Distance regular graphs fall into three families: primitive, antipodal, and bipar-tite. Each antipodal distance regular graph is a covering graph of a smaller (usually primitive) distance regular graph; the antipodal distance graphs of diameter three are covers of the complete graph, and are the first non-trivial case. Many of the known examples are connected with geometric objects, such as pro...

As an extension of the class of half condensed domains introduced by D.D. Anderson and Dumitrescu, we introduce and study the class of almost condensed domains. An integral domain D is almost condensed if whenever 0 ̸= z ∈ IJ with I, J ideals of D, there exist I ′, J ′ ideals of D such that I ′ ⊆ Iw, J ′ ⊆ Jw and zD = (I ′J )w. In 1983, D.F. Anderson and D.E. Dobbs [13] called an integral domain...

Abstract We study the statistical estimation problem of orthogonal group synchronization and rotation synchronization. The model is $Y_{ij} = Z_i^* Z_j^{*T} + \sigma W_{ij}\in{\mathbb{R}}^{d\times d}$ where $W_{ij}$ a Gaussian random matrix $Z_i^*$ either an or matrix, each $Y_{ij}$ observed independently with probability $p$. analyze iterative polar decomposition algorithm for $Z^*$ show it ha...

In this paper we study the fuzzy c-mean clustering algorithm combined with principal components method. Demonstratively analysis indicate that the new clustering method is well rather than some clustering algorithms. We also consider the validity of clustering method. Keywords—FCM algorithm, Principal Components Analysis, ClusI. FUZZY SET THEORETIC SIMILARITY MEASURES ONE of the most important ...

We continue the study in [11, 14] on the upper Lyapunov exponents for products of matrices. Here the matrix function M(x) is only assumed to be non-negative. In general, the variational formula about Lyapunov exponents we obtained in part I does not hold in this setting. Anyway we focus our interest on a special case where M(x) takes finite values M1, . . ., Mm. In this case we prove the variat...

Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,

Let Q(A) be number of comparisons done on input array A: (A) For 1 ≤ i < j < n let R ij be the event that rank i element is compared with rank j element. (B) X ij is the indicator random variable for R ij. That is, X ij = 1 if rank i is compared with rank j element, otherwise 0. Q(A) = ∑ 1≤i<j≤n X ij and hence by linearity of expectation,