LINEAR COMPLEXITY AND RANDOM SEQUENCES WITH PERIOD 2~n

Let (?)=(S,S,…)be a binary random sequence with period N=2~n,where S=(S_0,…,S_(N-1))is its one period with N independent and uniformly distributed binary random variables.The main results of this paper are as follows.1)Var c(?)=2-(2N+1)2~(-N)-2~(-2N);2)E|c(?)-c(?)|=[2~(c(?)+1)-2]2~(-N)for any sequence (?) with period 2~n;3)N-1+2~(-N)-(n/2+1-2~(-(N-n)))≤E[(?)c(?)]≤N-1+2~(-N)4)2-2~(-(N-1))≤E[(?)|c(?)-c(?)|]≤2-2~(-N)+n/2-2~(-(N-n)),where E and Var stand for taking expectation and variance respectively,c(?) is the linearcomplexity of the sequence (?) and W(b) the Hamming weight of one period of the seqnence (?).     

A NOTE ON THE L_p COMPARISON BETWEEN THE BOOTSTRAP AND RANDOM WEIGHTING

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COMPARING THE INDEPENDENCE OF DIFFERENT RANDOM NUMBER GENERATORS

Pseudo-random number generators have always been important in experimental design, computer simulation, cryptography and statistical analysis. This paper presents a method of comparing the degree of independence exhibited by various random number generators, a procedure, based on consideration of the largest (in modulus) non-unit eigenvalue of the observed Markov transition matrix, is used to assess the ‘randomness‘ of a random number generator.     

FORBIDDEN SUBGRAPHS,DEGREES,NEIGHBORHOOD UNIONS AND CIRCUMFERENCES OF GRAPHS

Combining forbidden subgraphs with degree restrictions and neighborhood unionrestrictions,respectively,we prove the following results:(1) Let G be a 2-connected graph of order n,and 3≤c≤n.If for each induced subgraphL of order four of G(?)|V_1(L)∩S_c|≥2 if L≌K_(1,3),and |V(L)∩S_c|≥1 if L≌P_4,then thecircumference of G is at least c,where V_1(L)is the set of vertices with degree 1 of L,S_c isthe set of vertices with degree at least c/2 of G and P_4 is a path of order 4.(2) Let G be a 2-connected graph of order n,and n≥s+2.If for each induced subgraphL of G isomorphic to K_(1,3)or P_4,d_L(u,v)=2(?)|N(u)∪N(v)|≥s,then the circumferencec (G) of G is at least s+2.Moreover,if n≥s+3 and s is odd,then c(G)≥s+3.     

FUNDAMENTALS OF THE ANALYTIC NETWORK PROCESS - MULTIPLE NETWORKS WITH BENEFITS,COSTS,OPPORTUNITIES AND RISKS

The general theory of the ANP enables one to deal with the benefits,opportunities,costs,andrisks(the BOCR merits)of a decision,by introducing the notion of negative priorites for C and Ralong with the rating(not comparison)of the top priority alternative synthesized for each of the fourmerits in terms of strategic criteria to enable one to combine the four B,O,C,and R values of eachalternative into a single outcome.Strategic criteria are very basic criteria individuals and groups useto assess whether they should make any of the many decisions they face in their daily operations.They do not depend on any particular decision for their priorities but are assessed in terms of the goalsand values of the individual or organization.Synthesis is made with two formulas,one multiplicativeand one additive subtractive that can give rise to negative overall priorities.This paper summarizesand illustrates basic complex decisions involving several control criteria under each of the BOCRmerits.