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 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.

The performance of Orthogonal Frequency Division Multiple Access (OFDMA) system degrades significantly in doubly dispersive channels. This is due to the fact that exponential sub-carriers do not match the singular functions of this type of channels. To solve this problem, we develop a system whose sub-carriers are chirp functions. This is equivalent to exploiting Fractional Fourier Transform (FrFT) instead of Fourier Transform (FT) in the structure of the aforementioned transmission scheme. We name the new system FrFT-OFDMA. The optimal angle of fractional Fourier Transform for each user depends on its channel parameters. Thus, the angles of Transform for different users are not necessarily identical. This destroys the orthogonality of users and generates Multi-User Interference (MUI). By analyzing MUI, we introduce quasi-orthogonality conditions where interference is negligible despite different angles of Transform. For non-orthogonal users, we propose a method to mitigate MUI. We present the efficiency of this method through comparative performance evaluation of the conventional system based on FT and the new system based on FrFT. We show that our proposed transmission scheme outperforms the traditional OFDMA system significantly in doubly dispersive channels and channels impaired by frequency offset.

This paper presents the results of the Identifying the binder and pigments used in the mural paintings in Rahim Abad Historic Garden and Mansion in Birjand. Birjand was one of the most important governmental strategic cities in Qajar era (1789–1925A.D) and an important branch area of ancient Silk Road which connected India to Europe. Though many monuments, especially historical gardens remained in Birjand. Rahim Abad Historic Garden and Mansion was the resident of Qaenat ruler to consider politics, businesses and accommodating foreign guests. The most important part in the Architectural decoration of Rahim Abad Historic Garden and Mansion is mirror-encrusted decorations, stucco and mural paintings. Due to diversity in building decorations and multiplicity of constructing periods in Rahim Abad Historic Garden and Mansion, identification of pigments used in mural paintings is a great evidential assistance in extracting chronological information. scanning electron microscopy in combination with energy dispersive X-ray microanalysis (SEM-EDX)، Fourier Transform infrared spectroscopy (FTIR), Polarized light microscopy (PLM), X-ray diffraction (XRD) and handheld X-Ray Florescence (micro-XRF) were used for the characterization of the compound and structure of the paint layers of samples taken from mural paintings. Accord This paper presents the results of the identification of the binder and pigments used in the mural paintings in Rahim Abad Historic Garden and Mansion in Birjand. Birjand was one of the most important governmental strategic cities in Qajar era (1789-1925 A.D.), and an important branch area of ancient Silk Road, which connected India to Europe. Many monuments, especially historical gardens have been remained in Birjand. Rahim Abad Historic Garden and Mansion is one of this gardens, which in the period of Amir Ismail Khan Shaukat Molk, was the location of Qaenat ruler to consider politics, businesses and accommodating foreign guests. The most important part in the Architectural decoration of Rahim Abad Historic Garden and Mansion is mirror-encrusted decorations, stucco and wall paintings. Due to diversity in building decorations and multiplicity of constructing periods in Rahim Abad Historic Garden and Mansion, identification of pigments and materials used in wall paintings is of a great evidential assistance in extracting chronological information. Wall painting is one of the Iran arts that based on the signs of old paint can be pursued to pre-history. One of the most important issues in the study of historical paintings, especially wall painting, is the identification of the nature of paintings used to decorate the walls. Pigments identification is also important not only from the perspective of archeology, but also in terms of the history of art and knowledge of degradation processes and the development of monument conservation strategies is also important. Scanning electron microscopy in combination with energy dispersive X-ray microanalysis (SEM-EDX) ،Fourier Transform infrared spectroscopy (FTIR), Polarized light microscopy (PLM), X-ray diffraction (XRD) and handheld X-Ray Florescence spectroscopy (micro-XRF) were used for the characterization of the compound and structure of the paint layers of samples taken from mural paintings. In fact, chemical and physical analysis, provides useful information from spectrum of pigments in a region and recognizing color preparation techniques and its application. Also before proceeding restoration, the accurate information from the chemical composition of materials used in object is required. According to the obtained results, mixture of gypsum and calcite as a substrate layer, red lead (Pb3O4), mixture of malachite (CuCO3.Cu(OH)2) and Prussian blue)Fe4(Fe[CN]6)3), ultramarine (Na8-10Al6Si6O24S2-4), and mixture of two metals, copper and zinc, as the pigments were used. Also, an adhesive like animal glue was that of common materials in Qajar period, as well as used to substrate color. Such pigments are further evidence that the mural painting of this monument are from the late Qajar. Oil was used as binder or varnish in this painting and there is in all of the samples. One of the interesting points of the materials used in the paintings was the application of a mixture of pigments to create colors with different tonalities. Another point is the use of imported pigments such as Prussian blue, along with other traditional pigments that were common in of that era. Also, the microscopic examination of golden color indicates the presence of chalcopyrite in this pigment. These compounds exist due to the corrosion of copper metal in golden color, and usually appears in golden colors obtained from two metals alloy, such as copper and zinc, by creating green color in a golden background.ing to the obtained results, mixture of gypsum and calcite as a preparatory layer, red lead (Pb3O4), mixture of malachite (CuCO3.Cu(OH)2) and Prussian blue ) Fe4(Fe[CN]6)3), ultramarine (Na8-10Al6Si6O24S2-4), and mixture of two metals, copper and zinc, as pigments were used. Also, an adhesive like animal glue was that of common materials in Qajar period, as well as used to substrate color. Such pigments are further evidence that the Mural Painting of this Monument are from the late Qajar. Oil was used as binder or varnish in this painting and there is in all of colors.

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.