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Let M ( X , A , mu ) $\mathcal{M}(X,\mathcal{A},\mu )$ be the ring of all real-valued measurable functions constructed over a measure space ( X , A , mu ) $(X,\mathcal{A},\mu )$ . A topology on M ( X , A , mu ) $\mathcal{M}(X,\mathcal{A},\mu )$ , called the F mu -topology, is introduced. It is realized that the component, the quasicomponent and the path component in this F mu -topology are identical. It turns out that the F mu -topology on M ( X , A , mu ) $\mathcal{M}(X,\mathcal{A},\mu )$ becomes connected if and only if mu is an atomic measure of a special type. It is also proved that the F mu -topology is first countable when and only when mu is a hemifinite measure. Finally, it is shown that the second countability of the F mu -topology is equivalent to the hemifiniteness of the measure mu together with the countable chain condition of the F mu -topology.
High-pressure synchrotron x-ray diffraction experiments combined with first-principles density functional theory (DFT) calculations on CaCu2O3compound were employed to investigate the structure up to ∼12 GPa. Rietveld refinement on ambient data indicates a weakly off stoichiometric composition Ca1.068Cu1.932O2.676, which indicates the presence of antisite Ca-Cu defects. There was no indication of structural phase transition, but a strong anisotropic elastic compression was observed, notably more significant along thec-axis than thea-andb-axes. While the experimental bulk modulus ∼54 GPa obtained matches well with the DFT calculated value (∼56 GPa), an anomalous stiffening of the bulk structure beyond ∼3-5 GPa was observed yielding the bulk modulus of ∼103 GPa. A simultaneous microstructural rearrangement was also observed experimentally in the form of bond lengths and bond angles exhibiting a change in trend in their pressure evolution at this range. The observed changes in the local coordination environments clearly suggesting a second order isosymmetric phase transition.
Forced Draft (FD) fans are an essential part of a thermal power plant and have to be used and maintained properly to ensure the safety and reliability of the plant. An unexpected breakdown of the FD fan may result in a generation loss of up to millions however the cost of power restoration and the penalty risk of a huge amount of the economic figure. This paper presents a real industrial case study on vibration based condition monitoring and bearing fault diagnosis of an FD forced draft fan. Multiple diagnostic techniques including vibration velocity, acceleration spectrum analysis, motor current signature analysis (MCSA), noise measurement, thermography, and wear debris analysis are employed. An early stage bearing defect is detected through high, frequency vibration analysis and is also confirmed by post maintenance measuring.This paper demonstrates that condition based maintenance can help to maintain high plant reliability and reduce unplanned downtime.
In a recent paper, Chatterjee, the author and Mohan posed the problem of determining all solutions of the Diophantine equation F_n=Φ(m), where F_n is the n-th Fibonacci number and Φ(m) counts the number of nonempty sets A ⊆{1, 2, …, m} for which (A) is relatively prime to m. In this paper, we prove that the Diophantine equation has the only solutions (n,m)=(1,1),(2,1),(3,2). The main tools used in this paper are lower bounds for linear forms in logarithms due to Matveev and Dujella-Pethő version of the Baker-Davenport reduction method in diophantine approximation.
Let X be a topological space. For each transfinite cardinal number ℵ_α, we define a topology C_ℵ_α(X) on the ring C(X). With ℵ_α=ℵ_0, C_ℵ_α(X) reduces to the space C_p(X). We prove that for ℵ_α≥ℵ_1, C_ℵ_α(X) is pathwise connected if and only if it is connected if and only if X is pseudocompact. Here, we define ℵ_α-separable space and furthermore, we show that X is ℵ_α-separable when and only when C_ℵ_α(X) is metrizable when and only when it is a sequential space. Later we introduce two new cardinal functions, namely cc_ℵ_α(X) and ac_ℵ_α(X) which turned out to be the character and pseudocharacter of C_ℵ_α(X) respectively. At the end of this article we show that a number cardinal functions associated with the space C_ℵ_α(X) are equal.
