Search results for "PROB"

(H,ρ)-induced dynamics and large time behaviors

2018

In some recent papers, the so called (H,ρ)-induced dynamics of a system S whose time evolution is deduced adopting an operatorial approach, borrowed in part from quantum mechanics, has been introduced. Here, H is the Hamiltonian for S, while ρ is a certain rule applied periodically (or not) on S. The analysis carried on throughout this paper shows that, replacing the Heisenberg dynamics with the (H,ρ)-induced one, we obtain a simple, and somehow natural, way to prove that some relevant dynamical variables of S may converge, for large t, to certain asymptotic values. This cannot be so, for finite dimensional systems, if no rule is considered. In this case, in fact, any Heisenberg dynamics im…

Work fluctuations in bosonic Josephson junctions

2016

We calculate the first two moments and full probability distribution of the work performed on a system of bosonic particles in a two-mode Bose-Hubbard Hamiltonian when the self-interaction term is varied instantaneously or with a finite-time ramp. In the instantaneous case, we show how the irreversible work scales differently depending on whether the system is driven to the Josephson or Fock regime of the bosonic Josephson junction. In the finite-time case, we use optimal control techniques to substantially decrease the irreversible work to negligible values. Our analysis can be implemented in present-day experiments with ultracold atoms and we show how to relate the work statistics to that…

A singular (p,q)-equation with convection and a locally defined perturbation

2021

Abstract We consider a parametric Dirichlet problem driven by the ( p , q ) -Laplacian and a reaction which is gradient dependent (convection) and the competing effects of two more terms, one a parametric singular term and a locally defined perturbation. We show that for all small values of the parameter the problem has a positive smooth solution.

A comprehensive probabilistic analysis of approximate SIR‐type epidemiological models via full randomized discrete‐time Markov chain formulation with…

2020

Spanish Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-P; Generalitat Valenciana, Grant/Award Number: APOSTD/2019/128; Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-P

A note on Jordan’s inequality

2020

Abstract In this paper we obtain some bounds in terms of polynomials for the function sin x x {{\sin x} \over x} , x ∈ [0, π].

Inverse problems for $p$-Laplace type equations under monotonicity assumptions

2016

We consider inverse problems for $p$-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying $\sigma_1 \geq \sigma_2$ and having the same nonlinear Dirichlet-to-Neumann map must be identical. The proof is based on a monotonicity inequality and the unique continuation principle for $p$-Laplace type equations. In higher dimensions, where unique continuation is not known, we obtain a similar result for conductivities close to constant.

Multiple Solutions for Fractional Boundary Value Problems

2018

Variational methods and critical point theorems are used to discuss existence and multiplicity of solutions for fractional boundary value problem where Riemann–Liouville fractional derivatives and Caputo fractional derivatives are used. Some conditions to determinate nonnegative solutions are presented. An example is given to illustrate our results.

Random Tensor Theory: Extending Random Matrix Theory to Mixtures of Random Product States

2012

We consider a problem in random matrix theory that is inspired by quantum information theory: determining the largest eigenvalue of a sum of p random product states in $${(\mathbb {C}^d)^{\otimes k}}$$ , where k and p/d k are fixed while d → ∞. When k = 1, the Marcenko-Pastur law determines (up to small corrections) not only the largest eigenvalue ( $${(1+\sqrt{p/d^k})^2}$$ ) but the smallest eigenvalue $${(\min(0,1-\sqrt{p/d^k})^2)}$$ and the spectral density in between. We use the method of moments to show that for k > 1 the largest eigenvalue is still approximately $${(1+\sqrt{p/d^k})^2}$$ and the spectral density approaches that of the Marcenko-Pastur law, generalizing the random matrix…

MonteCarlo Methods

2016

Análisis de la utilidad del algoritmo Gradient Boosting Machine (GBM) en la predicción del fracaso empresarial

2018

Este estudio, novedoso en cuanto a la utilizacion de la metodologia basada en la cultura de los algoritmos, prueba la capacidad de la tecnica ‘Gradient Boosting Machine’ (GBM) en la prediccion de l...