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.

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.