This paper is concerned with the relations between the differential invariants of a smooth manifold embedded in the Euclidean space and the square of the distance function from the manifold. In particular, we are interested in curvature invariants like the mean curvature vector and the second fundamental form. We find that these invariants can be computed in a very simple way using the third or...

In this paper, a hybrid inverse distance weighted (IDW) and the imperialist competitive algorithm (ICA) was proposed for grade estimations in mining projects. Indeed, coefficients of IDW equation, power, influence were modified by applying ICA algorithm. For this, an example solved using IDW, ordinary kriging, IDW-ICA. After successfully validating IDW-ICA, iron grades estimated Baba Ali mine, ...

Nonholonomic deformations of integrable equations of the KdV hierarchy are studied by using the expansions over the so-called “squared solutions” (squared eigenfunctions). Such deformations are equivalent to a perturbed model with external (self-consistent) sources. In this regard, the KdV6 equation is viewed as a special perturbation of KdV. Applying expansions over the symplectic basis of squ...

The bizarre coincidence (or is it a coincidence?) through which my wife and I are now living illustrates many of the physician pitfalls diagnosing one's own family subsequent perils or rewards knowing too much.

Distances in the well known fuzzy c-means algorithm of Bezdek (1973) are measured by the squared Euclidean distance. Other distances have been used as well in fuzzy clustering. For example, Jajuga (1991) proposed to use the L1-distance and Bobrowski and Bezdek (1991) also used the L∞-distance. For the more general case of Minkowski distance and the case of using a root of the squared Minkowski ...

PURPOSE To introduce a new approach to reconstruct a 3D model of the TMJ using magnetic resonance imaging (MRI) and cone-beam computed tomography (CBCT) registered images, and to evaluate the intra-examiner reproducibility values of reconstructing the 3D models of the TMJ. METHODS MRI and CBCT images of five patients (10 TMJs) were obtained. Multiple MRIs and CBCT images were registered using...

The row-wise multiple comparison procedure proposed in Hirotsu [Hirotsu, C., 1977. Multiple comparisons and clustering rows in a contingency table. Quality 7, 27–33 (in Japanese); Hirotsu, C., 1983. Defining the pattern of association in two-way contingency tables. Biometrika 70, 579–589] has been verified to be useful for clustering rows and/or columns of a contingency table in several applica...

We calculate the spin dependent structure function of the polarized virtual pho-ton g γ 1 (x, Q 2 , p 2), especially its hadronic part, using the OPE in the inverse powers of the target photon virtuality. Some model is accepted to achieve a correct analytical behaviour in the photon squared mass. This enables extrapolation to the case of a real photon.