Chaos forgets and remembers: Measuring information creation,destruction, and storage

The hallmark of deterministic chaos is that it creates information—the rate being given by the Kolmogorov–Sinai metric entropy. Since its introduction half a century ago, the metric entropy has been used as a unitary quantity to measure a system's intrinsic unpredictability. Here, we show that it naturally decomposes into two structurally meaningful components: A portion of the created information—the ephemeral information—is forgotten and a portion—the bound information—is remembered. The bound information is a new kind of intrinsic computation that differs fundamentally from information creation: it measures the rate of active information storage. We show that it can be directly and accurately calculated via symbolic dynamics, revealing a hitherto unknown richness in how dynamical systems compute.     

图的预解Estrada指标的界的估计（英文）

n阶图G的子图中心度,即后来著名的Estrada指标定义为EE（G）=∑_（i=1）~N e~（λ2）.其中λ_1,λ_2……λ_n为图G的特征值.作为复杂网络的一种中心性测度和一种分子结构描述符,Estrada指标在许多研究领域有着广泛的应用.最近,Estrada和High-ama引进了一种新的复杂网络中心度,即∑_（i=1）~n n-1n-1λ_i：他们称之为预解中心度,后来又被称为预解Estrada指标.本文主要利用图G的顶点数和边数给出了图G的预解Estrada指标的若干界.     

Existence and Concentration of Bound States of a Class of Nonlinear SchrSdinger Equations in R2 with Potential Tending to Zero at Infinity

In this paper, we establish the existence and concentration of solutions of a class of nonlinear Schr?dinger equation $$- \varepsilon ^2 \Delta u_\varepsilon + V\left( x \right)u_\varepsilon = K\left( x \right)\left| {u_\varepsilon } \right|^{p - 2} u_\varepsilon e^{\alpha _0 \left| {u_\varepsilon } \right|^\gamma } , u_\varepsilon > 0, u_\varepsilon \in H^1 \left( {\mathbb{R}^2 } \right),$$ where 2 < p < ∞, α ₀ > 0, 0 < γ < 2. When the potential function V (x) decays at infinity like (1 + |x|)^?α with 0 < α ≤ 2 and K(x) > 0 are permitted to be unbounded under some necessary restrictions, we will show that a positive H ¹(?²)-solution u _? exists if it is assumed that the corresponding ground energy function G(ξ) of nonlinear Schr?dinger equation $- \Delta u + V\left( \xi \right)u = K\left( \xi \right)\left| u \right|^{p - 2} ue^{\alpha _0 \left| u \right|^\gamma }$ has local minimum points. Furthermore, the concentration property of u _? is also established as ? tends to zero.     

(v,e)-图的正常λ-着色的最大数目的新界(英文)

设P（G，λ）表示图G的色多项式．给定正整数n，e和λ,记f（v，e，λ）=max{P（G，λ）：G是个v点e边的图}．本文得到f（v，e，λ）的新上界和f（v，e，3）的新下界．     

Relativistic quantum mechanic calculation of photoionization cross-section of hydrogenic and non-hydrogenic states using analytical potentials

Photoionization process is a subject of special importance in many areas of physics. Numerical methods must be used in order to obtain photoionization cross-sections for non-hydrogenic levels. The atomic data required to calculate them is huge so self-consistent calculations increase computing time considerably. Analytical potentials are a useful alternative because they avoid the iterative procedures typical in self-consistent models. In this work, we present a relativistic quantum calculation of photoionization cross-sections for isolated ions based on an analytical potential to obtain the required atomic data, which is valid both for hydrogenic and non-hydrogenic ions. Comparisons between our results and others obtained using either widely used analytical expressions for the cross-sections or more sophisticated calculations are done.     

不连续系统有界变差解对参数的连续依赖性

利用Henstock积分，讨论了一类不连续系统有界变差解对参数的连续依赖性及其它相关性质．     

On proving existence of feasible points in equality constrained optimization problems

Various algorithms can compute approximate feasible points or approximate solutions to equality and bound constrained optimization problems. In exhaustive search algorithms for global optimizers and other contexts, it is of interest to construct bounds around such approximate feasible points, then to verify (computationally but rigorously) that an actual feasible point exists within these bounds. Hansen and others have proposed techniques for proving the existence of feasible points within given bounds, but practical implementations have not, to our knowledge, previously been described. Various alternatives are possible in such an implementation, and details must be carefully considered. Also, in addition to Hansen’s technique for handling the underdetermined case, it is important to handle the overdetermined case, when the approximate feasible point corresponds to a point with many active bound constraints. The basic ideas, along with experimental results from an actual implementation, are summarized here. This work was supported in part by National Science Foundation grant CCR-9203730.     

Geodesics around oscillatons

Oscillatons are spherically symmetric solutions to the Einstein–Klein–Gordon equations. These solutions are non-singular, asymptotically flat, and with periodic time dependency. In this paper, we investigate the geodesic motion of particles moving around of an oscillatonic field. Bound orbits are found for particular values of the particles' angular momentum L and their initial radial position r ₀. It is found that the radial coordinate of such particles oscillates in time and we are able to predict the corresponding oscillating period as well as its amplitude. We carry out this study for the quadratic V(φ) = m _Φ Φ²/2 scalar field potential. We discuss possible ways to follow in order to connect this kind of studies with astrophysical observations.