Surface parameterization establishes bijective maps from a surface onto a topologically equivalent standard domain. It is well known that the spherical parameterization is limited to genus-zero surfaces. In this work, we design a new parameter domain, two-layered sphere, and present a framework for mapping high genus surfaces onto sphere. This setup allows us to transfer the existing applicatio...

2000 Mathematics Suject Classification. Primary 30F10, 30F50; Secondary 14H15, 20H10. Abstract. In this work we prove that the hyperelliptic branch locus of orientable Klein surfaces of genus g with one boundary component is connected and in the case of non-orientable Klein surfaces it has g+1 2 components, if g is odd, and g+2 2 components for even g. We notice that, for non-orientable Klein s...

We present a new approach toward the rational parametrization of canal surfaces. According to our previous work, every canal surface with rational (respectively polynomial) spine curve and rational (respectively polynomial) radius function is a rational (respectively polynomial) Pythagorean hodograph curve in R3,1. Drawing upon this formalism and utilizing the underlying Lorentzian geometry, th...

Kinematic surfaces form a general class of surfaces, including surfaces of revolution, helices, spirals, and more. Standard methods for fitting such surfaces are either specialized to a small subset of these surface types (either focusing exclusively on cylinders or exclusively on surfaces of revolution) or otherwise are basis-dependent (leading to scale-dependent results). Previous work has su...

background: the role of the hospital environment as a source of dissemination of pathogens is critical. environmental surfaces in the intensive care units (icus) are suitable for the growth of gram-negative bacteria that normally circulate between the environment and patients and can cause outbreaks of nosocomial infections. in this study, the prevalence of gram-negative bacilli in the environm...

titania nanotubes (tnt) prepared by anodization of ti foils were used for water splitting in a standalone cell. the concentration polarization between the anode side (1m naoh) and cathode side (0.5 m h2so4) ensured that the water splitting reaction could take place with no external bias and separate h2 and o2 evolution could be achieved. the destruction of tnt structures under 365 nm uv irradia...

in this paper, we consider weighted composition operators betweenmeasurable differential forms and then some classic properties of these operators are characterized.

The study of random surfaces as a generalization of Brownian motion, led to a renewed interest after the work of A. N. Polyakov[1]. In 1984, A. Billore, D.J. Gross and E. Marinari[2] applied Monte Carlo techniques to the numerical study of free random surfaces defined as a set of a fixed number of triangles embedded in a continuum space. This method, in practice, is a simulation of a microcanon...

Ellingsrud and Peskine showed in [ElP] that there are finitely many components of the Hilbert scheme of P containing smooth surfaces not of general type. The upper bound for the degree of such surfaces has recently been reduced to 105 (cf. [BF]). Quite a bit of work has been put into trying to construct such surfaces of high degree. So far the record is 15, which coincides with the conjectural ...

Previous work of the author has developed coordinates on bundles over the classical Teichmüller spaces of punctured surfaces and on the space of cosets of the Möbius group in the group of orientation-preserving homeomorphisms of the circle, and this work is surveyed here. Joint work with Dragomiř Sari´c is also sketched which extends these results to the setting of the Teichmüller space of the ...