Squareful numbers in hyperplanes
نویسندگان
چکیده
منابع مشابه
Sums of Three Squareful Numbers
We investigate the frequency of positive squareful numbers x, y, z 6 B for which x + y = z and present a conjecture concerning its asymptotic behaviour. Mathematics Subject Classification (2010). 11D45 (11P05, 14G05).
متن کاملGeneralized Catalan Numbers, Weyl Groups and Arrangements of Hyperplanes
For an irreducible, crystallographic root system Φ in a Euclidean space V and a positive integer m, the arrangement of hyperplanes in V given by the affine equations (α, x)= k, for α∈Φ and k=0, 1, . . . ,m, is denoted here by AΦ . The characteristic polynomial of AΦ is related in the paper to that of the Coxeter arrangement AΦ (corresponding to m=0), and the number of regions into which the fun...
متن کاملBinary quadratic forms with large discriminants and sums of two squareful numbers II
Let F = (F1, . . . , Fm) be an m-tuple of primitive positive binary quadratic forms and let UF(x) be the number of integers not exceeding x that can be represented simultaneously by all the forms Fj , j = 1, . . . ,m. Sharp upper and lower bounds for UF(x) are given, uniformly in the discriminants of the quadratic forms. As an application a problem of Erdös is considered. Let V (x) be the numbe...
متن کاملBayes Optimal Hyperplanes! Maximal Margin Hyperplanes
Maximal margin classifiers are a core technology in modern machine learning. They have strong theoretical justifications and have shown empirical successes. We provide an alternative justification for maximal margin hyperplane classifiers by relating them to Bayes optimal classifiers that use Parzen windows estimations with Gaussian kernels. For any value of the smoothing parameter (the width o...
متن کاملMedian hyperplanes in normed spaces
In this paper we deal with the location of hyperplanes in n{ dimensional normed spaces. If d is a distance measure, our objective is to nd a hyperplane H which minimizes points and d(x m ; H) = min z2H d(x m ; z) is the distance from x m to the hyperplane H. In robust statistics and operations research such an optimal hyperplane is called a median hyperplane. We show that for all distance measu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2012
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2012.6.1019