Results 1 to 10 of about 3,462,281 (263)
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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The study of solutions for several systems of PDDEs with two complex variables
Demonstratio Mathematica, 2023 The purpose of this article is to describe the properties of the pair of solutions of several systems of Fermat-type partial differential difference equations.
Xu Yi Hui, Liu Xiao Lan, Xu Hong Yan
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Negatively Invariant Sets and Entire Solutions [PDF]
Journal of Dynamics and Differential Equations, 2010 Negatively invariant compact sets of autonomous and nonautonomous dynamical systems on a metric space, the latter formulated in terms of processes, are shown to contain a strictly invariant set and hence entire solutions. For completeness the positively invariant case is also considered. Both discrete and continuous time systems are considered.
Kloeden, Peter E., Marín Rubio, Pedro
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Multiple interpolation with the fast-growing knots in the class of entire functions and its application [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 The conditions for the sequence of complex numbers (bn,k) are obtained, such that the interpolation problem g(k-1)(λn) = bn,k, k ∈ 1, s, n ∈ N, where |λk/λk+1| ≤ ∆ < 1, has a unique solution in some classes of entire functions g for which Mg(r) ≤ c1 exp (
I. Sheparovych
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Entire solutions for several complex partial differential-difference equations of Fermat type in ℂ2
Open Mathematics, 2021 By utilizing the Nevanlinna theory of meromorphic functions in several complex variables, we mainly investigate the existence and the forms of entire solutions for the partial differential-difference equation of Fermat type α∂f(z1,z2)∂z1+β∂f(z1,z2)∂z2m+f(
Gui Xian Min +3 more
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Axioms, 2021 This article is to investigate the existence of entire solutions of several quadratic trinomial difference equations f(z+c)2+2αf(z)f(z+c)+f(z)2=eg(z), and the partial differential difference equations f(z+c)2+2αf(z+c)∂f(z)∂z1+∂f(z)∂z12=eg(z),f(z+c)2+2αf ...
Hong Li, Hongyan Xu
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Entire solutions for several general quadratic trinomial differential difference equations
Open Mathematics, 2021 This paper is devoted to exploring the existence and the forms of entire solutions of several quadratic trinomial differential difference equations with more general forms.
Luo Jun, Xu Hong Yan, Hu Fen
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The Exact Solutions for Several Partial Differential-Difference Equations with Constant Coefficients
Mathematics, 2022 This article is concerned with the description of the entire solutions of several Fermat type partial differential-difference equations (PDDEs) μf(z)+λfz1(z)2+[αf(z+c)−βf(z)]2=1, and μf(z)+λ1fz1(z)+λ2fz2(z)2+[αf(z+c)−βf(z)]2=1, where fz1(z)=∂f∂z1 and fz2(
Hongyan Xu +2 more
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