Electrochemical (EC) data, in particular, when the magnitude of current is in range of nano and pico ampere, suffers from existence of environmental noises. In this work, a new modified SW voltammetric method for determination of Se(IV) is presented. Where signal-to-noise ratio has significantly (near to 620 times) increased by application of discrete FAST FOURIER Formation (FFT) method, background subtraction and two-dimensional integration of the electrode response over a selected potential range and time window. Also, the detection method can be used for direct and indirect determination of Se(IV) ions by measuring the changes in SW voltammogram (or admittance) of an gold ultramicroelectrode (in 0.05 M H3PO4 solution) caused by redox reaction or just adsorption of the Se(IV) ion on the electrode surface. In indirect detection, the analyte signal was calculated based on admittance changes related to inhibition of oxygen adsorption (by adsorbed of Se(IV) ions). Direct measurement was carried out in on an anodic stripping mode, after accumulation of the analytes on the electrode surface for 50 to 100 ms. In method, removal of oxygen from the studied solutions is not required. Calibration plots are given for solutions containing 10-8–10-7 M and 10-7–10-6 M of Se(IV) Se4+. The limit of detection is calculated to be 2.5 ´10-9 M. The relative standard deviation at concentration 3´10-8 M is 6 % for 5 reported measurements

Herein, FAST FOURIER TRANSFORMation square-wave VOLTAMMETRY (FFT-SWV) as a novel electrochemical determination technique was used to investigate the electrochemical behavior and determination of Riboflavin at the surface of a nanocomposite modified carbon paste electrode. The carbon paste electrode was modified by nanocomposite containing Samarium oxide (Sm2O3)/reduced graphene oxide (RGO) (2:1) to improve detection sensitivity of Riboflavin under optimal experimental conditions. Furthermore, the signal-to-noise ratio was significantly increased by application of discrete FAST FOURIER TRANSFORMation analysis, background subtraction and two-dimensional integration of the electrode response over the selected potential range and the time window. Obtained CYCLIC voltammograms demonstrated a diffusion-controlled reversible electron transfer reaction for Riboflavin in phosphate buffer solution (pH=7.2). The peak potential values were pH-dependent, involving the same numbers of protons and electrons. To obtain the maximum sensitivity, some effective parameters such as scan rate (10 mV/s), accumulation time (0.2 s) and potential (+400 mV), frequency (1420 Hz) and amplitude (20 mV) were optimized. As a result, determination of Riboflavin using FFT-SWV showed a linear range of response from 10 to 400 nM (R2=0.9993), with limit of detection of 0.86 nM. An acceptable recovery percent was also obtained for Riboflavin in human plasma samples as criteria of measurement applicability of the proposed modified electrode.

