Search results for "Calculus"

Electromagnetic Form Factors in the Time Like Domain

2008

The electromagnetic form factors in the time like domain can be accessed by the reaction p ¯ p → e + e − or its time inversed process. Despite a long standing experimental effort to determine these form factors, the precision in the knowledge of the ratio | G E | / | G M | ist still very poor in the time like domain. All world data suffer from limited statistics and therefore have used the hypothesis of | G E | = | G M | in order to extract a value for | G M | . While there is no theory argument for this hypothesis, recent JLAB data from polarisation transfer in elastic electron scattering show, that this hypothesis does not hold. Only a few data points allow the determination of | G E | / …

Biorthonormal-basis method for the vector description of optical-fiber modes

1998

This paper gives the theoretical basis for the development of real vector modal methods to describe optical-fiber modes. To this end, the vector wave equations, which determine the electromagnetic fields, are written in terms of a pair of linear, nonself-adjoint operators, whose eigenvectors satisfy biorthogonality relations. The key of our method is to obtain a matrix representation of the vector wave equations in a basis that is defined by the modes of an auxiliary system. Our proposed technique can be applied to fibers with any profile, even those with a complex refractive index. An example is discussed to illustrate our approach.

Deterministic and Random Vibration of Linear Systems with Singular Parameter Matrices and Fractional Derivative Terms

2021

Both time- and frequency-domain solution techniques are developed for determining the response of linear multi-degree-of-freedom systems exhibiting singular parameter matrices and endowed with derivative terms of noninteger orders modeled as rational numbers. This is done based on the Moore-Penrose matrix inverse theory, in conjunction with a state variable formulation and with a complex modal analysis treatment. It is worth noting that, for the class of systems considered herein, this treatment also yields decoupled governing equations, thus facilitating further their numerical solution. Next, a generalization of the standard frequency-domain input-output (excitation-response) relationship…

Vibration of damaged beams under a moving mass: theory and experimental validation

2004

Abstract A theoretical and experimental study of the response of a damaged Euler–Bernoulli beam traversed by a moving mass is presented. Damage is modelled through rotational springs whose compliance is evaluated using linear elastic fracture mechanics. The analytical solution is based on the series expansion of the unknown deflection in a basis of the beam eigenfunctions. The latter are calculated using the transfer matrix method, taking into account the effective mass distribution of the beam. The convective acceleration terms, often omitted in similar studies, are considered here for a correct evaluation of the beam–moving mass interaction force. The analytical solution is then validated…

Innovative modeling of tuned liquid column damper controlled structures

2016

In this paper a different formulation for the response of structural systems controlled by Tuned Liquid Column Damper (TLCD) devices is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it has been demonstrated that existing model may lead to inaccurate prediction of liquid motion, thus reflecting in a possible imprecise description of the structural response. For this reason the recently proposed fractional formulation introduced to model liquid displacements in TLCD devices, is here extended to deal with TLCD controlled structures under base excitations. As demonstrated through an extensive expe…

Single thermal zone balance solved by Transfer Function Method

2005

We present an algorithm that uses the Z-transform operator to face the problem of heat transmission in a single thermal zone composed by multilayered walls. The method is very flexible and could be adopted to calculate the transfer function coefficients able to simulate the thermal behaviour of a room in free floating. Knowing the transfer function coefficients, it is possible to simulate the dynamic profile of each inner surfaces temperature and furthermore of the inner air temperature. The proposed algorithm is fully described granting maximum clarity. The explicitness of all steps of the calculus make possible the definition of a method that is able to vary all of the calculus parameters…

1977

The thermal behavior of cycloalkanes (CH2)n with 12 ≤ n ≤ 84 prepared by metathesis reaction of cyclododecene, GPC separation of the oligomers, and hydrogenation has been investigated. The molar enthalpies of fusion being lower by a certain amount than those of the corresponding n-alkanes are a linear function of the chain length n. The entropy of fusion per CH2 increases with chain length in a not-linear mode (when plotted vs. 1/n). The melting points of the cycloalkanes are lower than those of the corresponding n-alkanes, the difference becoming smaller with increasing chain length.

Estimation of Uncertain Relations between Indeterminate Temporal Points

2000

Many database applications need to manage temporal information and sometimes to estimate relations between indeterminate temporal points. Indeterminacy means that we do not know exactly when a particular event happened. In this case, temporal points can be defined within some temporal intervals. Measurements of these intervals are not necessarily based on exactly synchronized clocks, and, therefore, possible measurement errors need to be taken into account when estimating the temporal relation between two indeterminate points. This paper presents an approach to calculate the probabilities of the basic relations (before, at the same time, and after) between any two indeterminate temporal poi…

Estrategias para la elaboración de modelos estadísticos de regresión

2011

Multivariable regression models are widely used in health science research, mainly for two purposes: prediction and effect estimation. Various strategies have been recommended when building a regression model: a) use the right statistical method that matches the structure of the data; b) ensure an appropriate sample size by limiting the number of variables according to the number of events; c) prevent or correct for model overfitting; d) be aware of the problems associated with automatic variable selection procedures (such as stepwise), and e) always assess the performance of the final model in regard to calibration and discrimination measures. If resources allow, validate the prediction mo…

Stochastic response determination of nonlinear oscillators with fractional derivatives elements via the Wiener path integral

2014

A novel approximate analytical technique for determining the non-stationary response probability density function (PDF) of randomly excited linear and nonlinear oscillators endowed with fractional derivatives elements is developed. Specifically, the concept of the Wiener path integral in conjunction with a variational formulation is utilized to derive an approximate closed form solution for the system response non-stationary PDF. Notably, the determination of the non-stationary response PDF is accomplished without the need to advance the solution in short time steps as it is required by the existing alternative numerical path integral solution schemes which rely on a discrete version of the…