fails to possess a solution in general if X is equal to any of the characteristic values X¡, ¿ = 1,2,3, , of the kernel __(x, y), it is not surprising that all treatments of (1) have been limited to the cases in which equation (2) is in some sense (to be made more precise later) a majorant for (1) when X =Xi, the smallest characteristic value of F"(x, y). Thus, if FT(x, y) is assumed to be posi...

Let f be a permutation of V (G). Define f (x, y)=|dG(x, y)−dG(f (x), f (y))| and f (G)= ∑ f (x, y) over all the unordered pairs {x, y} of distinct vertices of G. Let (G) denote the smallest positive value of f (G) among all the permutations f of V (G). The permutation fwith f (G)= (G) is called a near automorphism ofG. In this paper, we study the near automorphisms of cycles Cn and we prove tha...

fails to possess a solution in general if X is equal to any of the characteristic values X¡, ¿ = 1,2,3, , of the kernel __(x, y), it is not surprising that all treatments of (1) have been limited to the cases in which equation (2) is in some sense (to be made more precise later) a majorant for (1) when X =Xi, the smallest characteristic value of F"(x, y). Thus, if FT(x, y) is assumed to be posi...

Let f : X → Y f: \to Y </...

This paper describes an algorithm which finds the smallest set of smallest rings of a ring system without the necessity of finding all rings in the ring system. The algorithm first finds the smallest rings in which unused atoms occur and then progresses to find the smallest rings in which unused edges and faces occur until the smallest set of rings required to describe the complete ring system ...

(2) Minimality: The proof is by contradiction. Assume that Y is not a minimal spanning tree and among all minimum weight spanning trees, we pick Y1 which has the smallest number of edges which are not in Y . Consider the edge e which was first to be added by the algorithm to Y of those which are not in Y1. Y1 ∪ e forms a circuit. Being a tree, Y cannot contain all edges of this circuit. Therefo...

In this paper, we study sharp two-sided heat kernel estimates for a large class of symmetric reflected diffusions with jumps on the closure an inner uniform domain D D </mml:semantic...

Consider a group G such that there is no homomorphism f : G → {±1}. In that case, how close can we come to such a homomorphism? We show that if f has zero expectation, then the probability that f(xy) = f(x)f(y), where x, y are chosen uniformly and independently from G, is at most 1/2(1 + 1/ √ d), where d is the dimension of G’s smallest nontrivial irreducible representation. For the alternating...

Introduction: Slice encoding for metal artifact correction (SEMAC) [1] completely corrects metal-induced in-plane and through-plane distortions. The SEMAC imaging sequence (Fig. 1) augments a view-angle-tilting (VAT) [2] spin echo sequence with z-phase encoding. While the VATcompensation gradient suppresses the in-plane distortions, the throughplane distortions are corrected by combining multip...

It is well known that the smallest eigenvalue of the adjacency matrix of a connected ¿-regular graph is at least -d and is strictly greater than -d if the graph is not bipartite. More generally, for any connected graph G = (V JE), consider the matrix Q = D + A where D is the diagonal matrix of degrees in the graph G , and A is the adjacency matrix of G . Then Q is positive semi-definite, and th...