Isomorphism Relation Research Articles

Endomorphism algebras over weak (α, β)-Yetter–Drinfeld modules

Let H be a weak Hopf algebra with a bijective antipode, α, β ∈ Autweak Hopf(H) and M a finite-dimensional weak (α, β)-Yetter–Drinfeld module. Then in this paper we prove that the endomorphism algebras EndHs(M) and EndHt(M)opendowed with certain structures become algebras inH𝒲𝒴𝒟Hand we also study the isomorphic relations between different endomorphism algebras. We prove that EndHs(M) endowed with certain structures becomes an H-Azumaya algebra.

The limits of institutional isomorphism in the design of e-recruitment websites: a comparative analysis of the USA and Spain

The purpose of this study is to run a comparative analysis of the recruitment websites of the largest national companies of two different countries, Spain (companies within the IBEX 35 stock market index) and the USA (companies within the Dow Jones stock market index). Using an e-recruiting taxonomy of best practices with 27 attributes, we test the extent to which the selection of specific functionalities reflects different types of isomorphic relations due to socio-economic, technological or cultural forces. Our results show that (i) there is a high level of homogeneity within the two groups as regards the selection of e-recruitment attributes included in their websites and (ii) there are significant differences between DJIA and IBEX 35 e-recruitment attributes, showing low levels of alikeness among their websites. Results are discussed in terms of the institutional forces that may drive companies toward isomorphism in the design of their e-recruitment attributes and content.

On ‐complete equivalence relations on the generalized Baire space

Working with uncountable structures of fixed cardinality, we investigate the complexity of certain equivalence relations and show that if , then many of them are ‐complete, in particular the isomorphism relation of dense linear orders. Then we show that it is undecidable in whether or not the isomorphism relation of a certain well behaved theory (stable, NDOP, NOTOP) is ‐complete (it is, if , but can be forced not to be).

Isomorphism of finitely generated solvable groups is weakly universal

We show that the isomorphism relation for finitely generated solvable groups of class 3 is a weakly universal countable Borel equivalence relation. This improves on previous results. The proof uses a modification of a construction of Neumann and Neumann. Elementary arguments show that isomorphism of finitely generated metabelian or nilpotent groups can not achieve this Borel complexity. In this sense the result is sharp, though it remains open whether the relation is in fact universal.

Speaker variation in English prosodic boundary

This paper analyses the rate of inter-speaker consistency in the way multiple speakers render prosodic events when they read the same scripts. Prosodically labeled data of five speakers from the Boston Radio Speech Corpus (BURSC) are used to measure the degree of speaker variation in rendering prosodic boundaries. The results indicate that the average rate of consistency on the presence or absence of boundary tones 89.71%. For the rate of consistency for the levels of boundary tones, an average consistency of 79.25% is achieved when three levels of category (i.e., ip, IP and no boundary) are compared in pairs of speakers. The rate is lowered to 76.74% when a comparison of prosodic strength is made after both speakers in a pair agreed that there are phrasal tones on aligned words. When a pair of speakers both have a prosodic boundary on a given word, the agreement rate on the type of phrasal tones is 50.95%. The rate of speakers`` consistency in the presence of boundary tones is comparable to the rate of inter-transcriber reliability. The comparable rates with regard to locating prosodic boundaries in utterances by speakers and transcribers may be interpreted that the production and perception of prosodic phrasing are closely related to each other. The high rate of speakers`` consistency is interpreted to be affected by syntactic structures, in spite of the lack of isomorphic relations between prosodic phrasing and syntactic phrasing.

New concepts of fuzzy planar graphs

Fuzzy planar graph is an important subclass of fuzzy graph. Fuzzy planar graphs and its several properties are presented. A very close association of fuzzy planar graph is fuzzy dual graph. This is also defined and several properties of it are studied. Isomorphism on fuzzy graphs are well defined in literature. Isomorphic relation between fuzzy planar graph and its dual graph are established.

The variational formulation of a non-equilibrium traffic flow model: Theory and implications

The analysis and numerical solution of non-equilibrium traffic flow models in current literature are almost exclusively carried out in the hyperbolic conservation law framework, which requires a good understanding of the delicate and non-trivial Riemann problems for conservation laws. In this paper, we present a novel formulation of certain non-equilibrium traffic flow models based on their isomorphic relation with optimal control problems. This formulation extends the minimum principle observed by the LWR model. We demonstrate that with the new formulation, generic initial-boundary conditions can be conveniently handled and a simplified numerical solution scheme for non-equilibrium models can be devised. Besides deriving the variational formulation, we provide a comprehensive discussion on its mathematical properties and physical implications.

