The square root relationship of gas release in the early stage of desorption is widely used to provide a simple and fast estimation of the lost gas in coal mines. However, questions arise as to how the relationship wa...The square root relationship of gas release in the early stage of desorption is widely used to provide a simple and fast estimation of the lost gas in coal mines. However, questions arise as to how the relationship was theoretically derived, what are the assumptions and applicable conditions and how large the error will be. In this paper, the analytical solutions of gas concentration and fractional gas loss for the diffusion of gas in a spherical coal sample were given with detailed mathematical derivations based on the diffusion equation. The analytical solutions were approximated in case of small values of time and the error analyses associated with the approximation were also undertaken. The results indicate that the square root relationship of gas release is the first term of the approximation, and care must be taken in using the square root relationship as a significant error might be introduced with increase in the lost time and decrease in effective diameter of a spherical coal sample.展开更多
We verify that the total angular momentum 3-vector defined by the author [X. Zhang, Commun. Math.Phys. 206 (1999) 137] is equal to (0, 0, ma) forany time slice in both the Kerr and the Kerr-Newman spacetimes.
In this article we consider the kth-order discrete delay survival red blood cells model. The general form of the discrete dynamical system is rewritten as Xn＋l = f（Pn,δn,xn,... ,xn＋1） where Pn,δn converge to the...In this article we consider the kth-order discrete delay survival red blood cells model. The general form of the discrete dynamical system is rewritten as Xn＋l = f（Pn,δn,xn,... ,xn＋1） where Pn,δn converge to the parametric values P and 6. We show that when the parameters are replaced by sequences, the stability results of the original system still hold.展开更多
文摘The square root relationship of gas release in the early stage of desorption is widely used to provide a simple and fast estimation of the lost gas in coal mines. However, questions arise as to how the relationship was theoretically derived, what are the assumptions and applicable conditions and how large the error will be. In this paper, the analytical solutions of gas concentration and fractional gas loss for the diffusion of gas in a spherical coal sample were given with detailed mathematical derivations based on the diffusion equation. The analytical solutions were approximated in case of small values of time and the error analyses associated with the approximation were also undertaken. The results indicate that the square root relationship of gas release is the first term of the approximation, and care must be taken in using the square root relationship as a significant error might be introduced with increase in the lost time and decrease in effective diameter of a spherical coal sample.
文摘We verify that the total angular momentum 3-vector defined by the author [X. Zhang, Commun. Math.Phys. 206 (1999) 137] is equal to (0, 0, ma) forany time slice in both the Kerr and the Kerr-Newman spacetimes.
文摘In this article we consider the kth-order discrete delay survival red blood cells model. The general form of the discrete dynamical system is rewritten as Xn＋l = f（Pn,δn,xn,... ,xn＋1） where Pn,δn converge to the parametric values P and 6. We show that when the parameters are replaced by sequences, the stability results of the original system still hold.
