High spatial and temporal variability of the tropospheric wet refractivity index, makes it difficult to present an accurate model for this variable. Up to now, Radiosonde stations data have been used for monitoring atmosphere parameters. Furthermore, because of the sparse distribution of radiosonde stations to monitor the lower levels of the atmosphere, the numerical weather models do not have enough accuracies for atmospheric parameters. Using the GPS tropospheric delay measurements and tomography approaches, the wet refractivity index can be estimated. In this research, three-dimensional and four-dimensional basis-function tomography is used to demonstrate the distribution of wet refractivity index of the troposphere. In this model, SPHERICAL cap HARMONICS are used for the horizontal distribution of the wet refractivity index, and empirical orthogonal functions are used for the vertical distribution of the index. In addition, temporal changes are considered by correlating the unknown coefficients using fourier series. The region of study is in the west California State, and the wet refractivity index is retrieved from the wet tropospheric delay measurements. To validate the results, radiosonde profiles were compared to the tomographically retrieved profiles. The results show that wet refractivity indices can be retrieved using functional models with RMSE about 2. 4 ppm till 3. 9 in the four-dimensional method. The comparisons show that the four-dimensional retrieved profiles show improvement up to 34 and 42 percentages in mid-day tomography epochs compared to the three-dimensional tomography results. Also it can be seen that in mid-night epochs, the three-dimensional tomography has higher accuracy compared to four-dimensional method because of low variation of wet refractivity indices.

Diffusion tensor imaging (DTI) MRI is a noninvasive imaging method of the cerebral tissues whose fibers directions are not evaluated correctly in the regions of the crossing fibers. For the same reason, the high angular resolution diffusion images (HARDI) are used for estimation of the fiber direction in each voxel. One of the main methods to specify the direction of fibers is usage of the SPHERICAL deconvolution. The SPHERICAL deconvolution is a method which is very sensitive to noise and creates negative values in the orientation distribution function (ODF) of the fiber. To solve this problem, methods such as Laplace-Beltrami regularized SPHERICAL deconvolution (LB-SD), the gradient based SPHERICAL deconvolution (GB-SD) and the constrained SPHERICAL deconvolution (CSD) are used. In this paper, the method for SD based on Wiener filter (WB-SD) is presented. Regarding the results, the direction of the crossing fibers is specified correctly. The proposed algorithm has specified the direction of the fibers as zero degree with 4.9 standard deviation and 89.9 degree with 3.6 standard deviation against two crossing fibers with 90 degree angle.

