Kruskal’s extension solves the problem of the arrow of time of the “Schwarzschild solution” through combining two Hilbert manifolds by a singular coordinate transformation. We discuss the implications for the singularity problem and the definition of the mass point. The analogy set by Rindler between the Kruskal metric and the Minkowski spacetime is investigated anew. The question is answered, ...

This paper describes the comparison of the anova and the KruskalWallis test by means of the power when violating the assumption about normally distributed populations. The permutation method is used as a simulation method to determine the power of the test. It appears that in the case of asymmetric populations the non-parametric Kruskal-Wallis test performs better than the parametric equivalent...

Let f(n, r, k) be the minimal number such that every hypergraph larger than f(n, r, k) contained in ([n] r ) contains a matching of size k, and let g(n, r, k) be the minimal number such that every hypergraph larger than g(n, r, k) contained in the r-partite r-graph [n]r contains a matching of size k. The Erdős-Ko-Rado theorem states that f(n, r, 2) = (n−1 r−1 ) (r ≤ n 2 ) and it is easy to show...

We introduce a numerical measure on sets of partitions of finite sets that is linked to the Goodman-Kruskal association index commonly used in statistics. This measure allows us to define a metric on such partions used for constructing decision trees. Experimental results suggest that by replacing the usual splitting criterion used in C4.5 by a metric criterion based on the Goodman-Kruskal coef...

Face recognition in today's technological world, and face recognition applications attain much more importance. Most of the existing work used frontal face images to classify face image. However these techniques fail when applied on real world face images. The proposed technique effectively extracts the prominent facial features. Most of the features are redundant and do not contribute to repre...

We give a constructive proof of Kruskal’s Tree Theorem— precisely, of a topological extension of it. The proof is in the style of a constructive proof of Higman’s Lemma due to Murthy and Russell (1990), and illuminates the role of regular expressions there. In the process, we discover an extension of Dershowitz’ recursive path ordering to a form of cyclic terms which we call μ-terms. This all c...

We consider the poset SO(n) of all words over an n{element alphabet ordered by the subword relation. It is known that SO(2) falls into the class of Macaulay posets, i.e. there is a theorem of Kruskal{Katona type for SO(2). As the corresponding linear ordering of the elements of SO(2) the vip{order can be chosen. Daykin introduced the V {order which generalizes the vip{order to the n 2 case. He ...

The article is mainly concernedwith the Kruskal tree theorem and the following observation: there is a duality at the level of binary relations between well and noetherian orders. The first step here is to extend Kruskal theorem from orders to binary relations so that the duality applies. Then, we describe the theorem obtained by duality and show that it corresponds to a theorem by Ferreira and...

We present examples of flag homology spheres whose γvectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In these cases, we construct explicit simplicial complexes whose f -vectors are the γ-vectors in question. In another di...

It is shown that one can link in a continuous manner the Painlevé–Gullstrand partial extension to Kruskal–Szekeres maximal analytical extension, and thus exhibit of Schwarzschild metric unified picture. This done by finding coordinate system adopts two time coordinates, being proper congruence outgoing timelike geodesics, other ingoing both parametrized same energy per unit mass E. E range 1?E<...