Notes on Fréchet spaces by Woo Chorl Hong

“…Second, we give sufficient conditions for the expansion of a topological space by the sequential closure operator to be a Fréchet space and also a sufficient condition for a simple expansion of a topological space to be Fréchet. …”
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Persistent Homology Combined with Machine Learning for Social Network Activity Analysis by Zhijian Zhang, Yuqing Sun, Yayun Liu, Lin Jiang, Zhengmi Li

“…Then, based on the persistence entropy, this paper defines the Norm Entropy-NE(X) to represent the complexity of the topological features of the ego network, a larger NE(X) indicates a higher topological complexity, i.e., the higher the activity of the nodes, thus indicating the degree of activity of the nodes. …”
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Ecological network construction and optimization of typical resource-based regions, and strategies for the enhancement of multiple ecosystem services: Balancing function and struct... by Shaoqing Wang, Yanling Zhao, Qiyuan Wang, He Ren, Shichao Zhu, Jiarui Cao

“…The ecological functions of BESs performed better, but the topological structure and degree of coordination of DESs were better than those of BESs. …”
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A Surgery Issue: Cutting through the Architectural Fabric by Athina Angelopoulou

“…I start by rereading a topological body plan, used by surgeons as a guide for performing incisions. …”
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Some New Variants of Relative Regularity via Regularly Closed Sets by Sehar Shakeel Raina, A. K. Das

“…This notion of relative topological properties was introduced by Arhangel’skii and Ganedi in 1989. …”
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Induced Representation Method in the Theory of Electron Structure and Superconductivity by V. G. Yarzhemsky

“…It is proved that the nodal structure of topological superconductors in the case of multidimensional irreducible representations is defined by additional quantum numbers. …”
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Algorithms for Computing Wiener Indices of Acyclic and Unicyclic Graphs by Bo Bi, Muhammad Kamran Jamil, Khawaja Muhammad Fahd, Tian-Le Sun, Imran Ahmad, Lei Ding

“…Let G=VG,EG be a molecular graph, where VG and EG are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical/physical properties of the molecules. …”
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Lebesgue Measurability of Separately Continuous Functions and Separability by V. V. Mykhaylyuk

“…A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y, separately continuous function f:X×Y→ℝ and open set I⊆ℝ, the set f−1(I) is an Fσ-set) is studied. …”
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Mechanistic Pathways in Cyanide-Mediated Benzoin Condensation: A Comprehensive Electron Localisation Function (ELF) and Catastrophe Theory Analysis of the Umpolung Reaction by Michal Michalski, Slawomir Berski

“…This research investigates the mechanism of the cyanide-type umpolung reaction in benzoin condensation using topological analysis of ELF and catastrophe theory. …”
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Investigation of Dendrimer Structures by Means of K-Banhatti Invariants by Cheng-Gang Huo, Fozia Azhar, Abaid Ur Rehman Virk, Tariq Ismaeel

“…This study is about some new topological indices of dendrimer generations. Here, we calculate K Banhatti indices for five generations of dendrimers. …”
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Heat Transfer Potentiality and Flow Behavior in a Square Duct Fitted with Double-Inclined Baffles: A Numerical Analysis by Amnart Boonloi, Withada Jedsadaratanachai

“…Numerical analysis of heat transfer mechanisms and flow topologies for the heat exchanger square channel (HESC) installed with the double-inclined baffles (DIB) is reported. …”
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The Y-Index of Some Complement Graph Structures and Their Applications of Nanotubes and Nanotorus by Mohammed Alsharafi, Abdu Alameri, Yusuf Zeren, Mahioub Shubatah, Anwar Alwardi

“…Topological descriptors play a significant role in chemical nanostructures. …”
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Mechanism model of dynamic polyurethanes with two scales of nodes to regulate mechanical property by Yue Liu, Jinpeng Li, Litong Jia, Manyu Li, Yifan Diao, Zhenqi Han, Chenglei Yu, Tian Liu

“…This provides reference for prepare polyurethane with better mechanical properties in dynamic polyurethane industrial products through molecular topological structure design using same type of raw materials.…”
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The K-Theoretic Formulation of D-Brane Aharonov-Bohm Phases by Aaron R. Warren

“…The topological calculation of Aharonov-Bohm phases associated with D-branes in the absence of a Neveu-Schwarz B-field is explored. …”
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On IVF Approximating Spaces by Dingwei Zheng, Rongchen Cui, Zhaowen Li

“…We introduce the concept of IVF approximating spaces and obtain decision conditions that every IVF topological space is an IVF approximating space.…”
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Jewelry Art Modeling Design Method Based on Computer-Aided Technology by Yuan Li, Hai Wen

“…Moreover, in order to solve the situation that the given data points do not form a topological rectangular grid, an interpolation algorithm based on triangular BB surfaces is specially studied in this paper. …”
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Le modèle topologique des sociétés amazoniennes by Klaus Hamberger

“…The topological model of Amazonian societies. The article aims to outline, via a comparative analysis of social and spatial organization in Central Brazil, North-West Amazonia and Guyana, a topological model common to Amazonian societies. …”
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Connection-Based Multiplicative Zagreb Indices of Dendrimer Nanostars by Aqsa Sattar, Muhammad Javaid, Ebenezer Bonyah

“…Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. …”
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Parent Berry Curvature and the Ideal Anomalous Hall Crystal by Tixuan Tan, Trithep Devakul

“…At sufficiently high parent Berry curvature, we show that strong repulsive interactions generically lead to the formation of an anomalous Hall crystal: a topological state with spontaneously broken continuous translation symmetry. …”
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On maps: continuous, closed, perfect, and with closed graph by G. L. Garg, Asha Goel

“…This paper gives relationships between continuous maps, closed maps, perfect maps, and maps with closed graph in certain classes of topological spaces.…”
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