The interactions between topological covering spaces, homotopy and group structures in a fibered space exhibit an array of interesting properties. This paper proposes the formulation of finite covering space components of compact Lindelof variety in...
This paper describes a digital application designed for learning Space Groups of Symmetry (SGS). It teaches how to recognize the operations performed by the symmetry elements, both point (or 2D) operators (proper and improper rotations, including mir...
The algebraic as well as geometric topological constructions of manifold embeddings and homotopy offer interesting insights about spaces and symmetry. This paper proposes the construction of 2-quasinormed variants of locally dense p-normed 2-spheres...
Green spaces have been recognised for their positive impact on residents’ health and well-being. However, equitable access to these spaces remains a concern as certain social groups face barriers to reaching public green areas (PGS). Existing s...
Chirality depends on particular symmetries. For crystal structures it describes the absence of mirror planes and inversion centers, and in addition to translations, only rotations are allowed as symmetry elements. However, chiral space groups have ad...
This paper investigates the relationship between homology groups and warped product semi-slant submanifolds in Kenmotsu space forms. Some rigidity theorems for vanishing homology groups on warped product semi-slant submanifolds are obtained using the...
Social equity/inequity and equal/unequal rights to the city extend beyond the distribution of urban parks and green spaces, necessitating research on equitable accessibility to encompass a broader range of public spaces. However, previous research ha...
It is well known that every normed (even quasibarrelled) space is a Mackey space. However, in the more general realm of locally quasi-convex abelian groups an analogous result does not hold. We give the first examples of normed spaces which are not M...
In this paper, we establish a topological version of the notion of an Eilenberg–Mac Lane space. If X is a pointed topological space, π 1 ( X ) has a natural topology coming from the compact-open topology on the space of maps...
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions se...
Pile spacing is an important factor affecting the bearing capacity of concrete expansion pile (CEP) groups. In this study, a pile group was simulated and analyzed using ANSYS software R19.0. The influence of pile spacing on the bearing capacity of th...
In this paper, we characterize spaces of L∞-functions on a compact Hausdorff space that are invariant under a transitive and continuous group action. This work is analogous to established results concerning invariant spaces of continuous and me...
Topological photonics have developed in recent years since the seminal discoveries of topological insulators in condensed matter physics for electrons. Among the numerous studies, photonic Weyl nodes have been studied very recently due to their intri...
Let (X,ρ) be a metric space. A subset A of X resolves X if every point x∈X is uniquely identified by the distances ρ(x,a) for all a∈A. The metric dimension of (X,ρ) is the minimum integer k for which a set A of cardinality k res...
The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composabilit...
Protein packing within crystal lattices plays a critical role in determining molecular flexibility; therefore, the observed conformation and flexibility of protein side chains can vary depending on the crystal space group. Protein crystal dehydration...
The NT-CEP pile is an innovative type of pile that builds upon the conventional concrete straight-hole cast-in-place pile. It primarily consists of two components: the main pile and the bearing plate. The key factors influencing its load-bearing capa...
We present schemes for simulating Brownian bridges on complete and connected Lie groups and homogeneous spaces. We use this to construct an estimation scheme for recovering an unknown left- or right-invariant Riemannian metric on the Lie group from s...
Human personality (HP) is seen as an individual’s consistent patterns of feeling, thinking, and behaving by today’s psychological studies, in which HPs are characterized in terms of traits—in particular, as relatively enduring chara...
In this paper, we prove that, for compact warped product submanifolds Mn in an Euclidean space En+k, there are no stable p-currents, homology groups are vanishing, and M3 is homotopic to the Euclidean sphere S3 under various extrinsic restrictions, i...
Binary high temperature “Al3Mn” (T-phase) and its extensions in ternary systems were the subjects of numerous crystallographic investigations. The results were ambiguous regarding the existence or lack of the center of symmetry: both Pna2...
The spacing between piles plays a crucial role in determining the load-bearing capacity of CEP group pile foundations equipped with a bearing platform. In this research, five sets of six-pile models with different pile spacings were created using ANS...
With this report, the space group of [Zn(Nal)(DACH)2]Cl is corrected (Nal: nalidixic acid mono-anion; DACH: diaminocyclohexane) from its wrong description in the literature. In the correct, non-centrosymmetric space group P1, the crystal structure is...
Previously, we reported that inorganic–organic hybrid (C6H5CH2CH2NH3)2MnCl4 (Mn-PEA) is antiferromagnetic below 44 K by using magnetic susceptibility and neutron diffraction measurements. Generally, when an antiferromagnetic system is investiga...
Due to the interference of artifacts and the nonlinearity of electroencephalogram (EEG) signals, the extraction of representational features has become a challenge in EEG emotion recognition. In this work, we reduce the dimensionality of phase space...
