In this article we study HARMONIC ANALYSIS on the proper velocity (PV) gyrogroup using the gyrolanguage of analytic hyperbolic geometry. This PV addition is the relativistic addition of proper velocities in special relativity, and it is related with the hyperboloid model of hyperbolic geometry. The generalized HARMONIC ANALYSIS depends on a complex parameter zz and on the radius tt of the hyperboloid, and it comprises the study of the generalized translation operator, the associated convolution operator, the generalized Laplace–Beltrami operator and its eigenfunctions, the generalized Poisson transform and its inverse, the generalized Helgason–Fourier transform and its inverse, and Plancherel’s theorem. In the limit of large tt, t→+¥, the generalized HARMONIC ANALYSIS on the hyperboloid tends to the standard Euclidean HARMONIC ANALYSIS on RnRn, thus unifying hyperbolic and Euclidean HARMONIC ANALYSIS.

HARMONIC ANALYSIS has become an important issue in modern power systems. The widespread penetration of non-linear loads into the emergence of power systems has turned power quality ANALYSIS into an important operation issue under both steady state and transient conditions. This paper employs a Dynamic HARMONIC Domain (DHD) based framework for the dynamic HARMONIC ANALYSIS of VSC-HVDC systems. These systems are widely used in modern power systems in both distribution and transmission levels in order to provide voltage profile improvement, power flow control, and power loss reduction. In this paper, appropriate modeling of VSC-HVDC systems for HARMONIC propagation is performed by means of switching function which provides a connection between DC and AC sides. Also in this paper, dynamics related to DC side capacitor are taken into account which can greatly affect the transient response. In order to validate the results, the proposed method has been successfully tested on a test system and the obtained results are compared to those of a time-domain software, followed by a discussion on results.

In practical applications of inverters, unbalanced conditions may be occurred. For instance, semiconductor switches of a converter may not be exactly the same or switching circuit may be unbalanced. This unbalance leads to additional HARMONICs in the output of converter. The additional HARMONICs usually are not considered in the design of circuit, so cause many problems. For precise investigation of these HARMONICs, a new model of inverter based on switching functions is presented. With this model, analytical equations of HARMONICs in unbalanced switching are calculated. These analytical equations can be used for designing process such as investigation of optimal cases or elimination of undesired HARMONICs. The accuracy of the analytical calculations is verified by simulation results. As well, an experimental prototype is constructed to verify analytical results.

One of the most variability of atmospheric parameter is precipitation, which changes seasonally. It is important to understand exact characteristic of rainfall seasonal variable. Therefore, it is avoidable to study rainfall season in Hamedan province, because Hameden is one of the important centers of agriculture in Iran. In this research, the seasonal variability of rainfall is considered in Hamedan province. For this object, precipitation data spanning 30 years (1979-2009) were analysed to determine the onset and cessation, trend and seasonal variability of rainfall, based on the daily rainfall for there separated decades. The result of this study show the duration of rainfall is from early falls until end of spring in the first decade. This result indicated the duration of rainfall is long. In the second decade, there is no significant change in rainfall season, but only in some part of the province, the rainfall duration is shortfall and in the other part is long falls. Nevertheless, in the third decade there is considerable movement, i.e. the onset of rainfall duration has been in winter and cessation of rainfall duration has been in summer. It express that rainfall season has moved to summer slowly. The trend of rainfall duration has increasing trend. On the other hand, the duration length of rainfall is longer than before. In order to classify, rainfall seasonal variability is interpolated and the cluster ANALYSIS is done base on the “Oghlidos distance” and “Ward” integrated method. According to this method, Hamedan province is classified to 3 groups. The first group indicates the shortfall in the most parts, the second group indicates rainfall season onset is moved to winter, and in the third part the rainfall season hasn’t had change.

One of the factors that can be the link between our intentions and actions and their external consequences is human agency, which indicates the conscious design and intentional execution of actions by the individual in order to influence future events.Objective and Method: This research with a developmental approach of psychometric method and method 1, examines the psychometric indices of the Human Factor Characteristics Scale using the CLASSICAL theory of test score measurement and the graduated question-answer theory. The purpose of this study, which included high school students in Tehran, was selected by cluster sampling of 500 people as a sample size and statistical ANALYSIS was performed on 481 data. To collect the data, the ion Human Agent Characteristics Scale (2011) was used and the research questions were evaluated using IRTPRO and SPSS software.Results:The assumption of local independence based on Pearson x2 index was established by applying Simjima's calibrated question-answer theory and the assumption of being one-dimensional based on the ANALYSIS of multidimensional question-answer theory. Diagnosis parameters with question-answer approach and CLASSICAL approach Test score Both item 25 approach had the lowest and item 2 had the highest diagnosis parameter. The answer thresholds for all the questions were so far apart that no option was covered by the other option, and the options were independently selected by individuals at intervals of theta. The total scale was calculated with Cronbach's alpha of 0.945, intentionality of 0.894, foresight of 0.780, self-reactivity of 0.871 and rethinking of 0.762. Also, the role of each item in internal consistency was investigated by the loop method, which all questions had a favorable role in internal consistency of this scale. The value of the validity coefficient obtained from the question-answer theory was obtained by marginal method for intentionality 0.92, forethought 0.85, self-reaction 0.91, rethinking 0.83..

A prismatic beam made of a behaviorally nonlinear material is analyzed under a HARMONIC load moving with a known velocity. The vibration equation of motion is derived using Hamilton principle and Euler-Lagrange Equation. The amplitude of vibration, circular frequency, bending moment, stress and deflection of the beam can be calculated by the presented solution. Considering the response of the beam, in the sense of its resonance, it is found that there is no critical velocity when the behavior of the beam material is assumed to be physically nonlinear.

Increasing HARMONIC contamination is one of the concerns in power systems that has been more considered. On the other hand, the high cost of compensation can eliminate the possibility of compensation across the network. Regarding the restructuring of power systems, it is possible to provide the compensation cost by contaminating subscribers. In this paper, a new method for controlling the network HARMONIC level is presented using HARMONIC pricing. Determining the fair HARMONIC contribution at the point of common coupling voltage is the base of pricing method. In addition, a new index has been proposed to determine the HARMONIC contribution of the customer and utility to the HARMONIC contamination of the point of common coupling. By using this index, an accurate impression of the customer and utility contribution in all of the dominant HARMONIC levels is obtained. The simulation results on the IEEE 14-bus standard network illustrate the effectiveness of the proposed method for pricing based on fair contribution of customer and network. Also, the results show that by justly determining the HARMONIC contribution, the customers can be encouraged to reduce or control their HARMONIC level. Otherwise, by aggregating the penalty fees, HARMONIC filters can be installed at the desired location to control the network HARMONIC control.

In the main this paper introduces the concept of chromatic HARMONIC polynomials denoted, H (G; x) and chromatic HARMONIC indices denoted, H (G) of a graph G. The new concept is then applied to  nd-ing explicit formula for the minimum (maximum) chromatic HARMONIC polynomials and the minimum (maximum) chromatic HARMONIC index of certain graphs. It is also applied to split graphs and certain derivative split graphs.