Covering Spheres with Spheres
نویسنده
چکیده
Given a sphere of radius r > 1 in the n-dimensional Euclidean space, we study the coverings of this sphere with unit spheres. Our goal is to design a covering of the lowest covering density, which defines the average number of unit spheres covering a point in a bigger sphere. For growing n, we obtain the covering density of (n lnn)/2. This new upper bound is half the order n lnn established in the classical Rogers bound.
منابع مشابه
A Numerical Study of Flow and Heat Transfer Between Two Rotating Vertically Eccentric Spheres with Time- Dependent Angular Velocities
The transient motion and the heat transfer of a viscous incompressible flow contained between two vertically eccentric spheres maintained at different temperatures and rotating about a common axis with different angular velocities is numerically considered when the angular velocities are an arbitrary functions of time. The resulting flow pattern, temperature distribution, and heat transfer char...
متن کاملHeat Transfer in a Column Packed With Spheres
The purpose of the study is to investigate average and local surface heat transfer coefficients in a cylinder packed with spheres. Here the term «local» applies to a single sphere within the bed. Averages are derived from the sixteen different spheres that were instrumented and distributed throughout the bed. The experimental technique consisted of introducing a step - wise change in the temper...
متن کاملHermitian metric on quantum spheres
The paper deal with non-commutative geometry. The notion of quantumspheres was introduced by podles. Here we define the quantum hermitianmetric on the quantum spaces and find it for the quantum spheres.
متن کاملAny Finite Group Acts Freely and Homologically Trivially on a Product of Spheres
The main theorem states that if K is a finite CW-complex with finite fundamental group G and universal cover homotopy equivalent to a product of spheres X, then G acts smoothly and freely on X×Sn for any n greater than or equal to the dimension of X. If the G-action on the universal cover of K is homologically trivial, then so is the action on X × Sn. Ünlü and Yalçın recently showed that any fi...
متن کاملSynthesis of Carbon Spheres of Controlled Size by Hydrothermal Method
Carbon Spheres were fabricated by hydrothermal method and their structural properties were investigated. Carbon Spheres with average sizes around of 230, 320 and 430 nm were synthesized in different concentration of glucose aqueous solution and different hydrothermal reaction time. The temperature of 180 °C by a hydrothermal reaction was fixed in all of glucose concentration and hydrothermal re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete & Computational Geometry
دوره 38 شماره
صفحات -
تاریخ انتشار 2007