Discrepancy Estimate of Normal Vectors (the Case of Hyperbolic Matrices)
نویسندگان
چکیده
Let A be a t × t invertible matrix with integer entries and with eigenvalues |λi| 6 = 1, i ∈ [1, t]. In this paper we prove explicitly that there exists a vector α, such that discrepancy of the sequence {αA} n=1 is equal to O(N(logN)) for N −→ ∞. This estimate can be improved no more than on the logarithmic factor. Communicated by Robert F. Tichy Dedicated to the memory of Professor Edmund Hlawka
منابع مشابه
Automatic formulation of falling multiple flexible-link robotic manipulators using 3×3 rotational matrices
In this paper, the effect of normal impact on the mathematical modeling of flexible multiple links is investigated. The response of such a system can be fully determined by two distinct solution procedures. Highly nonlinear differential equations are exploited to model the falling phase of the system prior to normal impact; and algebraic equations are used to model the normal collision of this ...
متن کاملComparing Mean Vectors Via Generalized Inference in Multivariate Log-Normal Distributions
Abstract In this paper, we consider the problem of means in several multivariate log-normal distributions and propose a useful method called as generalized variable method. Simulation studies show that suggested method has a appropriate size and power regardless sample size. To evaluation this method, we compare this method with traditional MANOVA such that the actual sizes of the two methods ...
متن کاملSOLUTION-SET INVARIANT MATRICES AND VECTORS IN FUZZY RELATION INEQUALITIES BASED ON MAX-AGGREGATION FUNCTION COMPOSITION
Fuzzy relation inequalities based on max-F composition are discussed, where F is a binary aggregation on [0,1]. For a fixed fuzzy relation inequalities system $ A circ^{F}textbf{x}leqtextbf{b}$, we characterize all matrices $ A^{'} $ For which the solution set of the system $ A^{' } circ^{F}textbf{x}leqtextbf{b}$ is the same as the original solution set. Similarly, for a fixed matrix $ A $, the...
متن کاملDiscrepancy Estimate of Normal Vectors
is called the discrepancy of (xn)n=1. In 1954 Roth (see [DrTi], [KN]) proved that for any sequence in [0, 1) limN→∞ND(N)/ log N > 0. (2) Let A be an s × s invertible matrix with integer entries. A matrix A is said to be ergodic if for almost all α ∈ R the sequence {αA}n≥1 is uniformly distributed. A vector α ∈ R is said to be normal (A normal) if the sequence {αA}n≥1 is uniformly distributed. L...
متن کاملImplementation of Hyperbolic Tangent Function to Estimate Size Distribution of Rock Fragmentation by Blasting in Open Pit Mines
Rock fragmentation is one of the desired results of rock blasting. So, controlling and predicting it, has direct effects on operational costs of mining. There are different ways that could be used to predict the size distribution of fragmented rocks. Mathematical relations have been widely used in these predictions. From among three proposed mathematical relations, one was selected in this stud...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010