Related papers: More self-tuning solutions with $H_{MNPQ}$

We develop a geometric version of the inverse problem of the calculus of variations for discrete mechanics and constrained discrete mechanics. The geometric approach consists of using suitable Lagrangian and isotropic submanifolds. We also…

We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group -- subject to a Young tableaux $Y(s_1,\ldots ,s_k)$ with $k\geq 2$ rows -- in a $d$-dimensional…

We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…

In this paper, we prove that the closed Lagrangian self-shrinkers in $\mathbb{R}^4$ which are symmetric with respect to a hyperplane are given by the products of Abresch-Langer curves. As a corollary, we obtain a new geometric…

We consider the response of a multicomponent body to $n$ fields, such as electric fields, magnetic fields, temperature gradients, concentration gradients, etc., where each component, which is possibly anisotropic, may cross couple the…

Here we utilize a low-rank tensor model (LTM) as a function approximator, combined with the gradient descent method, to solve eigenvalue problems including the Laplacian operator and the harmonic oscillator. Experimental results show the…

We develop the BRST approach for all massless integer and half-integer higher spins in 4D Minkowski space, using the two component spinor nota- tion and develop the Lagrangian formulation for supersymmetric higher spin models. It is shown…

Let $(M,g)$ be a closed, connected and orientable Riemannian manifold with nonnegative Ricci curvature. Consider a Lagrangian $L(x,v):TM\to\R$ defined by $L(x,v):=\frac 12g_x(v,v)-\omega(v)+c$, where $c\in\R$ and $\omega$ is a closed…

Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…

In this paper we study the anisotropic incompressible Navier-Stokes equations with a logarithm damping $\alpha \log(e+|u|^2)|u|^2u$ in $H^{0.1}$, where we used new methods, new tools and Fourier analysis.

We are concerned with the homogenization of second-order linear elliptic equations with random coefficient fields. For symmetric coefficient fields with only short-range correlations, quantified through a logarithmic Sobolev inequality for…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

This paper considers various models of support vector machines with ramp loss, these being an efficient and robust tool in supervised classification for the detection of outliers. The exact solution approaches for the resulting optimization…

Doubly nonnegative (DNN) relaxation usually provides a tight lower bound for a mixed-binary quadratic program (MBQP). However, solving DNN problems is challenging because: (1) the problem size is $\Omega((n+l)^2)$ for an MBQP with $n$…

We present new analytical three-dimensional solutions of the magnetohydrostatic equations, which are applicable to the co-rotating frame of reference outside a rigidly rotating cylindrical body, and have potential applications to planetary…

This paper presents a Lagrangian approach to simulating multibody dynamics in a tensegrity framework with an ability to tackle holonomic constraint violations in an energy-preserving scheme. Governing equations are described using…

In this paper, we study the Lagrangian functions for a class of second-order differential systems arising from physics. For such systems, we present necessary and sufficient conditions for the existence of Lagrangian functions. Based on the…

We introduce a novel approach addressing global analysis of a difficult class of nonconvex-nonsmooth optimization problems within the important framework of Lagrangian-based methods. This genuine nonlinear class captures many problems in…

We extend the BRS and anti-BRS symmetry to the two point space of Connes' non-commutative model building scheme. The constraint relations are derived and the quantum Lagrangian constructed. We find that the quantum Lagrangian can be written…

Inspired by the so-called Palatini formulation of General Relativity and of its modifications and extensions, we consider an analogous formulation of the dynamics of a self-interacting gauge field which is determined by non-linear extension…