This paper aims to present the well-known spectral mapping theorem for multi-variable functions.

Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve ...

introduction lead-based shields are the most widely used attenuators in x-ray and gamma ray fields. the heavy weight, toxicity and corrosion of lead have led researchers towards the development of non-lead shields. materials and methods the purpose of this study was to design multi-layered shields for protection against x-rays and gamma rays in diagnostic radiology and nuclear medicine. in this...

The irreducible representations of the cubic space group are described and used to determine the mapping of continuum states to lattice states with non-zero linear momentum. The Clebsch-Gordan decomposition is calculated from the character table for the cubic space group. These results are used to identify multiparticle states which appear in the hadron spectrum on the lattice.

In this paper we present an algorithm for parameterizing arbitrary surfaces onto a quadrilateral domain defined by a collection of cubic cells. The parameterization inside each cell is implicit and thus requires storing no texture coordinates. Based upon this parameterization, we propose a unified representation of geometric and appearance information of complex models. The representation consi...

Sphere mapping is a useful tool for creating realistic computer-generated images. It is currently the only view-dependent texture mapping technique widely supported in hardware. Understanding how sphere mapping relates to other environment mapping techniques such as parabolic mapping and cubic mapping can help promote its use in the appropriate context. After an initial survey of texture mappin...

We describe the action of the automorphism group of the complex cubic x + y + x − xyz − 2 on the homology of its fibers. This action includes the action of the mapping class group of a punctured torus on the subvarieties of its SL(2, C) character variety given by fixing the trace of the peripheral element (socalled “relative character varieties”). This mapping class group is isomorphic to PGL(2...

* Correspondence: [email protected] Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia Abstract In this article, we propose to determine some stability results for the functional equation of cubic in random 2-normed spaces which seems to be a quite new and interesting idea. Also, we define the notion of continuity, approximate...