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Finite Commutative Chain Rings
A commutative ring with unit is called a chain ring if all its ideals form a chain under inclusion. All finite chain rings can be obtained in the following way: Let \(p\) be a prime, \(n,r>0\), \(f\in \mathbb{Z}_{p^n}[X]\) a monic polynomial, \(\deg(f)=r\) whose image in \(\mathbb{Z}_p[X]\) is irreducible and let \(\text{GR} (p^n,r): =\mathbb{Z}_{p^n ...
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Monopole-antimonopole chains and vortex rings [PDF]
We consider static axially symmetric solutions of SU(2) Yang-Mills-Higgs theory. The simplest such solutions represent monopoles, multimonopoles and monopole-antimonopole pairs. In general such solutions are characterized by two integers, the winding number m of their polar angle, and the winding number n of their azimuthal angle.
Kleihaus, Burkhard +2 more
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On Multiplicative Matrix Channels over Finite Chain Rings
Motivated by physical-layer network coding, this paper considers communication in multiplicative matrix channels over finite chain rings. Such channels are defined by the law $Y =A X$, where $X$ and $Y$ are the input and output matrices, respectively ...
Feng, Chen +3 more
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LIFTED CODES OVER FINITE CHAIN RINGS [PDF]
In this paper, we study lifted codes over finite chain rings.
Dougherty, Steven T. +2 more
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Full Classification of Finite Singleton Local Rings
The main objective of this article is to classify all finite singleton local rings, which are associative rings characterized by a unique maximal ideal and a distinguished basis consisting of a single element.
Sami Alabiad, Yousef Alkhamees
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1,3,5-Tri-p-tolylpentane-1,5-dione
In the crystal structure of the title compound, C26H26O2, the dihedral angle between the tolyl rings at each end of the 1,5-dione chain is 70.3 (1)°; the tolyl group at the middle of the chain makes dihedral angles of 67.8 (2) and 85.1 ...
You-Liang Shen
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Molecular Dynamics Simulation Study of Nonconcatenated Ring Polymers in a Melt: I. Statics
Molecular dynamics simulations were conducted to investigate the structural properties of melts of nonconcatenated ring polymers and compared to melts of linear polymers.
Alexander Y. Grosberg +11 more
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Commutative Chain Rings with Index of Nilpotency 5 and Residue Field
This paper gives a thorough characterization of chain rings with index of nilpotency 5 and residue field Fpm, where p represents a prime number, contributing valuable insights to the field of algebraic structures.
Alhanouf Ali Alhomaidhi +2 more
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Fluorescent probes allow dynamic visualization of phosphoinositides in living cells (left), whereas mass spectrometry provides high‐sensitivity, isomer‐resolved quantitation (right). Their synergistic use captures complementary aspects of lipid signaling. This review illustrates how these approaches reveal the spatiotemporal regulation and quantitative
Hiroaki Kajiho +3 more
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Chain rings and distributive rings
The author reports on joint work with \textit{G. Törner} [see f.e. Proc. Am. Math. Soc. 119, No. 2, 401-405 (1993; Zbl 0810.16020)].
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