Seismic data jitter sampling is one of the new seismic data acquisition methods developed recently to reduce seismic data acquisition costs. In this method, the number of seismic sources and receivers is less than the number determined by the Nyquist-Shannon Theorem. The Nyquist-Shannon theorem states that the sampling rate of a digital signal must be more than twice the bandwidth of the signal to avoid aliasing. To circumvent aliasing, the jitter sampling method uses compressed sensing technique. This technique is based on the principle that the sparsity of a signal can be used to recover it from fewer samples than required by the Nyquist–Shannon sampling theorem in two conditions. First, the signal needs to be sparse in some domains, like the frequency domain. Second, the signal must be randomly sampled in the main domain, like the time or space domain. In this type of data sampling method, the randomness of sampling appears as a white noise in the TRANSFORM domain. Therefore, it can be said that the compressed sensing method plays the role of a denoising technique in the TRANSFORMation domain. In conventional compressed sensing methods, it is assumed that the data is undersampled on a regular grid. FOURIER TRANSFORM, Curvelet TRANSFORM, and wavelet TRANSFORM are some of the TRANSFORMs that are used in these types of compressed sensing methods. On the other hand, sometimes in real seismic data acquisition, the shots and receivers cannot have a regular geometry due to the natural and civil obstacles. Therefore, sampling on a regular grid is not always possible in seismic data acquisition. This means that using the conventional compressed sensing method for seismic data regularization doesn’t seem to be an appropriate choice. To address this issue, some geophysicists have proposed to use discrete FOURIER TRANSFORM as the data TRANSFORMation technique in compressed sensing. Discrete FOURIER TRANSFORM does not require sampling on a uniquespace grid. However, this TRANSFORM is slow and needs a huge number of computations. In this paper, we used the non-uniquespace FAST FOURIER TRANSFORM instead of the discrete FOURIER TRANSFORM. The method doesn’t need a sampling scheme on a regular grid and is much FASTer than discrete FOURIER TRANSFORM. This method is based on the conventional FAST FOURIER TRANSFORM and an interpolation technique. The method can be applied on multidimensional pre-stack seismic data. Therefore, it can consider correlation between traces in different dimensions while interpolating the lost traces. On the other hand, a problem with fully random sampling is that there is no control over the locations of the samples on a signal. This means that, if a signal is sampled randomly, some parts of the signal may be oversampled while the other parts may not be sampled with enough points. This phenomenon may have a bad impact on the regularized result if the signal changes erratically. To avoid this situation, in this paper, a sampling protocol will be introduced to improve the control over random sampling. In this protocol, the samples are picked randomly in small windows over the length of the signal. In this sampling technique, the size of the windows and the number of random samples can be controlled easily. Moreover, the sampling scheme doesn’t need to be on a regular grid and the samples can be chosen anywhere along the signal. A set of 2D and 3D synthetic and 2D real seismic data were used to examine the performance of the proposed method. The results show that the method can regularize irregular seismic data properly.

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 work a novel method for the determination of tamoxifen in flow-injection systems has been developed. The FAST FOURIER TRANSFORM continuous CYCLIC VOLTAMMETRY (FFTCV) at gold microelectrode in flowing solution system was used for determination of tamoxifen in its pharmaceutical formulations. The developed technique is very simple, precise, accurate, time saving and economical, compared to all of the previously reported methods. The effects of various parameters on the sensitivity of the method were investigated. The best performance was obtained with the pH value of 2, scan rate value of 50V s-1, accumulation potential of 0 mV and accumulation time of 0.5s.  The proposed method has some advantages over other reported methods such as, no need for the removal of oxygen from the test solution, a picomolar detection limit, and finally the method is FAST enough for the determination of any such compound, in a wide variety of chromatographic methods. The method was linear over the concentration range of 1875-78000 pg/ml (r=0.9980) with a limit of detection and quantitation 37.1 and 200 pg/ml, respectively. We used this method to determination of tamoxifen in tablets.

Purpose: A new code based on Helmholtz decomposition is presented to separate longitudinal (pressure) and transverse (shear) components of a mixed wave field. This algorithm will help isolate shear or pressure components of an elastic wave to further concentrate on each specific wave and its physical characteristics, particularly in medical imaging instrument development and image processing techniques. Materials and Methods: Using the combination of FOURIER TRANSFORM and Helmholtz decomposition, first, the mathematical basis of the work is prepared. After reaching a usable formula, this basis is embedded in the Code written in MATLAB program. Then, various test data containing shear and pressure waves were created and fed to the Code to evaluate its ability to decompose the displacements into the shear and pressure waves. Results: This new algorithm successfully isolated the transverse and longitudinal wavefront of the mixed wavefield. The Code demonstrated 100% accuracy for separating the shear wave and more than 99% for the pressure wave. Moreover, the background noise was kept under 0. 03% in every step. Conclusion: The results show that using Helmholtz decomposition in FOURIER space on 3D data can help decompose a displacement field into its irrotational and solenoidal components with high accuracy. A weak dependency on wave thickness and contrast was observed, but the algorithm's accuracy never fell below 99%.

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.