The reciprocal complementary distance (RCD) matrix of a graphG is defined asRCD(G) = [rcij] where rcij = 1 1+D−dij if i 6= j and rcij = 0, otherwise, where D is the diameter of G and dij is the distance between the vertices vi and vj in G. The RCD-energy of G is defined as the sum of the absolute values of the eigenvalues of RCD(G). Two graphs are said to be RCDequienergetic if they have same R...

The aim of this note is to establish new spectral bounds for the harmonic matrix. The Harary matrix of given a connected graph G of order n, say RD(G), is an n-by-n symmetric matrix, such that (RD(G))ij =  1 dij , if i < j, 0 , if i = j, where dij denotes the distance between the vertices i and j [10, 11]. This matrix (originally known as reciprocal distance matrix [11]) is particulary well-k...

mathematical techniques. When the "objects" considered have specific properties, it is possible to envisage (and even to recommend) how to exploit these properties for performing dimensionality reduction. One example of this approach consists in replacing images of centro-symmetric particles by their rotational power spectrum (Crowther and Amos, 1971): the image is split into angular sectors, t...

The knowledge of two-temperature transport coefficients is of interest in the modelling of fluid flow and heat transfer processes in electric propulsion devices. Variations of species mole fraction, number density, specific enthalpy, specific heat at constant pressure, viscosity, electrical conductivity and thermal conductivity as a function of pressure, electron temperature and different degre...

An example is presented to show that the worst case complexity of Bertsekas small label rst strategy for the shortest path problem is exponential It becomes polynomial if when scanning a node i its successors j i are examined in the nondecreasing order of dij the distance between i and j

(ReceivedAzrgust 2a 1991) i!N)F*r)tiHiromitsu KoBAyAsHi=i815escartimaXigwt4-9-1Department of PhysiologicalDesignSciencesn"[il--diJ ispsc\ti1geAmasaigx.Anthropology, Kyushu Universityof

SUMMARY. In this paper, we consider the problem of comparing s controls to t test treatments using experimental units which are arranged in b blocks of size k. Methods are given for constructing highly A-and MV-efficient designs for such situations. The methods of construction given combine optimality results obtained for one way classification models with the optimal augmentation of blocks wit...

Let x1,…,xn be points in a metric space and define the distance matrix D?Rn×n by Dij=d(xi,xj). The Perron-Frobenius Theorem implies that there is an eigenvector v?Rn with non-negative entries associated to largest eigenvalue. We prove this nearly constant sense inner product vector 1?Rn large?v,1??12??v??2??1??2 each entry satisfies vi??v??2/4n. Both inequalities are sharp.

DYOPTYKA’s innovative solution for the reduction of speckle noise in projection displays, using a phase randomizing deformable mirror, is shown to achieve good performance both within a single 1 μs pulse duration and through sequences of such pulses.