Related papers: The commutative Moufang loops with minimum conditi…
The notion of conditional entropy is extended to noncomposite systems. The q-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the…
We first establish a sufficient condition for an additively idempotent semiring to be nonfinitely based. As applications, we exhibit several examples of additively idempotent semirings satisfying this condition, including a $4$-element…
Let $L$ be a commutative Moufang loop (CML) with multiplication group $\frak M$, and let $\frak F(L)$, $\frak F(\frak M)$ be the Frattini subgroup and Frattini subgroup of $L$ and $\frak M$ respectively. It is proved that $\frak F(L) = L$…
This paper provides a dynamical frame to study non-autonomous parabolic partial differential equations with finite delay. Assuming monotonicity of the linearized semiflow, conditions for the existence of a continuous separation of type II…
We provide necessary and sufficient conditions for the partial transposition of bipartite harmonic quantum states to be nonnegative. The conditions are formulated as an infinite series of inequalities for the moments of the state under…
We study emerging notions of quantum correlations in compound systems. Based on different definitions of quantumness in individual subsystems, we investigate how they extend to the joint description of a composite system. Especially, we…
For $g\geq 2$, let $\text{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g$. In this paper, we provide necessary and sufficient conditions for the existence of infinite metacyclic subgroups of…
Continuous variable entanglement is a manifestation of nonclassicality of quantum states. In this paper we attempt to analyze whether and under which conditions nonclassicality can be used as an entanglement criterion. We adopt the…
The entanglement criterion for continuous variable systems and the conditions under which the uncertainty relations are fulfilled are generalized to the case of a noncommutative (NC) phase-space. The quantum nature and the separability of…
By applying suitable centrality condition to non-commutative non-isospectral lattice modified Gel'fand-Dikii type systems we obtain the corresponding non-autonomous equations. Then we derive non-commutative q-discrete Painleve VI equation…
An explicit canonical construction of monopole connections on non trivial U(1) bundles over Riemann surfaces of any genus is given. The class of monopole solutions depend on the conformal class of the given Riemann surface and a set of…
For a finite loop $Q$, let $P (Q)$ be the set of elements that can be represented as a product containing each element of $Q$ precisely once. Motivated by the recent proof of the Hall-Paige conjecture, we prove several universal…
We prove that the composition of a quasi-nearly subharmonic function and a quasiregular mappings of bounded multiplicity is quasi-nearly subharmonic. Also, we prove that if $u\circ f$ is quasi-nearly subharmonic for all quasi-nearly…
We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral.…
Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient…
We compute the orders of free commutative Moufand loops of exponent 3 with $n\leq 7$ free generators and find embeddings of such loops into a loop of invertible elements of the free commutative alternative algebra with identity $x^3=0$.
We give examples of compactly supported Hamiltonian loops with non zero Calabi invariant on certain open symplectic manifolds.
Understanding what can be inferred about a multi-particle quantum system from only the knowledge of its subparts is a highly non-trivial task. Clearly, if the global system doesn't contain any information resource, nor do its subparts.…
The commutator calculus is one of the basic tools in group theory. However, its extension to the non-associative context, based on the usual definition of the lower central series of a loop, is not entirely satisfactory. Namely, the graded…
Quantumness and separability criteria for continuous variable systems are discussed for the case of a noncommutative (NC) phase-space. In particular, the quantum nature and the entanglement configuration of NC two-mode Gaussian states are…