In this paper we introduce two-wavelet constants for square integrable representations of homogeneous spaces. We establish the orthogonality relations for square integrable representations of homogeneous spaces which give rise to the existence of a unique self adjoint positive operator on the set of admissible wavelets. Finally, we show that this operator is a constant multiple of identity operator when G is a semidirect product group of a unimodular subgroup K and a closed subgroup H.

In recent years, many studies have been done on the use of surfactant to enhancement oil recovery from reservoirs,in which the performance of biosurfactant with chemical surfactant was compared. But so far no study has been conducted focusing on comparing the performance of biosurfactant with polymers as well as the effect of temperature on oil recovery. Therefore, the present study was dedicated to study the effect of temperature on the rhamnolipid biosurfactant performance using glass micromodel and to compare its performance with anionic polyacrylamide polymer. Thus, the results of the biosurfactant flooding tests were compared with saltwater and polyacrylamide flooding tests. Experiments were conducted at two temperature, 25 and 75 Celsius degrees, in two homogenous and non-homogenous micromodels. Results indicated that in the homogenous model, for two mentioned temperatures, enhanced oil recovery due to flooding with rhamnolipid biosurfactant was 48 and 62, respectively, in which there was 9 and 12. 7 percent improvement in compare to saltwater. Meanwhile, the results of polymer flooding showed 61 and 70 percent enhancement, respectively. The same results were obtained in non-homogenous model. The enhanced oil recovery due to rhamnolipid biosurfactant injection in two temperatures were 41 and 51 percent, respectively, which it is higher compared to saltwater and lower compared to polymer. In general, at higher temperature, oil recovery increased in both homogenous and non-homogenous models under three floods.

Metaheuristic algorithms have been increasingly used in different fields. The application of these algorithms for identifying and modelling natural phenomena such as flood and drought in terms of complexity and non-linear interactions can be considered as their capability in hydrology. In this paper, Symbiotic Organism Search (SOS) algorithm was first introduced, then its application in tuning fuzzy expert system, aiming to find the region of influence area of hydrometric stations in the Southern Caspian Sea Basin. This basin has regularly experienced flood events, causing human loss and properties damages every year. The outcome of this research is used to estimate floods, and subsequently, to design flood control structures. A total of 61 hydrometric stations were selected in the study area and their physical, climatic and hydrologic characteristics including area, perimeter, minimum elevation, maximum elevation, mean slope, stream length, slope of main stream, equivalent rectangle length, equivalent rectangle width, form factor, shape coefficient, Gravelious factor, round coefficient, and mean annual precipitation were determined. Results indicated that out of 16 parameters, area, mean elevation, form factor, Gravelious factor, and mean annual rainfall, were the most significant parameters in relation to flood by employing the SOS. These variables were used as the input variables into the fuzzy system and SOS algorithm to tune the fuzzy system. Finally, the efficiency of the SOS algorithm was evaluated using the linear torque heterogeneity statistic. Therefore, 61 influence areas were determined that show homogenous areas in 61 watersheds. Results indicated the performance of SOS in determining region of influence of the sub-basins in the study area. In addition, the geographical vicinity is not a suitable criterion for finding homogenous areas.

In this paper, the vertical displacement of a non-homogenous embankment dam is investigated and evaluated in both static and dynamic states using FLAC software. In this regard, initially, the results obtained from this software are validated against the results of conventional methods. Subsequently, using FLAC software and 100 selected models, the impact of important dam parameters such as crest and core height on the vertical displacement of the dam is studied under various conditions in both static and dynamic states. The data analysis approach in this work involves considering a parameter as a witness. The witness parameter remains constant, and assuming that it does not participate in the analysis, one effective parameter and one criterion parameter are chosen for discussion and examination. For example, if the dam base is chosen as the witness parameter, and its value is intended to be 165 meters, the results have shown that an increase in the height of the earth dam leads to an increase in vertical displacements under static and dynamic loadings.

In this paper, the applicability of Euler's homogenous equation method in detecting gravity anomalies from gravity or microgravity data is addressed. The stability of Euler solutions with respect to the window size, window position and choice of the structural index value (defining the anomaly attenuation rate) is analyzed and demonstrated using synthetic microgravity data created for different anomaly models. The analysis reveals that the optimum window size required to obtain the best solutions is a function of the source depth. The horizontal location parameters can be determined correctly if the window is located in the region of high derivatives regardless the assigned structural index v. Meanwhile, depth solution is linearly dependent on the structural index and incorrect choice of structural index leads to significant error in the estimated depth.

In this study, two methods of multivariate techniques and CV-Based test were employed for the identification of homogenous regions for low flow frequency analysis. First a group of 17 variables including climatologic, physiographic, geologic and hydrologic factors of 16 recording stations in Atrak river basin were analyzed using component analysis to find homogenous regions. The analysis indicated the high importance of 4 factors namely basin area, annual precipitation, percentage of pervious formation, and slope of the basin. Spatial variations of data were then interpreted with distance-grouping technique resulting in two homogenous regions. In addition, annual low flows of 7, 15, 30 and 60-day duration in each station were calculated and CV-Base test estimated based on the coefficient of variations. Results showed the non-homogeneity of the whole area, however two homogenous areas were determined using cluster analysis.