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Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
The behaviour of the Maxwell field near one of the spatial infinities of the Schwarzschild solution is analysed by means of the transport equations implied by the Maxwell equations on the cylinder at spatial infinity. Initial data for the…
A new class of conformal field theories is presented, where the background gravitational field is conformally flat. Conformally flat (CF) spacetimes enjoy conformal properties quite similar to the ones of flat spacetime. The conformal…
We provide a partially affirmative answer to the following question on robustness of polynomial stability with respect to sampling: ``Suppose that a continuous-time state-feedback controller achieves the polynomial stability of the…
Whether O(N)-invariant conformal field theory exists in five dimensions with its implication to higher-spin holography was much debated. We find an affirmative result on this question by utilizing conformal bootstrap approach. In solving…
We consider the application of logarithmic conformal field theory in finding solutions to the turbulent phases of 2-dimensional models of magnetohydrodynamics. These arise upon dimensional reduction of standard (infinite conductivity)…
A five-dimensional cosmological model including a single perfect fluid is studied in the framework of dynamical system analysis. All the critical points of the system with their stability properties are listed and some representative phase…
In this paper, we study diagonalizable hyperbolic systems in one space dimension. Based on a new gradient entropy estimate, we prove the global existence of a continuous solution, for large and nondecreasing initial data. Moreover, we show…
We rigorously show that a local spin system giving rise to a slow Hamiltonian dynamics is stable against generic, even time-dependent, local perturbations. The sum of these perturbations can cover a significant amount of the system's size.…
We study step-wise time approximations of non-linear hyperbolic initial value problems. The technique used here is a generalization of the minimizing movements method, using two time-scales: one for velocity, the other (potentially much…
In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be…
We present a scale-invariant theory, conformal gravity, which closely resembles the geometrodynamical formulation of general relativity (GR). While previous attempts to create scale-invariant theories of gravity have been based on Weyl's…
Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium…
Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…
When conformal field theories (CFTs) are perturbed by marginally relevant deformations, renormalization group (RG) flows ensue that can be studied with perturbative methods, at least as long as they remain close to the original CFT. In this…
The stability of the minisuperspace model of the early universe is studied by solving the Wheeler-DeWitt equation numerically. We consider a system of Einstein gravity with a scalar field. When we solve the Wheeler-DeWitt equation, we pick…
The constraint equations in Maxwell theory are investigated. In analogy with some recent results on the constraints of general relativity it is shown, regardless of the signature and dimension of the ambient space, that the "divergence of a…
The stability criteria for spatially flat homogeneous and isotropic cosmological dynamical system is investigated with the interaction of a scalar field endowed with a perfect fluid.In this paper, we depict the dynamical system perspective…
We study stable conditional measures for a certain equilibrium measure for hyperbolic endomorphisms, on basic sets with overlaps; we show that these conditional measures are geometric probabilities and measures of maximal stable dimension.…
Convergence to stationary solutions in fully nonlinear parabolic systems with general nonlinear boundary conditions is shown in situations where the set of stationary solutions creates a $C^2$-manifold of finite dimension which is normally…