The ionosphere is the ionized region of the atmosphere which is situated between 80 and 1200 km. Ionospheric delay is the major resource of error in GNSS positioning, Therefore knowledge of the ionospheric behavior is an important factor in this field. Total Electron Content (TEC) values may be considered as a key parameter to monitor the behavior of the ionospheric medium. Nowadays, continuous GNSS observations can provide an efficient tool to monitor timely ionospheric irregularities. Many scientists have investigated global ionospheric models on the basis of different observations data. For example, IGS Ionosphere Working Group produced daily TEC maps for user services from GNSS data. In this paper, we intend to utilize dual frequency GPS observations provided by Iranian Permanent GNSS Network (IPGN) to calculate TEC maps in Iran. For this purpose, data of 43 IPGN stations and about 180 IGS stations were processed with Bernese GPS software. This process was based on the use of SPHERICAL HARMONICS expansion up to degree and order 15 like the global one, to provide a model of TEC. In the meantime of using GPS data to calculate TEC maps, other resource of errors in GPS positioning such as satellite and receiver clock biases, tropospheric error and multipath error must be either removed, or at least significantly reduced. For this purpose, we used the geometry free linear combinations of pseudo ranges and carrier phases. For reducing the noise level of pseudo range observations we used the carrier phase smoothed pseudo range data as well. The processing method consists of several steps; code smoothing with phase observations, estimation of Differential Code Biases (DCBs), estimation of SPHERICAL harmonic coefficients and generation of TEC maps. Before code smoothing, the phase observations were pre- processed to remove the cycle slips. The used model assumes that the whole free electrons are concentrated on a thin SPHERICAL layer to an altitude varying between 250 and 450km. We chose the altitude equals to 450km in this paper. The obtained results show that the maximal TEC value measured over Iran is about 22 TECU, this value corresponds to the noon period (midday), where the sun is close to the zenith. The minimal TEC value varied around 5 TECU, it corresponds to the midnight period, and such values were obtained for the day of Jun 22, 2009. Iranian Ionosphere Model (IRIM) was created and compared with the different solutions delivered by the several IGS Ionosphere Associate Analysis Centers (IAACs) which are CODE, ESA, JPL and UPC. Despite different IAACs use various approaches, they provide TEC maps with resolution of 2 hours, 5o and 2.5o in UT, longitude and latitude respectively. In order to compare our obtained results with different IAACs TEC maps, we chose TEHN station from IPGN stations to generate and display TEC profiles. The differences between the various models are less than 6 TECU. The IRIM results had minimum differences with CODE TEC maps which both use SPHERICAL HARMONICS as their basic functions. The remained differences caused by the fact that when CODE TEC maps are estimated, the data from IPGN stations are not used. Calculated TEC values were thereafter applied to correct and improve the quality of the single frequency solutions in absolute and relative positioning modes. It is noted that ionosphere free (L3) solution results was considered as the reference solution. In absolute mode, we received the considerable improvements in horizontal and vertical components by using the IRIM instead of IGS models. In relative mode the comparison between the corrected L1 and L3 solutions showed that ignoring the ionospheric effects causes network contraction. Furthermore, the corrected L1 solution results using IRIM rather than IGS models were closer to the L3 solution results. Moreover, for baselines up to several hundreds of kilometers, deviations were better than 10cm in horizontal component.

This paper presents a new method based on the wavelet packet transform for the analysis of HARMONICS in power systems. The algorithm can simultaneously measure the rms value of current, voltage and power using wavelet packets transform. The advantage of the wavelet packets transform is that it can decompose a power signal into uniform frequency bands. This decomposition into uniform frequency bands helps for the identification of harmonic components and measure of harmonic parameters. The algorithm is validated using simulated waveforms from the full wave inverter bridge circuit.

The progressive application of non-linear loads in distribution systems (DS) increases current HARMONICS flow in DS's apparatuses, especially distribution transformers (DTs). Since DTs' operating temperature rises due to the HARMONICS flow, their loading should be reduced such that the hot spot temperature (HST) is preserved under its permissible value. This means that DTs' available capacity is influenced by load harmonic content. In this paper, a novel formulation for DTs' failure rate in the presence of HARMONICS is presented as a function of load harmonic contents. Using the suggested equivalent failure rate, DTs' available capacity in harmonic polluted DS is mathematically formulated. Additionally, the presence of the harmonic increases the HST, leading to DTs' aging acceleration. Therefore, the impact of harmonic components on DTs' aging is arithmetically modeled. To evaluate the efficacy of the suggested reliability model, it is applied to three distinct DTs having respectively industrial, commercial, and residential loads. The obtained results indicate that the available capacity of DTs with the same rated capacity would be different regarding to their load harmonic contents. On the other hand, it is comprehended from the achieved results that the aging acceleration factor (Faa) of the DTs increases owing to their load harmonic contents.

Studying the behaviour of supercavitation from the energy aspect can be divided into two sections. Studying the behavior of supercavitation in the flow field and in vicinity of the flow field. A large portion of field energy is kept in the field، and the rest of it distributed as noise (sound) out of the field. In this paper، harmonious structures of the field which are flowing as energy sources are decomposed by POD method (Proper Orthogonal Decomposition) and presented as spatial modes. The behavior of each mode and therefore behavior of supercavitation can be estimated by studying behavior of supercavitation in nearby area by decomposing the spatial modes via Helmholz decomposition to vectorial and Scalar potential function and then modelling of potential section of scalar to SPHERICAL HARMONICS. By investigating spatial modes، the first mode which has the highest energy is known as mean flow and by studying the intensity of SPHERICAL harmonic modes it can be shown that dipole source is an appropriate representative for field behavior in the nearby area and as a result supercavitation behavior in far feild.

