Programing Two-Dimensional Materials in Non-Euclidean Spaces

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

FUZZY HV -SUBSTRUCTURES IN A TWO DIMENSIONAL EUCLIDEAN VECTOR SPACE

In this paper, we study fuzzy substructures in connection withHv-structures. The original idea comes from geometry, especially from thetwo dimensional Euclidean vector space. Using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. We connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as Hv-groups...

Lines in n-Dimensional Euclidean Spaces

In this paper, we define the line of n-dimensional Euclidean space and we introduce basic properties of affine space on this space. Next, we define the inner product of elements of this space. At the end, we introduce orthogonality of lines of this space. provide the terminology and notation for this paper. (4) (a · b) · x = a · (b · x). (6) a · (x 1 + x 2) = a · x 1 + a · x 2. (7) (a + b) · x ...

Euclidean Structure in Finite Dimensional Normed Spaces

Packing hyperspheres in high-dimensional Euclidean spaces.

We present a study of disordered jammed hard-sphere packings in four-, five-, and six-dimensional Euclidean spaces. Using a collision-driven packing generation algorithm, we obtain the first estimates for the packing fractions of the maximally random jammed (MRJ) states for space dimensions d=4, 5, and 6 to be phi(MRJ) approximately 0.46, 0.31, and 0.20, respectively. To a good approximation, t...