Search

Recently, the authors constructed operators acting on a space of functions defined on [0,∞)$$ \left[0,\infty \right) $$ and preserving 1 and xj$$ {x}^j $$ for a given j∈ℕ$$ j\in \mathrm{\mathbb{N}} $$. To this end, they considered suitable modifications of the Post–Widder and gamma operators. They proved convergence results and established the associated Voronovskaja type formulas. In this paper, we give asymptotic expansions for the sequences of these operators. [ABSTRACT FROM AUTHOR]

The current research aims to assess the feasibility of groundwater resources in two soft and hard formations of the Shamil-Takht basin using logic and operators Fuzzy and Boolean in the GIS environment. For this purpose, eight and seven thematic layers in the soft and the hard formations were investigated and analyzed separately. The layers were prepared in a raster format in the GIS environment and then each of the layers was classified according to the values of usefulness obtained with Fuzzy membership degree and 0 and 1 Boolean values. In the next step, AND and Gamma operators for Fuzzy layers and Algebraic Multiplication operators for Boolean logic were used in combining layers. The groundwater potential map of the studied area was obtained from the desired pixels resulting from performing the operations at the output. Based on this, in Fuzzy logic, 77.1% of the area of soft formation and 11% of the area of hard formation, and in Boolean logic, 24.1% of the area of soft formation and 1.74% of the area of hard formation had the possibility of water sources. Areas with high potential of groundwater resources were in areas with low slope and cultivated and areas with weak potential of water resources were in areas with alluvial and sedimentary formations. Also, the field investigations confirm that the emerging springs and existing wells in the Shamil-Takht basin are located in the areas with the lowest slope and high density of the waterway.

Synthetic aperture radar (SAR) is a high-resolution imaging radar that works under any weather conditions without environmental constraints. It has wide applications in military and civilian fields. Maritime ship tracking based on SAR images mainly involves identifying a ship in a SAR image and monitoring its trajectory in subsequent SAR images, thus achieving the monitoring of the marine field. It is currently an important branch of remote sensing image information processing and has extremely important research value. This study aimed at the characteristics of coherent speckle noise in SAR images and the difficulty in capturing ships due to their large moving range.To improve the accuracy of ship tracking on the sea, an experimental scheme for ship tracking based on SAR images was designed. First, three pairs of continuous satellite SAR images were used to construct a dataset. Then, according to the characteristics of smallships on the sea and the layered structure of the SiamFC algorithm network, a SiamFC algorithm was proposed fortracking ships on the sea. Because of the relatively simple feature extraction network structure of SiamFC, which was more suitable for tracking small targets such as satellites and ships, this study adjusted the parameters of the SiamFC algorithm and trained and tested a model using a constructed dataset. The model was trained in a completely offline mode, and the tracking process did not update the model parameters. Only the trained parameters were used for tracking. The test results showed that the model is feasible. To achieve a better tracking effect, a gamma operator was introduced to enhance the SAR images. The coherent speckle noise in SAR images was reduced, enhancing the details of ship targets. This was mainly reflected in the fact that the grayscale value of the ocean was lower compared with ships and land after SAR image enhancement, resulting in a more pronounced shape and size of ships. The Gamma Map filtering algorithm was used to improve the model, which reduced a large amount of useless information in the image, the pressure of feature extraction, and the error of correlation convolution operation so that the model could effectively track the target according to the characteristics of the target. This effectively improved the performance of the model and solved the technical difficulties of SAR image tracking. Finally, the improved model was tested, and the experimental results showed that the average accuracy of the improved model on test set A increased from 12.7% to 19.6%. When the coincidence rate met at least 40%, the accuracy of the improved model reached 30%, which is an increase of more than 10%. When the test set was B, the average accuracy of the model increased from 39.0% to 41.7%. When the coincidence rate met at least 40%, the accuracy of the improved model increased from 55% to 61%, increasing by 6%. The improved method proposed in this study achieved the expected goal. The results showed that the ship tracking accuracy of this scheme was improved and that the new scheme had good tracking performance. [ABSTRACT FROM AUTHOR]

