Triangular B-splines are a new tool for modeling a broad class of objects defined over arbitrary, nonrectangular domains. They provide an elegant and unified representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additi...

Triangular B-splines are a new tool for modeling a broad class of objects deened over arbitrary, non-rectangular domains. They provide an elegant and uniied representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additio...

Introduction and Background: Ceramics are inorganic, nonmetallic materials, such as alumina, beryllia, or glassceramic, whose final characteristics are produced by subjection to high temperatures. Nanomaterials is a rapidly growing area of ceramics [1-3] and can be classified into the following categories: Nano-particles submicron or ultra micron size particles; Nano-fibers – nanometer (nm) siz...

This paper proposes an automated quadrilateral meshing technique based on the conversion of triangular meshes. Given a triangular mesh and a vector eld representing the desired directionality of quadrilateral elements, our new approach generates a well-shaped and well-aligned quadrilateral mesh. In the approach, the values of three scalar functions are rst calculated for each pair of adjacent t...

the level of dental and oral hygiene on elementary school age children is very low, so it can be increasing the incidence of dental and oral diseases which caused by various microorganisms. moutwash can keep dental and oral hygiene, but many commercial mouthwash is still used alcohol as their ingredients, which can be giving side effects, therefore, we still needed used alternative mouthwash, w...

objective: curcumin is extracted from curcuma longa and regulates the intracellular signal pathways which control the growth of cancerous cell, inflammation, invasion and apoptosis. curcumin molecules have special intrinsic features that can target the intracellular enzymes, genome (dna) and messengers (rna). a wide range of studies have been conducted on the physicochemical traits and pharmaco...

The spatial interpolation of property fields in 3D, such as the temperature, salinity, and organic content of ocean water, is an active area of research in the applied geosciences. Conventional interpolation methods have not adequately addressed anisotropy in these data. Thus, in our research we considered two interpolation methods based on a triangular prism volume element, as a triangular pri...

This note employs recurrence techniques to obtain entry-wise optimal inequalities for inverses of triangular matrices whose entries satisfy some monotonicity constraints. The derived bounds are easily computable.

In this paper, the triangular structures of a Hopf algebra A are discussed as a tensor Morita invariant. It is shown by many examples that triangular structures are useful for detecting whether module categories are monoidally equivalent or not. By counting and comparing the numbers of triangular structures, we give simple proofs of some results obtained in [25] without polynomial invariants.