Search

For the first time, this paper offers the Bayesian and E‐Bayesian estimation methods using the spacing function (SF) instead of the classical likelihood function. The inverse Lindley distribution, including its parameter and reliability measures, is discussed in this study through the mentioned methods, along with some other classical approaches. Six‐point and six‐interval estimations based on an adaptive Type‐I progressively censored sample are considered. The likelihood and product of spacing methods are used in classical inferential setups. The approximate confidence intervals are discussed using both classical approaches. For various parameters, the Bayesian methodology is studied by taking both likelihood and SFs as observed data sources to derive the posterior distributions. Moreover, the E‐Bayesian estimation method is considered by using the same data sources in the usual Bayesian approach. The Bayes and E‐Bayes credible intervals using both likelihood and SFs are also taken into consideration. Several Monte Carlo experiments are carried out to assess the performance of the acquired estimators, depending on different accuracy criteria and experimental scenarios. Finally, two data sets from the engineering and physics sectors are analyzed to demonstrate the superiority and practicality of the suggested approaches. [ABSTRACT FROM AUTHOR]

The Orlicz function-defined sequence spaces of functions by relative uniform convergence of sequences related to p -absolutely summable spaces are a new concept that is introduced in this article. We look at its various attributes, such as solidity, completeness, and symmetry. We also look at a few insertional connections involving these spaces. [ABSTRACT FROM AUTHOR]

This paper presents novel concepts in fuzzy topologies, namely q -rung orthopair picture fuzzy (q -ROPF) topology and q -rung orthopair picture fuzzy point (q -ROPFP). These concepts extended the existing notions in fuzzy topologies. We introduced a more relaxed form of continuity, called q ε -ROPF continuity, which allows for a flexible analysis of functions between q -ROPF topological spaces by incorporating an error bound ε. We define the q -neighborhood system for a q -ROPF point in a q -ROPF topological space and investigate the convergence of sequences of such points. Our results shed light on the behavior of functions and sequences in these spaces, as well as the conditions for uniqueness of limits within the realm of supports. This research has practical implications in control systems, providing valuable insights into the stability and robustness of the control strategies in the presence of small changes represented by the epsilon value. [ABSTRACT FROM AUTHOR]

Our model is based on an Euler-Bernoulli beam clamped at one end and subjected at its free end to a control in displacement and velocity. In this work, relative of the control parameters, we study the stabilization in displacement and then in energy of the model using a stable numerical scheme that we implement. This numerical scheme results from the Crank–Nicolson algorithm for the discretization in time and from the finite element method based on the approximation by Hermith cubic functions for the discretization in space. The study shows that, compared to the velocity control, the displacement control has an almost negligible effect on the stabilization of the beam. This result is confirmed later by a sensitivity study on the control parameters involved in our model. [ABSTRACT FROM AUTHOR]

In this paper, we study the stationary compressible nonisothermal nematic liquid crystal flows affected by the external force of general form in three-dimensional space. By using the contraction mapping principle, we prove the existence and uniqueness of strong solution around the constant state in some suitable function space. [ABSTRACT FROM AUTHOR]

Cell-free massive multi-input multi-output (MIMO) systems exhibit many characteristics that differ from those of traditional centralized massive MIMO systems, and there are still research gaps in the modeling of cell-free massive MIMO channels. In this paper, a geometry-based stochastic model (GBSM) that combines the double-ring model and hemisphere model to comprehensively consider the distribution of scatterers in the environment was proposed for cell-free massive MIMO channels. Combined with the line-of-sight (LoS) path, single scattering path, and double scattering path components, the channel matrix between the access points (APs) and the user was derived. The proposed model fully considers geometric parameters such as the arrival/departure direction, elevation angle, time delay, and distance, which can accurately characterize the channel. Then, we proved that the traditional channel model, standard block-fading model, and spatial basis expansion model (SBEM) adopted in a cell-free massive MIMO system could not describe the nonstationarity in the space, time, and frequency domains, whereas the proposed GBSM could. Statistical characteristics of the channel were analyzed, including the space cross-correlation function (CCF), time autocorrelation function (ACF), Doppler power spectral density (PSD), level crossing rate (LCR), and average fade duration (AFD). Then, we investigated the proposed model by simulating the space CCF, time ACF, Doppler PSD, LCR, and AFD under the conditions of two different scatterer densities. Through simulations and analyses, some new features of cell-free massive MIMO channels were identified, providing a theoretical basis for in-depth research on cell-free massive MIMO systems. Finally, the measurement-based scenario and the WINNER II channel model are compared to demonstrate that the GBSM is more practical to characterize real cell-free massive MIMO channels. [ABSTRACT FROM AUTHOR]