Previous studies on measuring the accessibility and equity of park green spaces (PGSs) often overlook differences in walking speeds across age groups, which may lead to research results that deviate from actual conditions. This study expands the curr...
The Visegrád Group (V4), as China’s key economic and trade partner in Central and Eastern Europe, plays a pivotal role in enhancing the effectiveness of sustainable development within the China-Central and Eastern Europe cooperation (Chi...
Time allocation is closely related to life quality and is a potential indicator of urban space utilization and sociospatial differentiation. However, existing time allocation studies focus on how time is allocated to various activities but pay less a...
8 June 2017
It has been suggested that certain residents, such as those with a low socioeconomic status, the elderly, and women, may benefit more from the presence of neighbourhood green space than others. We tested this hypothesis for age, gender, educational l...
Urban green spaces, as vital land use components, play a crucial role in promoting public mental health and well-being. This study investigates the differential restorative benefits and stress relief pathways in urban green spaces for populations wit...
In the course of investigating structural modifications of the 3-,4-connected net known as the Pt3O4 structure-type (waserite), a novel 4-,8-connected structure-type was discovered. This lattice is generated by replacing the 3-connected trigonal plan...
In the following, isomorphism of an arbitrary finite group of symmetry, non-crystallographic symmetry (quaternion groups, Pauli matrices groups, and other abstract subgroups), in addition to the permutation group, are considered. Application of fini...
Pile groups are designed to sustain complex loads in various engineering. During the design of a pile group, the obvious pile group effect should be considered for closely spaced pile groups. However, the group effect considered by different scholars...
A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a compl...
This paper is supposed to form a keystone towards a new and alternative approach to Fourier analysis over LCA (locally compact Abelian) groups G. In an earlier paper the author has already shown that one can introduce convolution and the Fourier&ndas...
Urbanization has been shown to cause biodiversity loss. However, its effects on butterfly taxonomic and functional diversity still need to be studied, especially in urban waterfront green spaces where mechanisms of impact still need to be explored. W...
We construct the free group over a non-Archimedean fuzzy metric space (X,M,∧) in the sense of George and Veeramani where ∧ is the minimum t-norm. The two main tools used are the concept of a scheme (for every non-empty subset S of N of even c...
The improper layout of urban public parks leads to the difference between citizens sharing or not sharing this kind of public resource, particularly in the historical districts of mountainous cities in China. The purpose of this study is to explore t...
The structure of topological spaces is analysed here through the lenses of fibrous preorders. Each topological space has an associated fibrous preorder and those fibrous preorders which return a topological space are called spatial. A special class o...
Let G be a monoid that acts on a topological space X by homeomorphisms such that there is a point x0∈X with GU=X for each neighbourhood U of x0. A subset A of X is said to be G-bounded if for each neighbourhood U of x0 there is a finite subset F of G...
The fundamental groups and homotopy decompositions of algebraic topology have applications in systems involving symmetry breaking with topological excitations. The main aim of this paper is to analyze the properties of homotopy decompositions in quot...
In this paper, we propose using quiver representations as a tool for understanding artificial neural network algorithms. Specifically, we construct these algorithms by utilizing the group algebra of a finite cyclic group as vertices and convolution t...
The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathem...
The continuous and injective embeddings of closed curves in Hausdorff topological spaces maintain isometry in subspaces generating components. An embedding of a circle group within a topological space creates isometric subspace with rotational symmet...
We show that the category of quantale-valued tolerance spaces is isomorphic to a category of quantale-valued convergence spaces. We define suitable quantale-valued closure functions and use them to characterize transitivity axioms. Furthermore, trans...
We introduce a multi-parameter family of bases in the Hilbert space L2(R) that are associated to a set of Hermite functions, which also serve as a basis for L2(R). The Hermite functions are eigenfunctions of the Fourier transform, a property that is,...
As a representation of Korea’s modern architecture, Kim Swoo Geun described the Space Group of Korea Building as an “enclosed but endless space”. The Space Group Building is currently Korea’s Registered Cultural Heritage No. 5...
We extend the theory of splits in finite metric spaces to infinite ones. Within this more general framework, we investigate the class of spaces having metrics that are integer-valued and totally split-decomposable, as well as the polyhedral complex s...
The crystal structures of red and blue-black tin(II) oxide, SnO, have been determined for the first time by single-crystal X-ray diffraction. Blue-black SnO crystallizes in the tetragonal space group P4/nmm, representing a layer structure consisting...
A holomorphically fibred space generates locally trivial bundles with positive dimensional fibers. This paper proposes two varieties of fibrations (compact and non-compact) in the non-uniformly scalable quasinormed topological (C, R) space admitting...
of 129