Gamma Operators Research Articles

Spacetime and inner space of spinors in the theory of superalgebraic spinors

We constructed gamma operators which are superalgebraic analogs of the Dirac gamma matrices as well as two additional gamma operators which have no analogs in the Dirac theory. We found a new mechanism of the left-right symmetry breaking which is absent in the usual theory of Dirac spinors. We constructed Lorentz invariant gamma operators from operators of creation and annihilation of spinors. These gamma operators are also analogs of the Dirac gamma matrices, however they are not related to Lorentz transformations but generate vector fields as affine spinor connections. We have shown that the theory is equivalent to an extended version of the Pati-Salam theory.

Landslide susceptibility zoning in a catchment of Zagros Mountains using fuzzy logic and GIS

Landslide is one of the dangerous types of natural hazards. This phenomenon causes damages in many countries every year. A detailed landslide hazard assessment is necessary to reduce these damages. This research aims to map the landslide susceptibility zoning (LSZ) using the fuzzy logic method and GIS in the Sorkhab basin as a part of the Zagros fold and thrust belt (FTB), northwestern Iran. All slide types were recorded in fieldwork as landslide inventory. Based on the results, four types, i.e., debris slide, earth slide, and rock fall and complex of landslides, was identified in the region. Then, the effect of each landslide contributing factor including topographical elevation heights, slope classes, aspect classes, geological units, proximity to faults, land covers, rainfall classes, and proximity to streams was constructed in GIS and subsequently normalized using fuzzy membership functions. Finally, by combining all standardized layers using the fuzzy gamma operator, a final map of LSZ was produced. The results showed that a 0.9 fuzzy gamma operator has a high accuracy for the LSZ map in the study area. Besides, the accuracy of the LSZ map revealed a strong relationship (R2) between susceptibility classes, and landslide inventory was calculated using a scatter plot equal to 0.79. Hence, the method represented an appropriate accuracy in predicting the landslide susceptibility in the study area.

Urban flood susceptibility zonation mapping using evidential belief function, frequency ratio and fuzzy gamma operator models in GIS: a case study of Greater Mumbai, Maharashtra, India

Greater Mumbai is one of the major sufferers of urban flood in India. In the present study, flood susceptibility zonation (FSZ) mapping of Greater Mumbai were performed using Geographical Information Systems (GIS) based models, evidential belief function (EBF), frequency ratio (FR), fuzzy gamma operator (FGO). For FSZ mapping, 12 conditioning factors were considered which included elevation, slope, plan curvature, topographic wetness index, stream power index, built-up index, geology, soil type, land use land cover, modified Fournier index, proximity to natural drainage and proximity to sewers and storm water drainage. The flood inventory database was divided into training and test data. The factor maps were integrated using GIS. The FSZ map was validated using area under curve (AUC) method. The AUC values of prediction rate using test data for FR, FGO, and EBF models were 0.7400, 0.7231 and 0.7268 respectively. The accuracy assessment of all three models shows fair prediction accuracy.

Approximation by Gamma type operators

In this study, we introduce newly defined Gamma operators which preserve constants and e2μ·, μ>0 functions. In accordance with this purpose, we focus on their approximation properties such as uniform convergence, rate of convergence, asymptotic formula, and saturation results. Superior properties of introduced operators have been tested both theoretically and numerically in certain senses to highlight the performance of the new constructions of Gamma operators.

On Stancu type generalization of (p,q)-Gamma operators

On Stancu type generalization of (p,q)-Gamma operators

Landslide susceptibility mapping by fuzzy gamma operator and GIS, a case study of a section of the national road n°11 linking Mateur to Béja (Nortshern Tunisia)

The purpose of this paper is to map the landslide susceptibility using the fuzzy gamma operator and GIS for the section of the national road n°11 linking Mateur to Beja. To minimize the subjectivity of the fuzzy logic approach, the frequency ratio was used to calculate the fuzzy membership. To locate the 147 landslides, Google Earth extracts analysis, and field survey has been done. In this cartography, nine factors controlling landslides were used: slope, aspect, curvature plane, curvature profile, distance to faults, distance to rivers, land use, rainfall, and lithology. Once the fuzziness is calculated in each factor using the frequency ratio (FR), the fuzzy gamma operator can be applied to these nine factors to produce the landslide susceptibility map. Finally, the choice of the nearest susceptibility map of reality is made by applying the ROC curve. By the analysis of the area under curve (AUC), it is seen that the prediction accuracy of model proves that the gamma value of 0.90 yielded the better prediction of landslide susceptibility map (0.89). Finally, our area of interest was classified based on the Jenks natural breaks classification method into five classes, such as non-susceptible zone, low susceptible zone, moderate susceptible zone, high susceptible zone, and very high susceptible zone. Landslide susceptibility mapping based on the fuzzy gamma operator presents a very acceptable result with a reliability of 89%.

