Conformal transformations are of much interest to modelers of physical phenomena as they provide many attractive mathematical properties such as locally preserving the isotropy of scales, invariance of the structure of the operators such as Laplacian under the transformation. It is known to atmosphere and ocean modelers as to generate coordinate transformations on the sphere using the analytic ...

The Leech lattice is the exceptional lattice in dimension 24. Soon after its discovery by Leech [9], it was conjectured that it is extremal for several geometric problems in R: the kissing number problem, the sphere packing problem, and the sphere covering problem. In 1979, Odlyzko and Sloane and independently Levenshtein solved the kissing number problem in dimension 24 by showing that the Lee...

We consider the problem of interpolating a smooth curve to a point sequence in the unit quaternion space U. This problem has application to object orientation interpolation in computer animation , sweep surface generation in solid modeling[7, 6]. Since the unit quaternions form the unit sphere 8 3 in p;4, a simple curve scheme using spherical biarcs is presented to solve this problem. The spher...

Solids of different shapes resonate according to their peculiar geometry. Although physics, for some fundamental shapes such as the cube and the sphere, provides explicit formulas for determining the modal frequencies, a general resonance analysis of 3-D shapes must be conducted using numerical methods. In this paper, Waveguide Meshes are used to model intermediate geometries between the cube a...

This study presents a qualitative analysis of social workers’ and their customers’ attitudes concerning control of alcohol use. Social workers and their customers were asked to comment on the following statements: Alcohol use is a private affair and I believe that social worker can influence customers’ alcohol use. The analytical focus is on how the two parties commented on the statements and d...

Dual photoelastic modulator polarimeters can measure light polarization, which is often described as a Stokes vector. By evaluating changes in polarization when light interacts with a sample, the sample Mueller matrix also can be derived, completely describing its interaction with polarized light. The choice of which and how many input Stokes vectors to use for sample investigation is under the...

This article addresses contemporary art as a means to investigate how, and to what extent, financial logic impacts upon the socio-cultural sphere. Its contribution is twofold: on the one hand, the article shows that contemporary art’s valuation practices increasingly reflect the logic of capitalization; on the other hand, it assesses the emancipatory potential of blockchain technology for the c...

To study nite Borel measures on the Riemann sphere invariant under a rational function R of degree greater than one, we decompose them in an R-invariant component measure supported on the Julia set and a nite number of mutually singular R-invariant component measures vanishing on the Julia set. The latter ones can be described easily. For a characterization of the former one, we use a general a...

Introduction: CSCs have been identified in prostate cancer (PCa), one of the most diagnosed malignancies in men over the world, for which radiation resistance is a major problem in the treatment of advanced stages. Cancer stem cells (CSCs) have the ability to self-renew and differentiate to give rise to heterogeneous phenotype of the tumor cells. It is believed that CSCs are ...

We give a simple procedure to estimate the smallest Lipshitz constant of a degree 1 map from a Riemannian 2-sphere to the unit 2-sphere, up to a factor of 10. Using this procedure, we are able to prove several inequalities involving this Lipshitz constant. For instance, if the smallest Lipshitz constant is at least 1, then the Riemannian 2-sphere has Uryson 1-Width less than 12 and contains a c...