Results 81 to 90 of about 497,650 (327)
On the Subdifferentiability of Convex Functions [PDF]
Proceedings of the American Mathematical Society, 1965 (Thus the subgradients of f correspond to the nonvertical supporting hyperplanes to the convex set consisting of all the points of E (DR lying above the graph of f.) The set of subgradients of f at x is denoted by of(x). If of(x) is not empty, f is said to be subdifferenticable at x.
Brøndsted, Arne, Rockafellar, R. T.
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Advanced Functional Materials, EarlyView.In situ TEM uncovers the atomic‐scale mechanisms underlying hydrogen‐driven γ‐Fe2O3→Fe3O4→FeO reduction. In γ‐Fe2O3, oxygen vacancies cluster around intrinsic Fe vacancies, leading to nanopore formation, whereas in Fe3O4, vacancy aggregation is suppressed, preserving a dense structure.
Yupeng Wu +14 more
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Inequalities via convex functions
International Journal of Mathematics and Mathematical Sciences, 1999 A general inequality is proved using the definition of convex functions. Many major inequalities are deduced as applications.
I. A. Abou-Tair, W. T. Sulaiman
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Advanced Functional Materials, EarlyView.The article reviews laser‐processed carbons from various precursors, processing mechanism and their application in advanced batteries. The laser process is chemical free, fast, and scalable, enabling improved battery performance and stability for Li, Na, and Zn battery technologies.
Sujit Deshmukh +2 more
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Results in semi-E-convex functions
Journal of Innovative Applied Mathematics and Computational Sciences, 2022 The concept of convexity and its various generalizations is important for quantitative and qualitative studies in operations research or applied mathematics.
Ayache Benhadid
doaj
Colloidal Crack Sintering Lithography for Light‐Induced Patterning of Particle Assemblies
Advanced Functional Materials, EarlyView.Colloidal crack sintering lithography (CCSL) is a microfabrication technique that uses light‐induced photothermal heating to trigger sintering and controlled cracking in polymer colloidal assemblies. Local structural changes generate microchannels and patterns, enabling direct writing of diverse topographic motifs.
Marius Schoettle +2 more
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Advanced Functional Materials, EarlyView.A spatiotemporal plasma–mediated laser processing approach is developed to fabricate ultrahigh–aspect ratio nanochannel arrays and corresponding perovskite nanowire arrays within transparent materials for optoelectronics devices. The laser‐fabricated nanochannels serve as templates for controlled perovskite infiltration and crystallization, enabling ...
Taijin Wang +3 more
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On HT-convexity and Hadamard-type inequalities
Journal of Inequalities and Applications, 2020 In the paper, the authors define a new notion of “HT-convex function”, present some Hadamard-type inequalities for the new class of HT-convex functions and for the product of any two HT-convex functions, and derive some inequalities for the arithmetic ...
Shu-Ping Bai, Shu-Hong Wang, Feng Qi
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Broadband, Flexible, Skin‐Compatible Carbon Dots/Graphene Photodetectors for Wearable Applications
Advanced Functional Materials, EarlyView.Broadband, flexible photodetectors integrating nitrogen‐rich carbon dots with single‐layer graphene on plastic substrates are demonstrated. A biocompatible chitosan–glycerol electrolyte enables efficient low‐voltage gating and on‐skin operation. The devices exhibit ultraviolet‐to‐near‐infrared response, mechanical robustness under bending, and verified
Nouha Loudhaief +20 more
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