In this work, we introduce weak Pata convex contractions and weak E -Pata convex contractions via simulation functions in metric spaces to prove some fixed point results for such mappings. Also, we consider an example related to weak Pata convex contractions. Consequently, our results generalize and unify some results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we mainly obtain an approximation theorem and generic convergence of solutions for inverse quasivariational inequality problems. First, we define the concept of the approximate solution to inverse quasivariational inequality problems under bounded rationality theory. Afterward, an approximation theorem that satisfies fairly mild assumptions is proved. Moreover, we establish a function space and discuss the convergence properties of solutions for inverse quasivariational inequality problems by the method of set-valued analysis. Finally, we prove that most of inverse quasivariational inequality problems are stable in the case of perturbation of the objective function. These results are new, which improve the corresponding outcomes of the recent literatures. [ABSTRACT FROM AUTHOR]

In this paper, we construct and investigate the space of null variable exponent second-order quantum backward difference sequences of fuzzy functions, which are crucial additions to the concept of modular spaces. The idealization of the mappings has been achieved through the use of extended s − fuzzy functions and this sequence space of fuzzy functions. This new space's topological and geometric properties and the mappings' ideal that corresponds to them are discussed. We construct the existence of a fixed point of Kannan contraction mapping acting on this space and its associated pre-quasi ideal. To demonstrate our findings, we give a number of numerical experiments. There are also some significant applications of the existence of solutions to nonlinear difference equations of fuzzy functions. [ABSTRACT FROM AUTHOR]

In this paper, we construct and investigate the space of weighted Gamma matrix of order r in Nakano sequence space of soft functions. The idealization of the mappings has been achieved through the use of extended s -soft functions and this sequence space of soft functions. This new space's topological and geometric properties, the multiplication mappings that stand in on it, and the mappings' ideal that correspond to them are discussed. We construct the existence of a fixed point of Kannan contraction mapping acting on this space and its associated prequasi ideal. Interestingly, several numerical experiments are presented to illustrate our results. Additionally, some successful applications to the existence of solutions of nonlinear difference equations of soft functions are introduced. [ABSTRACT FROM AUTHOR]

In general, we have constructed the operator ideal generated by extended s -fuzzy numbers and a certain space of sequences of fuzzy numbers. An investigation into the conditions sufficient for variable exponent Cesàro sequence space of fuzzy functions furnished with the definite function to create pre-quasi-Banach and closed is carried out. The R and the normal structural properties of this space are shown. Fixed points for Kannan contraction and nonexpansive mapping have been introduced. Lastly, we explore whether the Kannan contraction mapping has a fixed point in its associated pre-quasioperator ideal. The existence of solutions to nonlinear difference equations is illustrated with a few real-world examples and applications. [ABSTRACT FROM AUTHOR]

Multimedia teaching has the characteristics of flexibility, nonlinear structure, and the combination of multiple senses, which can fully mobilize the enthusiasm and initiative of students. Because the traditional piano teaching method is too old-fashioned and single, which is not conducive to stimulating students' interest in learning, the piano teaching is studied according to the methods of information technology, online education, and mixed teaching. This paper controls the rhythm of teaching through multimedia teaching technology, stimulates students' thirst for knowledge, and uses multimedia technology to enrich piano teaching resources to meet teaching needs. Then, by means of a questionnaire, the attitude of most of the high-efficiency students towards online piano teaching with multimedia technology is understood. At the same time, the cluster analysis system is used to analyze the online public opinion evaluation of the three teaching methods by collecting the network behavior of users in various distribution platforms on the Internet and analyzing the feature vector according to the function space formed by the relevant evaluation indicators. The accuracy of the system is above 82%, so the teaching evaluation is effective. Through the value evaluation model of the system, user dynamics can be accurately understood and applied to other fields. [ABSTRACT FROM AUTHOR]

