Results 51 to 60 of about 107,847 (314)
Journal of Combinatorial Theory, Series A, 1994 This paper gives another proof for the well-known fact, that the number of the well-formed orderings of \(n\) open and \(n\) closed parentheses is \({2n\choose n}/(n+1)\). The presented method works partitioning all the possible \({2n\choose n}\) orderings into classes of size \((n+1)\) such that every and each class contains exactly one well-formed ...
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Smart Nanogels as Enzyme‐Driven Nanomotors for Navigating Viscous Physiological Barriers
Advanced Functional Materials, EarlyView.Two families of urease‐powered nanomotors (NMs), with and without a p‐(2‐hydroxyethyl methacrylate) (p‐HEMA) shell, have been successfully prepared. Both types exhibit effective motion in highly viscous synovial fluid media at low urea concentrations (25 mM).
David Esporrín‐Ubieto +6 more
wiley +1 more source
Advanced Functional Materials, EarlyView.The relationship between the doping induced microstructure and thermal conductivity changes is elucidated for conjugated polymers. Eight conjugated polymers with different doping systems are studied, showing varied thermal conductivity responses based on structural order.
Jiali Guo +13 more
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Angewandte Chemie, EarlyView.Eu‐promoted PtSn2 catalysts leverage the redox activity of Eu and tailored acidity to reduce coke formation, enhancing selectivity and stability in propane dehydrogenation. This synergy significantly improves propylene yield and extends catalyst lifespan, providing an effective strategy for efficient PDH processes.
María I. Valls +10 more
wiley +2 more sources
Catalan Numbers for the Classroom?
Elemente der Mathematik, 1997 The author describes the experiences with 13-14 years old pupils in a project on Catalan numbers. She asserts that solving simple combinatorial problems plays an important role in developing thought processes, and should be practised throughout secondary school.
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A determinant property of Catalan numbers
Discrete Mathematics, 2000 Let \(M_k^t\) denote the \(k \times k\) (persymmetric) matrix having the consecutive Catalan numbers starting at \(c_t\) as row one, those starting at \(c_{t+1}\) as row two, etc. Now define \(G\) to be the infinite digraph with vertex set \({\mathbb{Z}} \times {\mathbb{Z}}\) and with directed arcs from \((i,j)\) to \((i+1,j)\), and to \({(i,j+1 ...
Jerzy Wojciechowski, Michael E. Mays
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Advanced Functional Materials, EarlyView.This review highlights recent advances in label‐free optical biosensors based on 2D materials and rationally designed mixed‐dimensional nanohybrids, emphasizing their synergistic effects and novel functionalities. It also discusses multifunctional sensing platforms and the integration of machine learning for intelligent data analysis.
Xinyi Li, Yonghao Fu, Yuehe Lin, Dan Du
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EDA Complex‐Driven Desaturation of Heterocyclic Carbonyl Compounds Enabled by HFIP
Angewandte Chemie, EarlyView.In this work, we report a novel light‐mediated desaturation strategy enabled by electron donor–acceptor complex formation. DFT and mechanistic studies reveal that the reaction proceeds via single‐electron transfer, hydrogen atom transfer, and base‐mediated deprotonation sequentially with pyridinium salt serving dually as oxidant and base, and ...
Rakesh Maiti +6 more
wiley +2 more sources
Two explicit formulas for the generalized Motzkin numbers
Journal of Inequalities and Applications, 2017 In the paper, by the Faà di Bruno formula, the authors establish two explicit formulas for the Motzkin numbers, the generalized Motzkin numbers, and the restricted hexagonal numbers.
Jiao-Lian Zhao, Feng Qi
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Parametric Catalan numbers and Catalan triangles
Linear Algebra and its Applications, 2013 Abstract Here presented a generalization of Catalan numbers and Catalan triangles associated with two parameters based on the sequence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan numbers are defined, which can be considered ...
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