Type Synthesis and Classification of 1-translational and 2-rotation Parallel Mechanism by Feng Yongping, Luo Yufeng, Shi Zhixin, Xie Dongfu

“…Using topological structure synthesis method Based on the POC set,the type synthesis of 1-translational and 2-rotation parallel mechanism is carried out. …”
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Compatible elements in partly ordered groups by Jirí Mockor, Angeliki Kontolatou

“…It is proved that if G is defined by a family of t-valuations of finite character, then G admits an SQDP if and only if it admits a quasi-divisor property and any finitely generated t-ideal is generated by two elements. A topological density condition in topological group of finitely generated t-ideals and/or compatible elements are proved to be equivalent to SQDP.…”
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Some Inequalities between General Randić-Type Graph Invariants by Imran Nadeem, Saba Siddique, Yilun Shang

“…The Randić-type graph invariants are extensively investigated vertex-degree-based topological indices and have gained much prominence in recent years. …”
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Derived categories and the analytic approach to general reciprocity laws. Part I by Michael Berg

“…We reformulate Hecke's open problem of 1923, regarding the Fourier-analytic proof of higher reciprocity laws, as a theorem about morphisms involving stratified topological spaces. We achieve this by placing Kubota's formulations of n-Hilbert reciprocity in a new topological context, suited to the introduction of derived categories of sheaf complexes. …”
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Representation and Reasoning of Three-Dimensional Spatial Relationships Based on R5DOS-Intersection Model Representation and Reasoning Based on R5DOS Model by Jian Li, Weijian Zhang, Yating Hu, Zhun Wang

“…This paper aims to disclose the compound topological and directional relationships of three simple regions in the three-dimensional (3D) space. …”
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Computing the Hosoya Polynomial of M-th Level Wheel and Its Subdivision Graph by Peng Xu, Muhammad Numan, Aamra Nawaz, Saad Ihsan Butt, Adnan Aslam, Asfand Fahad

“…Furthermore, we will derive two well-known topological indices for the abovementioned graphs, first Weiner index, and second hyper-Wiener index.…”
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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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Observing non-Hermiticity induced chirality breaking in a synthetic Hall ladder by Rui Ye, Yanyan He, Guangzhen Li, Luojia Wang, Xiaoxiong Wu, Xin Qiao, Yuanlin Zheng, Liang Jin, Da-Wei Wang, Luqi Yuan, Xianfeng Chen

“…Abstract Non-Hermitian topological photonics plays a key role in bridging topological matter with gain and loss engineering in optics. …”
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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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Hopf link invariants and integrable hierarchies by Chuanzhong Li, A. Mironov, A.Yu. Orlov

“…Furthermore, this Hopf generating function in the case of composite representations, which is a generating function of the 4-point functions in topological string (corresponding to the resolved conifold with branes on the four external legs), is a τ-function of the universal character (UC) hierarchy put on the topological locus. …”
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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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Rényi relative entropy based monogamy of entanglement in tripartite systems by Marwa Mannaï, Hisham Sati, Tim Byrnes, Chandrashekar Radhakrishnan

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