The purpose is to adapt to the current social development and promote the English translation teaching reform. Based on the theories of deep learning (DL), text classification (TC), and the Internet of Things (IoT), this work analyzes the current situation of English translation teaching. Additionally, 100 text categories are selected from the English text corpus of Northwestern Polytechnic University as the research objects. The data are classified by the DL-based TC method and analyzed by introducing the simulated annealing algorithm. Finally, the storage and security performance of the shared IoT system are described. The results show that the proposed TC method can overcome the performance loss caused by the function extraction method, greatly reducing the training time and function space. The storage and security performance of the shared IoT system to encrypt English text will increase with the number of model iterations. Therefore, this work designs the English translation teaching-oriented shared IoT system using a DL-based TC. The finding plays an important role in subsequent English translation and enriching the theory of IoT. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the long-time behavior of g -Navier-Stokes equations with weak dampnesss and time delay. The uniformly attracting sets of processes are obtained. On the basis of the method with asymptotic compactness, the existence of the uniform attractor for the equation is proved with the restriction of the forcing term belonging to translational compacted function space. [ABSTRACT FROM AUTHOR]

A Stevi c ′ -Sharma operator denoted by T ψ 1 , ψ 2 , φ is a generalization product of multiplication, differentiation, and composition operators. In this paper, we characterize the bounded and compact Stevi c ′ -Sharma operator T ψ 1 , ψ 2 , φ from a general class X of Banach function spaces into Zygmund-type spaces with some of the most convenient test functions on the open unit disk. Using several restrictive terms, we show that all bounded operators T ψ 1 , ψ 2 , φ from X into the little Zygmund-type spaces are compact. As an application, we show that our results hold up for some other domain spaces of T ψ 1 , ψ 2 , φ , such as the Hardy space and the weighted Bergman space. [ABSTRACT FROM AUTHOR]

In this paper, we will introduce and study several types of Kakeya inequalities by the maximal functions in Hardy spaces in ℝ n , n ≥ 2 , and we could obtain several inequalities associated with the Kakeya inequalities. We will show that M δ S α , β t f p ≲ p , n , φ , ε 1 / δ 5 n / r + 2 ε f p , when f x ∈ L p ℝ n and supp f ^ ξ ⊆ B 0 , 1 . [ABSTRACT FROM AUTHOR]

Regarding the concept of size function topology, this allows us to view the topological space X as a metric-like space. We prove the existence and uniqueness for a coupled fixed point of the map F : X × X ⟶ X satisfying some certain contractive conditions. [ABSTRACT FROM AUTHOR]

With the continuous development and improvement of university education, providing students with refined and comprehensive learning environment has come to be a problem of great importance and significance to the people. The state carries out quality-oriented education through a series of measures of education reform. These measures and standards not only help to improve the overall quality of students, but also put forward higher requirements for planning and architectural design of university campuses. In fact, the development of university campuses has been severely restricted by serious contradictions between the shortage of urban construction land and the expansion of middle school campuses. Therefore, in the case of limited construction land resources, how to integrate and optimize the building space and function of campus, improve the utilization rate of building space, make full use of the limited construction land, and create a rich and diverse space environment are difficult problems that are faced in the design of today's universities. In this paper, we discuss the integration strategy of main entrance space of university campus city through empirical research and put forward 4 value evaluation dimensions and 24 value evaluation factors. Moreover, we construct a numerical and geometric evaluation model, i.e., "CPCC," to complete the evaluation and optimization of the integration strategy. The purpose is to provide reference for the research object and same type of space on the interface of university campus city. We observed that the proposed CPCC model can effectively promote the historical process of the integration and symbiosis between the university campus and city. [ABSTRACT FROM AUTHOR]

