Search results for "Mathematica"

M.J. (Susie) Bayarri

2021

Finding Prediction Limits for a Future Number of Failures in the Prescribed Time Interval under Parametric Uncertainty

2012

Computing prediction intervals is an important part of the forecasting process intended to indicate the likely uncertainty in point forecasts. Prediction intervals for future order statistics are widely used for reliability problems and other related problems. In this paper, we present an accurate procedure, called ‘within-sample prediction of order statistics', to obtain prediction limits for the number of failures that will be observed in a future inspection of a sample of units, based only on the results of the first in-service inspection of the same sample. The failure-time of such units is modeled with a two-parameter Weibull distribution indexed by scale and shape parameters β and δ, …

Solving two‐armed Bernoulli bandit problems using a Bayesian learning automaton

2010

PurposeThe two‐armed Bernoulli bandit (TABB) problem is a classical optimization problem where an agent sequentially pulls one of two arms attached to a gambling machine, with each pull resulting either in a reward or a penalty. The reward probabilities of each arm are unknown, and thus one must balance between exploiting existing knowledge about the arms, and obtaining new information. The purpose of this paper is to report research into a completely new family of solution schemes for the TABB problem: the Bayesian learning automaton (BLA) family.Design/methodology/approachAlthough computationally intractable in many cases, Bayesian methods provide a standard for optimal decision making. B…

Robust Transmit Beamforming for Underlay D2D Communications on Multiple Channels

2020

Underlay device-to-device (D2D) communications lead to improvement in spectral efficiency by simultaneously allowing direct communication between the users and the existing cellular transmission. However, most works in resource allocation for D2D communication have considered single antenna transmission and with a focus on perfect channel state information (CSI). This work formulates a robust transmit beamforming design problem for maximizing the aggregate rate of all D2D pairs and cellular users (CUs). Assuming complex Gaussian distributed CSI error, our formulation guarantees probabilistically a signal to interference plus noise ratio (SINR) above a specified threshold. In addition, we al…

Reliable Underlay D2D Communications over Multiple Transmit Antenna Framework

2020

Robust beamforming is an efficient technique to guarantee the desired receiver performance in the presence of erroneous channel state information (CSI). However, the application of robust beamforming in underlay device-to-device (D2D) communication still requires further investigation. In this paper, we investigate resource allocation problem for underlay D2D communications by considering multiple antennas at the base station (BS) and at the transmitters of D2D pairs. The proposed design problem aims at maximizing the aggregate rate of all D2D pairs and cellular users (CUs) in downlink spectrum. In addition, our objective is augmented to achieve a fair allocation of resources across the D2D…

Relay selection in FDD amplify-and-forward cooperative networks

2017

In this paper, the problems of relay selection and distributed beamforming are investigated for bi-directional dual-hop amplify-and-forward frequency-division duplex cooperative wireless networks. When using individual per-relay maximum transmission power constraint, it has been proven that the relay selection and beamforming optimization problem becomes NP hard and requires exhaustive search to find the optimal solution. Therefore, we propose a computationally affordable sub-optimal multiple relay selection and beamforming optimization scheme based on the l1 norm squared relaxation. The proposed scheme performs the selection for the two transmission directions, simultaneously, while aiming…

A bending theory of thermoelastic diffusion plates based on Green-Naghdi theory

2017

Abstract This article is concerned with bending plate theory for thermoelastic diffusion materials under Green-Naghdi theory. First, we present the basic equations which characterize the bending of thin thermoelastic diffusion plates for type II and III models. The theory allows for the effect of transverse shear deformation without any shear correction factor, and permits the propagation of waves at a finite speed without energy dissipation for type II model and with energy dissipation for type III model. By the semigroup theory of linear operators, we prove the well-posedness of the both models and the asymptotic behavior of the solutions of type III model. For unbounded plate of type III…

Integration of a Dirac comb and the Bernoulli polynomials

2016

Abstract For any positive integer n , we consider the ordinary differential equations of the form y ( n ) = 1 − Ш + F where Ш denotes the Dirac comb distribution and F is a piecewise- C ∞ periodic function with null average integral. We prove the existence and uniqueness of periodic solutions of maximal regularity. Above all, these solutions are given by means of finite explicit formulae involving a minimal number of Bernoulli polynomials. We generalize this approach to a larger class of differential equations for which the computation of periodic solutions is also sharp, finite and effective.

Trial Methods for Nonlinear Bernoulli Problem

1997

In this article we consider a free boundary problem which is related to formation of waves on a fluid surface (for example the ship waves). We study the possibility to construct ‘trial’ methods where one solves a sequence of standard flow problems formulated in different geometries that converge to the final free boundary. Furthermore, we use the shape optimization techniques to analyse the convergence of the fixed point iteration near a fixed point. For stream function case we conclude that the fast convergence can be obtained by using non-standard boundary conditions and we present numerical results to confirm the analysis.

Equations-of-motion approach to the spin-12Ising model on the Bethe lattice

2006

We exactly solve the ferromagnetic spin- 1/2 Ising model on the Bethe lattice in the presence of an external magnetic field by means of the equations of motion method within the Green's function formalism. In particular, such an approach is applied to an isomorphic model of localized Fermi particles interacting via an intersite Coulomb interaction. A complete set of eigenoperators is found together with the corresponding eigenvalues. The Green's functions and the correlation functions are written in terms of a finite set of parameters to be self-consistently determined. A procedure is developed that allows us to exactly fix the unknown parameters in the case of a Bethe lattice with any coor…