Mild solutions to semilinear rough partial differential equations [PDF]
arXivWe provide an existence and uniqueness result for mild solutions to rough partial differential equations in the framework of the semigroup approach. Applications to stochastic partial differential equations driven by infinite dimensional Wiener processes and infinite dimensional fractional Brownian motion are presented as well.
arxiv
Soliton solution of the generalized fifth order Hirota-Satsuma equation coupled with KdV [PDF]
arXiv, 2016 We introduced a fifth-order partial differential equation as a generalization of Hirota-Satsuma coupled with KdV system. This equation is investigated based on tanh method. By applying the suitable independent variable in Hirota-Satsuma equation, we can convert this partial differential equations(PDE) into ordinary differential equations(ODE) .Solving ...
arxiv
Classification of acute myeloid leukemia based on multi‐omics and prognosis prediction value
Molecular Oncology, EarlyView.The Unsupervised AML Multi‐Omics Classification System (UAMOCS) integrates genomic, methylation, and transcriptomic data to categorize AML patients into three subtypes (UAMOCS1‐3). This classification reveals clinical relevance, highlighting immune and chromosomal characteristics, prognosis, and therapeutic vulnerabilities.
Yang Song +13 more
wiley +1 more source
Generalization of Sato equation and systems of multidimensional nonlinear Partial Differential Equations [PDF]
arXiv, 2002 This paper develops one of the methods for study of nonlinear Partial Differential equations. We generalize Sato equation and represent the algorithm for construction of some classes of nonlinear Partial Differential Equations (PDE) together with solutions parameterized by the set of arbitrary functions.
arxiv
Elementary Solutions for Certain Parabolic Partial Differential Equations [PDF]
, 1956 H. P. McKean
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Molecular Oncology, EarlyView.Presurgery 72‐h fasting in GB patients leads to adaptations of plasma lipids and polar metabolites. Fasting reduces lysophosphatidylcholines and increases free fatty acids, shifts triglycerides toward long‐chain TGs and increases branched‐chain amino acids, alpha aminobutyric acid, and uric acid.
Iris Divé +7 more
wiley +1 more source
Frequently Hypercyclic and Chaotic Behavior of Some First-Order Partial Differential Equation
Abstract and Applied Analysis, 2013 We study a particular first-order partial differential equation which arisen from a biologic model. We found that the solution semigroup of this partial differential equation is a frequently hypercyclic semigroup.
Cheng-Hung Hung, Yu-Hsien Chang
doaj +1 more source
Projective Geometry and PDE Prolongation [PDF]
arXivIn this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary differential equation into n first order equations. For partial differential equations there is a related process but it is
arxiv
Semilinear stochastic partial differential equations: central limit theorem and moderate deviations [PDF]
arXiv, 2019 In this paper, we establish a central limit theorem (CLT) and the moderate deviation principles (MDP) for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main results can be applied to stochastic partial differential equations of various types such as the stochastic Burgers ...
arxiv
Partial Differential Equations and Generalized Analytic Functions [PDF]
, 1951 Lipman Bers
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