Results 101 to 110 of about 1,388,710 (287)
Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations
Abstract and Applied Analysis, 2013 This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation.
Xiaoxiao Zheng, Yadong Shang, Yong Huang
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Advanced Materials Interfaces, EarlyView.When exposed to light of a defined wavelength, the photoisomerization of azobenzene chromophores leads to polymer reorientation, generating stresses that result in solvent‐facilitated localized delamination of the film from the substrate. Additionally, blisters that form spontaneously when exposed to an aqueous environment can be manipulated via ...
James Robert Benson +4 more
wiley +1 more source
Boundary Value Problems, 2010 We used what we called extended Fan's sub-equation method and a new compound Riccati equations rational expansion method to construct the exact travelling wave solutions of the Davey-Stewartson (DS) equations.
Hassan Zedan
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Spatial Homeotropic and Planar Liquid Crystal Alignment Patterning
Advanced Materials Interfaces, EarlyView.A voltage‐assisted two‐step photoalignment methodology achieves precise micro‐patterning of alternating planar and homeotropic liquid crystal domains. Applying an AC electric field during in situ laser illumination minimizes phase retardation, reducing the required exposure dose. This cooperative mechanism enables high‐resolution spatial patterning and
Mingye Li, Inge Nys, Jeroen Beeckman
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Well-posedness of an elliptic equation with involution
Electronic Journal of Differential Equations, 2015 In this article, we study a mixed problem for an elliptic equation with involution. This problem is reduced to boundary value problem for the abstract elliptic equation in a Hilbert space with a self-adjoint positive definite operator. Operator tools
Allaberen Ashyralyev +1 more
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Well-posedness of difference elliptic equation
Discrete Dynamics in Nature and Society, 1997 The exact with respect to step h∈(0,1] coercive inequality for solutions in Ch of difference elliptic equation is established.
Pavel E. Sobolevskii
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Advanced Materials Technologies, EarlyView.A closed U‐shaped microfluidic platform symmetrically embeds a single, size‐controlled HT29 colorectal cancer spheroid within a GFP‐HUVEC‐laden fibrin matrix. HT29 spheroids are associated with hyper‐branched endothelial network remodeling, while vascularized co‐culture is accompanied by anisotropic protrusive growth and EMT‐like marker changes in the ...
G. Cretti +4 more
wiley +1 more source
Zero‐Waste Manufacturing of Ophthalmic Lenses by Direct Fluidic Shaping in Arbitrary Domains
Advanced Materials Technologies, EarlyView.Conventional ophthalmic lens manufacturing discards up to 97% of material through subtractive processes. The Cookie Cutter algorithm extends Fluidic Shaping to arbitrary rim geometries. The framework prescribes a spatially varying boundary height that, under neutral buoyancy and surface tension, shapes curable polymer into spherocylindrical lenses that
Yotam Katzman +6 more
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Journal of Applied Mathematics, 2013 A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method ...
Yun-Mei Zhao, Ying-Hui He, Yao Long
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Heights on elliptic curves over number fields, period lattices, and complex elliptic logarithms [PDF]
This thesis presents some major improvements in the following computations: a lower bound for the canonical height, period lattices, and elliptic logarithms.
Thongjunthug, Thotsaphon
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