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

TESTING OF ROTATIONAL EXERCISE EQUIPMENT TO IMPROVE THE VESTIBULAR SYSTEM

The primary purpose of this study was to test the effect of training using the rotational exercise equipment developed in this study on the improvement of the vestibular system. In order to test the rotational exercise equipment developed in this study, 15 ordinary college students had trainings for 8 weeks and their nystagmus intensity was analyzed. The findings showed that the rotational training using the rotational exercise equipment affected vestibular balance, as it significantly decreased the slow phase velocity (SPV) immediately after rotational stimulation and reduced the recovery time of nystagmus to normal

Toxicological Evaluations of Rare Earths and Their Health Impacts to Workers: A Literature Review

In concert with the development of new materials in the last decade, the need for toxicological studies of these materials has been increasing. These new materials include a group of rare earths (RE). The use of RE nanotechnology is being considered in some green applications, to increase their efficiency by using nano-sized RE compounds, and therefore hazard evaluation and risk assessment are highly recommended. This review was conducted through an extensive contemplation of the literatures in toxicology with in vitro and in vivo studies. Major aspects reviewed were the toxicological evaluations of these elements and metallic compounds at the molecular and cellular level, animal and human epidemiological studies and environmental and occupational health impacts on workers. We also discuss the future prospect of industries with appliances using RE together with the significance of preventive efforts for workers’ health. To establish a safe and healthy working environment for RE industries, the use of biomarkers is increasing to provide sustainable measure, due to demand for information about the health risks from unfavorable exposures. Given the recent toxicological results on the exposure of cells, animals and workers to RE compounds, it is important to review the toxicological studies to improve the current understanding of the RE compounds in the field of occupational health. This will help to establish a sustainable, safe and healthy working environment for RE industries

Lifted codes and their weight enumerators

AbstractWe describe some structural results for codes over the rings Zp and use them to examine lifts of codes over these rings to Zpe and to codes over the p-adics. We determine the weight enumerator of all lifts of the length 8 Hamming code and the length 12 ternary Golay code. We show that all weight enumerators of the lifts of the length 24 Golay code can be determined after a finite computation