Existing environment mapping techniques include spherical mapping and cube mapping. These techniques have inherent flaws that cause sampling issues and aliasing. Continuous cube mapping is offered as an alternative environment mapping approach that effectively folds the cube onto the sphere, providing a better parameterization of cube mapping. We provide a hardware implementation.

The main result in this paper is the following linearization theorem. For each open set U in a complex Banach space E , there is a complex Banach space G°°(Í7) and a bounded holomorphic mapping gv: U —► G°°(U) with the following universal property: For each complex Banach space F and each bounded holomorphic mapping /: U —> F , there is a unique continuous linear operator T,\ G°°(U) —» F such t...

Let G be a Lie group and § a Banach space. A representation n of G on § is a mapping which assigns to every element x in G a bounded linear operator n(x) on § such that the following two conditions are fulfilled: (1) 7t(xy) = n(x) 7i(y) (x, y e G),n(l) = / and (2) the mapping (x, tp) ->uz(x)y) of G x § into § is continuous. (Here 1 is the unit element of G and I is the unit operator,) In partic...

We study metric spheres ( Z , d ) $(Z, d_{Z} )$ obtained by gluing two hemispheres of S 2 $\mathbb {S}^{2}$ along an orientation-preserving homeomorphism g : 1 → $g \colon \mathbb {S}^{1} \rightarrow {S}^{1}$ where $d_{Z}$ is the canonical distance that locally isometric to off seam. show if quasiconformally equivalent in geometric sense, then $g$ a welding with conformally removable curves. al...

In this paper, the dynamics of multicellular chopper are considered. The model is described by a continuous time three--dimensional autonomous system. Some basic dynamical properties such as Poincar'e mapping, power spectrum and chaotic behaviors are studied. Analysis results show that this system has complex dynamics with some interesting characteristics.

In this paper, we introduce a new class of set-valued mappings which is called MD-type mappings. This class of mappings is a set-valued case of a class of the D-type mappings. The class of D-type mappings is a generalization of nonexpansive mappings that recently introduced by Kaewkhao and Sokhuma. The class of MD-type mappings includes upper semi-continuous Suzuki type mappings, upper semi-con...

The theory of c-frames and c-Bessel mappings are the generalizationsof the theory of frames and Bessel sequences. In this paper, weobtain several equivalent conditions for dual of c-Bessel mappings.We show that for a c-Bessel mapping $f$, a retrievalformula with respect to a c-Bessel mapping $g$ is satisfied if andonly if $g$ is sum of the canonical dual of $f$ with a c-Besselmapping which  wea...

Staircase effect in metamagnetic transitions of charge and orbitally ordered manganites. Abstract This paper reports on peculiar metamagnetic transitions which take place in antiferromagnetic, charge and orbitally ordered (AFCOO) manganites. At very low temperatures, the virgin magnetization curves of some of these compounds exhibit several, sharp steps giving rise to a staircase-like shape. Th...