An (n, a, b)-perfect double cube is a b × b × b sized n-ary periodic array containing all possible a × a × a sized n-ary array exactly once as subarray. A growing cube is an array whose cj × cj × cj sized prefix is an (nj, a, cj)-perfect double cube for j = 1, 2, . . ., where cj = n v/3 j , v = a 3 and n1 < n2 < · · ·. We construct the smallest possible perfect double cube (a 256×256×256 sized ...

A (proper) coloring of a finite simple graph (G) is pe#ect if it uses exactly o(G) colors, where o(G) denotes the order of a largest clique in G. A coloring is locally-perfect [3] if it induces on the neighborhood of every vertex v a perfect coloring of this neighborhood. A graph G is perfect (resp. locally-petfect) if every induced subgraph admits a perfect (resp. locally-perfect) coloring. Pr...

We define generalizations of classical invariants of ramification, for coverings on a variety of arbitrary dimension over a local field of mixed characteristic. For an -adic sheaf, we define its Swan class as a 0-cycle class supported on the closed fiber. We present a formula for the Swan conductor of cohomology and its relative version. Let K be a complete discrete valuation field of character...

This study investigated the impact of oral pushed output on the learning and retention of English perfect tenses. During the study, a pre-test was administered to 22 freshmen majoring in English translation. The participants were randomly assigned to two groups. Then, for six sessions both groups received explicit instructions on English perfect tenses. Every session, the experimental group rec...

Let G be a connected graph with vertex set V (G) = {v1, v2, · · · , vν} , which may have multiple edges but have no loops, and 2 ≤ dG(vi) ≤ 3 for i = 1, 2, · · · , ν, where dG(v) denotes the degree of vertex v of G. We show that if G has an even number of edges, then the number of perfect matchings of the line graph of G equals 2, where n is the number of 3-degree vertices of G. As a corollary,...

Let V be a q-dimensional vector space. Fix a set B of q(q − 1) monomials in S(V ) of the form x where ik > 0 for all k. The generic element of S(V ) is conjugate under a suitable linear transformation to an element with support off of B. We prove this by showing the existence of a perfect matching with a unique weight in a certain weighted bipartite graph. Such a perfect matching corresponds to...

Let G be a graph with adjacency matrix A, let H(t) = exp(itA). G is called a periodic graph if there exists a time τ such that H(τ) is diagonal. If u and v are distinct vertices in G, we say that perfect state transfer occurs from u to v if there exists a time τ such that |H(τ)u,v| = 1. A necessary and sufficient condition for G is periodic is given. We give the existence for the perfect state ...

Sir.?The aims of your paper in regard to the public health, as set out in your New Year's issue, are excellent. And as everyone seems to be waking up at last to the fact that the housing question overshadows every other question in domestic politics, perhaps something will be accomplished. Questions of housing and health must not, however, be allowed to become the playthings of politics. Every ...