Analytical solutions for the two- and three-dimensional time-fractional telegraph equations by the method of separating variables

In this paper, a method of separating variables is effectively implemented for solving a time-fractional telegraph equation (TFTE) in two and three dimensions. We discuss and derive the analytical solution of the TFTE in two and three dimensions with nonhomogeneous Dirichlet boundary condition. This method can be extended to other kinds of the boundary conditions.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

Random telegraph noise in the photoluminescence of individual GaxIn1-xAs quantum dots in GaAs

We have investigated random telegraph noise in the photoluminescence from InGaAs quantum dots in GaAs. Dots switching among two and three levels have been measured. The experiments show that the switching InGaAs dots behave very similarly to switching InP dots in GaInP. but differently from the more commonly investigated colloidal dots. The switching is attributed to defects, and we show that the switching can be used as a monitor of the defect.

Fairground Music; Augustine Sleeping Before He Can Talk; Telegraph; Cathedral

Four poems.

Telegraph to H.K. Woodruff

Telegraph to H. K. Woodruff of St. Margaret's Island informing him of Samuel DeVeaux Woodruff's death. It is dated July 16, 1918 and signed "Welland".

Letter - Holmes' Burglar Alarm, Telegraph Company to S.D. Woodruff

Letter to S.D. Woodruff from the Holmes’ Burglar Alarm, Telegraph Company of New York stating that they will send a Mr. Whittaker over to make repairs or changes. There is a partial envelope included with this letter, Feb. 8, 1881.

Telegraph to S.D. Woodruff from W.H. Johnson of Alpena, Michigan

Telegraph to S.D. Woodruff from W.H. Johnson of Alpena, Michigan. He says “If I can have the refusal at the twenty five hundred until I can look, you can draw for the seventy two dollars”. The telegraph is torn, Mar. 5, 1880.

Telegraph to S.D. Woodruff from W. Johnson of Alpena, Michigan

Telegraph to S.D. Woodruff from W. Johnson of Alpena, Michigan stating that he has sent a New York draft for $2,500.00, May 27, 1881.

Telegram from Great North Western Telegraph Company of Canada to S.D. Woodruff from L. Cabot

Telegram from Great North Western Telegraph Company of Canada to S.D. Woodruff from L. Cabot stating that he will take the shares, Jan. 16, 1886.

Telegram from Great North Western Telegraph Company of Canada to S.D. Woodruff from L. Cabot stating that the draft for $5000.00 will be forwarded

Telegram from Great North Western Telegraph Company of Canada to S.D. Woodruff from L. Cabot stating that the draft for $5000.00 will be forwarded on Monday or Tuesday, Jan. 16, 1886.

Telegram from Montreal and Dominion Telegraph Companies’ Lines to Louis Cabot stating that Mr. Woodruff has arranged to transfer the shares

Telegram from Montreal and Dominion Telegraph Companies’ Lines to Louis Cabot stating that Mr. Woodruff has arranged to transfer the shares, Jan. 18, 1886.