In this paper, we define the space of functions Λ p -bounded variation on the plane and endow it with a norm under which it is a Banach space. In addition, we study some nonlinear integral equations and providing conditions for the functions and kernel involved in such equations under which we guarantee the existence and uniqueness in the space of functions of bounded variation in the sense of Shiba on the plane, Λ p B V I a b , ℝ . [ABSTRACT FROM AUTHOR]

The future pedagogical systems need anthropocentric inclusive educational programs in which the goal should be adjustable according to the knowledge requirements, intelligence, and learning objective of each student. Prioritizing these needs, innovative AI methods are required to assist and ensure the making of conscious educational decisions, in terms of clear identification and categorization with high accuracy of various forms of skills and knowledge of each student. This paper proposes a neuroevolution emerging technique that combines the searchability of evolutionary computation and the learning capability of a hybrid artificial neural networks method. Specifically, the proposed growing semiorganizing neural gas (GsONG) is a practical AI methodology utilizing advanced clustering techniques to enhance the learning experience by categorizing the true abilities, skills, and needs of learners, in an inclusive differentiated learning framework. It is a neural network architecture that includes competing and cooperating neurons with an unstructured mode whereby a cooperation-competition process delimits the topological neighborhood of neurons in a grid to identify patterns for which their classes are not known. To optimize the above process, a heuristic method was used that investigates the space of an objective function by regulating the optimal topologies of neurons that form pathway segments in a semi-contemplative manner. Based on the extensive experiments and results obtained from the GsONG clustering approach, the proposed algorithm can compensate with high accuracy for difficulties in multicriteria grouping and differentiation of uncertainty structures such as in small or tiny data sets. [ABSTRACT FROM AUTHOR]

On the premise of being familiar with ArcGIS Server technology, we build the architecture of the entire platform, including the basic support layer, data layer, service platform layer, and application layer, and build the entire environment of the platform. We make electronic maps through Arc Map, and collect, organize, and improve spatial data and attribute data, so as to achieve satisfactory accuracy and visual comfort. This study implements various map services under the Dojo framework, including basic map operations, information display and query, marker points, eagle eye diagrams, measurement, printing, and other functions, and uses JavaScript technology to improve user experience. We publish various services through ArcGIS Server, and realize fast and error-free invocation of each service. Based on the theory of runoff and runoff, ArcGIS software was used to study the hydrological information of the watershed, and to determine the catchment area threshold and hydrological response unit. Combined with the GIS spatial analysis method, the numerical simulation of rainfall and runoff in the study case area was carried out, and the variation of the annual rainfall-runoff coefficient was obtained. This study selects an area where stock planning was first proposed as the object of this research. Briefly, we introduce the construction of three-dimensional public space in a certain area, select thirteen typical three-dimensional public spaces as representatives for public evaluation, and explore their existing problems, mainly including the lack of adaptability of space functions and the lack of diversity in space design, privatization of operation management, low level of public perception, etc. Since then, in response to the public problems of the three-dimensional public space in a certain area, a targeted three-dimensional public space optimization strategy is proposed from the four levels of planning policy, urban design, management subject, and user subject. [ABSTRACT FROM AUTHOR]

The space of fractional Cauchy transforms plays a central role in classical complex analysis, harmonic analysis, and geometric measure theory. In this paper, we study the boundedness and compactness of product-type operators from the space of fractional Cauchy transforms to the Zygmund-type space in terms of the function theoretic characterization of Julia–Carathéodory type. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new theory of solving the multitarget control problem by introducing a machine learning framework in automatic driving and implementing the acquisition of excellent drivers' knowledge. Nowadays, there still exist some core problems that have not been fully realized by the researchers in automatic driving, such as the optimal way to control the multitarget objective functions of energy saving, safe driving, headway distance control, and comfort driving. It is also challenging to resolve the networks that automatic driving is relied on and to improve the performance of GPU chips on complex driving environments. According to these problems, we developed a new theory to map multitarget objective functions in different spaces into the same one and thus introduced a machine learning framework of SDL (super deep learning) for optimal multitarget control based on knowledge acquisition. We will present in this paper the optimal multitarget control by combining the fuzzy relationship of each multitarget objective function and the implementation of excellent drivers' knowledge acquired by machine learning. Theoretically, the impact of this method will exceed that of the fuzzy control method used in the automatic train. [ABSTRACT FROM AUTHOR]

