The structure of gauge-invariant ideals of labelled graph C∗C^*-algebras

In this paper, we consider the gauge-invariant ideal structure of a $C^*$-algebra $C^*(E,\mathcal{L},\mathcal{B})$ associated to a set-finite, receiver set-finite and weakly left-resolving labelled space $(E,\mathcal{L},\mathcal{B})$, where $\mathcal{L}$ is a labelling map assigning an alphabet to each edge of the directed graph $E$ with no sinks. Under the assumption that an accommodating set $\mathcal{B}$ is closed under taking relative complement, it is obtained that there is a one to one correspondence between the set of all hereditary saturated subsets of $\mathcal{B}$ and the gauge-invariant ideals of $C^*(E,\mathcal{L},\mathcal{B})$. For this, we introduce a quotient labelled space $(E,\mathcal{L},[\mathcal{B}]_R)$ arising from an equivalence relation $\sim_R$ on $\mathcal{B}$ and show the existence of the $C^*$-algebra $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ generated by a universal representation of $(E,\mathcal{L},[\mathcal{B}]_R)$. Also the gauge-invariant uniqueness theorem for $C^*(E,\mathcal{L},[\mathcal{B}]_R)$ is obtained. For simple labelled graph $C^*$-algebras $C^*(E,\mathcal{L},\bar{\mathcal{E}})$, where $\bar{\mathcal{E}}$ is the smallest accommodating set containing all the generalized vertices, it is observed that if for each vertex $v$ of $E$, a generalized vertex $[v]_l$ is finite for some $l$, then $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ is simple if and only if $(E,\mathcal{L},\bar{\mathcal{E}})$ is strongly cofinal and disagreeable. This is done by examining the merged labelled graph $(F,\mathcal{L}_F)$ of $(E,\mathcal{L})$ and the common properties that $C^*(E,\mathcal{L},\bar{\mathcal{E}})$ and $C^*(F,\mathcal{L},\bar{\mathcal{F}})$ share

Topological entropy and the AF core of a graph C∗-algebra

AbstractLet C∗(E) be the C∗-algebra associated with a locally finite directed graph E and AE be the AF core of C∗(E). For the topological entropy ht(ΦE) (in the sense of Brown–Voiculescu) of the canonical completely positive map ΦE on the graph C∗-algebra, it is known that if E is finiteht(ΦE)=ht(ΦE|AE)=hb(E)=hl(E), where hb(E) (respectively, hl(E)) is the block (respectively, the loop) entropy of E. In case E is irreducible and infinite, hl(E)⩽ht(ΦE|AE)⩽hb(Et) is known recently, where Et is the graph E with the edges directed reversely. Then by monotonicity of entropy, hl(E)⩽ht(ΦE) is clear. In this paper we show that ht(ΦE)⩽hb(Et) holds for locally finite infinite graphs E. The AF core AE is known to be stably isomorphic to the graph C∗-algebra C∗(E×cZ) of certain skew product E×cZ and we also show that ht(ΦE×cZ)=ht(ΦE|AE). Examples Ep (p>1) of irreducible graphs with ht(ΦEp)=logp are discussed

A Factor Analysis of Urban Railway Casualty Accidents and Establishment of Preventive Response Systems

AbstractSince the commencement of urban railways in 1974 and KTX service in 2014, the use of railways has been steadily increasing. The number of people using rail transportation has been steadily rising. As a result, this has also led to an increase in the number of passenger-related accidents that are occurring within railway stations. In an effort to prevent such accidents, much of the rail operation system is now automated. Nevertheless, the potential risks of railway accidents are very much present today. This study has utilized the railway accident databases of rail operators to allow for analysis of different types of railway accidents, age of accident victims, gender of accident victims, pedestrian facilities involved in accidents, passengers involved in accidents, and underlying causes of rail accidents. Based on these statistics and analyses, this paper proposes the development of a railway safety education program and the establishment of railway safety education centers as a means of preventing railway accidents

Eosinophilic Otitis Media: CT and MRI Findings and Literature Review

Eosinophilic otitis media (EOM) is a relatively rare, intractable, middle ear disease with extremely viscous mucoid effusion containing eosinophils. EOM is associated with adult bronchial asthma and nasal allergies. Conventional treatments for otitis media with effusion (OME) or for chronic otitis media (COM), like tympanoplasty or mastoidectomy, when performed for the treatment of EOM, can induce severe complications such as deafness. Therefore, it should be differentiated from the usual type of OME or COM. To our knowledge, the clinical and imaging findings of EOM of temporal bone are not well-known to radiologists. We report here the CT and MRI findings of two EOM cases and review the clinical and histopathologic findings of this recently described disease entity