scholarly journals On split Lie color triple systems

2019 ◽  
Vol 17 (1) ◽  
pp. 267-281
Author(s):  
Yan Cao ◽  
Jian Zhang ◽  
Yunan Cui
Keyword(s):  
Root System ◽  
Triple System ◽  
Natural Generalization ◽  
Maximal Length ◽  
Base Field ◽  
Triple Systems

Abstract In order to begin an approach to the structure of arbitrary Lie color triple systems, (with no restrictions neither on the dimension nor on the base field), we introduce the class of split Lie color triple systems as the natural generalization of split Lie triple systems. By developing techniques of connections of roots for this kind of triple systems, we show that any of such Lie color triple systems T with a symmetric root system is of the form T = U + ∑[α]∈Λ1/∼ I[α] with U a subspace of T0 and any I[α] a well described (graded) ideal of T, satisfying {I[α], T, I[β]} = 0 if [α] ≠ [β]. Under certain conditions, in the case of T being of maximal length, the simplicity of the triple system is characterized.

Catalytic Activity of Binary and Triple Systems Based on Redox Inactive Metal Compound, LiSt and Additives of Monodentate Ligands-Modifiers: DMF, HMPA and PhOH, in Selective Ethylbenzene Oxidation with Dioxygen

2016 ◽  
Vol 10 (3) ◽  
pp. 259-270
Author(s):  
Ludmila Matienko ◽  
◽  
Larisa Mosolova ◽  
Vladimir Binyukov ◽  
Gennady Zaikov ◽  
...  
Keyword(s):  
Catalytic Activity ◽  
Triple System ◽  
Metal Compound ◽  
Ethylbenzene Oxidation ◽  
Catalytic Systems ◽  
Triple Systems ◽  
Lithium Compound ◽  
Mechanism Of Catalysis ◽  
Monodentate Ligands

Mechanism of catalysis with binary and triple catalytic systems based on redox inactive metal (lithium) compound {LiSt+L2} and {LiSt+L2+PhOH} (L2=DMF or HMPA), in the selective ethylbenzene oxidation by dioxygen into -phenylethyl hydroperoxide is researched. The results are compared with catalysis by nickel-lithium triple system {NiII(acac)2+LiSt+PhOH} in selective ethylbenzene oxidation to PEH. The role of H-bonding in mechanism of catalysis is discussed. The possibility of the stable supramolecular nanostructures formation on the basis of triple systems, {LiSt+L2+PhOH}, due to intermolecular H-bonds, is researched with the AFM method.

scholarly journals Characterisation Results for Steiner Triple Systems and Their Application to Edge-Colourings of Cubic Graphs

2010 ◽  
Vol 62 (2) ◽  
pp. 355-381 ◽  
Author(s):  
Daniel Král’ ◽  
Edita Máčajov´ ◽  
Attila Pór ◽  
Jean-Sébastien Sereni
Keyword(s):  
Triple System ◽  
Steiner Triple System ◽  
Cubic Graphs ◽  
Steiner Triple Systems ◽  
Cubic Graph ◽  
Triple Systems ◽  
Forbidden Configurations ◽  
Edge Colourings

AbstractIt is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration C14. We find three configurations such that a Steiner triple system is affine if and only if it does not contain one of these configurations. Similarly, we characterise Hall triple systems using two forbidden configurations.Our characterisations have several interesting corollaries in the area of edge-colourings of graphs. A cubic graph G is S-edge-colourable for a Steiner triple system S if its edges can be coloured with points of S in such a way that the points assigned to three edges sharing a vertex form a triple in S. Among others, we show that all cubic graphs are S-edge-colourable for every non-projective nonaffine point-transitive Steiner triple system S.

scholarly journals On the Structure of Graded Leibniz Algebras

2015 ◽  
Vol 22 (01) ◽  
pp. 83-96 ◽  
Author(s):  
Antonio J. Calderón Martín ◽  
José M. Sánchez Delgado
Keyword(s):  
Arbitrary Dimension ◽  
Unit Element ◽  
Homogeneous Component ◽  
Maximal Length ◽  
Base Field ◽  
Leibniz Algebras ◽  
Arbitrary Base

We study the structure of graded Leibniz algebras with arbitrary dimension and over an arbitrary base field 𝕂. We show that any of such algebras 𝔏 with a symmetric G-support is of the form [Formula: see text] with U a subspace of 𝔏1, the homogeneous component associated to the unit element 1 in G, and any Ij a well described graded ideal of 𝔏, satisfying [Ij, Ik]=0 if j ≠ k. In the case of 𝔏 being of maximal length, we characterize the gr-simplicity of the algebra in terms of connections in the support of the grading.

scholarly journals Triple systems with a fixed number of repeated triples

1986 ◽  
Vol 41 (2) ◽  
pp. 180-187 ◽  
Author(s):  
C. A. Rodger
Keyword(s):  
Triple System ◽  
Fixed Number ◽  
Triple Systems ◽  
Partial Triple System

AbstractIn this paper, linear embeddings of partial designs into designs are found where no repeated blocks are introduced in the embedding process. Triple systems, pure cyclic triple systems, cyclic and directed triple systems are considered. In particular, a partial triple system with no repeated triples is embedded linearly in a triple system with no repeated triples.

