Method of Constructing Barker-Like Sequence on the Basis of Ideal Ring Bundle Families

2019 ◽  
Author(s):  
Oleg Riznyk ◽  
Natalya Kustra ◽  
Yurii Kynash ◽  
Roksolana Vynnychuk
Keyword(s):  
Ideal Ring

scholarly journals Investigation of Ring and Star Polymers in Confined Geometries: Theory and Simulations

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 242
Author(s):  
Joanna Halun ◽  
Pawel Karbowniczek ◽  
Piotr Kuterba ◽  
Zoriana Danel
Keyword(s):  
Star Polymers ◽  
Polymer Chains ◽  
The Other ◽  
Nano Particles ◽  
Dilute Solution ◽  
Confined Geometries ◽  
Density Profiles ◽  
Ideal Ring ◽  
Ring Polymer ◽  
Monomer Density

The calculations of the dimensionless layer monomer density profiles for a dilute solution of phantom ideal ring polymer chains and star polymers with f=4 arms in a Θ-solvent confined in a slit geometry of two parallel walls with repulsive surfaces and for the mixed case of one repulsive and the other inert surface were performed. Furthermore, taking into account the Derjaguin approximation, the dimensionless layer monomer density profiles for phantom ideal ring polymer chains and star polymers immersed in a solution of big colloidal particles with different adsorbing or repelling properties with respect to polymers were calculated. The density-force relation for the above-mentioned cases was analyzed, and the universal amplitude ratio B was obtained. Taking into account the small sphere expansion allowed obtaining the monomer density profiles for a dilute solution of phantom ideal ring polymers immersed in a solution of small spherical particles, or nano-particles of finite size, which are much smaller than the polymer size and the other characteristic mesoscopic length of the system. We performed molecular dynamics simulations of a dilute solution of linear, ring, and star-shaped polymers with N=300, 300 (360), and 1201 (4 × 300 + 1-star polymer with four arms) beads accordingly. The obtained analytical and numerical results for phantom ring and star polymers are compared with the results for linear polymer chains in confined geometries.

On (α + uβ)-constacyclic codes of length 4ps over 𝔽pm + u𝔽pm∗

2019 ◽  
Vol 18 (02) ◽  
pp. 1950023 ◽  
Author(s):  
Hai Q. Dinh ◽  
Bac T. Nguyen ◽  
Songsak Sriboonchitta ◽  
Thang M. Vo
Keyword(s):  
Principal Ideal ◽  
Constacyclic Codes ◽  
Constacyclic Code ◽  
Chain Ring ◽  
Principal Ideal Ring ◽  
Direct Sum ◽  
Ideal Ring ◽  
Unit Formula

For any odd prime [Formula: see text] such that [Formula: see text], the structures of all [Formula: see text]-constacyclic codes of length [Formula: see text] over the finite commutative chain ring [Formula: see text] [Formula: see text] are established in term of their generator polynomials. When the unit [Formula: see text] is a square, each [Formula: see text]-constacyclic code of length [Formula: see text] is expressed as a direct sum of two constacyclic codes of length [Formula: see text]. In the main case that the unit [Formula: see text] is not a square, it is shown that the ambient ring [Formula: see text] is a principal ideal ring. From that, the structure, number of codewords, duals of all such [Formula: see text]-constacyclic codes are obtained. As an application, we identify all self-orthogonal, dual-containing, and the unique self-dual [Formula: see text]-constacyclic codes of length [Formula: see text] over [Formula: see text].

Special Principal Ideal Rings and Absolute Subretracts

1991 ◽  
Vol 34 (3) ◽  
pp. 364-367 ◽  
Author(s):  
Eric Jespers
Keyword(s):  
Maximal Ideal ◽  
Principal Ideal ◽  
Identity Mapping ◽  
Principal Ideal Ring ◽  
Ideal Ring ◽  
Theoretic Version

AbstractA ring R is said to be an absolute subretract if for any ring S in the variety generated by R and for any ring monomorphism f from R into S, there exists a ring morphism g from S to R such that gf is the identity mapping. This concept, introduced by Gardner and Stewart, is a ring theoretic version of an injective notion in certain varieties investigated by Davey and Kovacs.Also recall that a special principal ideal ring is a local principal ring with nonzero nilpotent maximal ideal. In this paper (finite) special principal ideal rings that are absolute subretracts are studied.

