scholarly journals The Exact Linear Turán Number of the Sail

10.37236/9904 ◽  
2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Beka Ergemlidze ◽  
Ervin Győri ◽  
Abhishek Methuku
Keyword(s):  
The Other ◽  
Transversal Design ◽  
Additional Edge ◽  
Turán Number ◽  
Transversal Designs ◽  
Linear Hypergraph

A hypergraph is linear if any two of its edges intersect in at most one vertex. The sail (or $3$-fan) $F^3$ is the $3$-uniform linear hypergraph consisting of $3$ edges $f_1, f_2, f_3$ pairwise intersecting in the same vertex $v$ and an additional edge $g$ intersecting each $f_i$ in a vertex different from $v$. The linear Turán number $\mathrm{ex}_{\mathrm{lin}}(n, F^3)$ is the maximum number of edges in a $3$-uniform linear hypergraph on $n$ vertices that does not contain a copy of $F^3$. Füredi and Gyárfás proved that if $n = 3k$, then $\mathrm{ex}_{\mathrm{lin}}(n, F^3) = k^2$ and the only extremal hypergraphs in this case are transversal designs. They also showed that if $n = 3k+2$, then $\mathrm{ex}_{\mathrm{lin}}(n, F^3) = k^2+k$, and the only extremal hypergraphs are truncated designs (which are obtained from a transversal design on $3k+3$ vertices with $3$ groups by removing one vertex and all the hyperedges containing it) along with three other small hypergraphs. However, the case when $n =3k+1$ was left open. In this paper, we solve this remaining case by proving that $\mathrm{ex}_{\mathrm{lin}}(n, F^3) = k^2+1$ if $n = 3k+1$, answering a question of Füredi and Gyárfás. We also characterize all the extremal hypergraphs. The difficulty of this case is due to the fact that these extremal examples are rather non-standard. In particular, they are not derived from transversal designs like in the other cases.

scholarly journals List Coloring Hypergraphs

10.37236/401 ◽  
2010 ◽  
Vol 17 (1) ◽  
Author(s):  
Penny Haxell ◽  
Jacques Verstraete
Keyword(s):  
Chromatic Number ◽  
The Other ◽  
List Coloring ◽  
Other Hand ◽  
List Chromatic Number ◽  
Linear Hypergraphs ◽  
Linear Hypergraph

Let $H$ be a hypergraph and let $L_v : v \in V(H)$ be sets; we refer to these sets as lists and their elements as colors. A list coloring of $H$ is an assignment of a color from $L_v$ to each $v \in V(H)$ in such a way that every edge of $H$ contains a pair of vertices of different colors. The hypergraph $H$ is $k$-list-colorable if it has a list coloring from any collection of lists of size $k$. The list chromatic number of $H$ is the minimum $k$ such that $H$ is $k$-list-colorable. In this paper we prove that every $d$-regular three-uniform linear hypergraph has list chromatic number at least $(\frac{\log d}{5\log \log d})^{1/2}$ provided $d$ is large enough. On the other hand there exist $d$-regular three-uniform linear hypergraphs with list chromatic number at most $\log_3 d+3$. This leaves the question open as to the existence of such hypergraphs with list chromatic number $o(\log d)$ as $d \rightarrow \infty$.

The Turán Number of F3,3

2011 ◽  
Vol 21 (3) ◽  
pp. 451-456 ◽  
Author(s):  
PETER KEEVASH ◽  
DHRUV MUBAYI
Keyword(s):  
The Other ◽  
Turán Number

Let F3,3 be the 3-graph on 6 vertices, labelled abcxyz, and 10 edges, one of which is abc, and the other 9 of which are all triples that contain 1 vertex from abc and 2 vertices from xyz. We show that for all n ≥ 6, the maximum number of edges in an F3,3-free 3-graph on n vertices is $\binom{n}{3} - \binom{\lfloor n/2 \rfloor}{3} - \binom{\lceil n/2 \rceil}{3}$. This sharpens results of Zhou [9] and of the second author and Rödl [7].

scholarly journals On Symmetric Transversal Designs STD8[24; 3]'s

2010 ◽  
Vol 2010 ◽  
pp. 1-14
Author(s):  
Teppei Hatono ◽  
Chihiro Suetake
Keyword(s):  
Hadamard Matrix ◽  
Transversal Design ◽  
Generalized Hadamard Matrix ◽  
Symmetric Transversal Design ◽  
Transversal Designs

The existence of a class regular symmetric transversal design STDλ[3λ;3] is equivalent to a generalized Hadamard matrix of order 3u over GF(3). Let nλ be the number of nonisomorphic STDλ[3λ;3]'s. It is known that n1=1, n2=1, n3=4, n4=1, n5=0, n6≥20, and n7≥5. In this paper, it is shown that n8≥24.

scholarly journals LA INTEGRACIÓN MÁS QUE LA EDAD INFLUYE EN EL RENDIMIENTO DEL RAZONAMIENTO DEDUCTIVO.

