‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...

Three Bi2Sr2CaCu2O8 single crystals with di€erent annealing processes have been measured in terms of complex AC susceptibilities vn ˆ vn ÿ iv00 n (n ˆ 1; 3) to reveal the e€ect of ̄ux-pinning strength. The third harmonic susceptibility changes dramatically when the pinning strengths are di€erent due to di€erent annealing processes, although the fundamental susceptibilities are quite similar. Th...

The classical shell theory, first-order shear deformation theory, and third-order shear deformation theory are employed to study the natural frequencies of functionally graded cylindrical shells. The governing equations of motion describing the vibration behavior of functionally graded cylindrical shells are derived by Hamilton’s principle. Resulting equations are solved using the Navier-type s...

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for linearizability of a class of third order semi-linear ordinary differential equations, which is distinct from the classes available in the literature. Some examples are given and...

We review three approaches to mesh generation that are based on analyzing and accounting for the geometric structure of the domain. In the rst approach, due to Armstrong, the domain is partitioned into subdomains based on the medial-axis transform, a tool for analyzing spatial structures. In the second approach, due to Cox, the design history de nes a geometric structure of the domain. The desi...

A logical physical ontology is code theory, wherein reality is neither deterministic nor random. In light of Conway and Kochen’s free will theorem [1] and strong free will theorem [2], we discuss the plausibility of a third axiomatic option geometric language; the code theoretic axiom. We suggest freewill choices at the syntactically free steps of a geometric language of spacetime form the code...

The Space Group Visualizer (SGV) for all 230 3D space groups is a standalone PC application based on the visualization software CLUCalc. We first explain the unique geometric algebra structure behind the SGV. In the second part we review the main features of the SGV: The GUI, group and symmetry selection, mouse pointer interactivity, and visualization options. We further introduce the joint use...

We discuss recent work based on multiscale geometric analysis for the study of large data sets that lie in high-dimensional spaces but have low-dimensional structure. We present three applications: the first one to the estimation of intrinsic dimension of sampled manifolds, the second one to the construction of multiscale dictionaries, called geometric wavelets, for the analysis of point clouds...

In this work, a geometric invariant curve and surface normalization method is presented. Translation, scale and shear are normalized by Principal Component Analysis (PCA) whitening. Independent Component Analysis (ICA) and the third order moments are then employed for rotation and reflection normalization. By applying this normalization, curves and surfaces that are related by geometric transfo...