Let F (n, r, k) denote the maximum possible number of distinct edge-colorings of a simple graph on n vertices with r colors, which contain no monochromatic copy of Kk. It is shown that for every fixed k and all n > n0(k), F (n, 2, k) = 2k−1 and F (n, 3, k) = 3k−1, where tk−1(n) is the maximum possible number of edges of a graph on n vertices with no Kk, (determined by Turán’s Theorem). The case...

A sub-optimal decoder for finding K vectors close to a given origin in a lattice is presented. The algorithm operates by partitioning the search space and applying a list version of the sphere decoder, enabling efficient operation for lattices of dimensions m up to and exceeding 200. The decoder is well suited to finding K highly probable sequences for the estimation of a-posteriori probabiliti...

Consider the subband coder of figure 1, consisting of k = 0, 1, ..., M − 1 channels. Each channel has an analysis filter H k (z), a synthesis filter F k (z), down/up-sampling ratio m k , and a b k bit quantizer. The input is x[n], after passing through the analysis filters it becomes x k [n], and the subband signals are x k [n]. The subband coder is maximally decimated, M −1 k=0 m k = 1. (1) As...

THEOREM 1. Let K/Q be a number field, and let C/K be a smooth projective curve of genus at least 2. For each^class ^ e i / 1 (Gal (AT/AT), Aut(C)), let C% be the twist of C by x (cf. [11, X §3]) and le\Jx = J ac (Q be the Jacobian variety of Cx. There is a constant y = y{C/K) such that #C,( /Q^r7 a n k * ( K ) forallxeH{G2\{K/K),A\xi{C)). We illustrate this general theorem by applying it to a p...

This paper is comprised of two related parts. First we discuss which k-graph algebras have faithful gauge invariant traces, where the gauge action of T k is the canonical one. We give a sufficient condition for the existence of such a trace, identify the C *-algebras of k-graphs satisfying this condition up to Morita equivalence, and compute their K-theory. For k-graphs with faithful gauge inva...

By applying the melt-centrifugation, porosity and dislocations are introduced in microstructure of n-type Zintl phase Mg3+xSb1.5Bi0.49Te0.01leading to significantly low ?l (? 0.33 W m?1 K?1 at 723 K) enhanced zT 1.64 K).

in this paper, we introduce a considerable machinery which permits us to characterize a number of special (fuzzy) subsets in ag -groupoids. generalizing the concepts of (,q) -fuzzy bi-ideals (interior ideal), we define ( , ) k q -fuzzy bi-ideals, ( , ) k q -fuzzy left (right)-ideals and ( , ) k q -fuzzy interior ideals in ag -groupoids and discuss some fundamental aspects of these i...

We describe a class of geometric objects called k-omino towers that are created by stacking blocks of size k×1×1 on a convex base composed of these same k-omino blocks. These towers are equivalent to a class of fixed polyominoes or lattice animals, through the creation of a polyomino using the boundary of the two-dimensional vertical face of the tower. By applying a partition to the set of k-om...

For a given positive integer k, the k-circle formation problem asks set of autonomous, asynchronous robots to form disjoint circles having k each at distinct locations, centered fixed points in Euclidean plane. The are identical, anonymous, oblivious, and they operate Look–Compute–Move cycles. This paper studies its relationship with k-epf problem, generalized version embedded pattern which exa...

On “Increasing muscle extensibility...” Weppler CH, Magnusson SP. Phys Ther. 2010;90:438–449. This perspective article was very interesting and thought provoking; however, I was slightly skeptical about your conclusions in the section on neuromuscular relaxation. Specifi cally, I am having trouble reconciling my clinical experience with your suggestion that an increase in extensibility during a...