Product Cube Graphs over Finite Commutative Rings: Structural Properties
We define the Product Cube Graph PC(R) over a finite commutative ring R as a graph on nonzero elements and adjacency occurs when their product is a cube in R. We investigate its structural properties, including connectivity, diameter, clique structure, and bipartiteness. For finite fields F, PC(F) is completely characterized.
Nidhi Khandelwal +2 more
openaire +2 more sources
Entanglement, Space–Time Coordinates, and Bell's Inequalities in Photon–Polarization Experiments
This work presents a revised analysis of Bell‐type inequalities. It is argued that standard derivations of Bell‐type inequalities implicitly rely on additional assumptions beyond those originally stated, specifically concerning the cardinalities of the sets of measurements and photon‐pair properties.
Karl Hess, Jürgen Jakumeit
wiley +1 more source
Projections of Finite Commutative Rings with Identity
Associative rings R and R′ are said to be lattice-isomorphic if their subring lattices L(R) and L(R′) are isomorphic. An isomorphism of the lattice L(R) onto the lattice L(R′) is called a projection (or a lattice isomorphism) of the ring R onto the ring ...
Korobkov, S. S.
core +1 more source
On residual finiteness of monoids, their Schützenberger groups and associated actions [PDF]
RG was supported by an EPSRC Postdoctoral Fellowship EP/E043194/1 held at the University of St Andrews, Scotland.In this paper we discuss connections between the following properties: (RFM) residual finiteness of a monoid M ; (RFSG) residual finiteness ...
Ruskuc, Nik +3 more
core +1 more source
Musical Chemistry and Spectroscopy: Analogies Bridging Two Worlds in Multiple Dimensions
Music and spectroscopy speak the same language: that of fluctuations, line shapes, and ensembles. Herein, we establish useful analogies between music, chemistry, and spectroscopy, extending even to multidimensional and time‐resolved spectroscopies, with a mathematically‐grounded derivation and motivation.
Ricardo J. Fernández‐Terán
wiley +1 more source
On $k$-th unitary Cayley graphs over finite commutative rings: structure and decompositions
39 pages, 2 ...
Podestá, Ricardo A., Videla, Denis E.
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A Linear Generalization of the Nearly Gorenstein Property, With Applications to Veronese Subalgebras
ABSTRACT We study the nearly Gorenstein property for Veronese subalgebras of (semi‐)standard graded algebras. We introduce a condition (♮)$(\natural)$ for Cohen–Macaulay semi‐standard graded rings, motivated by the study of Ehrhart rings. We show that if a semi‐standard graded algebra R$ R$ satisfies (♮)$(\natural)$, then its Veronese subalgebras R(k)$
Sora Miyashita
wiley +1 more source
Aggregation and the Structure of Value
ABSTRACT Roughly, the view I call “Additivism” sums up value across time and people. Given some standard assumptions, I show that Additivism follows from two principles. The first says that how lives align in time cannot, in itself, matter. The second says, roughly, that a world cannot be better unless it is better within some period or another.
Weng Kin San
wiley +1 more source
Tensor Products and Quotient Rings which are Finite Commutative Principal Ideal Rings [PDF]
We give structure theorems for tensor products R⊕S, and quotient rings Q/I to be finite commutative principal ideal rings with identity, where Q is a polynomial ring and I is an ideal of Q generated by univariate polynomials.
Cazaran, Jilyana
core +1 more source
On Exponentially Long Prethermalization Timescales in Isolated Quantum Systems
ABSTRACT We study prethermalization in time‐independent quantum many‐body systems on a d$d$‐dimensional lattice with an extensive local Hamiltonian H=N+εP$H=N+\varepsilon P$, in the regime where ε≪1$\varepsilon \ll 1$. We prove that the prethermal timescale is exponential in ε0/ε$\varepsilon _0/\varepsilon$, where ε0$\varepsilon _0$ is an explicit ...
Matteo Gallone
wiley +1 more source

