Search results for "102"

Kirkman's tetrahedron and the fifteen schoolgirl problem

2011

We give a visual construction of two solutions to Kirkman's fifteen schoolgirl problem by combining the fifteen simplicial elements of a tetrahedron. Furthermore, we show that the two solutions are nonisomorphic by introducing a new combinatorial algorithm. It turns out that the two solutions are precisely the two nonisomorphic arrangements of the 35 projective lines of PG(3,2) into seven classes of five mutually skew lines. Finally, we show that the two solutions are interchanged by the canonical duality of the projective space.

Periodic and Nil Polynomials in Rings

1980

Let R be an associative ring and f(x1,…, xd) a polynomial in noncommuting variables. We say that f is periodic or nil in R if for all r1,…, rd ∈ R we have that f(r1,…, rd) is periodic, respectively nilpotent (recall that a ∈ R is periodic if for some integer ).

A non-linear Bishop–Phelps–BollobÁs type theorem

2018

Exact Quantum Query Complexity of $$\text {EXACT}_{k,l}^n$$

2017

In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly k or l of the n input bits given by an oracle are 1. We find an optimal algorithm (for some cases), and a nontrivial general lower and upper bound on the minimum number of queries to the black box.

The Variation of the Fractional Maximal Function of a Radial Function

2017

Abstract In this article, we study the regularity of the non-centered fractional maximal operator $M_{\beta}$. As the main result, we prove that there exists $C(n,\beta)$ such that if $q=n/(n-\beta)$ and $f$ is radial function, then $\|DM_{\beta}f\|_{L^{q}({\mathbb{R}^n})}\leq C(n,\beta)\|Df\|_{L^{1}({\mathbb{R}^n})}$. The corresponding result was previously known only if $n=1$ or $\beta=0$. Our proofs are almost free from one-dimensional arguments. Therefore, we believe that the new approach may be very useful when trying to extend the result for all $f\in W^{1,1}({\mathbb{R}^n})$.

Lower and Upper Probability Bounds for Some Conjunctions of Two Conditional Events

2018

In this paper we consider, in the framework of coherence, four different definitions of conjunction among conditional events. In each of these definitions the conjunction is still a conditional event. We first recall the different definitions of conjunction; then, given a coherent probability assessment (x, y) on a family of two conditional events \(\{A|H,B|K\}\), for each conjunction \((A|H) \wedge (B|K)\) we determine the (best) lower and upper bounds for the extension \(z=P[(A|H) \wedge (B|K)]\). We show that, in general, these lower and upper bounds differ from the classical Frechet-Hoeffding bounds. Moreover, we recall a notion of conjunction studied in recent papers, such that the res…

Pizza-cutter’s problem and Hamiltonian paths

2019

Summary. The pizza-cutter’s problem is to determine the maximum number of pieces that can be made with n straight cuts through a circular pizza, regardless of the size and shape of the pieces. For ...

Early development of filial preferences in the rabbit: implications of nursing- and pheromone-induced odour learning?

2008

Newborn rabbits, Oryctolagus cuniculus, discriminate between different categories of adult conspecifics on the basis of their abdominal odour cues. Whether these cues can support the development of filial preferences has not been adequately tested. Using a two-choice paradigm, we assessed the ability of 3–8-day-old pups to orient selectively to the mother versus an unfamiliar female, either spontaneously or after odour conditioning. In experiment 1, nonconditioned pups roamed indifferently over the mother and an unfamiliar female. In experiment 2, pups conditioned to a neutral odorant while nursing or with the mammary pheromone became attracted by the odorant. In experiment 3, pups that had…

Spin doctoring in British and German election campaigns: How the press is being confronted with a new quality of political PR

2000

The 1997 British and 1998 German general elections showed striking parallels and distinctive differences in the way Blair and Schroeder delivered their campaigns and defeated long-sitting conservative governments. Of vital importance was a new quality of political public relations called `spin doctoring'. In this, the British Labour Party served as a kind of role model for the German Social Democratic Party. This article traces the origins and different meanings of `spin doctoring' in both countries, distinguishes between media-related and non-media-related spin activities and analyses it against the background of the specific national contexts. The aims and methods of political spin doctor…

The Equationally-Defined Commutator in Quasivarieties Generated by Two-Element Algebras

2018

The notion of the equationally-defined commutator was introduced and thoroughly investigated in (Czelakowski, 2015). In this work the properties of the equationally-defined commutator in quasivarieties generated by two-element algebras are examined. It is proved: If a quasivariety Q is generated by a finite set of two-element algebras, then the equationally-defined commutator of Q is additive (Theorem 3.1) Moreover it satisfies the associativity law (Theorem 3.6). The second result is strengthened if the quasivariety is generated by a single two-element algebra 2: If Q = SP(2), then the equationally-defined commutator of Q universally validates one of the following laws: [x,y] = x^y or [x,y…