A theorem of J. Kruskal from 1977, motivated by a latent-class statistical model, established that under certain explicit conditions the expression of a third-order tensor as the sum of rank-1 tensors is essentially unique. We give a new proof of this fundamental result, which is substantially shorter than both the original one and recent versions along the original lines.

We discuss properties of conformal geodesics on general, vacuum, and warped product space-times and derive a system of conformal deviation equations. The results are used to show how to construct on the Schwarzschild-Kruskal space-time global conformal Gauss coordinates which extends smoothly and without degeneracy to future and past null infinity.

By using the modified Clarkson-Kruskal (CK) direct method, we construct a Bäcklund transformation of (2+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation. Through Bäcklund transformation , we get some new solutions of the BLMP equation, extend the results of previous literature.

RESUMO Esta pesquisa teve por objetivo principal avaliar a influência do tipo de geotêxtil reforço, solo, posição inserção reforço geossintético e energia compactação no comportamento mecânico solos reforçados com geotêxtil. avaliação foi baseada nos resultados dos ensaios Resistência à Compressão Não Confinada (RCNC) ao Cisalhamento Direto (τpico). Para da desses fatores mecânico, utilizaram-s...

We generalize the matroid-theoretic approach to greedy algorithms to the setting of poset matroids, in the sense of Barnabei, Nicoletti and Pezzoli (1998) [BNP]. We illustrate our result by providing a generalization of Kruskal algorithm (which finds a minimum spanning subtree of a weighted graph) to abstract simplicial complexes.

We deene well-partial-orderings on abstract algebras and give their order types. For every ordinal in an initial segment of Bachmann hierarchy there is one and only one (up to isomorphism) algebra giving the ordinal as order type. As a corollary, we show Kruskal-type theorems for various structures are equivalent to well-orderedness of certain ordinals.

We prove a vector space analog of a version of the Kruskal-Katona theorem due to Lovász. We apply this result to extend Frankl’s theorem on r-wise intersecting families to vector spaces. In particular, we obtain a short new proof of the ErdősKo-Rado theorem for vector spaces.

This paper uses simulation to explore the performance of a two-stage procedure where a preliminary Shapiro-Wilk test is used to choose between the ANOVA and Kruskal-Wallis tests as a three-sample location test. The results suggest that the two-stage procedure actually seems to be preferable when conducting such location tests.

Minimum spanning tree can be obtained for connected weighted edges with no negative weight using classical algorithms such as Boruvka’s, Prim’s and Kruskal. This paper presents a survey on the classical and the more recent algorithms with different techniques. This survey paper also contains comparisons of MST algorithm and their advantages and disadvantages.

Brain metastasis from breast cancer is an increasingly important clinical problem. Here we assessed the role of CD44/CD24 cells and pathways that regulate them, in an experimental model of brain metastasis. Notch signaling (mediated by g-secretase) has been shown to contribute to maintenance of the cancer stem cell (CSC) phenotype. Cells sorted for a reduced stem-like phenotype had a reduced ab...