Related papers: On $g$-functions for subshifts
We study several sufficient conditions for the existence of a L\'evy-Khinchin decomposition of generating functionals. We show that none of these conditions are equivalent and we show that such a decomposition does not always exist.
The existence of invariant generators for distributions satisfying a compatibility condition with the symmetry algebra is proved.
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
We characterize completely the Gneiting class of space-time covariance functions and give more relaxed conditions on the involved functions. We then show necessary conditions for the construction of compactly supported functions of the…
We consider distributions on $\mathbb{R}$ that can be written as the sum of a non-zero discrete distribution and an absolutely continuous distribution. We show that such a distribution is quasi-infinitely divisible if and only if its…
We prove both necessary and sufficient second order conditions of extrema for variational problems involving any higher order continuously twice differentiable Lagrangians with multi-valued dependent functions of several variables. Our…
The smooth function reconstruction needs to use derivatives. In 2010, we used the gradually varied derivatives to successfully constructed smooth surfaces for real data. We also briefly explained why the gradually varied derivatives are…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
We consider a class of discretionary stopping problems within the $G$-framework. We first establish the well-definedness of the stopping problem under the $G$-expectation, by showing the quasi-continuity of the stopped process. We then…
A central question in verification is characterizing when a system has invariants of a certain form, and then synthesizing them. We say a system has a $k$ linear invariant, $k$-LI in short, if it has a conjunction of $k$ linear (non-strict)…
A subequation on an open subset $X\subset \mathbb R^n$ is a subset $F$ of the space of $2$-jets on $X$ with certain properties. A smooth function is said to be $F$-subharmonic if all of its $2$-jets lie in $F$, and using the viscosity…
The main result of this paper shows a totally new necessary and sufficient condition to determine both real and complex zeros of derivative of all entire and meromorphic functions of one complex variable in the extended complex plane. By…
Let $G$ be a group with undecidable domino problem, such as $\mathbb{Z}^2$. We prove that all nontrivial dynamical properties for sofic $G$-subshifts are undecidable, that this is not true for $G$-SFTs, and an undecidability result for…
Consider the planar linear switched system $\dot x(t)=u(t)Ax(t)+(1-u(t))Bx(t),$ where $A$ and $B$ are two $2\times2$ real matrices, $x \in \R^2$, and $u(.):[0,\infty[\to\{0,1\}$ is a measurable function. In this paper we consider the…
In order to construct a representation of the tangle category one needs an enhanced R-matrix. In this paper we define a sufficient and necessary condition for enhancement that can be checked easily for any R-matrix. If the R-matrix can be…
It is well known that, the existence of a Lyapunov function is a sufficient condition for stability, asymptotic stability, or global asymptotic stability of an equilibrium point of an autonomous system $\dot{\mathbf{x}} = f(\mathbf{x})$. In…
In this note we give some new results concerning the subgroup commutativity degree of a finite group $G$. These are obtained by considering the minimum of subgroup commutativity degrees of all sections of $G$.
We consider the problem of equivalence of Gibbs states and equilibrium states for continuous potentials on full shift spaces $E^{\mathbb{Z}}$. Sinai, Bowen, Ruelle and others established equivalence under various assumptions on the…
New form of sufficient optimality condition is obtained in comparison with the Mangasarian sufficiency theorem. Both finite and infinite values of objective functional are allowed since concepts of overtaking and weakly overtaking…