2016 ◽  
Vol 1 (2) ◽  
pp. 221 ◽  
Author(s):  
Paula Álvarez Merino ◽  
Carmen Requena Hernández ◽  
Francisco Salto Alemany
Keyword(s):  
Life Cycle ◽  
Internal Consistency ◽  
Older Persons ◽  
Deductive Reasoning ◽  
General Rule ◽  
The Other ◽  
Transversal Design ◽  
Heuristic Rules ◽  
Abstraction Level ◽  
Palabras Clave

Abstract.This work merges from our interest for the evolution of deductive reasoning across the life cycle from youth to older age. With time, reasoning resources seem to be compromised and constrained, even if on the other side they seem more flexible. The literature on deductive reasoning considers that deduction only takes place between integrable premisses, that is, premisses whose elements share any categorematical term. The present research designed, applied and analyzed an instrument to measure deduction. The measure is based on integration as a general rule to deduce a conclusion from two premisses. The internal consistency of the instrument was .775 and its validity was approved by 10 experts. The transversal design had a sample of 37 young and 42 older persons, 12 of which had university degrees. Both young and old groups commit less failures with integrable elements than with non-integrable (p=.000), Importantly, the group of young reasoners show less correct answers differences between integrable and non-integrable inferences. As a conclusion, the high number of deductive errors among older persons in non integrable inferences can be explained because they seem to handle heuristic rules with a low abstraction level, of the kind: “if premisses are not integrable, then the inference is false”. The higher scores obtained by young reasoners with non integrable inferences is eventually explained in terms of the search for subjacent logical reasons in non integrable or even apparently incoherent inferential tasks.Keywords: Deduction, Aging reason, Integrable reasoning, Deductive reasonig measure instrumentResumen.El origen de este trabajo arranca del interés por conocer la evolución del razonamiento deductivo de la juventud a la vejez. Con el tiempo, los recursos razonadores parecen verse comprometidos y limitados, aunque por otra parte pueden aparecer más flexibles. La literatura sobre razonamiento deductivo considera que éste sucede sólo entre premisas que sean integrables. Del concepto de integración no existe una definición precisa aunque hay cierto acuerdo en considerar  que son integrables las premisas cuyos elementos comparten algún término categoremático. En la presente investigación se diseño, aplicó y analizó un instrumento para medir la deducción en base a  aplicar la integración como  regla general entre dos premisas para obtener la conclusión. La consistencia interna del instrumento fue de .775 y la validez de contenido fue aprobada por 10 expertos. El diseño transversal contó con una muestra de 37 jóvones y 42 personas mayores de las que 12 tenían estudios universitarios. El grupo de jóvenes y mayores comenten menos errores en los ítems integrables que en los no integrables (p = .000). Destacablemente, el grupo de jóvenes muestra menor diferencia de aciertos entre inferencias integrables y no integrables. Como conclusión, se explica el amplio número de errores deductivos de mayores en los ítems no integrables porque manejan reglas heurísticas de bajo nivel de abstracción del tipo: si las premisas no son integrables, la inferencia es falsa. El mayor acierto de los jóvenes con inferencias no integrables se explica eventualmente por la búsqueda de razones lógicas subyacentes ante una tarea aparentemente incoherente. Palabras Clave: Deducción, Razonamiento en la vejez, Razonamiento integrable, Razonamiento deductivo instrumento de medida

Stromatoporoids from the Famennian (Devonian) Wabamun Formation, Normandville oilfield, north–central Alberta, Canada

1988 ◽  
Vol 62 (03) ◽  
pp. 411-419 ◽  
Author(s):  
Colin W. Stearn
Keyword(s):  
Patch Reef ◽  
Abundant Species ◽  
The Other ◽  
North Central ◽  
Biotic Crisis