Vacuum and Spacetime Signature in the Theory of Superalgebraic Spinors

A new formalism involving spinors in theories of spacetime and vacuum is presented. It is based on a superalgebraic formulation of the theory of algebraic spinors. New algebraic structures playing role of Dirac matrices are constructed on the basis of Grassmann variables, which we call gamma operators. Various field theory constructions are defined with use of these structures. We derive formulas for the vacuum state vector. Five operator analogs of five Dirac gamma matrices exist in the superalgebraic approach as well as two additional operator analogs of gamma matrices, which are absent in the theory of Dirac spinors. We prove that there is a relationship between gamma operators and the most important physical operators of the second quantization method: number of particles, energy–momentum and electric charge operators. In addition to them, a series of similar operators are constructed from the creation and annihilation operators, which are Lorentz-invariant analogs of Dirac matrices. However, their physical meaning is not yet clear. We prove that the condition for the existence of spinor vacuum imposes restrictions on possible variants of the signature of the four-dimensional spacetime. It can only be (1, − 1 , − 1 , − 1 ), and there are two additional axes corresponding to the inner space of the spinor, with a signature ( − 1 , − 1 ). Developed mathematical formalism allows one to obtain the second quantization operators in a natural way. Gauge transformations arise due to existence of internal degrees of freedom of superalgebraic spinors. These degrees of freedom lead to existence of nontrivial affine connections. Proposed approach opens perspectives for constructing a theory in which the properties of spacetime have the same algebraic nature as the momentum, electromagnetic field and other quantum fields.

Convergence Estimates for Gamma Operator

Gamma operator is based on the gamma function and has interesting approximation properties. In the present note, we present some convergence estimates of the Gamma operators based on different modulus of continuities.

Identification of geochemical anomaly and gold potential mapping in the Sonakhan Greenstone belt, Central India: An integrated concentration-area fractal and fuzzy AHP approach

The present work combines Concentration-Area (C-A) fractal model with the Fuzzy Analytical Hierarchy Process (FAHP) on a GIS platform for mapping gold potential in the Sonakhan Greenstone Belt, India. A set of stream sediment geochemical data obtained over a part of the study area was used to delineate potential regions of gold mineralisation. In order to develop a suitable predictive model, the gold exploration target was taken as target (dependent variable) and concentration of pathfinder elements of gold such as Au, As, Ag, Hg, Sb and Se in the stream sediments were used as predictors (independent variables). The C-A fractal model was applied to the geochemical data of each element to decompose anomaly and background components of the spatial dispersion of element concentration in the study area. AHP combined with fuzzy set theory (FAHP) was used to determine the priority or, the weight of each evidential geochemical anomaly map. The Gold exploration targets are delineated by multiplying the weights with the respective fuzzy normalised geochemical anomaly map of the gold pathfinder elements and integrating the weighted geochemical evidential layers using fuzzy Gamma operator. The reliability of the outcome was assured by the coincidence of known gold mineralisation with the potential regions delineated in the final gold potential map. The areas with high potential are good targets for detailed exploration of gold in the region. The results highlight that (a) application C-A fractal model can effectively separate geochemical anomalies as it considers the spatial variation of the data unlike the conventional statistical methods which account only the frequency of the data, (b) the FAHP allows more flexibility in judgements of multiple decision makers in a group and reduces the inconsistency of the result which is essentially required in the knowledge-driven predictive mapping of mineral prospectivity.

(p,q)-gamma operators which preserve x^{2}

In this paper, we introduce (p,q)-gamma operators which preserve x^{2}, we estimate the moments of these operators, and establish direct and local approximation theorems of these operators. Then two approximation theorems about Lipschitz functions are obtained. The estimates on the rate of convergence and some weighted approximation theorems of the operators are also obtained. Furthermore, the Voronovskaja-type asymptotic formula is also presented.

