Search results for "Bernoulli"

A matrix-valued Bernoulli distribution

2006

AbstractMatrix-valued distributions are used in continuous multivariate analysis to model sample data matrices of continuous measurements; their use seems to be neglected for binary, or more generally categorical, data. In this paper we propose a matrix-valued Bernoulli distribution, based on the log-linear representation introduced by Cox [The analysis of multivariate binary data, Appl. Statist. 21 (1972) 113–120] for the Multivariate Bernoulli distribution with correlated components.

Non-fragile H  ∞  control for switched stochastic delay systems with application to water quality process

2013

SUMMARY In this paper, the problem of non-fragile observer-based H ∞  control for discrete-time switched delay systems is investigated. Both data missing and time delays are taken into account in the links from sensors to observers and from controllers to actuators. Because data missing satisfies the Bernoulli distribution, such problem is transformed into an H ∞  control problem for stochastic switched delay systems. Average dwell time approach is used to obtain sufficient conditions on the solvability of such problems. A numerical example and a real example for water quality control are provided to illustrate the effectiveness and potential applications of the proposed techniques. Copyrig…

Fractional visco-elastic Timoshenko beam from elastic Euler-Bernoulli beam

2014

The Euler–Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of the stress field or deflections of the elastic beam based on this theory. In contrast, Timoshenko theory is not so much used by engineers. However, in some cases, Euler–Bernoulli theory, which neglects the effect of transversal shear deformation, yields unacceptable results. For instance, when dealing with visco-elastic behavior, shear deformations play a fundamental role. Recent studies on the response evaluation of a visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads have been stressed that for better capturing of the visco-elastic behavior, a …

Stochastic dynamic analysis of structures with fractional viscoelastic constitutive laws

The main purpose of this thesis is to provide a new way to correctly perform stochastic analysis of structures with viscoelastic constitutive law. The reason for this kind of problem relates the fact that structures with viscoelastic materials are built in many areas of mechanical, civil and aerospace engineering. To perform this kind of stochastic analysis there are two fundamental problems. That is, the mechanical description of the viscoelastic phenomenon, and the correct representation of the external loads. Both of these problems are addressed and solved by the proposed modeling that involves some advanced mathematical tools. The reason to describe materials as viscoelastic is given by…

Compressed Drinfeld associators

2004

Drinfeld associator is a key tool in computing the Kontsevich integral of knots. A Drinfeld associator is a series in two non-commuting variables, satisfying highly complicated algebraic equations - hexagon and pentagon. The logarithm of a Drinfeld associator lives in the Lie algbera L generated by the symbols a,b,c modulo [a,b]=[b,c]=[c,a]. The main result is a description of compressed associators that satisfy the compressed pentagon and hexagon in the quotient L/[[L,L],[L,L]]. The key ingredient is an explicit form of Campbell-Baker-Hausdorff formula in the case when all commutators commute.

On the spatial spread of a pattern

1980

A simple process is considered for the spread of a pattern in a spatially distributed population. Expressions are given for the stochastic means, variances and covariances. Central limit theorems are obtained for the number of individuals that have the pattern, and the time needed for the pattern to reach the n-th subpopulation.

Stochastic response of fractional visco-elastic beams

2012

Reaalianalyyttistä lukuteoriaa

2016

Tämän tutkielman tarkoituksena on tutustuttaa lukija Bernoullin polynomeihin, Γ-funktioon ja lukuteoreettisiin Mertensin lauseisiin. Näiden lisäksi tutkitaan erästä lukuteoreettista tuloa, ja esitellään tähän tuloon liittyviä tiettävästi uusia tuloksia. Bernoullin polynomien avulla todistetaan erityisesti Euler-Maclaurinin lause, joka kertoo erilaisten summien ja integraalien välisestä yhteydestä. Γ-funktion avulla taas todistetaan Stirlingin kaava, joka antaa hyvän approksimaation kertoman n! kasvu- nopeudesta. Mertensin lauseista ensimmäinen kertoo, miten nopeasti lukua n pie- nempien alkulukujen käänteislukujen 1/p summa hajaantuu, kun kasvatetaan lukua n. Toinen Mertensin lause kertoo, …

Scala di efflusso del misuratore a cilindri in canale rettangolare a fondo orizzontale

2015

Disporre di un semplice strumento di misura della portata idrica è fondamentale nelle applicazioni di campo, soprattutto quando il sito di misura risulta essere non facilmente raggiungibile come, ad esempio, nelle stazioni di misura del trasporto solido e di erosione idrica. Il misuratore a cilindri, costituito da due semicilindri ad asse verticale che ostruiscono parzialmente il deflusso liquido, è uno strumento adatto a questo scopo. Nella memoria è presentata una relazione di derivazione teorica della scala delle portate del misuratore a cilindri. In particolare la relazione proposta ha origine dall’equazione di Bernoulli applicata tra la sezione a monte dello strumento, dove si misura i…

Demo 38. Soplando sobre papel y pelota de ping-pong (Bernoulli I)

2013

Objetivo: Demostrar que la presión disminuye en un fluido en movimiento.