Results 101 to 110 of about 51,997 (309)
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
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 +6 more
wiley +1 more source
Equivariant embedding theorems and topological index maps [PDF]
, 2010 The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections.
Heath Emerson +3 more
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Eccentricity-Based Topological Invariants of Some Chemical Graphs
Atoms, 2019 Topological index is an invariant of molecular graphs which correlates the structure with different physical and chemical invariants of the compound like boiling point, chemical reactivity, stability, Kovat’s constant etc.
Nazeran Idrees +2 more
doaj +1 more source
Effect of Optical Illumination on Bubble Nanodomains
Advanced Functional Materials, EarlyView.Stable surface‐confined nanoscale bubble domains are created and manipulated in PMN‐PT single crystals. Under above‐bandgap illumination, these bubble nanodomains remain unchanged. However, upon illumination cessation, they rapidly expand to switch the entire crystal surface, due to the accumulation of a large reservoir of electrons at the crystal ...
Haoze Zhang +8 more
wiley +1 more source
Computing forgotten topological index of zero-divisor graphs of commutative rings [PDF]
, 1996 The main objective of this paper is to calculate the forgotten topological index of the zero-divisor graph of Z(n). Let p, q and r be distinct prime numbers. We calculate the forgotten topological index of the ring Gamma(Z(n)) where n = p(alpha), pq, p(2)
Gursoy, Arif +6 more
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Advanced Functional Materials, EarlyView.A biomimetic aerogel conduit was engineered from a nanofiber of gelatin/poly(l‐lactic acid) doped with polypyrrole nanoparticles, integrated with tannic acid and Mg2+. This “electro‐ionic‐immune” strategy mimicked spinal cord properties, reduced calcium overload, inflammation, oxidative damage, promoted neural stem cell differentiation, suppressed ...
Qingxiang Liu +9 more
wiley +1 more source
Forgotten reduced neighborhood topological index [PDF]
Topological graph indices are the most important applications of graph theory. In the last few decades, such applications have been increasingly in use for mathematicians, chemists, pharmacologists.
Shalini, G. B. Sophia, Saleh, Anwar
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The Index Theorem of topological regular variation and its applications [PDF]
, 2009 We develop further the topological theory of regular variation of [N.H. Bingham, A.J. Ostaszewski, Topological regular variation: I. Slow variation, LSE-CDAM-2008-11].
Bingham, N.H. +3 more
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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 +3 more
doaj +1 more source