Currently, the existing techniques of evaluating quality of teaching quality colleges and universities within China are based on classical and statistical methods. However, these methods are unable to accurately reflect the real and actual evaluation of teaching quality. Furthermore, in this era of computerization, education has also revamped itself and is not limited to the conventional lecturing approach. Nowadays, English has become one of the most important skills for foreigners as countries move toward internationalization resulting in a huge amount of data being collected in educational databases, which remains unused. Powerful tools are required to improve the quality of English teaching and reap the benefits of big data generated in classrooms. In this paper, online analytical processing (OLAP) in combination with a support vector machine (SVM) classification algorithm is adopted, and then the algorithm constructs the linear optimal decision function in the feature space. Through the training of sample data by the SVM algorithm, relatively high-quality classification results can be obtained on the target object, especially for high-dimensional cases. The proposed approach has an extremely efficient application value. Compared with the existing methods, the error of evaluation results can be greatly improved, which leads to further improvement of accuracy in terms of evaluation results. [ABSTRACT FROM AUTHOR]

We have defined the variable exponent of the Cesàro complex function space of formal power series. We have constructed the prequasi-ideal generated by s -numbers and this new space of complex functions. We present some topological and geometric structures of this class of ideal. The existence of Caristi's fixed point is examined. Some geometric properties related to the fixed point theory are presented. Finally, real-world examples and applications show solutions to some nonlinear difference equations. [ABSTRACT FROM AUTHOR]

Let X , d , μ be a metric measure space endowed with a metric d and a non-negative Borel doubling measure μ. Let L be a non-negative self-adjoint operator on L 2 X . Assume that the (heat) kernel associated to the semigroup e − t L satisfies a Gaussian upper bound. In this paper, we prove that the Musielak–Orlicz–Hardy space H φ , L X associated with L in terms of the Lusin-area function and the Musielak–Orlicz–Hardy space H L , G , φ X associated with L in terms of the Littlewood–Paley function coincide and their norms are equivalent. To do this, we first establish the discrete characterization of these two spaces. It improves the known results in the literature. [ABSTRACT FROM AUTHOR]

We have defined and studied the weighted Nakano sequence spaces of fuzzy functions. We have constructed the ideal generated by extended s -fuzzy functions and the sequence spaces of fuzzy functions. We present some topological and geometric structures of this class of ideal and multiplication mappings acting on this sequence space of fuzzy functions. Moreover, the existence of Caristi's fixed point is examined. To show how the work is done, some examples and applications to the existence of solutions for a class of nonlinear summable and matrix equations are also talked about. [ABSTRACT FROM AUTHOR]

The three-dimensional organic growth features of buildings have been given more and more attention according to the unique view representation regulations of the indoor construction industry, in order to optimize the usage and allocation efficiency of building space. To explore the configuration structure of building function space, the three-dimensional box dimension algorithm is used to measure the fractal dimension of the indoor and outdoor form of building space, and the two-dimensional and three-dimensional fractal characteristics of building space are compared and analyzed; the method of the second derivative is utilized for the automatic recognition of fractal scale-free areas, aiming at the imprecise problem of the artificial judgment of scale-free areas in earlier fractal research of interior and outdoor forms of architectural space. The experimental results show that the second derivative method can effectively and automatically identify the scale-free region. The coefficients of linear fitting are above 0.990, and the indoor and outdoor forms of architectural space have clear fractal characteristics. After applying the method, the three-dimensional fractal dimension grows, indicating that the interior and outdoor form usage of architectural space in this area is generally effective and compact. [ABSTRACT FROM AUTHOR]

