相关论文: Getting results with negative thinking
In robust optimization, the uncertainty set is used to model all possible outcomes of uncertain parameters. In the classic setting, one assumes that this set is provided by the decision maker based on the data available to her. Only…
One can find lists of whole numbers having equal sum and product. We call such a creature a bioperational multiset. No one seems to have seriously studied them in areas outside whole numbers such as the rationals, Gaussian integers, or…
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…
We study the following problem. Given a multiset $M$ of non-negative integers, decide whether there exist and, in the positive case, compute two non-trivial multisets whose Minkowski sum is equal to $M$. The Minkowski sum of two multisets A…
A set of natural numbers will be called \emph{harmonic} if the reciprocals of its elements form a divergent series. An ultrafilter of the natural numbers will he called \emph{harmonic} if all each members are harmonic sets. The harmonic…
There are many papers studying properties of point sets in the Euclidean space $\mathbb{E}^m$ or on integer grids $\mathbb{Z}^m$, with pairwise integral or rational distances. In this article we consider the distances or coordinates of the…
We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions.
This report presents an expression for the number of a multiset's sub-multisets of a given cardinality as a function of the multiplicity of its elements. This is also the number of distinct samples of a given size that may be produced by…
Multisets are an intuitive extension of the traditional concept of sets that allow repetition of elements, with the number of times each element appears being understood as the respective multiplicity. Recent generalizations of multisets to…
Two of the pillars of combinatorics are the notion of choosing an arbitrary subset of a set with $n$ elements (which can be done in $2^n$ ways), and the notion of choosing a $k$-element subset of a set with $n$ elements (which can be done…
A numeral system is an infinite sequence of different closed normal $\lambda$-terms intended to code the integers in $\lambda$-calculus. H. Barendregt has shown that if we can represent, for a numeral system, the functions : Successor,…
A "numerical set-expression" is a term specifying a cascade of arithmetic and logical operations to be performed on sets of non-negative integers. If these operations are confined to the usual Boolean operations together with the result of…
We continue the exploration of various aspects of divisibility of ultrafilters, adding one more relation to the picture: multiplicative finite embeddability. We show that it lies between divisibility relations $\mid_M$ and…
The unity of mathematics has its power to compactify experiences in a form capable of being transferred and modified or adapted to new mathematical situations. Yet, we believe that the phrase "Unity of Mathematics" expresses a dream, an…
The number of tuples with positive integers pairwise relatively prime to each other with product at most $n$ is considered. A generalization of $\mu^{2}$ where $\mu$ is the M\"{o}bius function is used to formulate this divisor sum and…
For a set of nonnegative integers $A$, denote by $R_{A}(n)$ the number of unordered representations of the integer $n$ as the sum of two different terms from $A$. In this paper we partially describe the structure of the sets, which have…
We investigate the internal space of Bessel functions which is associated to the group Z of positive and negative integers defining their orders. As a result we propose and prove a new unifying formula (to be added to the huge literature on…
We study countable embedding-universal and homomorphism-universal structures and unify results related to both of these notions. We show that many universal and ultrahomogeneous structures allow a concise description (called here a finite…
Let R be the ring of S-integers of an algebraic function field (in one variable) over a perfect field, where S is finite and not empty. It is shown that for every positive integer N there exist elements of R that can not be written as a sum…
When we think of model ensembling or ensemble modeling, there are many possibilities that come to mind in different disciplines. For example, one might think of a set of descriptions of a phenomenon in the world, perhaps a time series or a…