Upscaling based on the bandwidth of the kernel function is a flexible approach to upscale the data because the cells will be coarse-based on variability. The intensity of the coarsening of cells in this method can be controlled with bandwidth. In a smooth variability region, a large number of cells will be merged, and vice versa, they will remain fine with severe variability. Bandwidth variatio...

We give some theorems of bi-Lipschitz or C sufficiency of jets which are expressed by means of transversality with respect to some strata of a stratification satisfying the (L) condition of T. Mostowski. This enables us to prove that the number of metric types of intersection of smooth transversals to a stratum of an (a) regular stratification of a subanalytic set is finite.

String theory has already motivated, suggested, and sometimes well-nigh proved a number of interesting and sometimes unexpected mathematical results, such as mirror symmetry. A careful examination of the behavior of string propagation on (mildly) singular varieties similarly suggests a new type of (co)homology theory. It has the ‘good behavior’ of the well established intersection (co)homology ...

In 1893 J. J. Sylvester [8] posed the following celebrated problem: Given a finite collection of points in the affine plane, not all lying on a line, show that there exists a line which passes through precisely two of the points. Sylvester’s problem was reposed by Erdős in 1944 [4] and later that year a proof was given by Gallai [6]. Since then, many proofs of the Sylvester-Gallai Theorem have ...

To implement a method measuring anaerobic capacity within the field of training control, the reproducibility of the results is of deciding significance. In this study, we examined the test-retest-reliability of the most commonly used method for measuring anaerobic capacity to date, modified according to Monod and Scherrer, on a motorized treadmill. Ten healthy, athletically active, male partici...

A complete graph is the graph in which every two vertices are adjacent. For a graph G = (V,E), the complete width of G is the minimum k such that there exist k independent sets Ni ⊆ V , 1 ≤ i ≤ k, such that the graph G obtained from G by adding some new edges between certain vertices inside the sets Ni, 1 ≤ i ≤ k, is a complete graph. The complete width problem is to decide whether the complete...

An intersection representation of a graph G is a function f : V…G† ! 2 (where S is any set) with the property that uv A E…G† if and only if f …u†V f …v†0h. The size of the representation is jSj. The intersection number of G is the smallest size of an intersection representation of G. The intersection number can be expressed as an integer program, and the value of the linear relaxation of that p...

Conductor is a numerical invariant of a variety over a local field measuring the wild ramification of the inertia action on the l-adic etale cohomology. In [3], S.Bloch proposes a conjectural formula, Conjecture 1.9, which we call the conductor formula of Bloch. To formulate it, he defines another numerical invariant as the degree of the self-intersection class, which is defined using the local...

[1] A. Arabia, Faisceaux pervers sur les varie?te?s alge?briques complexes. Correspondance de Springer, [2] A. Arabia, Introduction a‘ l?homologie d?intersection [3] A. Beilinson, J. Bernstein, P. Deligne, Faisceaux pervers, in: Analyse et topologie sur les espaces singuliers, Aste?risque 100, 1982. [4] A. Borel et. al., Intersection Cohomology, Birka?user Progress in Math. 50, 1984, SB 2083. [...

in this paper we will determine the multiple point manifolds of certain self-transverse immersions in euclidean spaces. following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to dold manifold $v^5$ or a boundary. we will show there is an immersion of $s^7times p^2$ in $mathbb{r}^{13...