In this paper, we consider new and general models for imperfect sources of randomness, and show how to obtain quasi-random sequences from such sources. Intuitively, quasi-random sequences are sequences of almost unbiased elements over a finite set. Our model is as follows: Let A be a finite set whose number of elements is a power of 2. Let 1/|A| ≤ δ < 1 be a constant. The source outputs an elem...

Abstract We present an extension of the projection method proposed by Challis et al. (Int J Solids Struct 45(14–15):4130–4146, 2008) for constrained level set-based topology optimisation that harnesses Hilbertian velocity extension-regularisation framework. Our chooses a normal set function as linear combination (1) orthogonal operator applied to extended objective shape sensitivity and (2) wei...

Let \(\mathcal {H}\) be a complex Hilbert space and let A positive operator on {H}\). We obtain new bounds for the A-numerical radius of operators in semi-Hilbertian {B}_A(\mathcal {H})\) that generalize improve existing ones. Further, we estimate an upper bound \(\mathbb {A}\)-operator seminorm \(2\times 2\) matrices, where {A}=\text{ diag }(A,A)\). The obtained here generalizes earlier relate...

It is shown that localization of eigenfunctions in the Wigner band random matrix model with increasing diagonal elements can be related to localization in a band random matrix model with random diagonal elements. The relation is obtained by making use of a result of a generalization of Brillouin-Wigner perturbation theory, which shows that reduced Hamiltonian matrices with relatively small dime...

We give an account on Otto’s geometrical heuristics for realizing, on a compact Riemannian manifold M , the L Wasserstein distance restricted to smooth positive probability measures, as a Riemannian distance. The Hilbertian metric discovered by Otto is obtained as the base metric of a Riemannian submersion with total space, the group of diffeomorphisms of M equipped with the Arnol’d metric, and...

We give model theoretic criteria for the existence of∃∀ and∀∃formulas in the ring language to define uniformly the valuation rings O of models (K,O) of an elementary theory Σ of henselian valued fields. As one of the applications we obtain the existence of an ∃∀-formula defining uniformly the valuation rings O of valued henselian fields (K,O) whose residue class field k is finite, pseudofinite,...

Schizophrenic patients suffer from hallucination which its causality is not yet fully understood. This paper attempts to approach this mystery from the perspective of quantum mechanical theories. A novel approach has been adopted to demonstrate the hallucination as a time evolution of percepts basis states in the Hilbertian consciousness which are desynchronised from the time in real world. The...

In this article we give enhancements of several functional techniques to forecast sulfur dioxide levels near a power plant. The data are considered as a time series of curves. Assuming a lag-one dependence, the predictions are computed using the functional kernel (with local bandwith) and the linear autoregressive Hilbertian model. We carry out the estimation with a so-called “historical matrix...