We consider inverse problems in Hilbert spaces under correlated Gaussian noise, and use a Bayesian approach to find their regularized solution. focus on mildly ill-posed with fractional using novel wavelet-based vaguelette–vaguelette approach. It allows us apply sequence space methods without assuming that all operators are simultaneously diagonalizable. The results proved for more general base...

In classical mechanics, Galilean covariance and the principle of relativity are completely equivalent and hold for all possible dynamical processes. In contrast, in relativistic physics the situation is much more complex. It will be shown that Lorentz covariance and the principle of relativity are not completely equivalent. The reason is that the principle of relativity actually only holds for ...

This work presents a parametrized family of distances, namely the Alpha Procrustes on set symmetric, positive definite (SPD) matrices. The distances provide unified formulation encompassing both Bures-Wasserstein and Log-Euclidean between SPD We show that are Riemannian corresponding to metrics manifold matrices, which encompass Wasserstein metrics. is then generalized Hilbert-Schmidt operators...

Polynomials in differentiation operators are considered. Joint covariance with respect to Darboux transformations of a pair of such polynomials (Lax pair) as a function of one-field is studied. Methodically, the transforms of the coefficients are equalized to Frechèt differential (first term of the Taylor series on prolonged space) to establish the operator forms. In the commutative (Abelian) c...

The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry tr...

This article deals with the issue of reducing the spectral dimension of a hyperspectral image using principal component analysis (PCA). To perform this dimensionality reduction, we propose the addition of spatial information in order to improve the features that are extracted. Several approaches proposed to add spatial information are discussed in this article. They are based on mathematical mo...

In this paper we formulate new curvature functions on Sn via integral operators. For certain even orders, these curvature functions are equivalent to the classic curvature functions defined via differential operators, but not for all even orders. Existence result for antipodally symmetric prescribed curvature functions on Sn is obtained. As a corollary, the existence of a conformal metric for a...

The rate of H-convergence of truncations of stochastic infinite-dimensional systems du = [Au + B(u)]dt + G(u)dW, u(0, ·) = u0 ∈ H with nonrandom, local Lipschitz-continuous operators A,B and G acting on a separable Hilbert space H, where u = u(t, x) : [0, T ] × ID → IRd (ID ⊂ IRd) is studied. For this purpose, some new kind of monotonicity conditions on those operators and an existing H-series ...