Related papers: Order polarities
As probabilistic systems gain popularity and are coming into wider use, the need for a mechanism that explains the system's findings and recommendations becomes more critical. The system will also need a mechanism for ordering competing…
As in our previous work [1] we address the problem to determine the splitting of the normal bundle of rational curves. With apolarity theory we are able to characterize some particular subvarieties in some Hilbert scheme of rational curves,…
We will define the Alexander duality for strongly stable ideals. More precisely, for a strongly stable ideal $I \subset \Bbbk[x_1, \ldots, x_n]$ with ${\rm deg}(\mathsf{m}) \le d$ for all $\mathsf{m} \in G(I)$, its dual $I^* \subset…
We describe polar homology groups for complex manifolds. The polar k-chains are subvarieties of complex dimension k with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincare residue…
Studying and understanding social networks is crucial for accurately defining ideological polarization, since they enable precise modeling of social structures. One of the limitations of many methods for quantifying polarization on networks…
Let $E/F$ be a cyclic Galois extension of degree $p^l$ with Galois group $G$. It is shown that the Galois module structure of both sides of the Kummer pairing (for Kummer extensions of $E$) are the same. In other words, we show that the…
The electric polarization induced by local polar domains of two types (phase separation domains of magnetic nature and structure-distorted domains) has been observed in YCrO3 single crystals. These domains form a superparaelectric state.…
Many physical systems involve two types of orientational order, which are coupled together. For example, ferroelectric nematic liquid crystals have coupled polar and nematic order, and tilted hexatic phases have coupled polar and hexatic…
Using a materials by design approach, the authors find a class of ordered oxynitride piezoelectrics with perovskite structure. They predict that ordered YSiO2N and YGeO2N are characterized by large nonlinear optic responses and by some of…
We classify all division algebras that are principal Albert isotopes of a cyclic Galois field extension of degree $n>2$ up to isomorphisms. We achieve a ``tight'' classification when the cyclic Galois field extension is cubic. The…
The complexity of a pair $(X,B)$ is an invariant that relates the dimension of $X$, the rank of the group of divisors, and the coefficients of $B$. If the complexity is less than one, then $X$ is a toric variety. We prove that if the…
The first steps towards linearisation of partial orders and equivalence relations are described. The definitions of partial orders and equivalence relations (on sets) are formulated in a way that is standard in category theory and that…
Preclones are described as the closed classes of the Galois connection induced by a preservation relation between operations and matrix collections. The Galois closed classes of matrix collections are also described by explicit closure…
A poset can be regarded as a category in which there is at most one morphism between objects, and such that at most one of Hom(c,c') and Hom(c',c) is nonempty for distinct objects c,c'. If we keep in place the latter axiom but allow for…
The aim of this paper is to present an extension theorem for the functions separately holomorphic on generalized (N,k)-crosses with pluripolar singularities.
In solid state physics, any symmetry breaking is known to be associated with emergence of an order parameter. However, the order parameter for molecular and crystal chirality, which is a consequence of parity and mirror symmetry breaking,…
Existing polarization theories have mostly been concerned with Shannon's information measures, such as Shannon entropy and mutual information, and some related measures such as the Bhattacharyya parameter. In this work, we extend…
For any length category, we establish a set of rules (necessary and sufficient) that ensure a partial order on the isomorphism classes of simple objects such that the category is equivalent to the category of finite dimensional…
This paper introduces a definition of ideological polarization of an electorate around a particular central point. The definition is flexible about the location or boundaries of the center. Using US survey data, the paper shows how this…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…