Hazard zoning for spatial planning using GIS-based landslide susceptibility assessment: a new hybrid integrated data-driven and knowledge-based model

The popular use of geographical information system (GIS) technology in landslide assessment ensures good, accurate and fast results with less cost and manages mass movements and identifies safe areas for the development of new settlements. In the literature, different methods have been applied in landslide susceptibility assessment using various models. In these studies, the methods are either expert knowledge-based or data-driven approaches. These two approaches produce different outcomes based on their specific characteristics. Thus, the simultaneous use of a set of methods using fusion techniques at the decision-level improves the results. This study aims to investigate and identify a landslide zonation model by combining different methods in GIS and integrate the results (incorporated in the decision level) to achieve optimum accuracy. In this study, landslide hazard mapping was performed using knowledge-based models such as simple additive weighting (SAW) and fuzzy gamma operator and data-driven models namely radial basis function link network (RBFLN) and probabilistic neural network (PNN). Evaluation results indicate that data-driven methods have better performance than knowledge-based methods based on expert opinion. The SAW method also has a better result than other knowledge-based methods, such as fuzzy gamma. The assessment results of the randomly selected landslide control points indicate that PNN, SAW, RBFLN and fuzzy gamma have accuracies of 82.3, 69.62, 65.39 and 61.26% in landslide zoning, respectively. Meanwhile, weighted mean, maximum, median and minimum were used to incorporate the results in decision-level fusion; results show improved accuracies of 70.53, 83.5, 67.39 and 60.27% for each criterion, respectively.

Approximation properties of (p,q)-Gamma operators

Approximation properties of (p,q)-Gamma operators

Evaluation of landslide susceptibility models: A comparative study on the part of Western Ghat Region, India

The present research focuses on evaluating the effectiveness of landslide susceptibility using fuzzy gamma operator (FGO) and analytical hierarchy process (AHP) model in part of Western Ghat, India. The landslide inventory data and various causative factors were used to generate the landslide susceptibility index (LSI) map using geospatial technology. The LSI map classified into five classes and finally validated by Area Under Curve (AUC) method for accuracy assessment. The AUC result of success and prediction rates depicts that FGO model has high accuracy value than AHP model. However, both models are highly correlated (r = 0.976). Among the all causative factors slope, lithology, land use land cover, geomorphology and lineament proximity are strongly correlated (r = >0.9) with the landslide susceptibility between the two models. The research outcome will be helpful for future spatial planning in the study region.

Application of fuzzy logic approach for wind erosion hazard mapping in Laghouat region (Algeria) using remote sensing and GIS

Abstract Wind erosion is one of the most serious environmental problems in Algeria that threatens human activities and socio-economic development. The main goal of this study is to apply a fuzzy logic approach to wind erosion sensitivity mapping in the Laghouat region, Algeria. Six causative factors, obtained by applying fuzzy membership functions to each used parameter, are considered: soil, vegetation cover, wind factor, soil dryness, land topography and land cover sensitivity. Different fuzzy operators (AND, OR, SUM, PRODUCT, and GAMMA) are applied to generate wind-erosion hazard map. Success rate curves reveal that the fuzzy gamma (γ) operator, with γ equal to 0.9, gives the best prediction accuracy with an area under curve of 85.2%. The resulting wind-erosion sensitivity map delineates the area into different zones of five relative sensitivity classes: very high, high, moderate, low and very low. The estimated result was verified by field measurements and the high statistically significant value of a chi-square test.

Szász–Gamma Operators Based on Dunkl Analogue

In this article, we introduce Szasz–Gamma operators based on Dunkl analogue. We discuss basic approximation results in terms of the classical Korovkin theorem and modulus of continuity. For our operators, we investigate local approximation results by means of Peetre’s K-functional, second order modulus of smoothness, the Lipschitz class and the Lipschitz maximal function. Next, we present weighted approximation theorems by means of a Korovkin type theorem and weighted modulus of continuity. Lastly, A-Statistical approximation result and rate of convergence for functions with derivative of bounded variation are also studied.

A novel framework for the potential assessment of utility-scale photovoltaic solar energy, application to eastern Iran

This paper presents a framework to assess the potential of photovoltaic solar energy for utility-scale installations. In order to achieve this purpose, the framework incorporates spatial planning and performance simulation of photovoltaic power systems into the potential assessment process. Birjand County where is a suitable region for the deployment of photovoltaic technologies because of its climatic conditions was selected asa case study. The installation of solar power plants asa subset of infrastructure facilities should have the conformity to the standards of land-use planning. At the first step, the set of factors (27 criteria) influencing on the site selection of photovoltaic power plants was defined. After the detection of unsuitable areas, they were excluded from the county map by Boolean logic. Remaining areas were rated based on the technical, socio-economic, environmental criteria by using different fuzzy membership functions. Then, these rated areas were mapped. To determine the optimal sites for the grid-connected installations of photovoltaic, the fuzzified maps were overlaid by fuzzy gamma operator. Then, the pixels of final map were classified into five groups regarding to their fuzzy value. The results show that optimal places for the installation of photovoltaic power plants account for 0.5 percent (2005 hectares) of Birjand’s territory. The results of geo-spatial modeling of this thesis were verified by using satellite images. To estimate the capacity of electricity production from photovoltaic power plants, a 46.2kW- photovoltaic installation was designed and its performance and energy output was simulated under climatic and geographical conditions of Birjand. The estimated energy output of photovoltaic power plants in optimal sites of Birjand County (1781.6GWh/year) not only can supply the electrical demand of Southern Khorasan Province but also, the excess generated electricity can export to other provinces and neighboring countries such as Pakistan and Afghanistan.

