Results 91 to 100 of about 3,892,377 (304)

Topological aspects of some dendrimer structures

Nanotechnology Reviews, 2018
A numerical number associated to the molecular graph G that describes its molecular topology is called topological index. In the study of QSAR and QSPR, topological indices such as atom-bond connectivity index, Randić connectivity index, geometric index,
Aslam Adnan, Jamil Muhammad Kamran, Gao Wei, Nazeer Waqas   +3 more
doaj   +1 more source

Computation of Topological Indices of Some Special Graphs

Mathematics, 2018
There are several chemical indices that have been introduced in theoretical chemistry to measure the properties of molecular topology, such as distance-based topological indices, degree-based topological indices and counting-related topological indices ...
Mohammed Salaheldeen Abdelgader, Chunxiang Wang, Sarra Abdalrhman Mohammed   +2 more
doaj   +1 more source

Topological Index Theory for surfaces in 3–manifolds [PDF]

Geometry & Topology, 2010
The disk complex of a surface in a 3-manifold is used to define its {\it topological index}. Surfaces with well-defined topological index are shown to generalize well-known classes, such as incompressible, strongly irreducible, and critical surfaces.
openaire   +4 more sources

Optical Signature of Moiré Superlattices Formed by Twisted SrTiO3 Membranes

Advanced Functional Materials, EarlyView.
We discover optical signatures from bonded interfaces in twisted SrTiO3 moiré superlattices, including low‐frequency Raman vibrational modes and strong second‐harmonic generation, consistent with strong interlayer coupling inferred from cross‐sectional electron microscopy and ab initio calculations. ABSTRACT Moiré superlattices formed at the interfaces
T. A. M. Ragib Shahriar, Fumikazu Murakami, Xing He, Konnor Koons, Xinyan Li, Bumseop Kim, Shihan Qin, Varun Harbola, Jochen Mannhart, Yimo Han, Ruijuan Xu, Shengxi Huang, Andrew M. Rappe, Hanyu Zhu   +13 more
wiley   +1 more source

From Photoalignment to Structured Light: Liquid Crystal Platforms for Beam Shaping and Complex Wavefronts

Advanced Functional Materials, EarlyView.
Photoaligned and photopatterned liquid crystal platforms provide programmable control of optical phase, polarization, and spin‐orbit interactions, enabling compact generation of structured light and complex wavefronts. This review highlights how tailored molecular orientations transform simple beams into designed optical fields, opening versatile ...
Le Zhou, Tingjun Zhong, Sijie Liu, Pouya Nosratkhah, Ke Xu, Yuzhen Zhao, Kristiaan Neyts   +6 more
wiley   +1 more source

Two‐Photon Grayscale Lithography (2GL) of High Mechanical and Optical Quality 3D Silica Glass Microstructures

Advanced Functional Materials, EarlyView.
Two‐photon grayscale lithography (2GL) enables high‐speed and precise 3D printing of thermolyzed silica glass microstructures with optical‐grade surface quality, high quality factors, and mechanical strength utilizing a custom‐made pre‐glass resist based on polyhedral oligomeric silsesquioxane (POSS) modified with a high‐sensitivity Norrish type II ...
Jonathan L. G. Schneider, Jiajie Liang, Paul Somers, Martin Wegener, Jens Bauer   +4 more
wiley   +1 more source

Functionalizing Micro‐to‐Mesoscopic Electrode Architectures for Regulating Electron Transfer Behaviors in Electrocatalysis

Advanced Functional Materials, EarlyView.
A systematic review is conducted to assess the influence of electrode architecture across micro‐ to mesoscopic length scales on electron‐transfer pathways in electrocatalysis. We discuss the structure‐activity relationships in electrocatalytic applications, including resource recovery and environmental remediation, and provide cost‐effective, efficient
Manshu Zhao, Jiaojiao Zhang, Shideng Yuan, Xinmeng Yu, Keming Wan, Xiaoguang Duan, Zhining Wang   +6 more
wiley   +1 more source

On the extremal cactus graphs for variable sum exdeg index with a fixed number of cycles

AKCE International Journal of Graphs and Combinatorics, 2020
The variable sum exdeg index, introduced by Vukičević [Croat. Chem. Acta 84 (2011) 87–91] for predicting the octanol-water partition coefficient of certain chemical compounds, of a graph G is defined as where a is any positive real number different from ...
Mubeen Javaid, Akbar Ali, Igor Milovanović, Emina Milovanović   +3 more
doaj   +1 more source

On the Forgotten Topological Index of Signed Graphs

Ukrainian Mathematical Journal
UDC 519.17 The forgotten topological index denoted by $F(G)$ of a graph $G=(V,E)$ is defined as follows:  $F(G)=\displaystyle\sum\nolimits_{i=1}^{n}\!d_v^3,$ where $d_v$ denotes the degree of the vertex $v.$ We extend the notion of forgotten topological index to signed graphs and  introduce the $MS$-index of a signed graph.
Shariefuddin Pirzada, Mir Riyaz Ul Rashid   +1 more
openaire   +1 more source

Noncommutative topology and the world’s simplest index theorem [PDF]

Proceedings of the National Academy of Sciences, 2010
In this article we outline an approach to index theory on the basis of methods of noncommutative topology. We start with an explicit index theorem for second-order differential operators on 3-manifolds that are Fredholm but not elliptic. This low-brow index formula is expressed in terms of winding numbers. We then proceed to show how it is derived as a
openaire   +3 more sources