First passage percolation: The stationary case

Summary If the passage time of the edges of the ^d lattice are stationary, ergodic and have finite moment of orderp>d, then a.s. the set of vertices that can be reached within timet, has an asymptotic shape ast.     

Computing Finite Semigroups, I: The First Row

New precedence results are obtained for finite, not necessarily commutative semigroups, which are used to further sharpen existing algorithms for the computation of finite semigroups. The results in this first part describe the first row of the multiplication table in detail and provide a numerical profile with which it can be compared to other rows.     

Computing Finite Semigroups,II: The First Nonconstant Row

New precedence results are obtained for finite, not necessarily commutative semigroups, which are used to further sharpen existing algorithms for the computation of finite semigroups. The results in this second part assume a left zero element, describe the first nonconstant row of the multiplication table in detail, and provide a numerical profile with which it can be compared to other rows.     

Memoir: My Cambridge Years

The Ramanujan Journal -     

The First Biharmonic Steklov Eigenvalue: Positivity Preserving and Shape Optimization

We consider the Steklov problem for the linear biharmonic equation. We survey existing results for the positivity preserving property to hold. These are connected with the first Steklov eigenvalue. We address the problem of minimizing this eigenvalue among suitable classes of domains. We prove the existence of an optimal convex domain of fixed measure.     

Area Spaces: First Steps

We show that a Riemannian manifold of dimension at least 3 can be recovered from the space of boundaries of rectifiable integral 2-currents (the “lcycles”) equipped with the filling area distance, and discuss possible approaches to “spaces with area structures”.     

Versik processes: First steps

A. M. Versik defined a property of finite-state stationary stochastic processes that formally is slightly weaker than D. S. Ornstein’s very weak Bernoulli (VWB) property. Versik conjectured his property was equivalent withVWB. The conjecture is false. We construct a zero entropy Versik process that is not loosely Bernoulli (LB) and, by taking a skew product of this process with the two-shift, we produce aK process that is Versik but notVWB. Our technique for constructing a non-LB process differs from the few known methods.     

The First Fundamental Theorem of Calculus

<正>The Fundamental Theorem of Calculus establishes a connection between the two branches of calculus:differential calculus and integral calculus.Integral calculus arose from the area problem.Differential calculus arose from the tangent problem.Two parts seem unrelated.But the great Mathematician Newton realized that differentiation and integration are inverse processes.So the Fundamental Theorem of Calculus gives the pre-     

A Vision for What Science Education Should Be Like for the First 25 Years of a New Millennium

Robert Yager is a native Iowan who was worked at the University of Iowa since 1956. He has served as president of seven national associations, including the National Science Teachers Association, School Science and Mathematics Association, the National Association of Biology Teachers, the Association for the Education of Teachers of Science, the National Association for Research in Science Teaching, Section Q of the American Association for the Advancement of Science, and the National Association of Science‐Technology‐Society. Yager has directed over 100 projects supported by the National Science Foundation, several research projects supported by the U.S. Department of Education, and several project evaluations. The University of Iowa has one of the largest graduate programs in the U.S., while also focusing on in‐service programs for science teachers and a model preservice program (which enjoyed NSF support for a 10‐year period). Yager has published over 500 books, monographs, and research reports. Currently, he is active with several research projects in Korea, Japan, Thailand, Malaysia, Israel, and Estonia.     

一阶最优性条件研究

本对由Botsko的关于多变量函数取极值的一阶导数检验条件定理^[1]进行了分析研究，给出了更实用而简捷的差别条件。最后，举出若干例子予以说明。