This paper deals with the period T of pseudorandom number sequence gener- ated by subtract- with borrow (SWB ). For the selected base b,legs r > s it is shown that T is dependent only on b, r and s and equal to the...This paper deals with the period T of pseudorandom number sequence gener- ated by subtract- with borrow (SWB ). For the selected base b,legs r > s it is shown that T is dependent only on b, r and s and equal to the order of b with respect to m = br- bs + 1 provided that m and A, which is determined by initial values x1,s’’’ ,xr and initial borrow value cr+1, are coprime. For b = 231-1 this paper searches the field 0 < r ≤ 300, r-s ≤ 10 and finds out all the pairs of (r, s) for which m is prime. In addition, the periods of SWB corresponding to b = 231-1 and these pairs (r, s) are aIso calculated. Besed on data obtained, generators of SWB with extremely long period could be designed.展开更多
A method is put forward to establish the lower hounds for some n-color classical Ramsey numbersR(q,q,…,q) = Rn(q). With this method six new explicit lower bounds R4 (4) ≥458, R3(5)3≥242, R3(6)≥ 1070, R3(7)≥ 1214,...A method is put forward to establish the lower hounds for some n-color classical Ramsey numbersR(q,q,…,q) = Rn(q). With this method six new explicit lower bounds R4 (4) ≥458, R3(5)3≥242, R3(6)≥ 1070, R3(7)≥ 1214, R3(8)≥2834and R3(9)≥ 5282 are obtained using a computer.展开更多
文摘This paper deals with the period T of pseudorandom number sequence gener- ated by subtract- with borrow (SWB ). For the selected base b,legs r > s it is shown that T is dependent only on b, r and s and equal to the order of b with respect to m = br- bs + 1 provided that m and A, which is determined by initial values x1,s’’’ ,xr and initial borrow value cr+1, are coprime. For b = 231-1 this paper searches the field 0 < r ≤ 300, r-s ≤ 10 and finds out all the pairs of (r, s) for which m is prime. In addition, the periods of SWB corresponding to b = 231-1 and these pairs (r, s) are aIso calculated. Besed on data obtained, generators of SWB with extremely long period could be designed.
基金Project supported by Guangxi Natural Science Foundation.
文摘A method is put forward to establish the lower hounds for some n-color classical Ramsey numbersR(q,q,…,q) = Rn(q). With this method six new explicit lower bounds R4 (4) ≥458, R3(5)3≥242, R3(6)≥ 1070, R3(7)≥ 1214, R3(8)≥2834and R3(9)≥ 5282 are obtained using a computer.
