The gluing technique is used to construct hypersurfaces in Euclidean space having approximately constant prescribed mean curvature. These surfaces are perturbations of unions of finitely many spheres of the same radius assembled end-to-end along a line segment. The condition on the existence of these hypersurfaces is the vanishing of the sum of certain integral moments of the spheres with respe...

A closed formula for ultimate bound estimation in LTI systems with non–vanishing perturbations is presented. The formula, based on geometrical properties of the system, provides an alternative to Lyapunov’s second method based study. Although it is not proven that the bound obtained is always less conservative than the Lyapunov’s bound, some examples are introduced where the estimations are sig...

A scheme is proposed to achieve chaos synchronization for mutual coupled systems via partial stability theory. Under this scheme, three criteria are given to ensure chaos synchronization. The first criterion applies to the case without system perturbation and the other two apply to systems possessing vanishing and nonvanishing perturbations, respectively. Finally, coupled Lorenz systems are sim...

Starting from a uniform d-wave superconducting phase we study the energy cost due to imposed unidirectional defects with a vanishing pairing amplitude. Both renormalized mean-field theory and variational Monte Carlo calculations within the t–J model yield that the energies of inhomogeneous and uniform phases are very close to each other. This suggests that small perturbations in the microscopic...

We show that the Gauss-Bonnet term is the only consistent curvature squared interaction in the Randall-Sundrum model and various static and inflationary solutions can be found. And from metric perturbations around the RS background with a single brane embedded, we also show that for a vanishing Gauss-Bonnet coefficient, the brane bending allows us to reproduce the 4D Einstein gravity at the lin...

We study the leading term of the holonomy map of a perturbed plane polynomial Hamiltonian foliation. The non-vanishing of this term implies the non-persistence of the corresponding Hamiltonian identity cycle. We prove that this does happen for generic perturbations and cycles, as well for cycles which are commutators in Hamiltonian foliations of degree two. Our approach relies on the Chen’s the...

We present a stability result for a class of non-trivial self-similarly vanishing solutions to a 3D Hele-Shaw moving boundary problem with surface tension and single-point suction. These solutions are domains that bifurcate from the trivial spherical solution. The moving domains have a geometric centre located at the suction point and they are axially symmetric. We show stability with respect t...

In this paper we study the effect of external perturbations on a networked control system. We start by assuming that the nonnetworked system without perturbation is exponentially stable. Then, for fast enough networks we show that if the perturbation is bounded the networked system is ultimately bounded and if the perturbation is vanishing then the networked system is asymptotically stable. We ...

Cross-correlations between Cosmic Microwave Background (CMB) temperature and polarization anisotropies $\mu$-spectral distortions have been considered to measure (squeezed) primordial scalar bispectra in a range of scales inaccessible primary CMB bispectra. In this work we address whether it is possible constrain tensor non-Gaussianities with these cross-correlations. We find that only statisti...

We investigate the classical stability of the higher-dimensional Schwarzschild black holes against linear perturbations, in the framework of a gauge-invariant formalism for gravitational perturbations of maximally symmetric black holes, recently developed by the authors. The perturbations are classified into the tensor, vector, and scalar-type modes according to their tensorial behaviour on the...