scholarly journals A characterization of the Arf property for quadratic quotients of the Rees algebra

2019 ◽  
Vol 19 (07) ◽  
pp. 2050127 ◽  
Author(s):  
Alessio Borzì
Keyword(s):  
Numerical Semigroup ◽  
Rees Algebra ◽  
Numerical Duplication

We provide a characterization of the Arf property in both the numerical duplication of a numerical semigroup and in a member of a family of quotients of the Rees algebra studied in [V. Barucci, M. D’Anna and F. Strazzanti, A family of quotients of the Rees algebra, Commun. Algebra 43(1) (2015) 130–142].

scholarly journals Characterization of Graphs Associated with Numerical Semigroups

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 557 ◽  
Author(s):  
Muhammad Ahsan Binyamin ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Nida Munawar Khan ◽  
Adnan Aslam ◽  
Yongsheng Rao
Keyword(s):  
Undirected Graph ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Vertex Set

Let Γ be a numerical semigroup. We associate an undirected graph G ( Γ ) with a numerical semigroup Γ with vertex set { v i : i ∈ N \ Γ } and edge set { v i v j ⇔ i + j ∈ Γ } . In this article, we discuss the connectedness, diameter, girth, and some other related properties of the graph G ( Γ ) .

scholarly journals The ideal duplication

2021 ◽  
Author(s):  
Danny Troia
Keyword(s):  
Numerical Semigroup ◽  
New Construction ◽  
Relative Ideal ◽  
Numerical Duplication ◽  
The Ideal

AbstractIn this paper we present and study the ideal duplication, a new construction within the class of the relative ideals of a numerical semigroup S, that, under specific assumptions, produces a relative ideal of the numerical duplication $$S\bowtie ^b E$$ S ⋈ b E . We prove that every relative ideal of the numerical duplication can be uniquely written as the ideal duplication of two relative ideals of S; this allows us to better understand how the basic operations of the class of the relative ideals of $$S\bowtie ^b E$$ S ⋈ b E work. In particular, we characterize the ideals E such that $$S\bowtie ^b E$$ S ⋈ b E is nearly Gorenstein.

scholarly journals Numerical semigroups of small and large type

2021 ◽  
pp. 1-20
Author(s):  
Deepesh Singhal
Keyword(s):  
Numerical Semigroup ◽  
Frobenius Number ◽  
Numerical Semigroups ◽  
Natural Numbers ◽  
Type Formula ◽  
Explicit Characterization ◽  
Large Type ◽  
Number Formula ◽  
Genus Formula

A numerical semigroup is a sub-semigroup of the natural numbers that has a finite complement. Some of the key properties of a numerical semigroup are its Frobenius number [Formula: see text], genus [Formula: see text] and type [Formula: see text]. It is known that for any numerical semigroup [Formula: see text]. Numerical semigroups with [Formula: see text] are called almost symmetric, we introduce a new property that characterizes them. We give an explicit characterization of numerical semigroups with [Formula: see text]. We show that for a fixed [Formula: see text] the number of numerical semigroups with Frobenius number [Formula: see text] and type [Formula: see text] is eventually constant for large [Formula: see text]. The number of numerical semigroups with genus [Formula: see text] and type [Formula: see text] is also eventually constant for large [Formula: see text].

scholarly journals Characterization of Graphs Associated with the Ideal of Numerical Semigroups

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Peng Xu ◽  
Muhammad Ahsan Binyamin ◽  
Adnan Aslam ◽  
Wajid Ali ◽  
Hasan Mahmood ◽  
...  
Keyword(s):  
Undirected Graph ◽  
Numerical Semigroup ◽  
Numerical Semigroups ◽  
Vertex Set ◽  
The Ideal

Let I be an ideal of a numerical semigroup Λ. We define an undirected graph GIΛ with vertex set vi:i∈Λ∖I∗=Λ∖I−0 and edge set vivj⟺i+j∈I. The aim of this article is to discuss the connectedness, girth, completeness, and some other related properties of the graph GIΛ.

The numerical duplication of a numerical semigroup

2012 ◽  
Vol 87 (1) ◽  
pp. 149-160 ◽  
Author(s):  
M. D’Anna ◽  
F. Strazzanti
Keyword(s):  
Numerical Semigroup ◽  
Numerical Duplication

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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