Related papers: Consistent Initialization of the Laplace Transform
This is an intuitive introduction to classic sliding mode control that shows how the associated assumptions and condition for its use arise in the context of a derivation of the method. It derives a controller that obviates the need for the…
Constrained optimization problems where both the objective and constraints may be nonsmooth and nonconvex arise across many learning and data science settings. In this paper, we show for any Lipschitz, weakly convex objectives and…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
Consider a spectrally positive L\'evy process $Z$ with log-Laplace exponent $\Psi$ and a positive continuous function $R$ on $(0,\infty)$. We investigate the entrance from $\infty$ of the process $X$ obtained by changing time in $Z$ with…
We consider a one-Laplace equation perturbed by $p$-Laplacian with $1<p<\infty$. We prove that a weak solution is continuously differentiable ($C^{1}$) if it is convex. Note that similar result fails to hold for the unperturbed one-Laplace…
We use the practical framework for abstract perturbed saddle point problems recently introduced by Hong et al. to analyze the mixed formulation of the Hodge Laplace problem. We compose two parameter-dependent norms in which the uniform…
A new approach of implementing initial and boundary conditions for the lattice Boltzmann method is presented. The new approach is based on an extended collision operator that uses the gradients of the fluid velocity. The numerical…
Zero-One Composite Optimization (0/1-COP) is a prototype of nonsmooth, nonconvex optimization problems and it has attracted much attention recently. The augmented Lagrangian Method (ALM) has stood out as a leading methodology for such…
Optimization is a critical tool for addressing a broad range of human and technical problems. However, the paradox of advanced optimization techniques is that they have maximum utility for problems in which the relationship between the…
Form factors of a simple system have been calculated in various forms of relativistic quantum mechanics, using a single-particle current. Their comparison has shown large discrepancies. The comparison is extended here to instant- and…
This work establishes the existence and uniqueness of solutions to the initial-value problem for the geometric transport equation $$ \frac{\mathrm{d}}{\mathrm{d} t}T_t+\mathcal{L}_b T_t=0 $$ in the class of $k$-dimensional integral or…
In this paper we investigate possible approaches to study general time-inconsistent optimization problems without assuming the existence of optimal strategy. This leads immediately to the need to refine the concept of time-consistency as…
This article describes an absolutely stable, first-order constraint solverfor multi-rigid body systems that calculates (predicts) constraint forces for typical bilateral and unilateral constraints, contact constraints with friction, and…
In a series of papers \cite{LSJR16, PP17, LPP}, it was established that some of the most commonly used first order methods almost surely (under random initializations) and with step-size being small enough, avoid strict saddle points, as…
In this paper, we study the initial-value problem for two first order systems in non-conservative form. The first system arises in elastodynamics and belongs to the class of strictly hyperbolic, genuinely nonlinear systems. The second…
In this study, a method for predicting unsteady aerodynamic forces under different initial conditions using a limited number of samples based on transfer learning is proposed, aiming to avoid the need for large-scale high-fidelity…
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…
In this paper the small-amplitude motion of multiple superposed viscous fluids is studied as a linearized initial-value problem. The analysis results in a closed set of equations for the Laplace transformed amplitudes of the interfaces that…
We suggest a new statement of the inverse spectral problem for Sturm--Liouville-type operators with constant delay. This inverse problem consists in recovering the coefficient (often referred to as potential) of the delayed term in the…
This short note is motivated by an attempt to understand the distinction between the Laplace operator and the hyperbolic Laplacian on the unit ball of $\mathbb{R}^n$, regarding the Lipschitz continuity of the solutions to the corresponding…