Background: In nuclear medicine application often it is required to use computational methods for evaluation of organ absorbed dose. Monte Carlo simulation and phantoms have been used in many works before. The shape, size and volume in organs are varied, and this variation will produce error in dose calculation if no correction is applied. Materials and Methods: A computational framework for constructing individual phantom for dosimetry was performed on five liver CT scan data sets of Japanese normal individuals. The Zubal phantom was used as an original phantom to be adjusted by each individual data set. This registration was done by SPHERICAL HARMONICS (SH) and Thin-Plate Spline methods. Hausdorff distance was calculated for each case.Results: Result of Hausdorff distance for five individual phantoms showed that before registration ranged from 140.9 to 192.1, and after registration it changed to 52.5 to 76.7. This was caused by index similarity ranged from %56.4 to %70.3. Conclusion: A new and automatic three-dimensional (3D) phantom construction approach was suggested for individual internal dosimetry simulation via SPHERICAL HARMONICS (SH) and Thin-Plate Spline methods. The results showed that the individual comparable phantom can be calculated with acceptable accuracy using geometric registration. This method could be used for race-specific statistical phantom modeling with major application in nuclear medicine for absorbed dose calculation.

Polishing is considered as the last and most important step in the manufacturing of optical components. Computer control polishing (CCP) methods are usually used to polish complex surfaces. In this method, material removal is controlled at each point, depending on error at that point. In contact polishing mechanism, tool feed rate is often controlled to eliminate local errors. It means that the higher the tool feed rate, the lower the material removal would be and vice versa. Tool influence function (TIF), which is defined as the instantaneous material removal under the polishing tool for a given tool motion, is the most important parameter in CCP and its predictability during the polishing process leads to reliable result. In this study, a new SPHERICAL tool which can polish complex surfaces by using a 3-axis CNC machine is presented. Because of SPHERICAL geometry of both tool and work piece, tool, material removal rate is variable because of changing the angle between tool axis and surface normal vector which leads to variation of relative speed. Tool influence function which depends on tool engagement’s angle was modeled based on Preston equation. Moreover, the simulation is modeled based on discretization of tool path. To evaluate the methodology, some polishing experimental tests were performed. The experimental results show that a 130 mm SPHERICAL convex lens with initial surface roughness of 1.114 micrometer for PV was decreased to 395 nm for PV using the CCP method developed in this study.

One of the power quality concerns that have received most attention is the problem of HARMONICS which are generated by widely dispersed single phase nonlinear loads.Such loads cause harmonic distortion of voltages and currents in a power distribution system. In order to fully understand the problem of harmonic distortion, an effective means of identifying the harmonic patterns generated by different types of nonlinear loads is considered. This paper presents the application of fractal analysis for analyzing various harmonic current waveforms generated by typical nonlinear loads such as personal computer, fluorescent lights and uninterruptible power supply. The fractal technique provides both time and spectral information of the nonlinear load harmonic patterns. The analysis results shows that the various harmonic current waveforms can be easily identified from the characteristics of the fractal features. This investigation proves that the fractal technique is a useful tool for identifying harmonic current waveforms and forms a basis towards the development of the harmonic load recognition system.

In this research article, new fuzzy K-algebras, namely, SPHERICAL fuzzy K-algebras and (∈ , ∈ ∨ q)-SPHERICAL fuzzy K-algebras are constructed. Certain properties of these SPHERICAL fuzzy K-structures are investigated. The behavior of SPHERICAL fuzzy K-algebras under homomorphism is characterized. The SPHERICAL fuzzy K-algebra with thresholds is also delineated.