AN UPPER BOUND ON DENSITY FOR PACKINGS OF COLLARS ABOUT HYPERPLANES IN Hn
نویسنده
چکیده
We consider packings of radius r collars about hyperplanes in H. For such packings, we prove that the Delaunay cells are truncated ultra-ideal simplices which tile H. If we place n+1 hyperplanes in H each at a distance of exactly 2r to the others, we could place radius r collars about these hyperplanes. The density of these collars within the corresponding Delaunay cell is an upper bound on density for all packings of radius r collars.
منابع مشابه
BIODESULFURIZATION OF SIMULATED LIGHT FUEL OIL BY A NATIVE ISOLATED BACTERIA BACILLUS CEREUS HN
In the present paper, the biodesulfurization of simulated light fuel oil (i.e., dibenzothiophene (DBT) in dodecane) and untreated kerosene with a high total sulfur content has been studied by a native isolated bacterium named Bacillus cereus HN. The influences of various parameters such as the reaction temperature (T), biocatalyst cell density, oil phase fraction (OFP), and initial DBT concentr...
متن کاملNew Conjectural Lower Bounds on the Optimal Density of Sphere Packings
Sphere packings in high dimensions interest mathematicians and physicists and have direct applications in communications theory. Remarkably, no one has been able to provide exponential improvement on a 100-year-old lower bound on the maximal packing density due to Minkowski in d-dimensional Euclidean space R. The asymptotic behavior of this bound is controlled by 2 in high dimensions. Using an ...
متن کاملAn Upper Bound on the First Zagreb Index in Trees
In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.
متن کاملAn Upper Bound Approach for Analysis of Hydroforming of Sheet Metals
Considering a kinematical velocity admissible field, the upper bound method has beenused for predicting the amount of pressure in hydroforming of sheet metals. The effects of workhardening, friction and blank size have been considered in pressure prediction. Also the effect ofsheet thickness variation has been considered in the present work formulations. The relation betweenpressure and punch s...
متن کاملWavelet Based Estimation of the Derivatives of a Density for a Discrete-Time Stochastic Process: Lp-Losses
We propose a method of estimation of the derivatives of probability density based on wavelets methods for a sequence of random variables with a common one-dimensional probability density function and obtain an upper bound on Lp-losses for such estimators. We suppose that the process is strongly mixing and we show that the rate of convergence essentially depends on the behavior of a special quad...
متن کامل