相关论文: On circuits and serial symmetric basis-exchange in…
We investigate the role of exchange bridges in molecular magnets. We explore their effects on the distribution of the valence electrons and their contribution to the exchange processes. The present study is focused on a spin-half dimer with…
Recently, the relationship between matroids and generalized rough sets based on relations has been studied from the viewpoint of linear independence of matrices. In this paper, we reveal more relationships by the predecessor and successor…
In this paper we address two of the major foundational questions in the theory of matroids over rings. First, we provide a cryptomorphic axiomatisation, by introducing an analogue of the base polytope for matroids. Second, we describe a…
The period changes of contact binaries obtained by the analysis of eclipse minima timing are found mostly chaotic in nature. However, they are representable by a few cyclic changes superposed on a secular change. The cyclic changes are…
If $C_1$ and $C_2$ are circuits in a matroid $M$ with $e_1$ in $C_1-C_2$ and $e$ in $C_1\cap C_2$, then $M$ has a circuit $C_3$ such that $e\in C_3\subseteq (C_1\cup C_2)-e$. This strong circuit elimination axiom is inherently asymmetric. A…
Experimental observations of an almost symmetric electronic circuit show complicated sequences of bifurcations. These results are discussed in the light of a theory of imperfect global bifurcations. It is shown that much of the dynamics…
We investigate two-neutrino double beta decay ($2\nu\beta\beta$) in chiral effective field theory. We find contributions from weak magnetism and double-weak pion-exchange at next-to-leading-order in the chiral power counting. We discuss the…
Transport phenomena in parallel coupled scatterers are studied by transfer matrix formulism. We derive a simple recurrence relation for transfer matrix of one-dimensional two-terminal systems consisting of $N$ arbitrary scattering unit…
In 2004, Ehrenfeucht, Harju, and Rozenberg showed that any graph on a vertex set $V$ can be obtained from a complete graph on $V$ via a sequence of the operations of complementation, switching edges and non-edges at a vertex, and local…
Matroids and semigraphoids are discrete structures abstracting and generalizing linear independence among vectors and conditional independence among random variables, respectively. Despite the different nature of conditional independence…
We investigate the strong Rayleigh property of matroids for which the basis enumerating polynomial is invariant under a Young subgroup of the symmetric group on the ground set. In general, the Grace-Walsh-Szeg\H{o} theorem can be used to…
In this paper, first steps are taken towards characterising lattices of cyclic flats $\mathcal{Z}(M)$ that belong to matroids $M$ that can be represented over a prescribed finite field $\mathbb{F}_q$. Two natural maps from $\mathcal{Z}(M)$…
We generalize the well-studied notion of a modular pair of a finite matroid to arbitrary families of sets in infinite matroids, and use it to develop the theory of infinite matroids in several as-yet-unexplored areas. Our results include a…
In this paper, we are mainly interested in the two questions "which are the commutative rings on which every finitely presented modules is [Formula: see text]-periodic (respectively, [Formula: see text]-periodic)?". It is proved that these…
The double exchange model describing interactions of itinerant electrons with localized spins is usually used to explain ferromagnetism in metals. We show that for a variety of crystal lattices of different dimensionalities and for a wide…
We show that the number of linear spaces on a set of $n$ points and the number of rank-3 matroids on a ground set of size $n$ are both of the form $(cn+o(n))^{n^2/6}$, where $c=e^{\sqrt 3/2-3}(1+\sqrt 3)/2$. This is the final piece of the…
This is a continuation of the early paper concerning matroid base polytope decomposition. Here, we will present sufficient conditions on $M$ so its base matroid polytope $P(M)$ has a {\em sequence} of hyperplane splits. The latter yields to…
In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e.…
The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic…
We report the results of Monte Carlo simulations with the aim to clarify the microscopic origin of exchange bias in the magnetization hysteresis loops of a model of individual core/shell nanoparticles. Increase of the exchange coupling…