485 research outputs found
Asymptotics of the number of threshold functions on a two-dimensional rectangular grid
Let , . It is well-known that the number of
(two-dimensional) threshold functions on an rectangular grid is
{eqnarray*} t(m,n)=\frac{6}{\pi^2}(mn)^2+O(m^2n\log{n})+O(mn^2\log{\log{n}})=
\frac{6}{\pi^2}(mn)^2+O(mn^2\log{m}). {eqnarray*} We improve the error term by
showing that t(m,n)=\frac{6}{\pi^2}(mn)^2+O(mn^2). $
The arithmetic derivative and Leibniz-additive functions
An arithmetic function is Leibniz-additive if there is a completely
multiplicative function , i.e., and for
all positive integers and , satisfying
for all positive integers and . A motivation for the present study is
the fact that Leibniz-additive functions are generalizations of the arithmetic
derivative ; namely, is Leibniz-additive with . In this paper,
we study the basic properties of Leibniz-additive functions and, among other
things, show that a Leibniz-additive function is totally determined by the
values of and at primes. We also consider properties of
Leibniz-additive functions with respect to the usual product, composition and
Dirichlet convolution of arithmetic functions
The effect of lifting date, packing. storing and watering on the field survival and growth of Scots pine seedlings.
Allocation of rehabilitation measures provided by the Social Insurance Institution in Finland: A register linkage study
Effects of multidisciplinary inpatient rehabilitation for chronic back or neck pain: a register-linkage study of sickness absences and analgesic purchases in an occupational cohort
Microbiology of Bartholin's Duct Abscess
Objective: The aim of the study was to determine the currently most
frequent microbial findings in Bartholin's duct abscess
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