Results 1 to 10 of about 11,651,840 (352)
Adaptive regularization using the entire solution surface.
Biometrika, 2009 Several sparseness penalties have been suggested for delivery of good predictive performance in automatic variable selection within the framework of regularization. All assume that the true model is sparse. We propose a penalty, a convex combination of the L1- and L∞-norms, that adapts to a variety of situations including sparseness and nonsparseness ...
Wu S, Shen X, Geyer CJ.
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Entire solutions for the heat equation
Electronic Journal of Differential Equations, 2021 We consider the solutions of the heat equation $$ \partial_t F = \partial_z^2 F $$ which are entire in z and t (caloric functions). We examine the relation of the z-order and z-type of an entire caloric function \(F(t, z)\), viewed as function of z, to its t-order and t-type respectively, if it is viewed as function of \(t\). Also, regarding the zeros \
Vassilis G. Papanicolaou +2 more
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On the growth of entire solution of a nonlinear differential equation [PDF]
Mathematica Bohemica, 2020 In the paper we consider the growth of entire solution of a nonlinear differential equation and improve some existing results.
Indrajit Lahiri, Shubhashish Das
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LIMITING DIRECTIONS FOR ENTIRE SOLUTIONS OF A
Mathematical ReportsLet us consider f as being an entire solution of the differential-difference equation G(z, f)+h(z)fm(z) = 0, (m ∈ N), where h(z) is a transcendental entire function and G(z, f) is a differential-difference polynomial in f with entire coefficients.
Yezhou Li, Zhixue Liu, Heqing Sun
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Remarks on two fourth order elliptic problems in whole space
Proceedings of the Edinburgh Mathematical Society, 2014 We are interested in entire solutions for the semilinear biharmonic equation $\Delta^{2}u=f(u)$ in $\R^N$, where $f(u)=e^{u}$ or $-u^{-p}\ (p>0)$. For the exponential case, we prove that any classical entire solution verifies $-\Delta u>0$ without any ...
Lai, Baishun, Ye, Dong
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Entire Solution of a Singular Semilinear Elliptic Problem
Journal of Mathematical Analysis and Applications, 1996 Betrachtet wird die singuläre semilineare elliptische Gleichung \[ \Delta u+ p(x)u^{-\gamma} = 0\quad \text{für} \quad x\in \mathbb{R}^n,\;\gamma>0,\;n\geq 3 \] mit einer homogenen Dirichletschen Randbedingung. Gilt \(p(x)>0\) für \(x\in\mathbb{R}^n\) und \(\int^\infty_0 t \varphi (t)dt0\) auf \(\overline \Omega\) [\textit{A. C. Lazer} und \textit{P. J.
A. V. Lair, A. W. Shaker
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Rigidity for general semiconvex entire solutions to the sigma-2 equation [PDF]
Duke mathematical journal, 2021 We show that every general semiconvex entire solution to the sigma-2 equation is a quadratic polynomial. A decade ago, this result was shown for almost convex solutions.
R. Shankar, Yu Yuan
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Entire Solutions of Linear Systems of Moment Differential Equations and Related Asymptotic Growth at Infinity [PDF]
Differential Equations and Dynamical Systems, 2021 The general entire solution to a linear system of moment differential equations is obtained in terms of a moment kernel function for generalized summability, and the Jordan decomposition of the matrix defining the problem.
A. Lastra
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AIMS Mathematics, 2022 This article is concerned with the existence of entire solutions for the following complex second order partial differential-difference equation $ \left(\frac{\partial^2 f(z_1, z_2)}{\partial z_1^2}+\frac{\partial^2 f(z_1, z_2)}{\partial z_2^2 ...
Wenju Tang, Keyu Zhang, Hongyan Xu
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Entire solution in an ignition nonlocal dispersal equation: Asymmetric kernel [PDF]
, 2017 This paper mainly focuses on the front-like entire solution of a classical nonlocal dispersal equation with ignition nonlinearity. Especially, the dispersal kernel function J may not be symmetric here.
Li Zhang, Wan-Tong Li, Zhi-Cheng Wang
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