We investigated mechanistic differences in antigen presentation between murine MHC class I variants H-2K(b) and H-2K(bm)8. H-2K(bm)8 differs from H-2K(b) by four residues at the floor of the peptide-binding site, affecting its B pocket which interacts with the second (P2) residue of the peptide. The rest of the molecule, including the T cell receptor (TCR)-contacting residues, is identical to H...

Tibor Gallai conjectured that the edge set of every connected graph G on n vertices can be partitioned into ⌈n/2⌉ paths. Let Gk be the class of all 2k-regular graphs of girth at least 2k − 2 that admit a pair of disjoint perfect matchings. In this work, we show that Gallai’s conjecture holds in Gk, for every k ≥ 3. Further, we prove that for every graph G in Gk on n vertices, there exists a par...

In this correspondence, we present a systematic and closed form construction of complex orthogonal spacetime block codes from complex orthogonal designs of rates (k+1)=2k for 2k 1 or 2k transmit antennas for any positive integer k.

A graph G is k-crossing-critical if cr(G)≥k, but cr(G∖e)<k for each edge e∈E(G), where cr(G) the crossing number of G. It known that latest upper bound a 2k+8k+47 when δ(G)≥3, and 2k+35 δ(G)≥4, δ(G) minimum degree In this paper, we mainly show any with n vertices, cr(G)≤2k+8 cr(G)≤2k−k/2n+35/6 δ(G)≥5.

In this paper we study products and sums divisible by central binomial coefficients. We show that 2(2n+ 1) ( 2n n ) ∣∣∣∣ (6n 3n )( 3n n ) for all n = 1, 2, 3, . . . . Also, for any nonnegative integers k and n we have ( 2k k ) ∣∣∣∣ (4n+ 2k + 2 2n+ k + 1 )( 2n+ k + 1 2k )( 2n− k + 1 n ) and ( 2k k ) ∣∣∣∣ (2n+ 1)(2n n ) Cn+k ( n+ k + 1 2k ) , where Cm denotes the Catalan number 1 m+1 ( 2m m ) = (...

In this paper, we prove that for any positive integers k, n with k ≥ 2, the graph P k n is a divisor graph if and only if n ≤ 2k + 2, where P k n is the k power of the path Pn. For powers of cycles we show that C n is a divisor graph when n ≤ 2k + 2, but is not a divisor graph when n ≥ 2k + bk2 c+ 3, where C k n is the k th power of the cycle Cn. Moreover, for odd n with 2k + 2 < n < 2k + bk2 c...