Gamma-Ray Burst Afterglows: Effects of Radiative Corrections and Nonuniformity of the Surrounding Medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be due to continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, viz., $n_{ext}\propto R^{-k}$, we analytically study the effects of the first-order radiative correction and the nonuniformity of the medium on a GRB afterglow. We first derive a new relation among the observed time, the shock radius and the fireball's Lorentz factor: $t_\oplus=R/4(4-k)\gamma^2c$, and also derive a new relation among the comoving time, the shock radius and the fireball's Lorentz factor: $t_{co}=2R/(5-k)\gamma c$. We next study the evolution of the fireball by using the analytic solution of Blandford and McKee (1976). The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is $p=2.5$, implied from the spectra of GRBs, the X-ray afterglow of GRB970616 is well fitted by assuming $k=2$.Comment: 17 pages, no figures, Latex file, MNRAS in pres

A dubiety-determining based model for database cumulated anomaly intrusion

The concept of Cumulated Anomaly (CA), which describes a new type of database anomalies, is addressed. A typical CA intrusion is that when a user who is authorized to modify data records under certain constraints deliberately hides his/her intentions to change data beyond constraints in different operations and different transactions. It happens when some appearing to be authorized and normal transactions lead to certain accumulated results out of given thresholds. The existing intrusion techniques are unable to deal with CAs. This paper proposes a detection model, Dubiety-Determining Model (DDM), for Cumulated Anomaly. This model is mainly based on statistical theories and fuzzy set theories. It measures the dubiety degree, which is presented by a real number between 0 and 1, for each database transaction, to show the likelihood of a transaction to be intrusive. The algorithms used in the DDM are introduced. A DDM-based software architecture has been designed and implemented for monitoring database transactions. The experimental results show that the DDM method is feasible and effective