scholarly journals Free Poisson fields and their automorphisms

2016 ◽  
Vol 15 (10) ◽  
pp. 1650196 ◽  
Author(s):  
Leonid Makar-Limanov ◽  
Ualbai Umirbaev
Keyword(s):  
Universal Enveloping Algebra ◽  
Arbitrary Field ◽  
Group Of Automorphisms ◽  
Cremona Group ◽  
Enveloping Algebra ◽  
Ideal Ring ◽  
Poisson Fields ◽  
Poisson Field

Let [Formula: see text] be an arbitrary field of characteristic [Formula: see text]. We prove that the group of automorphisms of a free Poisson field [Formula: see text] in two variables [Formula: see text] over [Formula: see text] is isomorphic to the Cremona group [Formula: see text]. We also prove that the universal enveloping algebra [Formula: see text] of a free Poisson field [Formula: see text] is a free ideal ring and give a characterization of the Poisson dependence of two elements of [Formula: see text] via universal derivatives.

Explicit Formulas Describing: The Binary Operations Calculus In \(E_{a,b}\)

2011 ◽  
Vol 2 (3) ◽  
pp. 16
Author(s):  
Chillali Abdelhakim ◽  
Mohamed Charkani
Keyword(s):  
Elliptic Curve ◽  
Principal Ideal ◽  
Group Homomorphism ◽  
Explicit Formulas ◽  
Principal Ideal Ring ◽  
Binary Operations ◽  
Ideal Ring

In this work we study the elliptic curve over theartinian principal ideal ring \(A=\mathbf{F}_q[\epsilon]\), \((\epsilon^3=0)\). More precisely, we establish a group homomorphism betweens \((\mathbf{F}_q^2,+)\) and theabelian group \(E_{a,b}\) of elliptic curve. For cryptographyapplications, we give meany various explicit formulas describingthe binary operations calculus in \(E_{a,b}\).

When is every module with essential socle a direct sum of automorphism-invariant modules?

2019 ◽  
Vol 19 (10) ◽  
pp. 2050185
Author(s):  
Shahabaddin Ebrahimi Atani ◽  
Saboura Dolati Pish Hesari ◽  
Mehdi Khoramdel
Keyword(s):  
Commutative Ring ◽  
Principal Ideal ◽  
Essential Extension ◽  
Principal Ideal Ring ◽  
Von Neumann ◽  
Simple Modules ◽  
Direct Sum ◽  
Finite Dimensional ◽  
Ideal Ring ◽  
Von Neumann Regular

The purpose of this paper is to study the structure of rings over which every essential extension of a direct sum of a family of simple modules is a direct sum of automorphism-invariant modules. We show that if [Formula: see text] is a right quotient finite dimensional (q.f.d.) ring satisfying this property, then [Formula: see text] is right Noetherian. Also, we show a von Neumann regular (semiregular) ring [Formula: see text] with this property is Noetherian. Moreover, we prove that a commutative ring with this property is an Artinian principal ideal ring.

QUASI-MORPHIC RINGS

2007 ◽  
Vol 06 (05) ◽  
pp. 789-799 ◽  
Author(s):  
V. CAMILLO ◽  
W. K. NICHOLSON
Keyword(s):  
Principal Ideal ◽  
Principal Ideal Ring ◽  
Bezout Ring ◽  
Ideal Ring ◽  
Left And Right ◽  
Regular Rings

A ring R is called left morphic if R/Ra ≅ l (a) for each a ∈ R, equivalently if there exists b ∈ R such that Ra = l (b) and l (a) = Rb. In this paper, we ask only that b and c exist such that Ra = l (b) and l (a) = Rc, and call R left quasi-morphic if this happens for every element a of R. This class of rings contains the regular rings and the left morphic rings, and it is shown that finite intersections of principal left ideals in such a ring are again principal. It is further proved that if R is quasi-morphic (left and right), then R is a Bézout ring and has the ACC on principal left ideals if and only if it is an artinian principal ideal ring.

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