Related papers: V-shaped action functional with delay
This paper studies the stabilization and safety problems of nonlinear time-delay systems. Following both Razumikhin and Krasovskii approaches, we propose novel control Lyapunov functions/functionals for the stabilization problem and novel…
A previously established correspondence between definite-parity real functions and inner analytic functions is generalized to real functions without definite parity properties. The set of inner analytic functions that corresponds to the set…
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…
Action recognition from still images is an important task of computer vision applications such as image annotation, robotic navigation, video surveillance and several others. Existing approaches mainly rely on either bag-of-feature…
Differential forms on an odd symplectic manifold form a bicomplex: one differential is the wedge product with the symplectic form and the other is de Rham differential. In the corresponding spectral sequence the next differential turns out…
In this paper we provide a different approach for existence of the variational solutions of the gradient flows associated to functionals on Sobolev spaces studied in \cite{BDDMS20}. The crucial condition is the convexity of the functional…
This book is an extension of my doctoral dissertation, focusing on techniques for analyzing stability (dissipativity) and achieving stabilization of linear systems that are characterized by non-trivial distributed delays. It specifically…
An alternative characterization of Minkowski--Lyapunov functions is derived. The derived characterization enables a computationally efficient utilization of Minkowski--Lyapunov functions in arbitrary finite dimensions. Due to intrinsic…
This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…
In this paper, subsystems with shadowing property for $\mathbb{Z}^{k}$-actions are investigated. Let $\alpha$ be a continuous $\mathbb{Z}^{k}$-action on a compact metric space $X$. We introduce the notions of pseudo orbit and shadowing…
As a robot senses and selects actions, the world keeps changing. This inference delay creates a gap of tens to hundreds of milliseconds between the observed state and the state at execution. In this work, we take the natural generalization…
This paper constructs a foundation to analyze semi-group actions, group actions, filtrations, and decompositions in a unified manner. In fact, though the studies of decomposition can be applied to foliated spaces and group actions, they can…
A form of Sobolev inequalities for the symmetric gradient of vector-valued functions is proposed, which allows for arbitrary ground domains in $\mathbb R ^n$. In the relevant inequalities, boundary regularity of domains is replaced with…
The structure of one-loop divergences of two-dimensional dilaton-Maxwell quantum gravity is investigated in two formalisms: one using a convenient effective action and the other a unique effective action. The one-loop divergences (including…
In a joint paper, Jean Petitot together with the authors of the present paper described the functional geometry of the visual cortex as the symplectization of a contact form to describe the family of cells sensitive to position, orientation…
Despite the rapid progress of vision-language-action (VLA) models, the prevailing practice of predicting action chunks as discrete waypoints remains structurally misaligned with the intrinsic continuity of physical motion. This…
We consider nonautonomous cyclic systems of delay differential equations with variable delay. Under suitable feedback assumptions, we define an (integer valued) Lyapunov functional related to the number of sign changes of the coordinate…
The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…
We establish estimates and representations for the remainders of Taylor approximations of the spectral action functional $V\mapsto\tau(f(H_0+V))$ on bounded self-adjoint perturbations, where $H_0$ is a self-adjoint operator with…
In this paper, the relations between the Yang-Baxter equation and affine actions are explored in detail. In particular, we classify solutions of the Yang-Baxter equations in two ways: (i) by their associated affine actions of their…