1,284 research outputs found

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

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

    Support Vector Number Reduction: Survey and Experimental Evaluations

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    Critical appraisal of metabolic dysfunction-associated steatotic liver disease: Implication of Janus-faced modernity

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    The existing term non-alcoholic fatty liver disease (NAFLD) has raised substantial concerns due to its inherent disadvantages of using exclusionary diagnostic criteria and the stigmatizing word ‘fatty.’ Three pan-national liver associations set out to explore a new nomenclature to replace both NAFLD and its suggested alternative, metabolic (dysfunction)-associated fatty liver disease (MAFLD). They surveyed if a change in nomenclature and/or definition is favored and which nomenclature best communicates disease characteristics and increases awareness. In lieu of NAFLD/MAFLD, metabolic dysfunction-associated steatotic liver disease (MASLD) has been chosen, and an umbrella term, steatotic liver disease (SLD), encompassing the whole spectrum of liver disease, has been proposed. It has been suggested that cardiometabolic risk factors should be considered when categorizing SLD patients. Furthermore, a new subcategory, MASLD with increased alcohol intake (MetALD), casts light on a neglected group of patients with moderate or more alcohol consumption. The importance of metabolic dysfunction was acknowledged in this new nomenclature, but the precise contribution of metabolic dysfunction and alcohol consumption to the development and progression of SLD remains unclear. Herein, we review hepatologists’ and endocrinologists’ perspectives on the new nomenclature, along with its possible impact on clinical practice. Although it is premature to predict the settlement of the new nomenclature, this review may help build more evidence for a soft landing of it in the future

    Tribological characteristics of high strength low alloy steel under various environmental conditions

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    High strength low alloy steel has excellent heat resistance and high strength. As it is commonly used as gun barrel material, a long service life and superior wear resistance are necessary for steel components. Here we investigated the wear characteristics of high strength low alloy steel surfaces under various environmental conditions, using a pin-on-disk wear test. Oxidation and wear debris effects on the coefficient of friction (COF) of the alloy steel were examined under air and argon (Ar) gas flow at atmospheric conditions
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