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Four (1,-1, 0)-matrices of order m, X = (x ij), Y = (y ij), Z = (z ij), U = (u ij) satisfying will be called semi Williamson type matrices of order m. In this paper we prove that if there exist Williamson type matrices of order n 1 ;: :: ;n k then there exist semi Williamson type matrices of order N = Q k j=1 n rj j , where r j are non-negative integers. As an application, we obtain a W(4N;2N)....

We consider a class of graph problems introduced in a paper of Goemans and Williamson that involve finding forests of minimum edge cost. This class includes a number of location/routing problems; it also includes a problem in which we are given as input a parameter k, and want to find a forest such that each component has at least k vertices. Goemans and Williamson gave a 2-approximation algori...

We give examples of reducible characteristic cycles for irreducible HarishChandra modules for U(p, q) by analyzing a four-dimensional singular subvariety of C. We relate this singularity to the Kashiwara-Saito singularity arising for Schubert varieties for GL(8,C) with reducible characteristic cycles, as well as recent related examples of Williamson. In particular, this gives another explanatio...

We consider a class of graph problems introduced in a paper of Goemans and Williamson that involve finding forests of minimum edge cost. This class includes a number of location/routing problems; it also includes a problem in which we are given as input a parameter k, and want to find a forest such that each component has at least k vertices. Goemans and Williamson gave a 2-approximation algori...

Although there has been much speculation about psychopaths' distinctive use of speech, to date there have been no published data documenting that psychopaths communicate any di€erently than others. This study examined the clinical observation that psychopathic speech is poorly integrated compared to that of controls. 39 inmates from a Wisconsin state penitentiary were asked to produce two stori...