Results 81 to 90 of about 33,094 (273)

Derivatives of Multivariate Bernstein Operators and Smoothness with Jacobi Weights

Journal of Applied Mathematics, 2012
Using the modulus of smoothness, directional derivatives of multivariate Bernstein operators with weights are characterized. The obtained results partly generalize the corresponding ones for multivariate Bernstein operators without weights.
Jianjun Wang, Zuoxiang Peng, Shukai Duan, Jia Jing   +3 more
doaj   +1 more source

Multimodal Structural Color Graphics Based on Colloidal Photonic Microdome Arrays

Advanced Functional Materials, EarlyView.
A hybrid photonic system combining colloidal crystals and microscale domes is designed to achieve four switchable optical states via the interplay of Bragg reflection and TIR interference. The graphics composed of the photonic microdome arrays provide tunable, angle‐sensitive structural coloration and concealed‐to‐revealed transitions, offering a ...
Jun‐Gu Kang, Hwan‐Young Lee, Chaerim Son, Hyeonbin Jo, Shin‐Hyun Kim   +4 more
wiley   +1 more source

Fully Bio‐Based Gelatin Organohydrogels via Enzymatic Crosslinking for Sustainable Soft Strain and Temperature Sensing

Advanced Functional Materials, EarlyView.
Enzymatically crosslinked gelatin‐based organohydrogels, fabricated through a fully bio‐based and scalable process, exhibit exceptional strain and temperature sensing capabilities with minimal interference from environmental humidity. These transparent, stretchable, and ionically conductive materials operate without synthetic fillers or dopants.
Pietro Tordi, Adrián Tamayo, Yeonsu Jeong, Bin Han, Tamer Al Kayal, Aida Cavallo, Massimo Bonini, Paolo Samorì   +7 more
wiley   +1 more source

Adaptive 4D‐Printed Vascular Stents With Low‐Temperature‐Activated and Intelligent Deployment

Advanced Functional Materials, EarlyView.
Microarchitected coronary artery stents were fabricated using a polycaprolactone (PCL)‐based shape memory polymer (SMP) composite via projection micro‐stereolithography (PµSL) 4D printing. By incorporating diethyl phthalate (DEP) as a plasticizer, the thermal transition temperature (Ttran) was modulated to about 37°C, enabling rapid and autonomous ...
Yannan Li, Yifan Pan, Chikahiro Imashiro, Chaolun Xu, Jianxian He, Jingao Xu, Kewei Song, Ze Zhang, Chen Gao, Junbo Jiang, Runhuai Yang, Kayo Hirose, Shinjiro Umezu   +12 more
wiley   +1 more source

Geometric characterization of generalized Hajłasz-Sobolev embedding domains

Advances in Nonlinear Analysis
In this article, the authors study the embedding properties of Hajłasz-Sobolev spaces with generalized smoothness on Euclidean domains, whose regularity is described via a smoothness weight function ϕ:[0,∞)→[0,∞)\phi :\left[0,\infty )\to \left[0,\infty ).
Li Ziwei, Yang Dachun, Yuan Wen
doaj   +1 more source

Characterization of Best Algebraic Approximation by an Algebraic Modulus of Smoothness

Journal of Approximation Theory, 1997
Denoting by \( x \oplus h \) the weighted addition given by \( x \oplus h = x \sqrt{1-h^2} + \sqrt{1-x^2}h, \forall x, h \in [-1, 1], \) the author considers the difference operator of \( r\) th order of the function \( f: [-1, 1] \rightarrow \mathbb{R}, \) defined by \( \Delta_h^r f = (\Delta_h\circ\ldots\circ\Delta_h)(f), \) (\(r \) times) where \( (\
openaire   +1 more source

A Biologically‐Architected Wear and Damage‐Resistant Nanoparticle Coating From the Radular Teeth of Cryptochiton stelleri

Advanced Functional Materials, EarlyView.
The ultrahard teeth of mollusks that feed on rocky substrates contain a wear‐resistant coating on their surfaces consisting of densely packed mesocrystalline magnetic nanoparticles within an organic matrix. These coatings display significant hardness and toughness through their highly controlled mesocrystalline architectures.
Taifeng Wang, Yu Chen, Ezra Sarmiento, Taige Hao, Atsushi Arakaki, Michiko Nemoto, Pablo Zavattieri, David Kisailus   +7 more
wiley   +1 more source

Toughening β‐Ga2O3 via Mechanically Seeded Dislocations

Advanced Functional Materials, EarlyView.
β‐Ga2O3 is promising for next‐generation semiconductors but its brittleness limits flexible and high‐precision applications. Here, mechanically seeded dislocations introduced by surface deformation improved damage tolerance in (001) β‐Ga2O3. Nanoindentation and characterization show dislocations suppress cleavage cracks by enabling stable plastic ...
Zanlin Cheng, Jiawen Zhang, Peng Gao, Guosong Zeng, Xufei Fang, Wenjun Lu   +5 more
wiley   +1 more source

A Modulus of Continuity for a Class of Quasi-Smooth Functions [PDF]

Proceedings of the American Mathematical Society, 1985
Let Z be the Zygmund class of functions f on [-1,1] such that \(f(- 1)=f(1)=0\) and \(| \Delta^ 2_ hf| \leq 2h.\) Let \(\omega (h)=\sup_{f\in Z}\sup_{| x-y| \leq h}| f(x)-f(y)|.\) Theorem. \[ \omega (h)\leq h \log_ 2\{2eK/(h \log_ 2 e)\}; \] here \(K=\sup_{f\in Z}\sup_{x}| f(x)\). A preceding result of \textit{A. F. Timan} [Izv. Akad.
openaire   +1 more source

Extensive Review of Materials for Next‐Generation Transparent Batteries and Their Design Strategies

Advanced Functional Materials, EarlyView.
Review explores emerging materials and design strategies for transparent batteries, examining electrodes, electrolytes, separators, and device architectures optimized for high electrochemical performance, mechanical flexibility, and optical transparency.
Atul Kumar Mishra, Shuvaraj Ghosh, Malkeshkumar Patel, Sourov Hossain, Ju‐Hyung Yun, Joondong Kim   +5 more
wiley   +1 more source