With xij we denote the value of variable j (j = 1, ..., p) for sample i (i = 1, ..., n); xi is the set of variables for sample i and x is the set of variables for all samples. Some of the n samples are known to belong to Class 1 (n1 samples) and the others to Class 2 (n2, n1 +n2 = n); the proportion of samples from Class 1 and 2 is denoted by k1 = n1/n and k2 = n2/n, respectively, and yi = {−1,...

let e be an edge of a g connecting the vertices u and v. define two sets n1 (e | g) andn2(e |g) as n1(e | g)= {xv(g) d(x,u) d(x,v)} and n2(e | g)= {xv(g) d(x,v) d(x,u) }.thenumber of elements of n1(e | g) and n2(e | g) are denoted by n1(e | g) and n2(e | g) ,respectively. the szeged index of the graph g is defined as sz(g) ( ) ( ) 1 2 n e g n e g e e    . inthis paper we compute the sz...

High harmonic generation is studied in gas species, namely pure H2, N2 and their mixture 1:1 ratio. Observation of orders from 17H to 35H are well resolved. Harmonic spectrum produced H2 obtained, but the signal weaker compared that mixture. yield enhanced H2. The maximum photon energy can reach calculated with know cutoff formula. experiment calculation results close agreement. In N2:H2, highe...

The rank of the matrix multiplication operator for n×n matrices is one of the most studied quantities in algebraic complexity theory. I prove that the rank is at least 3n2−o(n2). More precisely, for any integer p ≤ n− 1 the rank is at least (3− 1 p+1 )n2 − (1 + 2p 2p p−1 ) )n. The previous lower bound, due to Bläser, was 5 2 n2−3n (the case p = 1). The new bounds improve Bläser’s bound for all ...

Optical emission spectra ~OES! from CH4/N2 rf plasmas, which are used for the deposition of nitrogen-containing hydrogenated amorphous carbon ~a-C:H:N! thin films, have been characterized. Previously unidentified spectral lines have been assigned to atomic N. Further identified species include CH, H, H2, N2, N2 1 , N, and CN. Variations between spectra from the pure CH4 or N2 plasmas and the mi...

Richard Wilson conjectured in 1974 the following asymptotic formula for the number of n-vertex Steiner triple systems: STS(n) = ( (1 + o(1)) n e2 )n2 6 . Our main result is that STS(n) ≤ ( (1 + o(1)) n e2 )n2 6 . The proof is based on the entropy method. As a prelude to this proof we consider the number F (n) of 1factorizations of the complete graph on n vertices. Using the KahnLovász theorem i...

We show that necessary and sufficient conditions for the existence of a semi-evenly partite star factorization of the symmetric complete tripartite digraph K~I,n2,n3 are (i) k is even, k 2 4 and (ii) nl = n2 = n3 == 0 (mod k(k -1)/3) for k == 0 (mod 6) and nl = n2 = n3 == 0 (mod k(k 1)) for k == 2,4 (mod 6).

UNLABELLED The ability to reduce atmospheric nitrogen (N2) to ammonia, known as N2 fixation, is a widely distributed trait among prokaryotes that accounts for an essential input of new N to a multitude of environments. Nitrogenase reductase gene (nifH) composition suggests that putative N2-fixing heterotrophic organisms are widespread in marine bacterioplankton, but their autecology and ecologi...

effect of controlled atmospheres (cas) at various concentrations of co2, n2 and o2 on the lethal times of tribolium castaneum and trogoderma granarium was investigated at 20 and 30 ºc. experiments were performed using a recirculatory multi-flask apparatus. the results revealed that, the shortest times (0.1, 0.3 and 0.9 day for adults, larvae and pupae, respectively) required to obtain 50% morta...

For a positive integer N , let s(N) be the side length of the minimum square into which N unit squares can be packed. This paper shows that, for given real numbers a, b ≥ 2, no more than ab− (a + 1− dae)− (b + 1− dbe) unit squares can be packed in any a′ × b′ rectangle R with a′ < a and b′ < b. From this, we can deduce that, for any integer N ≥ 4, s(N) ≥ min{d√Ne, √ N − 2b√Nc + 1 + 1}. In parti...