In this paper, we propose a new residual analysis method using FOURIER SERIES TRANSFORM into fuzzy time SERIES model for improving the forecast- ing performance. This hybrid model takes advantage of the high predictable power of fuzzy time SERIES model and FOURIER SERIES TRANSFORM to t the esti- mated residuals into frequency spectra, select the low-frequency terms, lter out high-frequency terms, and then have well forecasting performance. Two numerical examples are given to show that our proposed model can be applied with the best forecasting performance than the other models.

Introduction: Clinical performance of light cured resin composites is related to their degree of polymerization. The purpose of this study was to compare the degree of conversion of packable and hybrid composites by FTIR (FOURIER TRANSFORM Infrared Spectroscopy).Materials & Methods: In this experimental study, 40 composite disks were prepared in two groups from Z250 and P60 composites. Each group was divided into four subgroups (2mm thickness cured with QTH unit, 2mm thickness cured with LED unit, 5mm thickness cured with QTH unit, and 5mm thickness cured with LED unit). Then samples were evaluated by FTIR to determine the degree of conversion (DC). Data were analyzed by Kolmogorov-Smirnov and three way ANOVA.Results: There was not a significant difference among the DC of the materials tested. LED significantly increased the degree of conversion of materials tested (P<0.001). DC values were significantly greater in 2mm diameter samples vs 5mm ones (P<0.001).Conclusion: The use of incremental technique in deep cavities restored with these composites is suggested. Also using LED is advised for curing composites because of a better result.

In this research, active control of vibrations of a simply supported rectangular plate is investigated by a new method. At first, differential equation of motion of a plate with piezoelectric patches is developed by means of classical plate theory in order to apply in this method, and a local function is used for applying the mass and stiffness effects. Then, natural frequencies and modeshapes of the plate with patches are obtained using FOURIER SERIES. A PID controller is designed and closed loop poles are calculated. Forced response of the system and mode shapes will be calculated using Laplace TRANSFORM. The effect of PID on active control of plate is investigated simply for the first time. Some examples are presented to illustrate the validity of this method.

In this manuscript, we review fractal calculus and the analogues of both local FOURIER TRANSFORM with its related properties and FOURIER convolution theorem are proposed with proofs in fractal calculus. The fractal Dirac delta with its derivative and the fractal FOURIER TRANSFORM of the Dirac delta is also defined. In addition, some important applications of the local fractal FOURIER TRANSFORM are presented in this paper such as the fractal electric current in a simple circuit, the fractal second order ordinary differential equation, and the fractal Bernoulli-Euler beam equation. All discussed applications are closely related to the fact that, in fractal calculus, a useful local fractal derivative is a generalized local derivative in the standard calculus sense. In addition, a comparative analysis is also carried out to explain the benefits of this fractal calculus parameter on the basis of the additional alpha parameter, which is the dimension of the fractal set, such that when α,= 1, we obtain the same results in the standard calculus.

Digital holographic Microscopy is a non-destructive and label-free method that provides quantitative phase information in biological and industrial applications. High coherence light sources, such as lasers, are commonly used in digital holographic microscopes. Parasitic -interference fringes and speckle noise in high-coherence sources as well as complex configurations reduce the accuracy of the phase measurements. In this paper, a common-path and low-coherence digital holographic microscopy with a FOURIER TRANSFORM-based spectroscopy is introduced. The low-coherence source used here is an LED and the common path configuration is used based on splitting the wavefront by Fresnel biprism. Reconstruction of the hologram is analyzed using the FOURIER method. In addition, The spectral line shape of the LED is obtained simultaneously with the FOURIER TRANSFORM of the visibility of the recorded fringes. The ability to simultaneously perform quantitative phase imaging and FOURIER TRANSFORM spectroscopy makes this system unique in the real-time study of biological samples in micron size.