 7 figures; Journal of combinatorics, 201

Anderson Impurity in Helical Metal

We use a trial wave function to study the spin-1/2 Kondo effect of a helical metal on the surface of a three-dimensional topological insulator. While the impurity spin is quenched by conduction electrons, the spin-spin correlation of the conduction electron and impurity is strongly anisotropic in both spin and spatial spaces. As a result of strong spin-orbit coupling, the out-of-plane component of the impurity spin is found to be fully screened by the orbital angular momentum of the conduction electrons.Comment: The published versio

Molecular Cloning, Characterization, and Expression Analysis of the CXCR4 Gene from Turbot: Scophthalmus maximus

Chemokine receptor 4 (CXCR4) belongs to the large superfamily of G protein-coupled receptors. The EST sequence of CXCR4 from turbot (Scophthalmus maximus L.) was obtained from a subtractive cDNA library. In the present study, the full-length cDNA sequence of turbot CXCR4 was obtained, and sequence analysis indicated that its primary structure was highly similar to CXCR4 from other vertebrates. Quantitative real-time PCR demonstrated that the highest expression level of turbot CXCR4 was in the spleen following injection with physiological saline (PS). After turbot were challenged with Vibrio harveyi, the lowest expression level of CXCR4 was detected at 8 hours in the spleen and 12 hours in the head kidney, and then increased gradually to 36 hours. These findings suggested that CXCR4 may play a significant role in the immune response of turbot

{μ-6,6′-Dimeth­oxy-2,2′-[ethane-1,2-diylbis(nitrilo­methyl­idyne)]diphenolato-1κ4 O 6,O 1,O 1′,O 6′:2κ4 O 1,N,N′,O 1′}(methanol-1κO)(perchlorato-1κO)copper(II)sodium(I)

The mol­ecule of the title compound, [CuNa(C18H18N2O4)(ClO4)(CH3OH)], is almost planar with mean deviation of 5.2 (8)°. The coordination environment of the CuII ion is distorted square-planar and it is N2O2-chelated by the 6,6′-dimeth­oxy-2,2′-[ethane-1,2-diylbis(nitrilo­methyl­idyne)]diphenolate Schiff base ligand. The Na atom is chelated by the four O atoms of the Schiff base ligand, and coordinated by a methanol mol­ecule and a perchlorate anion. The six-coordinate Na atom adopts a distorted octa­hedral coordination geometry. The O atoms of the perchlorate anion are disordered over two sites with site-occupancy factors of 0.697 (5) and 0.303 (5). O—H⋯O hydrogen bonding occurs