C*-Algebras, Dynamics, and Classification

Classification is a central theme in mathematics, and a particularly rich one in the theory of operator algebras. Indeed, one of the first major results in the theory is Murray and von Neumann’s type classification of factors (weakly closed self-adjoint algebras of operators on Hilbert space with trivial center), and one of its modern touchstones is the mid-1970s Connes-Haagerup classification of amenable factors with separable predual. Several significant themes in the classification theory of norm-separable C‡-algebras have emerged since the work of Connes-Haagerup, and these were the focus of our workshop. They include Elliott’s program to classify separable nuclear C‡-algebras via K-theoretic invariants, the role of C‡-algebras in the classification of orbit equivalence relations of discrete countable group actions, and the more recent contact between descriptive set theorists and operator algebraists which seeks to quantify the Borel complexity of the isomorphism relation for various natural classes of algebras.

The Variational Formulation of a Non-equilibrium Traffic Flow Model: Theory and Implications

The analysis and numerical solution of non-equilibrium traffic flow models in current literature are almost exclusively carried out in the hyperbolic conservation law framework, which requires a good understanding of the delicate and non-trivial Riemann problem for conservation laws. In this paper, we present a novel formulation of certain non-equilibrium traffic flow models based on their isomorphic relation with optimal control problems. This formulation extends the minimum principle observed by the LWR model. We demonstrate that with the new formulation, generic initial-boundary conditions can be conveniently handled and a simplified numerical solution scheme for non-equilibrium models can be devised. Besides deriving the variational formulation, we provide a comprehensive discussion on its mathematical properties and physical implications.

TWISTED TENSOR PRODUCT MODULES OVER MÖBIUS TWISTED TENSOR PRODUCT NONLOCAL VERTEX ALGEBRAS

This is the third part in a series of papers developing a twisted tensor product theory for nonlocal vertex algebras and its modules. In this paper we introduce and study twisted tensor product modules over Möbius twisted tensor product nonlocal vertex algebras. Among the main results, we find the isomorphic relation between the opposite Möbius twisted tensor product nonlocal vertex algebra and twisted tensor product of opposite Möbius nonlocal vertex algebras. And we also establish the isomorphism between two twisted tensor product contragredient modules. Furthermore, we study iterated twisted tensor product modules over iterated twisted tensor product nonlocal vertex algebras and find conditions for constructing an iterated twisted tensor product module of three factors.

An integrational response to Searlean realism, or how language does not relate to consciousness

The relationship between language and a science of consciousness is rarely treated as crucial for the field's metatheory (i.e., its underlying philosophical assumptions about the role and nature of language). John Searle is among those thinkers who has given language due attention as part of his realist philosophy, and semantic questions turn out to be in the forefront of his plea for a scientific approach to the phenomenon of consciousness. This paper will consider Searle's philosophy of language in the light of an integrational theory of communication (Harris 1981, 1996, 1998). It is argued here that Searlean realism is grounded in a “reocentric” conception of the world, which (wrongly) assumes an isomorphic relation between language and what language refers to.

The isomorphism relation for separable $C*$-algebras

We prove that the isomorphism relation for separable C ∗ -algebras, the rela- tions of complete and n-isometry for operator spaces, and the relations of unital n-order isomorphisms of operator systems, are Borel reducible to the orbit equivalence relation of a Polish group action on a standard Borel space.

Turbulence, orbit equivalence, and the classification of nuclear C* -algebras

Abstract. We bound the Borel cardinality of the isomorphism relation for nuclear simple separable C* -algebras: It is turbulent, yet Borel reducible to the action of the automorphism group of the Cuntz algebra 𝒪 2 $\mathcal {O}_2$ on its closed subsets. The same bounds are obtained for affine homeomorphism of metrizable Choquet simplexes. As a by-product we recover a result of Kechris and Solecki, namely, that homeomorphism of compacta in the Hilbert cube is Borel reducible to a Polish group action. These results depend intimately on the classification theory of nuclear simple C* -algebras by K $\mathrm {K}$ -theory and traces. Both of necessity and in order to lay the groundwork for further study on the Borel complexity of C* -algebras, we prove that many standard C* -algebra constructions and relations are Borel, and we prove Borel versions of Kirchberg's 𝒪 2 $\mathcal {O}_2$ -stability and embedding theorems. We also find a C* -algebraic witness for a K σ $K_\sigma $ hard equivalence relation.

