Results 41 to 50 of about 8,945 (319)
Hardware acceleration of number theoretic transform for zk‐SNARK
Engineering Reports, EarlyView., 2023 An FPGA‐based hardware accelerator with a multi‐level pipeline is designed to support the large‐bitwidth and large‐scale NTT tasks in zk‐SNARK. It can be flexibly scaled to different scales of FPGAs and has been equipped in the heterogeneous acceleration system with the help of HLS and OpenCL.
Haixu Zhao +6 more
wiley +1 more source
Ellipticity and Regularity for Periodic Nonlinear Equations [PDF]
Proceedings of the American Mathematical Society, 1969 The composition of two strongly elliptic linear operators with suitably differentiable coefficients is also strongly elliptic. This fact has been used [3, pp. 178-181] to yield a particularly simple proof of the regularity of weak solutions of periodic strongly elliptic linear equations.
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Discontinuous Galerkin Finite Element Approximation of Nonlinear Second-Order Elliptic and Hyperbolic Systems [PDF]
, 2006 We develop the convergence analysis of discontinuous Galerkin finite element approximations to second-order quasilinear elliptic and hyperbolic systems of partial differential equations of the form, respectively, $-\sum_{\alpha=1}^d \partial_{x_\alpha ...
Suli, Endre +5 more
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Homogenization of singular elliptic systems with nonlinear conditions on the interfaces [PDF]
, 2020 We prove existence and homogenization results for elliptic problems involving a singular lower order term and defined on a domain with interfaces having a nonlinear response.
Amar Micol, Giuseppe Riey
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Mathematics, 2022 This article is the further work of previous papers and also the first study to adopt the elliptic integral approach to solve the forced nonlinear structural acoustic problem.
Yiu-Yin Lee
doaj +1 more source
Second‐Harmonic Hyper‐Mie Optical Activity Enables Closed‐Loop Chiral Photochemistry
Advanced Materials, EarlyView.Nonlinear chiral photochemistry is demonstrated in CdTe/CdO nanohelices, where circularly polarized infrared light both drives and tracks photo‐oxidation via second‐harmonic scattering. This closed‐loop process reveals real‐time structural evolution, including shell fracturing and core exposure, accompanied by a transition from hyper‐Mie to hyper ...
Hoyeon Choi +6 more
wiley +1 more source
Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems [PDF]
, 2011 Morse Index Theorems for elliptic boundary value problems in multi-dimensions are proved under various boundary conditions. The theorems work for star-shaped domains and are based on a new idea of measuring the "oscillation" of the trace of the set of ...
Deng, Jian +1 more
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Near‐Unity Chiral Lasing Enabled by Quasi‐Bound States in the Continuum
Advanced Materials, EarlyView.Nanoimprinted chiral array that supports bound states in the continuum is doped with an efficient non‐chiral molecule (Rhodamine‐B) acting as gain medium to produce fully circularly polarized lasing emission. The chiral lasing wavelength can be tuned across the emission band of Rhodamine‐B by adjusting the coating thickness of the TiO2 high refractive ...
Jose Mendoza‐Carreño +5 more
wiley +1 more source
A Symmetrization Result for Nonlinear Elliptic Equations
Revista Matemática Complutense, 2004 The authors consider the following problem \[ -\Delta_pu=c|u|^{p-2}u+f\text{ in }\Omega\qquad u=0\text{ on }\partial\Omega,\tag{1} \] where \(\Delta_p\) is the \(p\)-Laplacian operator, \(p>1\), and \(c,f\) are bounded given functions. Under some natural assumptions on the data of (1), the authors prove that the rearrangement of \(u\) can be estimated ...
FERONE, VINCENZO, MESSANO, BASILIO
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Numerical Homogenization and Correctors for Nonlinear Elliptic Equations [PDF]
SIAM Journal on Applied Mathematics, 2004 The authors study numerical homogenization techniques for nonlinear elliptic equatiuons involving operators with homogeneous random coefficients. They use a heterogeneous multiscale approach and establish convergence results in the framework of G-convergence. Numerical examples illustrate the performance of the suggested method for convection-diffusion
Yalchin Efendiev, Alexander Pankov
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