Publications related to Linear differential equation

Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The cons ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2023

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Rafael Vazquez Hernandez

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Fast in vivo assay of creatine kinase activity in the human brain by P-31 magnetic resonance fingerprinting

Lijing Xin, Daniel Wenz, Mark Stephan Widmaier, Songi Lim

A new and efficient magnetisation transfer P-31 magnetic resonance fingerprinting (MT-P-31-MRF) approach is introduced to measure the creatine kinase metabolic rate kCK

{k}_{\mathrm{CK}}

between phosphocreatine (PCr) and adenosine triphosphate (ATP) i ...

WILEY2023

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Le Chen, Cheuk Yin Lee, David Jean-Michel Candil

We consider nonlinear parabolic stochastic PDEs on a bounded Lipschitz domain driven by a Gaussian noise that is white in time and colored in space, with Dirichlet or Neumann boundary condition. We establish existence, uniqueness and moment bounds of the r ...

New York2023

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Victor Panaretos, Neda Mohammadi Jouzdani

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

Amsterdam2023

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Giancarlo Ferrari Trecate, Luca Furieri, Clara Lucía Galimberti, Liang Xu

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem from the discretiz ...

2023

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

Serge Vaudenay, Bénédikt Minh Dang Tran

Witness encryption is a cryptographic primitive which encrypts a message under an instance of an NP language and decrypts the ciphertext using a witness associated with that instance. In the current state of the art, most of the witness encryption construc ...

Springer2023

Homogeneous catalysis with nitrous oxide

Kay Severin

Nitrous oxide (N2O; ‘laughing gas’) is a powerful oxidant, but chemical transformations are hampered by the inert character of this gas. Recent advances in using N2O as an oxidant in metal-catalyzed reactions are discussed. The focus will be on reactions t ...

Elsevier2023

Fast global spectral methods for three-dimensional partial differential equations

Daniel Kressner, Christoph Max Strössner

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...

OXFORD UNIV PRESS2022

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

Junming Duan

The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary differe ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Linear differential equation

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Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Fast in vivo assay of creatine kinase activity in the human brain by P-31 magnetic resonance fingerprinting

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

Homogeneous catalysis with nitrous oxide

Fast global spectral methods for three-dimensional partial differential equations

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

Homogeneous catalysis with nitrous oxide

Extractable Witness Encryption for the Homogeneous Linear Equations Problem

An analytical solution of the isentropic vortex problem in the special relativistic magnetohydrodynamics

Fast in vivo assay of creatine kinase activity in the human brain by P-31 magnetic resonance fingerprinting

Parabolic stochastic PDEs on bounded domains with rough initial conditions: moment and correlation bounds

Heteroclinic orbits for a system of amplitude equations for orthogonal domain walls

Fast global spectral methods for three-dimensional partial differential equations

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Hamiltonian Deep Neural Networks Guaranteeing Non-Vanishing Gradients by Design