Related papers: Frequency-dependent stability for Gabor frames
We report on a frequency ratio measurement of a ${}^{199}$Hg-based optical lattice clock referencing a ${}^{87}$Sr-based clock. Evaluations of lattice light shift, including atomic-motion-dependent shift, enable us to achieve a total…
We experimentally investigate the stability of a quantum gas with repulsive interactions in an optical 1D lattice subjected to periodic driving. Excitations of the gas in the lowest lattice band are analyzed across the complete stability…
We describe an optical frequency stabilization scheme of a microwave oscillator that is used for the interrogation of primary caesium fountain clocks. Because of its superior phase noise properties, this scheme, which is based on an…
We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when…
We prove that stability conditions on the derived category of a product of curves of positive genus are uniquely determined by their central charge and the phase of skyscraper sheaves. As an application, we construct stability conditions on…
In this paper, we study perturbation of Hilbert-Schmidt frames under structured modifications, where the perturbation takes the form of replacing finitely or infinitely many frame elements. We establish explicit criteria under which the…
Improvements in atom-light coherence are foundational to progress in quantum information science, quantum optics, and precision metrology. Optical atomic clocks require local oscillators with exceptional optical coherence due to the…
The topic of this paper are (multi-window) Gabor frames for signals over finite Abelian groups, generated by an arbitrary lattice within the finite time-frequency plane. Our generic approach covers simultaneously multi-dimensional signals…
Compact optical clocks with high stability are essential for next-generation frequency standard field applications, from navigation to geodesy, yet existing vapor cell clock systems have remained confined to fractional instabilities over…
This paper establishes integral representations of mild solutions of impulsive Hilfer fractional differential equations with impulsive conditions and fluctuating lower bounds at impulsive points. Further, the paper provides sufficient…
We report the role of $\mathcal{PT}$-symmetry in switching characteristics of a highly nonlinear fiber Bragg grating (FBG) with cubic-quintic-septic nonlinearities. We demonstrate that the device shows novel bi-(multi-) stable states in the…
Cubature formulas (CFs) based on radial basis functions (RBFs) have become an important tool for multivariate numerical integration of scattered data. Although numerous works have been published on such RBF-CFs, their stability theory can…
In this paper we establish the stability of the functional equation $$f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y)),\;\; x,y \in G, $$where $G$ is an abelian group.
In the present work, we introduce a new $\mathcal{PT}$-symmetric variant of the Klein-Gordon field theoretic problem. We identify the standing wave solutions of the proposed class of equations and analyze their stability. In particular, we…
The problem of phase retrieval is to determine a signal $f\in \mathcal{H}$, with $\mathcal{H}$ a Hilbert space, from intensity measurements $|F(\omega)|$, where $F(\omega):=\langle f , \varphi_\omega\rangle$ are measurements of $f$ with…
Controlled frames and g-frames were considered recently as generalizations of frames in Hilbert spaces. In this paper we generalize some of the known results in frame theory to controlled g-frames. We obtain some new properties of…
Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the…
We survey some aspects of stability conditions both in general and on the derived category of coherent sheaves on a surface, with applications to the birational geometry of certain holomorphic symplectic varieties.
This paper investigates stability analysis of flapping flight. Due to time-varying aerodynamic forces, such systems do not display fixed points of equilibrium. The problem is therefore approached via a limit cycle analysis based on Floquet…
We study quotients of mapping class groups (\Gamma_{g,1}) of oriented surfaces with one boundary component by terms of their Johnson filtrations, and we show that the homology of these quotients with suitable systems of twisted coefficients…