Two points, one limit: Homogenization techniques for two-point local algebras

We study several algebras generated by convolution, multiplication and flip operators on Lp(R), their Calkin counterparts and derive new isomorphism relations. We introduce a new class of homogenization strong limits, compatible with the flip operator and which explore the properties of the Fourier transform in Lp(R), when p≠2.

Isomorphism relations on computable structures

AbstractWe study the complexity of the isomorphism relation on classes of computable structures. We use the notion of FF-reducibility introduced in [9] to show completeness of the isomorphism relation on many familiar classes in the context of all equivalence relations on hyperarithmetical subsets of ω.

A hierarchy of tree-automatic structures

AbstractWe considerωn-automatic structures which are relational structures whose domain and relations are accepted by automata reading ordinal words of lengthωnfor some integern≥ 1. We show that all these structures areω-tree-automatic structures presentable by Muller or Rabin tree automata. We prove that the isomorphism relation forω2-automatic (resp.ωn-automatic forn> 2) boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups) is not determined by the axiomatic system ZFC. We infer from the proof of the above result that the isomorphism problem forωn-automatic boolean algebras,n≥ 2, (respectively, rings, commutative rings, non commutative rings, non commutative groups) is neither a-set nor a-set. We obtain that there exist infinitely manyωn-automatic, hence alsoω-tree-automatic, atomless boolean algebras, which are pairwise isomorphic under the continuum hypothesis CH and pairwise non isomorphic under an alternate axiom AT, strengthening a result of [14].

The Hierarchy of Equivalence Relations on the Natural Numbers Under Computable Reducibility

The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computable reducibility hierarchy, comparing and contrasting it with the Borel reducibility hierarchy from descriptive set theory. Meanwhile, the notion of computable reducibility appears well suited for an analysis of equivalence relations on the c.e.\ sets, and more specifically, on various classes of c.e.\ structures. This is a rich context with many natural examples, such as the isomorphism relation on c.e.\ graphs or on computably presented groups. Here, our exposition extends earlier work in the literature concerning the classification of computable structures. An abundance of open questions remains.

The classification of torsion-free abelian groups of finite rank up to isomorphism and up to quasi-isomorphism

The isomorphism and quasi-isomorphism relations on the p p -local torsion-free abelian groups of rank n ≥ 3 n\geq 3 are incomparable with respect to Borel reducibility.

Preserving mappings in fuzzy predicate logics

In this article, we develop the method of diagrams for fuzzy predicate logics and give a characterization of different kinds of preserving mappings in terms of diagrams. Our work is a contribution to the model-theoretic study of fuzzy predicate logics. We present a reduced semantics and we prove a completeness theorem of the logics with respect to this semantics. The main concepts being studied are the Leibniz congruence and the structure-preserving relation. On the one hand, the Leibniz congruence of a model identifies the elements that are indistinguishable using equality-free atomic formulas and parameters from the model. A reduced structure is the quotient of a model modulo this congruence. On the other hand, the structure-preserving relation between two structures plays the same role that the isomorphism relation plays in classical predicate languages with equality.

The conjugacy problem in ergodic theory

All common probability preserving transformations can be represented as elements of MPT, the group of measure preserving transformations of the unit interval with Lebesgue measure. This group has a natural Polish topology and the induced topology on the set of ergodic transformations is also Polish. Our main result is that the set of ergodic elements T in MPT that are isomorphic to their inverse is a complete analytic set. This has as a consequence the fact that the isomorphism relation is also a complete analytic set and in particular is not Borel. This is in stark contrast to the situation of unitary operators where the spectral theorem can be used to show that conjugacy relation in the unitary group is Borel. This result explains, perhaps, why the problem of determining whether ergodic transformations are isomorphic or not has proven to be so intractable. The construction that we use is general enough to show that the set of ergodic T ’s with nontrivial centralizer is also complete analytic. On the positive side we show that the isomorphism relation is Borel when restricted to the rank one transformations, which form a generic subset of MPT. It remains an open problem to nd a good explicit method of checking when two rank one transformations are isomorphic. In Memoriam: Prior to the