Fuzzy gamma operator model for preparing landslide susceptibility zonation mapping in parts of Kohima Town, Nagaland, India

Growing population and expansion of settlements over hilly areas have largely increased the impact of landslide. This paper deals with the use of Geoinformatics technology and Fuzzy Gamma Operator model to map the landslide susceptibility zones in part of Kohima Town, Nagaland. For this study, eight landslide inducing parameters such as slope gradient, slope aspect, curvature, elevation, land use and land cover, drainage density, lineament density, and topographical wetness index were considered and prepared with the help of toposheet, high resolution satellite imagery such as World View II, LISS IV, DEM data and field data. Landslide inventory was the first step for the geospatial database generation which involves the mapping of past landslide details. Landslide susceptibility maps were generated by calculating relationship between the landslide inducing factors with past landslide locations using frequency ratio and fuzzy gamma operator model. The ratios were normalized between the range of 0 and 1 to obtain fuzzy membership values. The landslide susceptibility zonation (LSZ) map were prepared by integrating all the causative factors with fuzzy membership values and classified into five different susceptibility classes based on Jenks natural breaks classification viz. very high (37.51%), high (32.21%), moderate (20.97%), low (7.97%), and very low (1.34%). The LSZ map were compared with the landslide inventory map and validated with best prediction accuracy using area under curve (AUC) with the accuracy level and R-Index.

Fuzzy fusion of geological and geophysical data for mapping hydrocarbon potential based on GIS

Effective fusion of multiple data, including geographical, geological, geophysical, geochemical and dynamic data for hydrocarbon potential mapping, involves both a fusion algorithm and a convenient modelling platform. In this study, fuzzy logic and a geographical information system (GIS) are used to fuse geological and geophysical interpretations in mapping the gas potential of the Kazakhstan Marsel Territory Carboniferous system based on the assumed gas-accumulation model. Non-linear membership functions are used to transform the input data, while the gamma operator is used to combine the multiple datasets. Finally, the Carboniferous system targets, the Visean (C 1 v) and Serpukhovian (C 1 sr) units, are mapped. Gas testing in situ validated our results.

Knowledge-Driven Prospectivity Mapping for Granite-Related Polymetallic Sn–F–(REE) mineralization, Bushveld Igneous Complex, South Africa

This paper presents mineral prospectivity mapping to identify potential new exploration ground for polymetallic Sn–F–REE mineralization associated with the Bushveld granites of the Bushveld Igneous Complex, South Africa. The Lebowa Granite Suite, commonly known as the Bushveld granites, is host to a continuum of polymetallic mineralization with a wide range of metal assemblages (Sn–Mo–W–Cu–Pb–Zn–As–Au–Ag–Fe–F–U–REE), ranging from a high-temperature to a low-temperature magmatic hydrothermal mineralizing environment. The prospectivity map was generated by fuzzy logic modeling and a selection of targeting criteria (or spatial proxies) based on a conceptual mineral system highlighting critical processes responsible for the formation of the polymetallic mineralization. The spatial proxies include proximity to differentiated granites (as heat and metal-rich fluid sources), Rb geochemical map (fluid-focusing mechanism such as fractionation process), principal component maps (PC 4 Y–Th and PC 14 Sn–W, fluid pathways for both high- and low-temperature mineralization) and proximity to roof rocks (traps for fluids). Logarithmic functions were used to rescale rasterized evidential maps into continuous fuzzy membership scores in a range of [0, 1]. The evidential maps were combined in two-staged integration matrix using fuzzy AND, OR and gamma operators to produce the granite-related polymetallic Sn–F–(REE) prospectivity map. The conceptual mineral system model and corresponding prospectivity model developed in this study yielded an encouraging result by delineating the known mineral deposits and occurrences of Sn–F–(REE) mineralization that were not used to assign weights to the evidential maps. The prospectivity model predicted, on average, 77% of the known mineral occurrences in the BIC (i.e., 56 of 73 Sn occurrences, 12 of 15 F occurrences and 6 of 8 REE occurrences). Based on this validation, 13 new targets were outlined in this study.

On the degree of approximation by modified gamma operators

On the degree of approximation by modified gamma operators