scholarly journals A characterization of a class of non-binary matroids

1990 ◽  
Vol 49 (2) ◽  
pp. 181-189 ◽  
Author(s):  
James G Oxley
Keyword(s):  
Binary Matroids

A characterization of n-connected splitting matroids

2014 ◽  
Vol 07 (04) ◽  
pp. 1450060
Author(s):  
P. P. Malavadkar ◽  
M. M. Shikare ◽  
S. B. Dhotre
Keyword(s):  
Binary Matroid ◽  
Binary Matroids ◽  
Splitting Operation

The splitting operation on an n-connected binary matroid may not yield an n-connected binary matroid. In this paper, we characterize n-connected binary matroids which yield n-connected binary matroids by the generalized splitting operation.

scholarly journals Idealness of k-wise intersecting families

2020 ◽  
Author(s):  
Ahmad Abdi ◽  
Gérard Cornuéjols ◽  
Tony Huynh ◽  
Dabeen Lee
Keyword(s):  
Chromatic Number ◽  
Common Element ◽  
Binary Matroids ◽  
Projective Geometries ◽  
Intersecting Families ◽  
Cycle Covers ◽  
Binary Clutters

Abstract A clutter is k-wise intersecting if every k members have a common element, yet no element belongs to all members. We conjecture that, for some integer $$k\ge 4$$ k ≥ 4 , every k-wise intersecting clutter is non-ideal. As evidence for our conjecture, we prove it for $$k=4$$ k = 4 for the class of binary clutters. Two key ingredients for our proof are Jaeger’s 8-flow theorem for graphs, and Seymour’s characterization of the binary matroids with the sums of circuits property. As further evidence for our conjecture, we also note that it follows from an unpublished conjecture of Seymour from 1975. We also discuss connections to the chromatic number of a clutter, projective geometries over the two-element field, uniform cycle covers in graphs, and quarter-integral packings of value two in ideal clutters.

scholarly journals Circuit-Difference Matroids

10.37236/9314 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
George Drummond ◽  
Tara Fife ◽  
Kevin Grace ◽  
James Oxley
Keyword(s):  
Disjoint Union ◽  
Symmetric Difference ◽  
Binary Matroids ◽  
Regular Matroid

One characterization of binary matroids is that the symmetric difference of every pair of intersecting circuits is a disjoint union of circuits. This paper considers circuit-difference matroids, that is, those matroids in which the symmetric difference of every pair of intersecting circuits is a single circuit. Our main result shows that a connected regular matroid is circuit-difference if and only if it contains no pair of skew circuits. Using a result of Pfeil, this enables us to explicitly determine all regular circuit-difference matroids. The class of circuit-difference matroids is not closed under minors, but it is closed under series minors. We characterize the infinitely many excluded series minors for the class.

scholarly journals ℓ-matrices and a characterization of binary matroids

1974 ◽  
Vol 8 (2) ◽  
pp. 139-145 ◽  
Author(s):  
Robert E. Bixby
Keyword(s):  
Binary Matroids

Non-Binary Matroids Having At Most Three Non-Binary Elements

1994 ◽  
Vol 3 (3) ◽  
pp. 355-369 ◽  
Author(s):  
Manoel Lemos
Keyword(s):  
Binary Matroids

An element e of a matroid M is called non-binary when M\e and M/e are both non-binary matroids. Oxley in [5] gave a characterization of the 3-connected non-binary matroids without non-binary elements. In this paper, we will construct all the 3-connected matroids having 1, 2 or 3 non-binary elements.

scholarly journals On the Excluded Minors for Matroids of Branch-Width Three

10.37236/1648 ◽  
2002 ◽  
Vol 9 (1) ◽  
Author(s):  
Petr Hliněný
Keyword(s):  
Computer Assisted ◽  
Binary Matroids ◽  
Alternative Characterization ◽  
Excluded Minor ◽  
Practical Algorithm ◽  
Branch Width ◽  
A Minor ◽  
Excluded Minors

Knowing the excluded minors for a minor-closed matroid property provides a useful alternative characterization of that property. It has been shown in [R. Hall, J. Oxley, C. Semple, G. Whittle, On Matroids of Branch-Width Three, submitted 2001] that if $M$ is an excluded minor for matroids of branch-width $3$, then $ M$ has at most $14$ elements. We show that there are exactly $10$ such binary matroids $M$ (7 of which are regular), proving a conjecture formulated by Dharmatilake in 1994. We also construct numbers of such ternary and quaternary matroids $ M$, and provide a simple practical algorithm for finding a width-$3$ branch-decomposition of a matroid. The arguments in our paper are computer-assisted — we use a program $MACEK$ [P. Hliněný, The MACEK Program, http://www.mcs.vuw.ac.nz/research/macek, 2002] for structural computations with represented matroids. Unfortunately, it seems to be infeasible to search through all matroids on at most $14$ elements.

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 144-145
Author(s):  
B. H. Kear ◽  
J. M. Oblak
Keyword(s):  
Stable Phase ◽  
Nickel Base Superalloy ◽  
Alloy 718 ◽  
Commercial Alloy ◽  
Precipitate Morphology ◽  
Continuous Precipitation ◽  
Nickel Base ◽  
Base Superalloy ◽  
Strengthening Precipitate

A nickel-base superalloy is essentially a Ni/Cr solid solution hardened by additions of Al (Ti, Nb, etc.) to precipitate a coherent, ordered phase. In most commercial alloy systems, e.g. B-1900, IN-100 and Mar-M200, the stable precipitate is Ni3 (Al,Ti) γ′, with an LI2structure. In A lloy 901 the normal precipitate is metastable Nis Ti3 γ′ ; the stable phase is a hexagonal Do2 4 structure. In Alloy 718 the strengthening precipitate is metastable γ″, which has a body-centered tetragonal D022 structure.Precipitate MorphologyIn most systems the ordered γ′ phase forms by a continuous precipitation re-action, which gives rise to a uniform intragranular dispersion of precipitate particles. For zero γ/γ′ misfit, the γ′ precipitates assume a spheroidal.

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