Results 131 to 140 of about 213,970 (327)
, 2012 A topological graph is \emph{$k$-quasi-planar} if it does not contain $k$ pairwise crossing edges. A topological graph is \emph{simple} if every pair of its edges intersect at most once (either at a vertex or at their intersection). In 1996, Pach, Shahrokhi, and Szegedy \cite{pach} showed that every $n$-vertex simple $k$-quasi-planar graph contains at ...
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Advanced Functional Materials, EarlyView.Strong exciton‐photon coupling is achieved by integrating porphyrin ligand‐based MOF nanoparticles in optical cavities, as evidenced by pronounced polariton branch anticrossing. The porous nature of the resonator enables precise, reversible tuning via vapor pressure, unlocking unprecedented chemical‐environment controlled dynamic polaritonic platforms ...
Beatriz de Sola‐Báez +7 more
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Advanced Functional Materials, EarlyView.Nanoscale‐grooved indium gallium oxide (IGO) semiconductors, patterned via thermal nanoimprint lithography (NIL) using CD/DVD templates, are integrated into electrolyte‐gated transistor biosensors to overcome Debye length limitations. Precisely engineered concave–convex nanostructures modulate local electrostatic potentials, extend the effective Debye ...
Jong Yu Song +5 more
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Embeddings of 3-connected 3-regular planar graphs on surfaces of non-negative Euler characteristic
, 2019 Kengo Enami
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Advanced Functional Materials, EarlyView.This study presents a dynamic interaction between liquid resins and photopolymerized structures enabled by an in situ light‐writing setup. By controlling a three‐phase interface through localized photopolymerization, which provides physical confinement for the remaining uncured resin regions, the approach establishes a programmable pathway that ...
Kibeom Kim +3 more
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Kramers–Wannier Duality and Random-Bond Ising Model
EntropyWe present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators ...
Chaoming Song
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Journal of Combinatorial Theory, Series B, 1998 Given four distinct vertices in a 4-connected planar graph \(G\), we characterize when the graph \(G\) contains a \(K_4\)-subdivision with the given vertices as its degree three vertices. This result implies the following conjecture of Robertson and Thomas: a 5-connected planar graph has no \(K_4\)-subdivision with specified degree three vertices, if ...
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Novel Functional Materials via 3D Printing by Vat Photopolymerization
Advanced Functional Materials, EarlyView.This Perspective systematically analyzes strategies for incorporating functionalities into 3D‐printed materials via Vat Photopolymerization (VP). It explores the spectrum of achievable functionalities in recently reported novel materials—such as conductive, energy‐storing, biodegradable, stimuli‐responsive, self‐healing, shape‐memory, biomaterials, and
Sergey S. Nechausov +3 more
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A spherical fuzzy planar graph approach to optimize wire configuration in transformers
Frontiers in PhysicsIn this modern era, graph theory has become an integral part of science and technology. It has enormous applications in handling various design-based problems.
Hao Guan +5 more
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