Properties Of Morphisms Research Articles

О пространствах Чу над категорией 𝑆𝑆 − 𝐴𝑐𝑡

We prove the general properties of morphisms of Chu spaces and functors with a value in the category 𝐶ℎ𝑢(𝑆𝑆 − 𝐴𝑐𝑡) of Chu spaces over the category 𝑆𝑆 − 𝐴𝑐𝑡. As a consequence, for the category 𝐶ℎ𝑢(𝑆𝑆 −𝐴𝑐𝑡) the existence of coproducts and some products is proved, monomorphisms and epimorphisms are characterized; in terms of this category the characteristics of separable and complete separable Chu spaces are given.

Measuring Social Network De-Anonymizability by Means of Morphism Property

Anonymization techniques have tranquilized current social network users in terms of privacy leakage, however, it does not radically prevent adversaries from de-anonymizing users, as they may map the users to an un-anonymized network. Till now, researchers share a common thread in such de-anonymization attack: unveiling conditions leading to successful de-anonymization under the chosen network model. However, it has not yet been well understand how the structural property in different network models intrinsically determines de-anonymizability. We address the above issue in this paper by making the two contributions: (i) We discover that the automorphic degree and homomorphic degree of social networks determine their de-anonymizability universally. The automorphic degree characterizes the distinguishability of the users in a network, while the homomorphic degree models the similarities of users between two networks. We conclude that a smaller automorphic degree and a larger homomorphic degree conduce to a higher de-anonymizability. Such model-independent phenomenon refreshes us with a latitudinal study as it generalizes the essential commonness of de-anonymization in different network models. (ii) We derive explicit parametric bounds of the de-anonymizability for three classic network models, showing that such bounds correspond well to our conclusion about morphism property. We then algorithmically and experimentally show that such theoretical results literally make sense to adversaries. Such longitudinal study, including welding theory, algorithm and validation, promises applicability of our results on morphism property in real cases.

Categories and semigroups

The aim of this paper is to consider the correspondence between the classification of morphisms in categories and the classes of semigroups with idempotents, in particular, we establish a mutual corresponding theorem of three classes of categories and the classes of left (right) abundant, two-sided abundant semigroups and regular semigroups. We first apply the nine axioms (P1)–(P9) which characterize cancellation and split properties of morphisms in a category to classify categories into three subclasses: idempotent ample ([Formula: see text]-, for short) categories, balanced categories and normal categories. The intrinsic relationship between these categories and their cone semigroups is investigated. It is proved that the cone semigroup of an [Formula: see text]-category is left abundant and vice versa, the category of principal left ∗-ideals of a left abundant (not necessarily right abundant) semigroup is an [Formula: see text]-category. Similar results for balanced categories and abundant semigroups are reproved and strengthened. As a consequence, we employ categorical terms to characterize those abundant semigroups in which the regular elements form a regular subsemigroup. Therefore, the significant theory of normal categories and regular semigroups devoted by K. S. S. Nambooripad is generalized to arbitrary abundant semigroups and even to left and right abundant semigroups, respectively.

A uniform treatment of Grothendieck's localization problem

Let $f\colon Y \to X$ be a proper flat morphism of locally noetherian schemes. Then the locus in $X$ over which $f$ is smooth is stable under generization. We prove that, under suitable assumptions on the formal fibers of $X$, the same property holds for other local properties of morphisms, even if $f$ is only closed and flat. Our proof of this statement reduces to a purely local question known as Grothendieck's localization problem. To answer Grothendieck's problem, we provide a general framework that gives a uniform treatment of previously known cases of this problem, and also solves this problem in new cases, namely for weak normality, seminormality, $F$-rationality, and the ‘Cohen–Macaulay and $F$-injective’ property. For the weak normality statement, we prove that weak normality always lifts from Cartier divisors. We also solve Grothendieck's localization problem for terminal, canonical, and rational singularities in equal characteristic zero.

Nets of graded $C^*$-algebras over partially ordered sets

The paper deals with $C^*$-algebras generated by a net of Hilbert spaces over a partially ordered set. The family of those algebras constitutes a net of $C^*$-algebras over the same set. It is shown that every such an algebra is graded by the first homotopy group of the partially ordered set. We consider inductive systems of $C^*$-algebras and their limits over maximal directed subsets. We also study properties of morphisms for nets of Hilbert spaces as well as nets of $C^*$-algebras.

Short and biased introduction to groupoids

The algebraic part of an approach to groupoids started by Zakrzewski is presented together with some new results on formal properties of morphisms.

