A characterization of the Razak-Jacelon algebra

Combing Elliott, Gong, Lin and Niu's result and Castillejos and Evington's result, we see that if $A$ is a simple separable nuclear monotracial C$^*$-algebra, then $A\otimes\mathcal{W}$ is isomorphic to $\mathcal{W}$ where $\mathcal{W}$ is the Razak-Jacelon algebra. In this paper, we give another proof of this. In particular, we show that if $\mathcal{D}$ is a simple separable nuclear monotracial $M_{2^{\infty}}$-stable C$^*$-algebra which is $KK$-equivalent to $\{0\}$, then $\mathcal{D}$ is isomorphic to $\mathcal{W}$ without considering tracial approximations of C$^*$-algebras with finite nuclear dimension. Our proof is based on Matui and Sato's technique, Schafhauser's idea in his proof of the Tikuisis-White-Winter theorem and properties of Kirchberg's central sequence C$^*$-algebra $F(\mathcal{D})$ of $\mathcal{D}$. Note that some results for $F(\mathcal{D})$ is based on Elliott-Gong-Lin-Niu's stable uniqueness theorem. Also, we characterize $\mathcal{W}$ by using properties of $F(\mathcal{W})$. Indeed, we show that a simple separable nuclear monotracial C$^*$-algebra $D$ is isomorphic to $\mathcal{W}$ if and only if $D$ satisfies the following properties:(i) for any $\theta\in [0,1]$, there exists a projection $p$ in $F(D)$ such that $\tau_{D, \omega}(p)=\theta$,(ii) if $p$ and $q$ are projections in $F(D)$ such that $0<\tau_{D, \omega}(p)=\tau_{D, \omega}(q)$, then $p$ is Murray-von Neumann equivalent to $q$,(iii) there exists a homomorphism from $D$ to $\mathcal{W}$.Comment: added references, fixed typos, 23 page

Study of quasi-distributed optical fiber methane sensors based on laser absorption spectrometry

The coal industry plays an important role in the economic development of China. With the increase of coal mining year by year, coal mine accidents caused by gas explosion also occur frequently, which poses a serious threat to the life safety of absenteeism and national property safety. Therefore, high-precision methane fiber sensor is of great significance to ensure coal mine safety. This paper mainly introduces two kinds of quasi-distributed gas optical fiber sensing systems based on laser absorption spectroscopy. The gas fiber optic sensor based on absorption spectrum has high measurement accuracy, fast response and long service life. One is quasi-distributed optical fiber sensing system based on spatial division multiplexing (SDM) technology and the other is quasi-distributed optical fiber sensing system based on optical time domain reflection and time division multiplexing(TDM) technology

A New HDG Method for Dirichlet Boundary Control of Convection Diffusion PDEs II: Low Regularity

In the first part of this work, we analyzed a Dirichlet boundary control problem for an elliptic convection diffusion PDE and proposed a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution. For the case of a 2D polygonal domain, we also proved an optimal superlinear convergence rate for the control under certain assumptions on the domain and on the target state. In this work, we revisit the convergence analysis without these assumptions; in this case, the solution can have low regularity and we use a different analysis approach. We again prove an optimal convergence rate for the control, and present numerical results to illustrate the convergence theory

A Simple Demonstration of the Doppler Effect in Sound

The example which is perhaps most frequently cited as an illustration of the Doppler effect is the change of pitch of a locomotive bell or whistle or of a street-car gong in rapid motion, particularly as heard by a person on board a car passing rapidly in the opposite direction on a parallel track. To the use of this illustration Professor R. W. Wood objects on the ground that scarcely one person in ten has any distinct recollection of having noticed the phenomena unless his attention has been directed to it

Quantifying and Transferring Contextual Information in Object Detection

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Complete genome sequence of a sub-subgenotype 2.1i isolate of classical swine fever virus from China

Citation: Zhang, B., Mi, S., Bao, F., Guo, H., Tu, C., Shi, J., & Gong, W. (2017). Complete genome sequence of a sub-subgenotype 2.1i isolate of classical swine fever virus from China. Genome Announcements, 5(14). doi:10.1128/genomeA.00127-17The complete genome sequence of a sub-subgenotype 2.1i isolate of classical swine fever virus (CSFV), GD317/2011, was determined. Notably, GD317/2011 is distant from the sub-subgenotype 2.1b isolate HEBZ at genes of Erns, E1, E2, P7, NS2, NS5A and the 3=-nontranslated region (3=-NTR) but is closely related to that at genes of Npro, Core, NS3, NS4A, NS4B, and NS5B. © 2017 Zhang et al