Steiner triple systems of order 19 constructed from the Steiner triple system of order 9

1983 ◽  
Vol 94 (1-2) ◽  
pp. 89-92 ◽  
Author(s):  
Alan R. Prince
Keyword(s):  
Standard Method ◽  
Triple System ◽  
Isomorphism Class ◽  
Automorphism Groups ◽  
Steiner Triple System ◽  
Steiner Triple Systems ◽  
Triple Systems ◽  
Isomorphism Classes

SynopsisA standard method of constructing Steiner triple systems of order 19 from the Steiner triple system of order 9 gives rise to 212 different such systems. It is shown that there are just three isomorphism classes amongst these systems. Representatives of each isomorphism class are described and the orders of their automorphism groups are determined.

scholarly journals Codes, Lattices and Steiner Systems

10.37236/1291 ◽  
1997 ◽  
Vol 4 (1) ◽  
Author(s):  
Patrick Solé
Keyword(s):  
Root System ◽  
Binary Code ◽  
The Other ◽  
Steiner Triple Systems ◽  
Steiner Systems ◽  
Classification Schemes ◽  
Triple Systems

Two classification schemes for Steiner triple systems on 15 points have been proposed recently: one based on the binary code spanned by the blocks, the other on the root system attached to the lattice affinely generated by the blocks. It is shown here that the two approaches are equivalent.

scholarly journals An empirical fit for viscoelastic simulations of tertiary tides

2019 ◽  
Vol 491 (1) ◽  
pp. 264-271
Author(s):  
Yan Gao ◽  
Silvia Toonen ◽  
Evgeni Grishin ◽  
Tom Comerford ◽  
Matthias U Kruckow
Keyword(s):  
Time Scales ◽  
Stellar Evolution ◽  
Triple System ◽  
Mass Ratio ◽  
Empirical Expression ◽  
Triple Systems ◽  
Tidal Interactions ◽  
The Subject ◽  
Computationally Expensive ◽  
The Masses

ABSTRACT Tertiary tides (TTs), or the continuous tidal distortion of the tertiary in a hierarchical triple system, can extract energy from the inner binary, inducing within it a proclivity to merge. Despite previous work on the subject, which established that it is significant for certain close triple systems, it is still not a well-understood process. A portion of our ignorance in this regard stems from our inability to integrate a simulation of this phenomenon into conventional stellar evolution codes, since full calculations of these tidal interactions are computationally expensive on stellar evolution time-scales. Thus, to attain a better understanding of how these TTs act on longer time-scales, an empirical expression of its effects as a function of parameters of the triple system involved is required. In this work, we evaluate the rate at which TTs extract energy from the inner binary within a series of constructed hierarchical triple systems under varying parameters, and study the rate at which the inner binary orbital separation shrinks as a function of those parameters. We find that this rate varies little with the absolute values of the masses of the three component objects, but is very sensitive to the mass ratio of the inner binary q, the tertiary radius R3, the inner binary orbital separation a1, the outer orbital separation a2, and the viscoelastic relaxation time of the tertiary τ. More specifically, we find that the percentage by which a1 shrinks per unit time can be reasonably approximated by (1/a1)(da1/dt) = (2.22 × 10−8 yr−1)4q(1 + q)−2(R3/100 R⊙)5.2(a1/0.2 au)4.8(a2/2 au)−10.2 (τ/0.534 yr)−1.0. We also provide tests of how precise this fitting function is.

Construction of Steiner Triple Systems Having Exactly One Triple in Common

1974 ◽  
Vol 26 (1) ◽  
pp. 225-232 ◽  
Author(s):  
Charles C. Lindner
Keyword(s):  
Triple System ◽  
Steiner Triple System ◽  
Steiner Triple Systems ◽  
Triple Systems

A Steiner triple system is a pair (Q, t) where Q is a set and t a collection of three element subsets of Q such that each pair of elements of Q belong to exactly one triple of t. The number |Q| is called the order of the Steiner triple system (Q, t). It is well-known that there is a Steiner triple system of order n if and only if n ≡ 1 or 3 (mod 6). Therefore in saying that a certain property concerning Steiner triple systems is true for all n it is understood that n ≡ 1 or 3 (mod 6). Two Steiner triple systems (Q, t1) and (Q, t2) are said to be disjoint provided that t1 ∩ t2 = Ø. Recently, Jean Doyen has shown the existence of a pair of disjoint Steiner triple systems of order n for every n ≧ 7 [1].

Hermitian generalized Jordan triple systems and certain applications to field theory

2014 ◽  
Vol 29 (13) ◽  
pp. 1450071 ◽  
Author(s):  
Noriaki Kamiya ◽  
Matsuo Sato
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Triple System ◽  
Structure Theorem ◽  
Triple Systems ◽  
Jordan Triple System ◽  
Mathematical Properties ◽  
Jordan Triple Systems ◽  
Chern Simons

We define Hermitian generalized Jordan triple systems and prove a structure theorem. We also give some examples of the systems and study mathematical properties. We apply a Hermitian generalized Jordan triple system to a field theory and obtain a Chern–Simons gauge theory.

scholarly journals A STRUCTURE THEORY OF (−1,−1)-FREUDENTHAL KANTOR TRIPLE SYSTEMS

2009 ◽  
Vol 81 (1) ◽  
pp. 132-155 ◽  
Author(s):  
NORIAKI KAMIYA ◽  
DANIEL MONDOC ◽  
SUSUMU OKUBO
Keyword(s):  
Triple System ◽  
Lie Superalgebras ◽  
Structure Theory ◽  
Triple Systems ◽  
Jordan Triple System

AbstractIn this paper we discuss the simplicity criteria of (−1,−1)-Freudenthal Kantor triple systems and give examples of such triple systems, from which we can construct some Lie superalgebras. We also show that we can associate a Jordan triple system to any (ε,δ)-Freudenthal Kantor triple system. Further, we introduce the notion of δ-structurable algebras and connect them to (−1,δ)-Freudenthal Kantor triple systems and the corresponding Lie (super)algebra construction.

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