12,620 research outputs found
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
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