On Gieseker stability for Higgs sheaves

In this article we review the notion of Gieseker stability for torsion-free Higgs sheaves. This notion is a natural generalization of the classical notion of Gieseker stability for torsion-free coherent sheaves. Here we prove some properties of Higgs sheaves that are similar to the classical ones for torsion-free coherent sheaves over projective algebraic manifolds. In particular, we show that Gieseker stability for torsion-free Higgs sheaves can be defined using only Higgs subsheaves with torsion-free quotients; we also prove that a direct sum of two Higgs sheaves is Gieseker semistable if and only if the Higgs sheaves are both Gieseker semistable with equal normalized Hilbert polynomial; then we prove that a classical property of morphisms between Gieseker semistable sheaves also holds in the Higgs case; as a consequence of this and because of an existing relation between Mumford–Takemoto stability and Gieseker stability for Higgs sheaves, we obtain certain properties concerning the existence of Hermitian-Yang–Mills metrics, simplesness and extensions. Finally, we make some comments about Jordan–Hölder and Harder–Narasimhan filtrations for Higgs sheaves.

The morphism property of subelliptic equations on the roto-translation group

We establish the morphism property of subelliptic equations for mappings with bounded distortion whose domain lies in the roto-translation group and whose range is the Heisenberg group. This implies that every nonconstant locally bounded mapping with bounded distortion whose domain and range lie in the roto-translation group is continuous, open, and discrete.

Palindromic sequences generated from marked morphisms

Fixed points u=φ(u) of marked and primitive morphisms φ over arbitrary alphabet are considered. We show that if u is palindromic, i.e., its language contains infinitely many palindromes, then some power of φ has a conjugate in class P. This class was introduced by Hof et al. (1995) in order to study palindromic morphic words. Our definitions of marked and well-marked morphisms are more general than the ones previously used by Frid (1999) or Tan (2007). As any morphism with an aperiodic fixed point over a binary alphabet is marked, our result generalizes the result of Tan. Labbé (2014) demonstrated that already over a ternary alphabet the property of morphisms to be marked is important for the validity of our theorem. The main tool used in our proof is the description of bispecial factors in fixed points of morphisms provided by Klouda (2012).

Equivalence of the Category of Precubical Sets and the Category of Transitional Chu Spaces With Preservation of the Openness Property of Morphisms

We use directed algebraic topology for establishing categorical relationships between two geometrical models of concurrency, precubical sets and transitional Chu spaces. We study the universal dicovering functor from the category of precubical sets to the category of simply diconnected counterparts of precubical sets. We prove that the category of transitional Chu spaces is equivalent to the category of simply diconnected precubical sets and show that the openness of morphisms is preserved. Bibliography :1 9titles. Illustrations :7 figures.

On k-abelian avoidability

We consider a recently defined notion of the k-abelian equivalence of words, giving some basic results and concentrating on avoidability problems. This equivalence relation counts the numbers of factors of length k for a fixed natural number k. We ask for the size of a smallest alphabet for which k-abelian squares or cubes can be avoided. For 2-abelian squares, the answer is four, as in the case of abelian words; while for 2-abelian cubes, we only have strong evidence that the answer is two, as it is in the case of words. In addition, we point out a few properties of morphisms supporting the view that it might be difficult to find solutions to our questions by simply iterating a morphism. Bibliography: 17 titles.

Lax–Hopf formula and Max-Plus properties of solutions to Hamilton–Jacobi equations

We state and prove a “Lax–Hopf formula” characterizing viable capture basins of targets investigated in viability theory and derive a “Max-Plus” morphism of capture basins with respect to the target. Capture basins are used to define “viability solutions” to Hamilton–Jacobi equations satisfying “trajectory conditions” (initial, boundary or Lagrangian conditions). The Max-Plus morphism property of Lax–Hopf formula implies the fact that the solution associated with inf-convolution of trajectory conditions is the inf-convolution of the solutions for each trajectory condition. For instance, Lipschitz regularization or decreasing envelopes of trajectory condition imply the Lipschitz regulation or decreasing envelopes of the solutions.

New critical points for the liquid phase and the construction of thermodynamics depending on the interaction potential

A mechanism for the inheritance of properties of spectra by differential spectra is developed and applied to prove geometric properties of morphisms of differential algebraic varieties.

Inheritance of properties of spectra

A mechanism for the inheritance of properties of spectra by differential spectra is developed and applied to prove geometric properties of morphisms of differential algebraic varieties.

