A construction for partially ordered sets

A construction I(S) is defined which corresponds to the intuitive notion of the set of places in which new elements can be inserted into a given poset S. It is given the minimal possible ordering. It turns out that if the base sets are chains the construction produces the corresponding interval orders. for whose dimensions there exist good estimates. In this paper we make the dual restriction that the height of the underlying set is ?1. Under this assumption we find a bound for the dimension of I(S) in general and a precise value if the set consists of two antichains all the elements of one lying above all those of the other.     

On copowers of an ordered skew field

It is shown that the double of an ordered skew fieldE over a subfieldK, which is its own bicentralizer, can again be ordered, and a corresponding result for groups is deduced.     

A Solution of Conway's Fried Potato Problem

In order to fry it as expeditiously as possible, Conway wishesto slice a given convex potato into n pieces by n–1 successiveplane cuts (just one piece being divided by each cut), so asto minimize the greatest inradius of the pieces. We show thatone has to employ equally-spaced parallel cuts, choosing thedirection of the cuts parallel to the planes of support whichdetermine the minimum width of a well-defined, rounded potato.We also show some examples and discuss two variations of theoriginal problem.     

The kurzweil construction of an integral in ordered spaces

This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space T with respect to an ordered group valued measure are proved in this paper.     

Toward a Characterization of Conway's Group Co3

In this paper, Conway's group, Co₃, is characterized among simplegroups of even type with e(G) = 3, by a restriction on the p-localstructure for some odd prime p for which m_2,p(G) = 3. 2000 MathematicsSubject Classification 20D05.     

On characterizations of the ordered field of real numbers

This self-contained note could find classroom use in an introductory course on analysis. It is proved that an ordered field F is complete (that is, order-isomorphic to the field of real numbers) if and only if each bounded monotonic sequence in F converges in F. Also established is the key tool that an ordered field is complete if and only if it is Archimedean and Cauchy-complete, along with a number of characterizations of Archimedean fields.     

A class of stochastic games with ordered field property

It is shown that discounted general-sum stochastic games with two players, two states, and one player controlling the rewards have the ordered field property. For the zero-sum case, this result implies that, when starting with rational data, also the value is rational and that the extreme optimal stationary strategies are composed of rational components.     

Computational methods for Conway's Game of Life cellular automaton

The cellular automaton model of computation has drawn the interest of researchers from different disciplines including computer science, biology, mathematics, economy, biochemistry and philosophy. Although a cellular automaton is based on a set of simple rules, over time complex patterns may evolve. We present computational methods for implementing and optimizing a well known two-state cellular automaton, Conway's Game of Life, on a 16-core Intel Xeon. The evaluation is based on three multicore algorithms. The first algorithm is coherent and utilizes shared memory and barrier synchronization. The remaining two algorithms are distributed and utilize private memories and explicit core-to-core message passing. We provide a link to our open source simulation software.     

An investigation on ordered algebraic hyperstructures

In this paper, we present some basic notions of simple ordered semihypergroups and regular ordered Krasner hyperrings and prove some results in this respect. In addition, we describe pure hyperideals of ordered Krasner hyperrings and investigate some properties of them. Finally, some results concerning purely prime hyperideals are proved.     

An alternative Gentzenisation of

In this paper, we give a sequent calculus for the positive contraction‐less relevant logic and we give a proof that it is cut‐free without the use of the truth constant t. Based on , we re‐prove the decidability of the logic .     

An example on ordered Banach algebras

Let be a complex unital Banach algebra. We consider the Banach algebra ordered by the algebra cone , and investigate the connection between results on ordered Banach algebras and the right bound of the numerical range of elements in .

     

Testing homogeneity with an ordered alternative in a two-factor layout by combiningp-values

Two-factor experiments in which both factors are ordinal are considered. If it is believedapriori that the mean response is nondecreasing in each factor with the other held fixed, then one may test for a treatment effect by testing homogeneity with the appropriate ordered alternative. The likelihood ratio test has been developed in the literature, but the level probabilities needed to implement the test have only been determined in a few special cases by Monte Carlo techniques. A test obtained by combining thep-values from a test concerning the rows and a test concerning the columns is studied. Fisher's method of combiningp-values is recommended. It is shown that the likelihood ratio test is more powerful, but if one does not want to obtain Monte Carlo estimates of the level probabilities, then the procedure proposed here should be considered.This research was supported by the National Institutes of Health under Grant 1R01GM42584-01. Part of this work is taken from the first author's dissertation submitted in partial fulfillment for the Ph.D. degree at the University of Missouri-Columbia.     

A bartlett-type adjustment for the likelihood ratio statistic with an ordered alternative

For testing the equality of normal variances with an increasing alternative, under the null hypothesis the likelihood ratio test statistic is asymptotically distributed as a mixture of chi-squared distributions. In this paper a Bartlett-type adjustment is proposed to improve the approximation of the null distribution of the likelihood ratio test statistic with an ordered alternative.     

An alternative quadratic formula

Mathematische Semesterberichte - One would usually expect that a subject such as the quadratic equation which is known since Babylonian times would not offer any interesting new aspect...     

An alternative givens ordering

Summary A new Givens ordering is shown, empirically and by an approximate theoretical analysis, to take appreciably fewer stages than the standard scheme. Sharper error bounds than Gentleman's ensue, and the scheme is better suited to parallel computation. Other schemes, less efficient but more easily analysed, are discussed. The effect of a possible limit in practice on the number of simultaneous computations is considered.     

An alternative Daugavet property

We introduce a strictly weaker version of the Daugavet property as follows: a Banach space X has this alternative Daugavet property (ADP in short) if the norm identity

(aDE)