We modify the definition of spherical knotoids to include a framing, in analogy framed knots, and define further modification that includes secondary 'coframing' obtain 'biframed' knotoids. exhibit topological spaces whose ambient isotopy classes are one-to-one correspondence with biframed respectively. then show how allow us generalize quantum knot invariants knotoid setting, leading construct...

We present the result of an eight-year didactic experiment in two primary school classes involving comparative geometry activities: a comparison between Euclidean plane and spherical that took place over five years. Following experiment, three years on from end final questionnaires were administered codified order to evaluate project’s effect pupils’ performance attitude, especially with regard...

We consider a nonhomogeneous polyharmonic equation on the unit sphere in three-dimensional Euclidean space. Sobolev spherical spaces act as functional classes which solutions to are sought. It is proved that for given right-hand side of equation, orthogonal identically-one function, solution exists space and unique there. establish small variations under consideration, its change little corresp...

Recently the general orthogonal planes split with respect to any two pure unit quaternions f, g ∈ H, f = g = −1, including the case f = g, has proved extremely useful for the construction and geometric interpretation of general classes of double-kernel quaternion Fourier transformations (QFT) [7]. Applications include color image processing, where the orthogonal planes split with f = g = the gr...

Order parameters based on spherical harmonics and Fourier coefficients already play a significant role in condensed matter research in the context of systems of spherical or point particles. Here, we extend these types of order parameter to more complex shapes, such as those encountered in nanoscale self-assembly applications. To do so, we build on a powerful set of techniques that originate in...

Oriented matroids have long been of use in various areas of combinatorics [BLS93]. Gelfand and MacPherson [GM92] initiated the use of oriented matroids in manifold and bundle theory, using them to formulate a combinatorial formula for the rational Pontrjagin classes of a differentiable manifold. MacPherson [Mac93] abstracted this into a manifold theory (combinatorial differential (CD) manifolds...

Recommended Citation Malata, A. M. (2004). The development and evaluation of a childbirth education program for Malawian women. Retrieved from

In this paper, a combination of the braneworld scenario and covariant de Rham-Gabadadze-Tolley (dRGT) massive Gravity theory is proposed. In this setup, the five-dimensional bulk graviton is considered to be massive. The five dimensional nonlinear ghost-free massive gravity theory affects the 3-brane dynamics and the gravitational potential on the brane. Following the solutions with spherical s...

In previous work, semi-supervised Fuzzy c-means (ssFCM) was used as an automatic classification technique to classify the Nottingham Tenovus Breast Cancer (NTBC) dataset as no method to do this currently exists. However, the results were poor when compared with semi-manual classification. It is known that the NTBC data is highly non-normal and it was suspected that this affected the poor result...