Uncertainty evaluation is an important task in almost all activities in the field of calibration and standard conformity assessment. Evaluation of uncertainty is a process in which the statistical characteristics (mainly the first and second moments,i. e. the average and the standard deviation) of the result of a measurement are estimated based on those of contributing factors. The result of this process is used to determine how appropriate a measurement is for a specific application. The measurement uncertainty influences the result of binary decisions made on conformity assessment, calibration and many other applications in the fields of jurisdiction, commerce, law enforcement or healthcare. Another important application of uncertainty evaluation, is to evaluate and validate mathematical or computer models simulating real world phenomena. For example, an uncertainty evaluation process can be utilized to quantify the error characteristics of a simulation software. Many techniques have been introduced and practiced for uncertainty evaluation. The applicability of each method relies upon the measurement model, possibility of performing repeated simulations and availability of statistical data. In this paper, we examine a celebrated uncertainty propagation method, namely,the polynomial chaos Expansion in the uncertainty evaluation of measurements described by a rigorous mathematical model. These measurement processes have been conventionally studied using sensitivity coefficients which can be calculated via partial derivatives. The two approaches are compared in an illustrative example.

Let G be a signed graph, where G = (V; E) is the underlying simple graph and  : E(G) → {± 1} is the sign function on E(G). In this paper, we obtain k-th signed spectral moments and k-th signed Laplacian spectral moments of a signed graph G , together with coe cients of their signed characteristic polynomial and signed Laplacian characteristic polynomial are calculated.

Recently Rather et al. [18] considered the Generalized polar derivative and studied the relative position of zeros of the Generalized polar derivative with respect to the zeros of the polynomial. In this paper, by taking into account the size of the constant term and the leading coefficient of the polynomial $P(z)$, we obtain some lower bound estimates for the Generalized polar derivative of certain polynomials, which refine and generalize various results due to Aziz and Rather, Malik, Tur\'{a}n, Dubinin, Govil and others.

Statistical methods are practical and unavoidable in analysis of physical and engineering results. Study of anufacturing errors and uncertainties in construction of radio frequency structures is one of cases which statistical quantities is used. In this paper, we quantify uncertainty in the cutoff frequency of a waveguide using the chaos polynomial expansion method. Different distributions for uncertainty in the waveguide width are considered. We then investigate the effect of the distributions on the waveguide cutoff frequency. Using statistical quantities, we determine the amount of acceptable error during the construction of the waveguide such that it does not affect the wavequide performance.

Multipactor(MP) is an unwanted phenomenon which is occurred in the radio frequency vacuum devices. Research to find a convenient method to lower the MP threshold or move it away from the operational range is an important key in the design of microwave components. In this regard, the accuracy of predicting the MP threshold is essential. In the simulation of MP, the secondary electron yield model is typically built in the commercial code; CST code. The accuracy of the results of MP simulation is mainly determined by the variation of secondary electron yield model. Therefore, in this paper, we calculate the effect of the variation of the secondary electron yield on the results of the MP simulation. For this purpose, the Generalized polynomial chaos method is employed using Python programming. This method is based on an orthogonal polynomial expansion. Here, MP in the rectangular waveguide, Cornell Electron Storage Ring input coupler, is studied.

Non-homogeneous mixture and unintentional flaws during the production stage have always given rise to uncertainties in the structural response of composite materials. This is intensified in the composites reinforced with natural fibers due to the natural origin of the fibers. In this study, an uncertainty analysis of the frequency response of a unidirectional flax/epoxy composite, as one of the common natural fiber composites, were carried out. The variability of the fiber elastic properties, fiber density, fiber volume fraction, and the misalignment of ply orientations were considered as the uncertainty sources. The uncertain input variables were divided into normal and uniform variables through the Anderson-Darling test, based on the various experimental data acquired from the literature. Due to the high number of uncertain input variables, a computationally efficient response surface approach based on the polynomial chaos expansion was adopted and modified accordingly to take the multi-type stochasticity of the input parameters into account. Moreover, the uncertainty analysis results obtained from the response surface method were validated by the direct Monte Carlo simulation, and the accuracy and efficiency of the surrogate model were demonstrated.

The fabrication tolerances for a coaxial to WG1800 waveguide coupler cause the variations of its electromagnetic parameter such as the working frequency. In order to investigate the effect of these uncertainty on the electromagnetic parameters, Monte Carlo method is usually used, which is very time consuming. In this paper, the Generalized polynomial chaos (gPC) method is first used for study the effect of variations of dimensions of a WR187 rectangular cavity on the resonant frequency. To assessment the accuracy of this method, these results are compared with the Monte Carlo and the theory methods. In the second step, the effect of variations of dimensions of a coaxial to WG1800 waveguide coupler on its frequency is investigated using the gPC Method.

This article deals with two new subclasses of analytic and bi-univalent functions in the open unit disk, which is defined  by applying subordination principle between analytic functions and the Generalized Bivariate Fibonacci polynomials. Bounds for coefficients $\left|a_{2}\right|$ and $\left|a_{3}\right|$ of functions in these subclasses are estimated in terms of Generalized Bivariate Fibonacci polynomials. In addition, the Fekete-Szeg\"{o} problem is handled for the members of these subclasses and several consequences and examples of the main results are presented. The results of article generalize some of the previously published papers in the literature.