Stromatoporoids are the principal framebuilding organisms in the patch reef that is part of the reservoir of the Normandville field. The reef is 10 m thick and 1.5 km2in area and demonstrates that stromatoporoids retained their ability to build reefal edifices into Famennian time despite the biotic crisis at the close of Frasnian time. The fauna is dominated by labechiids but includes three non-labechiid species. The most abundant species isStylostroma sinense(Dong) butLabechia palliseriStearn is also common. Both these species are highly variable and are described in terms of multiple phases that occur in a single skeleton. The other species described areClathrostromacf.C. jukkenseYavorsky,Gerronostromasp. (a columnar species), andStromatoporasp. The fauna belongs in Famennian/Strunian assemblage 2 as defined by Stearn et al. (1988).

D. The Line Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 207-244
Author(s):  
R. P. Kraft
Keyword(s):  
Variable Stars ◽  
The Other ◽  
Line Spectrum ◽  
Afternoon Session ◽  
Empirical Information ◽  
Pulsating Variable Stars ◽  
Almost Continuous ◽  
Informal Approach

(Ed. note:Encouraged by the success of the more informal approach in Christy's presentation, we tried an even more extreme experiment in this session, I-D. In essence, Kraft held the floor continuously all morning, and for the hour and a half afternoon session, serving as a combined Summary-Introductory speaker and a marathon-moderator of a running discussion on the line spectrum of cepheids. There was almost continuous interruption of his presentation; and most points raised from the floor were followed through in detail, no matter how digressive to the main presentation. This approach turned out to be much too extreme. It is wearing on the speaker, and the other members of the symposium feel more like an audience and less like participants in a dissective discussion. Because Kraft presented a compendious collection of empirical information, and, based on it, an exceedingly novel series of suggestions on the cepheid problem, these defects were probably aggravated by the first and alleviated by the second. I am much indebted to Kraft for working with me on a preliminary editing, to try to delete the side-excursions and to retain coherence about the main points. As usual, however, all responsibility for defects in final editing is wholly my own.)

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

Observing programme for the 24-inch/36-inch Schmidt telescope

1966 ◽  
Vol 24 ◽  
pp. 337
Author(s):  
W. Iwanowska
Keyword(s):  
The Other ◽  
Schmidt Telescope ◽  
Flint Glass

A new 24-inch/36-inch//3 Schmidt telescope, made by C. Zeiss, Jena, has been installed since 30 August 1962, at the N. Copernicus University Observatory in Toruń. It is equipped with two objective prisms, used separately, one of crown the other of flint glass, each of 5° refracting angle, giving dispersions of 560Å/mm and 250Å/ mm respectively.

A hard choice for Tomasello

2020 ◽  
Vol 43 ◽  
Author(s):  
Philip Pettit
Keyword(s):  
Joint Action ◽  
The Other ◽  
Hard Choice ◽  
Margaret Gilbert ◽  
Michael Bratman ◽  
Human Sense ◽  
Sense Of Obligation

Abstract Michael Tomasello explains the human sense of obligation by the role it plays in negotiating practices of acting jointly and the commitments they underwrite. He draws in his work on two models of joint action, one from Michael Bratman, the other from Margaret Gilbert. But Bratman's makes the explanation too difficult to succeed, and Gilbert's makes it too easy.

A study of cometary eruptions through OH radio-lines

1999 ◽  
Vol 173 ◽  
pp. 249-254
Author(s):  
A.M. Silva ◽  
R.D. Miró
Keyword(s):  
Short Duration ◽  
Growth Curves ◽  
The Other ◽  
Initial Mass ◽  
Radio Lines ◽  
Other Hand ◽  
Sudden Rise

AbstractWe have developed a model for theH2OandOHevolution in a comet outburst, assuming that together with the gas, a distribution of icy grains is ejected. With an initial mass of icy grains of 108kg released, theH2OandOHproductions are increased up to a factor two, and the growth curves change drastically in the first two days. The model is applied to eruptions detected in theOHradio monitorings and fits well with the slow variations in the flux. On the other hand, several events of short duration appear, consisting of a sudden rise ofOHflux, followed by a sudden decay on the second day. These apparent short bursts are frequently found as precursors of a more durable eruption. We suggest that both of them are part of a unique eruption, and that the sudden decay is due to collisions that de-excite theOHmaser, when it reaches the Cometopause region located at 1.35 × 105kmfrom the nucleus.

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