Related papers: Commutator formulas for gradient Ricci shrinker an…
We study the growth of matter density perturbations delta_m for a number of viable f(R) gravity models that satisfy both cosmological and local gravity constraints, where the Lagrangian density f is a function of the Ricci scalar R. If the…
In this paper, we extend the work of Cao-Chen [9] on Bach-flat gradient Ricci solitons to classify $n$-dimensional ($n\ge 5$) complete $D$-flat gradient steady Ricci solitons. More precisely, we prove that any $n$-dimensional complete…
The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms. For example, stable solutions of gradient descent (GD) correspond to flat minima, which have been…
The stability requirements for a noncommutative scalar field coupled to gravity is investigated through the positive energy theorem. It is shown that for a noncommutative scalar with a polynomial potential, the stability conditions are…
We improve certain degree bounds for Grobner bases of polynomial ideals in generic position. We work exclusively in deterministically verifiable and achievable generic positions of a combinatorial nature, namely either strongly stable…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
This note presents a non-rigorous study of the linear response for an SRB (or `natural physical') measure $\rho$ of a diffeomorphism $f$ in the presence of tangencies of the stable and unstable manifolds of $\rho$. We propose that…
This paper addresses issues concerning asymptotic stability testing and controller design for the two-dimensional Rosser model in Differential-Algebraic-Equations systems (DAEs). We present sufficient stability criteria based on the…
In this paper we give a new sufficient condition for a general stability of Kronecker coefficients, which we call it additive stability. It was motivated by a recent talk of J. Stembridge at the conference in honor of Richard P. Stanley's…
Motivated by the dark energy issue, a minisuperspace approach to the stability for modified gravitational models in a four dimensional cosmological setting are investigated. Specifically, after revisiting the $f(R)$ case, $R$ being the…
Conditions are given which, subject to a genericity condition on the Ricci tensor, are both necessary and sufficient for a 3-metric to arise from a static spacetime metric.
Let $(M, g, f, \tau)$ be a complete Ricci shrinker satisfying $\textrm{Ric}+\nabla^2f=\frac{g}{2\tau}$ and let $R$ denote its scalar curvature. For a confined function $V$ on $M$, we obtain a lower bound for the lowest eigenvalue of the…
We consider a novel class of $f(\R)$ gravity theories where the connection is related to the conformally scaled metric $\hat g_{\mu\nu}=C(\R)g_{\mu\nu}$ with a scaling that depends on the scalar curvature $\R$ only. We call them C-theories…
We propose a new version of the scalar Weak Gravity Conjecture (WGC) which would apply to any scalar field coupled to quantum gravity. For a single scalar it is given by the differential constraint $V''\leq…
In this paper, we establish the stability and superstability of $J^*-$derivations in $J^*-$algebras for the generalized Jensen--type functional equation $$rf(\frac{x+y}{r})+rf(\frac{x-y}{r})= 2f(x).$$ Finally, we investigate the stability…
This paper derives a necessary and sufficient condition for the coincidence of Harmonic residual vectors and the residual vector in GMRES. The properties of the harmonic Ritz values at the stagnation of GMRES were described in the…
In this study, we provide some classifications for half-conformally flat gradient $f$-almost Ricci solitons, denoted by $(M, g, f)$, in both Lorentzian and neutral signature. First, we prove that if $||\nabla f||$ is a non-zero constant,…
In this announcement, we exhibit the second variation of Perelman's $\lambda$ and $\nu$ functionals for the Ricci flow, and investigate the linear stability of examples. We also define the "central density" of a shrinking Ricci soliton and…
In this paper we give necessary and sufficient conditions on the compatibility of a $k$th order homogeneous linear elliptic differential operator $\mathbb{A}$ and differential constraint $\mathcal{C}$ for solutions of \begin{align*}…
In this paper, we consider the stability of discrete-time linear switched systems with a common non-strict Lyapunov matrix.