Finding The Sign Of A Function Value By Binary Cellular Automaton

Given a continuous function $f(x)$, suppose that the sign of $f$ only has finitely many discontinuous points in the interval $[0,1]$. We show how to use a sequence of one dimensional deterministic binary cellular automata to determine the sign of $f(\rho)$ where $\rho$ is the (number) density of 1s in an arbitrarily given bit string of finite length provided that $f$ satisfies certain technical conditions.Comment: Revtex, uses amsfonts, 10 page

Effective algebraic degeneracy

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}

The Complete Characterization of Fourth-Order Symplectic Integrators with Extended-Linear Coefficients

The structure of symplectic integrators up to fourth-order can be completely and analytical understood when the factorization (split) coefficents are related linearly but with a uniform nonlinear proportional factor. The analytic form of these {\it extended-linear} symplectic integrators greatly simplified proofs of their general properties and allowed easy construction of both forward and non-forward fourth-order algorithms with arbitrary number of operators. Most fourth-order forward integrators can now be derived analytically from this extended-linear formulation without the use of symbolic algebra.Comment: 12 pages, 2 figures, submitted to Phys. Rev. E, corrected typo

Finite Generation of Canonical Ring by Analytic Method

In the 80th birthday conference for Professor LU Qikeng in June 2006 I gave a talk on the analytic approach to the finite generation of the canonical ring for a compact complex algebraic manifold of general type. This article is my contribution to the proceedings of that conference from my talk. In this article I give an overview of the analytic proof and focus on explaining how the analytic method handles the problem of infinite number of interminable blow-ups in the intuitive approach to prove the finite generation of the canonical ring. The proceedings of the LU Qikeng conference will appear as Issue No. 4 of Volume 51 of Science in China Series A: Mathematics (www.springer.com/math/applications/journal/11425)

Higher Order Force Gradient Symplectic Algorithms

We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to similarly iterated higher order algorithms based on the standard Forest-Ruth algorithm. We gauge the accuracy of each algorithm by comparing the step-size independent error functions associated with energy conservation and the rotation of the Laplace-Runge-Lenz vector when solving a highly eccentric Kepler problem. For orders 6, 8, 10 and 12, the new algorithms are approximately a factor of $10^3$, $10^4$, $10^4$ and $10^5$ better.Comment: 23 pages, 10 figure

Interpersonal Competence and Service Leadership

According to the Hong Kong Institute of Service Leadership and Management, interpersonal competence is an important component of an effective service leader. The present paper introduces a lecture embedded in a service leadership subject that focuses on promoting students’ interpersonal competence. Several topics are covered in this lecture. First, concepts and theories about interpersonal competence are introduced. Second, the relevance of interpersonal competence to service leadership is outlined. Third, methods of developing interpersonal competence are presented, particularly different conflict management strategies and assertiveness skills. Finally, conclusions and reflections on students’ own interpersonal competence and its relevance to the service leadership in one’s professional field are discussed. Different activities have been designed and incorporated in the lecture to facilitate students’ active learning and self-reflection. Students are also encouraged to explore their own ways to promote the development of interpersonal competence

Prosocial Norms as a Positive Youth Development Construct: A Conceptual Review

Prosocial norms like reciprocity, social responsibility, altruism, and volunteerism are ethical standards and beliefs that youth development programs often want to promote. This paper reviews evolutionary, social-cognitive, and developmental theories of prosocial development and analyzes how young people learn and adopt prosocial norms. The paper showed that very few current theories explicitly address the issue of how prosocial norms, in form of feelings of moral obligations, may be challenged by a norm of self-interest and social circumstances when prosocial acts are needed. It is necessary to develop theories which put prosocial norms as a central construct, and a new social cognitive theory of norm activation has the potential to help us understand how prosocial norms may be applied. This paper also highlights how little we know about young people perceiving and receiving prosocial norms and how influential of school policies and peer influence on the prosocial development. Lastly, while training of interpersonal competence (e.g., empathy, moral reasoning, etc.) was commonly used in the youth development, their effectiveness was not systematically evaluated. It will also be interesting to examine how computer and information technology or video games may be used in e-learning of prosocial norms

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Recognition for Positive Behavior as a Critical Youth Development Construct: Conceptual Bases and Implications on Youth Service Development

Recognition for positive behavior is an appropriate response of the social environment to elicit desirable external behavior among the youth. Such positive responses, rendered from various social systems, include tangible and intangible reinforcements. The following theories are used to explain the importance of recognizing positive behavior: operational conditioning, observational learning, self-determination, and humanistic perspective. In the current work, culturally and socially desirable behaviors are discussed in detail with reference to Chinese adolescents. Positive behavior recognition is especially important to adolescent development because it promotes identity formation as well as cultivates moral reasoning and social perspective thinking from various social systems. The significance of recognizing positive behavior is illustrated through the support, tutorage, invitation, and subsidy provided by Hong Kong's social systems in recognition of adolescent volunteerism. The practical implications of positive behavior recognition on youth development programs are also discussed in this work