The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains th...The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied展开更多
Carbon dots （C-dots）, since their first discovery in 2004 by Scrivens et al. during purification of single-walled carbon nano- tubes, have gradually become a rising star in the fluorescent nanoparticles family, due ...Carbon dots （C-dots）, since their first discovery in 2004 by Scrivens et al. during purification of single-walled carbon nano- tubes, have gradually become a rising star in the fluorescent nanoparticles family, due to their strong fluorescence, resistance to pbotobleaching, low toxicity, along with their abundant and inexpensive nature. In the past decade, the procedures for prepar- ing C-dots have become increasingly versatile and facile, and their applications are being extended to a growing number of fields. In this review, we focused on introducing the biological applications of C-dots, hoping to expedite their translation to the clinic.展开更多
文摘The single birth process is a Markov chain, either time-continuous or time-discrete, valuedin the non-negative integers: the system jumps with positive rate from k to k + 1 but not tok +j for all j 2 (this explains the meaning of 'single birth') . However, there is no restrictionfor the jumps from k to k - j(1 j< k). This note mainly deals with the uniqueness problemfor the time-continuous processes with an extension: the jumps from k to k + 1 may also beforbidden for at most finite number of k. In both cases (time-continuous or -discrete), thehitting probability and the first moment of the hitting time are also studied
基金the support for this work from the National Science and Technology Major Project of China(2012ZX-10004801-003-007,2012AA022603)
文摘Carbon dots （C-dots）, since their first discovery in 2004 by Scrivens et al. during purification of single-walled carbon nano- tubes, have gradually become a rising star in the fluorescent nanoparticles family, due to their strong fluorescence, resistance to pbotobleaching, low toxicity, along with their abundant and inexpensive nature. In the past decade, the procedures for prepar- ing C-dots have become increasingly versatile and facile, and their applications are being extended to a growing number of fields. In this review, we focused on introducing the biological applications of C-dots, hoping to expedite their translation to the clinic.