The current research aims to assess the feasibility of groundwater resources in two soft and hard formations of the Shamil-Takht basin using logic and operators Fuzzy and Boolean in the GIS environment. For this purpose, eight and seven thematic layers in the soft and the hard formations were investigated and analyzed separately. The layers were prepared in a raster format in the GIS environment and then each of the layers was classified according to the values of usefulness obtained with Fuzzy membership degree and 0 and 1 Boolean values. In the next step, AND and Gamma operators for Fuzzy layers and Algebraic Multiplication operators for Boolean logic were used in combining layers. The groundwater potential map of the studied area was obtained from the desired pixels resulting from performing the operations at the output. Based on this, in Fuzzy logic, 77.1% of the area of soft formation and 11% of the area of hard formation, and in Boolean logic, 24.1% of the area of soft formation and 1.74% of the area of hard formation had the possibility of water sources. Areas with high potential of groundwater resources were in areas with low slope and cultivated and areas with weak potential of water resources were in areas with alluvial and sedimentary formations. Also, the field investigations confirm that the emerging springs and existing wells in the Shamil-Takht basin are located in the areas with the lowest slope and high density of the waterway. [ABSTRACT FROM AUTHOR]

In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.

Identifying landslide-prone areas is an essential step in assessing landslide risk and reducing landslide damage. In this paper, GIS-based spatial analysis has been used to prepare the landslide susceptibility (LS) map in the north of Lorestan province in western Iran. For this purpose, three main criteria and their sub-criteria were identified as causative factors including geology and topography (i.e., distance from the fault, lithology, slope, aspect, and elevation), climate (i.e., rainfall and distance from the river), and environmental parameters (i.e., distance from the road, land-cover, NDVI). One hundred thirty-six known landslides were randomly divided into training (≅ 70%) and validation (≅ 30%) datasets. This study is based on the integration of popular analytic hierarchy process (AHP), frequency ratio (FR), and the fuzzy gamma operator (FGO) techniques. AHP was utilized to prioritize causal factors and fuzzy technique was applied in two stages of factor map fuzzification and calculation of sub-criteria maps and then overlap of fuzzified map layers. The fuzzy membership (FM) values were determined based on the FR method, which was normalized between the ranges of 0 and 1. Finally, LS zoning maps were estimated in five susceptibility classes (very low, low, moderate, high, and very high). Validation processes by comparing the three output maps with the layer of validation landslides in the study area and area under receiver operating characteristic curve confirm that the gamma value of 0.9 (AUC = 0.88) offers a more accurate LS map compared to other gamma values. The results of this study will be reliable for landslide risk reduction strategies. [ABSTRACT FROM AUTHOR]

The present paper deals with new modification of Gamma operators preserving polynomials in Bohman-Korovkin sense and study their approximation properties: Voronovskaya type theorems, weighted approximation and rate of convergence are captured. The effectiveness of the newly modified operators according to classical ones are presented in certain senses as well. Numerical examples are also presented, highlighting the performance of the new constructions of Gamma operators in the context of one dimensional approximation. [ABSTRACT FROM AUTHOR]

Abstract The present paper deals with reconstruction of Gamma operators preserving some exponential functions and studies their approximation properties: uniform convergence, rate of convergence, asymptotic formula and saturation. The effectiveness of new operators compared to classical ones is presented in certain senses as well. The last section is devoted to numerical results which compare the effectiveness of new constructions of Gamma operators.

The research focuses on how hybrid renewable energy facilities can be addressed within the spatial planning system by adopting an approach that minimizes the problems related to the sustainability of energy. The study aims to develop a spatial model based on parameters for the site selection processes of hybrid renewable energy facilities relying on wind, solar, and biomass energy sources within the spatial planning system in Turkey. The integration of fuzzy logic approach and Geographic Information Systems (GIS) tools has been proposed to establish a spatially applicable methodological framework. The methodology focuses on the neighborhood scale in terms of planning level and covers the Karatay district, where the hybrid renewable energy potential is high. The research findings indicate that the GAMMA operator used in the methodology provides the most optimal areas with a value of γ = 0.90 and generates site selections for hybrid renewable energy facilities based on the source with the highest suitability index in single-source utilization. Additionally, the operator determines the best alternative in terms of resources in different hybrid scenarios. In this context conducted in Karatay district, it was found that the highest suitability index in terms of hybrid applications is associated with biomass-solar energy combinations. [ABSTRACT FROM AUTHOR]

