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1
Content available remote

On the roots of certain sequences of congruences

100%
Berend D.
Acta Arithmetica
|
1994
|
tom 67
|
nr 1
97-104
2
Content available remote

On some arithmetical properties of middle binomial coefficients

64%
Berend D., Harmse J.
Acta Arithmetica
|
1998
|
tom 84
|
nr 1
31-41
3
Content available remote

Uniform decompositions of polytopes

64%
Berend D., Bromberg L.
Applicationes Mathematicae
|
2006
|
tom 33
|
nr 2
243-252
EN
We design a method of decomposing convex polytopes into simpler polytopes. This decomposition yields a way of calculating exactly the volume of the polytope, or, more generally, multiple integrals over the polytope, which is equivalent to the way suggested in Schechter, based on Fourier-Motzkin elimination (Schrijver). Our method is applicable for finding uniform decompositions of certain natural families of polytopes. Moreover, this allows us to find algorithmically an analytic expression for the distribution function of a random variable of the form $∑_{i=1}^{d}c_{i}X_{i}$, where $(X₁,..., X_{d})$ is a random vector, uniformly distributed in a polytope.
4
Content available remote

On a result of Mahler on the decimal expansions of (nα)

64%
Berend D., Boshernitzan M.
Acta Arithmetica
|
1994
|
tom 66
|
nr 4
315-322
5
Content available remote

Probabilistic comparison of weighted majority rules

51%
Berend D., Bromberg L., Sapir L.
Applicationes Mathematicae
|
2012
|
tom 39
|
nr 2
151-167
EN
This paper studies a bi-parametric family of decision rules, so-called restricted distinguished chairman rules, which contains several one-parameter classes of rules considered previously in the literature. Roughly speaking, these rules apply to a variety of situations where the original committee appoints a subcommittee. Moreover, the chairman of the subcommittee, who is supposed to be the most competent committee member, may have more voting power than other jurors. Under the assumption of exponentially distributed decision skills, we obtain an analytic formula for the probability of any restricted distinguished chairman rule being optimal. We also study, for arbitrary fixed voting power of the chairman, the connection between the probability of the rule being optimal and the size of the subcommittee.
6
Content available remote

Actions of sets of integers on irrationals

32%
Berend D.
Acta Arithmetica
|
1987
|
tom 48
|
nr 3
275-306
7
Content available remote

Density modulo 1 in local fields

26%
Berend D.
Acta Arithmetica
|
1989
|
tom 52
|
nr 3
267-282
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