Markov chains and dynamical systems: the open system point of view

Abstract. This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one component that we get from a dynamical system on a product system, when losing information on the other component. We show that passing from the deterministic dynamics to the random one is character- ized by the loss of algebra morphism property; it is also characterized by the loss of reversibility. In the continuous time framework, we show that the solu- tions of stochastic dierential equations are actually deterministic dynamical systems on a particular product space. When losing the information on one component, we recover the usual associated Markov semigroup.

Pointwise characterizations of Besov and Triebel–Lizorkin spaces and quasiconformal mappings

In this paper, the authors characterize, in terms of pointwise inequalities, the classical Besov spaces B ˙ p , q s and Triebel–Lizorkin spaces F ˙ p , q s for all s ∈ ( 0 , 1 ) and p , q ∈ ( n / ( n + s ) , ∞ ] , both in R n and in the metric measure spaces enjoying the doubling and reverse doubling properties. Applying this characterization, the authors prove that quasiconformal mappings preserve F ˙ n / s , q s on R n for all s ∈ ( 0 , 1 ) and q ∈ ( n / ( n + s ) , ∞ ] . A metric measure space version of the above morphism property is also established.

Characterizing Artin stacks

We study properties of morphisms of stacks in the context of the homotopy theory of presheaves of groupoids on a small site Open image in new window . There is a natural method for extending a property P of morphisms of sheaves on Open image in new window to a property \({\mathcal{P}}\) of morphisms of presheaves of groupoids. We prove that the property \({\mathcal{P}}\) is homotopy invariant in the local model structure on Open image in new window when P is stable under pullback and local on the target. Using the homotopy invariance of the properties of being a representable morphism, representable in algebraic spaces, and of being a cover, we obtain homotopy theoretic characterizations of algebraic and Artin stacks as those which are equivalent to simplicial objects in Open image in new window satisfying certain analogues of the Kan conditions. The definition of Artin stack can naturally be placed within a hierarchy which roughly measures how far a stack is from being representable. We call the higher analogues of Artin stacks n-algebraic stacks, and provide a characterization of these in terms of simplicial objects. A consequence of this characterization is that, for presheaves of groupoids, n-algebraic is the same as 3-algebraic for all n ≥ 3. As an application of these results we show that a stack is n-algebraic if and only if the homotopy orbits of a group action on it is.

Dirac Sigma Models

We introduce a new topological sigma model, whose fields are bundle maps from the tangent bundle of a 2-dimensional world-sheet to a Dirac subbundle of an exact Courant algebroid over a target manifold. It generalizes simultaneously the (twisted) Poisson sigma model as well as the G/G-WZW model. The equations of motion are satisfied, iff the corresponding classical field is a Lie algebroid morphism. The Dirac Sigma Model has an inherently topological part as well as a kinetic term which uses a metric on worldsheet and target. The latter contribution serves as a kind of regulator for the theory, while at least classically the gauge invariant content turns out to be independent of any additional structure. In the (twisted) Poisson case one may drop the kinetic term altogether, obtaining the WZ-Poisson sigma model; in general, however, it is compulsory for establishing the morphism property.

Conjugacy and episturmian morphisms

Episturmian morphisms generalize Sturmian morphisms. Here, we study some intrinsic properties of these morphisms: invertibility, presentation, cancellativity, unitarity, characterization by conjugacy. Most of them are generalizations of known properties of Sturmian morphisms. But we present also some results on episturmian morphisms that have not already been stated in the particular case of Sturmian morphisms: characterization of the episturmian morphisms that preserve palindromes, new algorithms to compute conjugates. We also study the conjugation of morphisms in the general case and show that the monoid of invertible morphisms on an alphabet containing at least three letters is not finitely generated. Résumé Les morphismes épisturmiens généralisent les morphismes sturmiens. Ici, nous étudions des propriétés intrinsèques de ces morphismes: inversibilité, unitarité, régularité, caractérisation par conjugaison. La plupart de ces résultats sont des généralisations de résultats connus sur les morphismes sturmiens. Mais nous présentons aussi des résultats non encore établis pour les morphismes sturmiens: caractérisations des morphismes épisturmiens qui préservent les palindromes, nouveaux algorithmes pour calculer des conjugués. Nous donnons également des résultats généraux sur la conjugaison et montrons que le monoı̈de des morphismes inversibles sur un alphabet d'au moins trois lettres n'est pas finiment engendré. Mots Clés. Combinatoire des mots; Morphismes sturmiens; Conjugaison; Présentation; Morphismes inversibles

The morphism property for mappings with bounded distortion on the Heisenberg group

The morphism property for mappings with bounded distortion on the Heisenberg group