#### 62 Citations

Kobe University Repository : Kernel タイトル Tit le A metric discrepancy result with given speed 著者

- 2018

It is known that the discrepancy DN{kx} of the sequence {kx} satisfies NDN{kx} = O ( (log N)(log log N) ) a.e. for all ε > 0, but not for ε = 0. For nk = θ, θ > 1 we have NDN{nkx} ≤ (Σθ + ε)(2N log… Expand

On Weyl products and uniform distribution modulo one

- Mathematics, Medicine
- Monatshefte fur Mathematik
- 2018

The main result are matching lower and upper bounds for such products in terms of the star-discrepancy of the underlying points $$\omega $$ω, thereby improving earlier results obtained by Hlawka. Expand

A metric discrepancy result with given speed

- Mathematics
- 2017

It is known that the discrepancy $${D_N\{kx\}}$$DN{kx} of the sequence $${\{kx\}}$${kx} satisfies $${ND_N\{kx\} = O((\log N){(\log \log N)}^{1+\varepsilon})}$$NDN{kx}=O((logN)(loglogN)1+ε) a.e. for… Expand

Homogenization of Neumann boundary data with fully nonlinear operator

- Mathematics
- 2013

In this paper we study periodic homogenization problems for solutions of fully nonlinear PDEs, in half-spaces with oscillatory Neumann boundary data. We show the existence, uniqueness of the… Expand

On the law of the iterated logarithm for the discrepancy of 〈nkx〉

- Mathematics
- 2008

Abstract.By a well known result of Philipp (1975), the discrepancy DN(ω) of the sequence (nkω)k≥1 mod 1 satisfies the law of the iterated logarithm under the Hadamard gap condition nk + 1/nk ≥ q > 1… Expand

Local Discrepancies in the Problem of the Distribution of the Sequence
$$\{k\alpha\}$$

- 2021

Abstract The paper deals with local discrepancies in the problem of the distribution of the sequence $$\{k\alpha\}$$ , i.e., with the remainder terms in asymptotic formulas for the number of points… Expand

Minimal Graphs with Respect to Geometric Distance Realizability

- Mathematics, Computer Science
- Discuss. Math. Graph Theory
- 2021

It is proved that, for infinitely many n, the number of non-isomorphic n-vertex minimal non-unit-distance graphs is at least exponential in n. Expand

Centralized and Decentralized Warehouse Logistics Collaboration

- Business, Computer Science
- Manuf. Serv. Oper. Manag.
- 2020

The value of collaboration is bound in a decentralized multisupplier multiretailer setting, where several suppliers ship to several retailers through a shared warehouse, and out to the public through a distributed network of retailers. Expand

Equidistribution of orbits of isometries on compact Riemannian manifolds

- Mathematics
- 2020

Abstract Let S be a finitely generated semigroup of isometries of a compact Riemannian manifold. We present a simple argument to prove that, if there exists a point x whose orbit S x is dense, then… Expand