(d) Suppose list1 contains N1 elements and list2 contains N2 elements. The first while loop is executed O(N1) times. The body of this loop takes O(N1) since GetNextItem takes O(1) and InsertItem takes O(N1). So, the complexity of the first loop is O(N1N1). The second while loop is executed O(N2) times. The body of that loop takes O(N1+N2) time since GetNextItem takes O(1), RetrieveItem takes O(...

The effects of several N-sulfonyl-polyamines, including N1-dansyl-spermine (N1-DnsSpm) and N1-(n-octanesulfonyl)-spermine (N1-OsSpm), were studied at recombinant N-methyl-D-aspartate (NMDA) receptors expressed in Xenopus laevis oocytes. N1-DnsSpm and N1-OsSpm inhibited NMDA receptors and were approximately 1000-fold more potent than spermine in oocytes voltage-clamped at -70 mV. Block by N1-Dns...

In this paper a deterministic algorithm for the length reduction problem is presented. This algorithm enables a new tool for performing fast convolution in sparse data. While the regular fast convolution of vectors V1, V2 whose sizes are N1, N2 respectively, takes O(N1 log N2) using FFT, the proposed algorithm performs the convolution in O(n1 log n1), where n1 is the number of non-zero values i...

Let X be a complex Fano manifold of arbitrary dimension, and consider a prime divisor D ⊂ X. We denote by N1(D,X) the linear subspace of N1(X) spanned by numerical classes of curves contained in D, i.e. N1(D,X) = i∗(N1(D)) where i∗ : N1(D) → N1(X) is the push-forward of one-cycles induced by the inclusion i : D →֒ X. The codimension of N1(D,X) in N1(X) equals the dimension of the kernel of the r...

Let F (m; n1, n2) denote the number of lattice walks from (0, 0) to (n1, n2), always staying in the first quadrant {(n1, n2); n1 ≥ 0, n2 ≥ 0} and having exactly m steps, each of which belongs to the set {E = (1, 0),W = (−1, 0), NE = (1, 1), SW = (−1,−1)}. Ira Gessel conjectured that F (2n; 0, 0) = 16 (1/2)n(5/6)n (2)n(5/3)n . We pose similar conjectures for some other values of (n1, n2), and gi...

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...

a. N1 = {(i1, i2, . . . , in) : ik ∈ Ik for all k ∈ {1, 2, . . . , n}} and b. N2 = {(x1, x2, . . . , xn) : ∑n k=1 xk = 0}. Proof. To prove (a), it suffices to show, by Proposition 1, that N1 is nonempty and x + ry ∈ N1 for all r ∈ R and all x, y ∈ N1. For the first condition, (0, 0, . . . , 0) ∈ N1 since Ik is a subgroup of R containing the additive identity 0 for all k ∈ {1, 2, . . . , n}. Tha...

Site-specific modification of the N1-position of purine was explored at the nucleoside and oligomer levels. 2'-deoxyinosine was converted into an N1-2,4-dinitrophenyl derivative 2 that was readily transformed to the desired N1-substituted 2'-deoxyinosine analogues. This approach was used to develop a post-synthetic method for the modification of the endocyclic N1-position of purine at the oligo...