In this article, we introduce a generalization of Gamma operators based on a function ρ having some properties and prove quantitative Voronovskaya and quantitative Grüss type Voronovskaya theorems via weighted modulus of continuity. [ABSTRACT FROM AUTHOR]

Let I be a finite or infinite interval and ω (f ′ , δ) = sup | x − y | ≤ δ | f ′ (x) − f ′ (y) | be the modulus of continuity of f ′ for f (x) ∈ C 1 (I) = { f : f ′ ∈ C (I) }. Let [ a , b ] ⊂ I be a finite close interval. In this paper we derive the best asymptotic constant defined by C = lim sup n → ∞ sup f ∈ C 1 (I) sup x ∈ [ a , b ] n | L n (f , x) − f (x) | ω (f ′ , 1 n ) where f is not a linear function of x and L n (f , x) are a class of positive linear operators. The results are applied to some well-known operators including Szász–Mirakyan operator, Gamma operator, Baskakov operator and B-spline operator. [ABSTRACT FROM AUTHOR]

This paper aims to study the preservation of log-concavity for Bernstein-type operators. In particular, attention is focused on positive linear operators, defined on the positive semi-axis, admitting a probabilistic representation in terms of a process with independent increments. This class includes the classical Gamma, Szász, and Szász–Durrmeyer operators. With respect to the first and second operators, the results of this paper correct two erroneous counterexamples in [10]. As a main tool in our results we use stochastic order techniques. Our results include, as a particular case, the log-concavity of certain functions related to the incomplete Gamma function. [ABSTRACT FROM AUTHOR]

Abstract: This paper aims to study the preservation of log-concavity for Bernstein-type operators. In particular, attention is focused on positive linear operators, defined on the positive semi-axis, admitting a probabilistic representation in terms of a process with independent increments. This class includes classical Gamma, Szász and Szász-Durrmeyer operators. As a main tool in our results we use stochastic orders techniques. Our results include, as a particular case, the log-concavity of certain functions related to the gamma incomplete function. [Copyright &y& Elsevier]

Recently M.W.Müller [9] gave the Gamma quasi-interpolants and obtained approximation equivalence theorems with Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. In this paper we obtain characterizations on simultaneous approximation for left. Gamma quasi-interpolants with Due to image rights restrictions, multiple line equation(s) cannot be graphically displayed. [ABSTRACT FROM AUTHOR]

Abstract: We present a characterization of the approximation errors of the Post–Widder and the Gamma operators in , with a weight with arbitrary real . Characteristics of two types are used — weighted -functionals of the approximated function itself and the classical fixed-step moduli of smoothness taken on simple modifications of it. [ABSTRACT FROM AUTHOR]

Recently Müller introduced the left Gamma quasi-interpolants and obtained an approximation equivalence theorem with ωφ2r (f, t)p.Guo extended the results with ωφλ2rλ(f, t)∞. In this paper we will improve the previous results and give a weighted simultaneous approximation equivalence theorem with ωφλ2rλ(f, t)∞ which unified classical modulus and Ditzian-Totick modulus. [ABSTRACT FROM AUTHOR]

We introduce modified gamma operators in polynomial weighted spaces of differentiable functions and give approximation theorems for them. [ABSTRACT FROM AUTHOR]

Abstract: The weighted approximation errors of the Post-Widder and the Gamma operators are characterized for functions in with a weight , . Direct and strong converse theorems are proved. Two types of characteristics are used—weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it. [Copyright &y& Elsevier]

Recently some classical operator quasi-interploants were introduced to obtain much faster convergence. Müller [8] gave Gamma left quasi-interpolants and obtained approximation equivalence theorem with ω 2rφ (f; t)p. In this paper we extend above result from two side in L∞: one is we study weight approximation, the other we use modulus ω 2rφλ (f; t) ∞ which unified classical modulus and Ditzian-Totik modulus. [ABSTRACT FROM AUTHOR]