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By using the central limit theorem, it is possible to consider the Fourier’s transform of a stochastic process with independent increments as a Gaussian random variable of which the mathematical expectation and the variance are respectively integrals of the mean and the variance of this process. One can then use this result to analyze the statistical properties of linear feedback systems in the frequency domain, that is to say in terms of transfer functions. The advantage of this approach is that one can deal with linear systems subject to squared white noises, in a very simple manner.

Paper aims to determinate caking paper manuscript cause through studying of the manuscript components, bio-deterioration and physio-chemical deterioration factor. It will facilitate manuscripts and paper conservators to understand paper blocking and caking phenomenon.

The manuscript condition has been diagnosed by focusing on adhesion and fossilization regions. To achieve this, some methods of analysis and examination were used, such as visual examination, digital microscopy and scanning electron microscope were used to studying surface changes. X-ray diffraction and Fourier transform infrared microscopy were used to determinate of cellulose crystallinity, ink composition and identify the binding medium.

The results revealed the use of cotton pulp, and calcium carbonate was among the fillers that were used to improve the properties of paper. The crystallization of cellulose was lower in the first and last papers than the papers located in the heart of the manuscript. The most important reasons that led to the papers caking was the presence of fungi A. niger, Cladosporium sp, Chaetomium sp, by secreting some enzymes in combination with some other factors such as difference variation in temperature and moisture.

All deterioration factors participate with each other until rule the damage circle of the papers because one factor alone cannot stick the papers. It was inferred from the examinations and analyzes that were conducted for the samples.

A new method of spectral analysis has been proposed for non‐stationary harmonic analysis of corrosion processes. The current of a model circuit has been considered which would simulate a first‐order electrode reaction proceeding in conditions of a linearly changing electrode potential with a superimposed sinusoid signal. It has been shown that the Fourier transformation approach does not reflect the amplitude changes of harmonic components as a function of constant potential. In addition, it has been shown mathematically that application of Gabor transformation in spectral analysis is a means of obtaining the correct frequency components. The Gabor transform correctly reflects amplitude changes of harmonic components as a function of potential. Digital analysis of current changes by Gabor transformation unequivocally confirmed the usability of this method for harmonic analysis of corrosion processes.

This paper presents a modification of the classical boundary integral equation method (BIEM) for two‐dimensional potential boundary‐value problem. The proposed modification consists in describing the boundary geometry by means of Hermite curves. As a result of this analytical modification of the boundary integral equation (BIE), a new parametric integral equation system (PIES) is obtained. The kernels of these equations include the geometry of the boundary. This new PIES is no longer defined on the boundary, as in the case of the BIE, but on the straight line for any given domain. The solution of the new PIES does not require boundary discretization as it can be reduced merely to an approximation of boundary functions. To solve this PIES a pseudospectral method has been proposed and the results obtained compared with exact solutions.

Describes a passive, open‐path infrared gas detector that utilises thermal background radiation as the source. Explains its mode of operation, provides a specification and considers its route to market.

Static converters generate current harmonics in power grids. For numerous studies, analytical frequency modeling is preferred to carry out their harmonic modeling in the context of sizing by optimization. However, a design by optimization has to consider other constraints, e.g. modeling constraints and operating constraints. In this way, this paper aims to focus on applying an analytical frequency modeling on the sizing by optimization of an aircraft electrical power channel.

The paper aims to size a multiphysical system by optimization. In this way, the sizing of an aircraft electrical power channel by optimization has been carried out. The models of all the channel components are analytical. Specifically, the frequency model of the power electronics is based on Tran et al. (2016) and is made of equalities and inequalities. Due to this modeling choice, the optimization satisfies hundreds of constraints, such as modeling constraints and static converter operating constraints. Furthermore, transient constraints are only verified after optimization.

The difficulty is the modeling of the system by taking into account nonlinear implicit equations having several solutions. A solution is the addition of inequality constraints to the model to guide the implicit solving. Furthermore, this greatly helps the optimization algorithm to find the good operating mode of the static converter, at steady state. This aspect is indispensable to validate the sizing model.

The number of the configurations per operating period of the static converters is defined a priori and limited.

The analytical model for the sizing is formulated as a constrained optimization problem. Its solving and the sizing by optimization are carried out by the same optimization algorithm.

Describes a hybrid formulation solution based on variational techniques, where unknown functions are combined with a set of Fourier trigonometric expansions. The unknown functions refer to the toroidal shell distortion in the longitudinal direction when the shell is submitted to generalised in‐plane forces in the linear‐elastic stress field. This set of functions is solved from a system of differential equations, having calculated the eigenvalues and corresponding eigenvectors in the complex field from the system equations matrix. For this purpose the MAPLE^® mathematical solver was used. This module led to an analytical solution, which is exact for each Fourier term used in the global solution. The final results agree very well with finite element method or other solutions obtained using a total expansion of trigonometric functions in the longitudinal and meridional directions.

The theory which is addressed in this paper is that we should not be surprised to come across fractals in the analysis of some dynamic systems involving human factors. Moreover, in substance, fractals in human behaviour is acceptable. For the convenience of the reader a primary background to some models of fractional Brownian motions which can be found in the literature is given, and then the main features of the complex‐valued model, via a random walk in the complex plane, recently introduced by the author are recalled. The practical meaning of the model is exhibited. The parallel of the central limit theorem here is Levy’s stability. If it is supposed that human decision‐makers work via an observation process which combines the Heisenberg principle and a quantization principle in the measurement, then fractal dynamics appears to be quite in order. The relation with the theory of relative information is exhibited. The conjecture is then the following: could this model explain why fractals appear in finance, for instance?

Teaches by example the application of finite element templates in constructing high performance elements. The example discusses the improvement of the mass and geometric stiffness matrices of a Bernoulli‐Euler plane beam. This process interweaves classical techniques (Fourier analysis and weighted orthogonal polynomials) with newer tools (finite element templates and computer algebra systems). Templates are parameterized algebraic forms that uniquely characterize an element population by a “genetic signature” defined by the set of free parameters. Specific elements are obtained by assigning numeric values to the parameters. This freedom of choice can be used to design “custom” elements. For this example weighted orthogonal polynomials are used to construct templates for the beam material stiffness, geometric stiffness and mass matrices. Fourier analysis carried out through symbolic computation searches for template signatures of mass and geometric stiffness that deliver matrices with desirable properties when used in conjunction with the well‐known Hermitian beam material stiffness. For mass‐stiffness combinations, three objectives are noted: high accuracy for vibration analysis, wide separation of acoustic and optical branches, and low sensitivity to mesh distortion and boundary conditions. Only the first objective is examined in detail.

In the present paper, the three-phase-lag (3PHL) model, Green-Naghdi theory without energy dissipation (G-N II) and Green-Naghdi theory with energy dissipation (G-N III) are used to study the influence of the gravity field on a two-temperature fiber-reinforced thermoelastic medium.

The analytical expressions for the displacement components, the force stresses, the thermodynamic temperature and the conductive temperature are obtained in the physical domain by using normal mode analysis.

The variations of the considered variables with the horizontal distance are illustrated graphically. Some comparisons of the thermo-physical quantities are shown in the figures to study the effect of the gravity, the two-temperature parameter and the reinforcement. Also, the effect of time on the physical fields is observed.

To the best of the author’s knowledge, this model is a novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium, and gravity plays an important role in the wave propagation of the field quantities. It explains that there are significant differences in the field quantities under the G-N II theory, the G-N III theory and the 3PHL model because of the phase-lag of temperature gradient and the phase-lag of heat flux.