Let Pi, 1≤i≤5, be prime numbers. It is proved that every integer N that satisfies N=5 （mod 24） can be written as N=p1^2＋p2^2＋P3^2＋p4^2 ＋p5^2, where │√N5-Pi│≤N^1/2-19/850＋∈.
This article proposes algorithms to determine an optimal choice of the Reed-Solomon forward error correction （FEC） code parameters （n,k） to mitigate the effects of packet loss on multimedia traffic caused by buffe...This article proposes algorithms to determine an optimal choice of the Reed-Solomon forward error correction （FEC） code parameters （n,k） to mitigate the effects of packet loss on multimedia traffic caused by buffer overflow at a wireless base station. A network model is developed that takes into account traffic arrival rates, channel loss characteristics, the capacity of the buffer at the base station, and FEC parameters. For Poisson distributed traffic, the theory of recurrent linear equations is applied to develop a new closed form solution of low complexity of the Markov model for the buffer occupancy. For constant bit rate （CBR） traffic, an iterative procedure is developed to compute the packet loss probabilities after FEC recovery.展开更多
We use the large sieve inequality with sparse sets of moduli to prove a new estimate for exponential sums over primes. Subsequently, we apply this estimate to establish new results on the binary Goldbach problem where...We use the large sieve inequality with sparse sets of moduli to prove a new estimate for exponential sums over primes. Subsequently, we apply this estimate to establish new results on the binary Goldbach problem where the primes are restricted to given arithmetic Drogressions.展开更多
文摘Let Pi, 1≤i≤5, be prime numbers. It is proved that every integer N that satisfies N=5 （mod 24） can be written as N=p1^2＋p2^2＋P3^2＋p4^2 ＋p5^2, where │√N5-Pi│≤N^1/2-19/850＋∈.
文摘This article proposes algorithms to determine an optimal choice of the Reed-Solomon forward error correction （FEC） code parameters （n,k） to mitigate the effects of packet loss on multimedia traffic caused by buffer overflow at a wireless base station. A network model is developed that takes into account traffic arrival rates, channel loss characteristics, the capacity of the buffer at the base station, and FEC parameters. For Poisson distributed traffic, the theory of recurrent linear equations is applied to develop a new closed form solution of low complexity of the Markov model for the buffer occupancy. For constant bit rate （CBR） traffic, an iterative procedure is developed to compute the packet loss probabilities after FEC recovery.
文摘We use the large sieve inequality with sparse sets of moduli to prove a new estimate for exponential sums over primes. Subsequently, we apply this estimate to establish new results on the binary Goldbach problem where the primes are restricted to given arithmetic Drogressions.