This paper establishes the reality of a fixed point of Kannan's prequasinorm contraction mapping on the variable exponent function space of complex variables, demonstrating that it satisfies the property (R) and possesses a prequasinormal structure. We have established the presence of a fixed point of Kannan prequasinorm nonexpansive mapping on it and Kannan prequasinorm contraction mapping in the prequasi-Banach operator ideal, created by this function space and s -numbers. Finally, we provide some applications for solutions to summable equations and illustrate instances to corroborate our findings. [ABSTRACT FROM AUTHOR]

Using some new techniques, the necessary and sufficient conditions for Kadec-Klee property of Orlicz function spaces equipped with s-norms are presented. An original method that was used in the process of inquiry and the obtained results also systematically complete and broaden the characterization of Kadec-Klee property of Orlicz spaces. [ABSTRACT FROM AUTHOR]

Let θ ≥ 0 and p · be a variable exponent, and we introduce a new class of function spaces L p · , θ in a probabilistic setting which unifies and generalizes the variable Lebesgue spaces with θ = 0 and grand Lebesgue spaces with p · ≡ p and θ = 1. Based on the new spaces, we introduce a kind of Hardy-type spaces, grand martingale Hardy spaces with variable exponents, via the martingale operators. The atomic decompositions and John-Nirenberg theorem shall be discussed in these new Hardy spaces. [ABSTRACT FROM AUTHOR]

In this article, we introduce and study a new class of operators defined on a Cartesian product of ideal spaces of measurable functions. We use the general approach of the theory of vector lattices. We say that an operator T : E × F ⟶ W defined on a Cartesian product of vector lattices E and F and taking values in a vector lattice W is orthogonally biadditive if all partial operators T y : E ⟶ W and T x : F ⟶ W are orthogonally additive. In the first part of the article, we prove that, under some mild conditions, a vector space of all regular orthogonally biadditive operators O B A r E , F ; W is a Dedekind complete vector lattice. We show that the set of all horizontally-to-order continuous regular orthogonally biadditive operators is a projection band in O B A r E , F ; W . In the last section of the paper, we investigate orthogonally biadditive operators on a Cartesian product of ideal spaces of measurable functions. We show that an integral Uryson operator which depends on two functional variables is orthogonally biadditive and obtain a criterion of the regularity of an orthogonally biadditive Uryson operator. [ABSTRACT FROM AUTHOR]

The topological and geometric behaviors of the variable exponent formal power series space, as well as the prequasi-ideal construction by s -numbers and this function space of complex variables, are investigated in this article. Upper bounds for s -numbers of infinite series of the weighted n th power forward and backward shift operator on this function space are being investigated, with applications to some entire functions. [ABSTRACT FROM AUTHOR]

The deployment of cache and computing resources in 5G mobile communication networks is considered as an important way to reduce network transmission delay and redundant content transmission and improve the efficiency of content distribution and network computing processing capacity, which has been widely concerned and recognized by academia and industry. Aiming at the development trend of cache and computing resource allocation in 5G mobile communication networks, in order to improve the efficiency of content cache and reduce network energy consumption, a 5G network cache optimization strategy based on Stackelberg game was proposed, which modeled network operators and content providers as multimaster and multislave Stackelberg game model. Providers buy base station storage space from network operators to cache popular content. In this paper, we construct the strategy space and profit function of the two sides of the game and prove the existence of Nash equilibrium solution among content providers given a set of base station rental prices of network operators. In this paper, distributed iterative algorithm is used to solve the game model, and the optimal base station pricing of network operators and the optimal base station occupancy rate of content providers are obtained. [ABSTRACT FROM AUTHOR]

In this article, we define a kind of truncated maximal function on the Heisenberg space by M γ c f x = sup 0 < r < γ 1 / m B x , r ∫ B x , r f y d y. The equivalence of operator norm between the Hardy-Littlewood maximal function and the truncated maximal function on the Heisenberg group is obtained. More specifically, when 1 < p < ∞ , the L p norm and central Morrey norm of truncated maximal function are equal to those of the Hardy-Littlewood maximal function. When p = 1 , we get the equivalence of weak norm L 1 ⟶ L 1 , ∞ and M ̇ 1 , λ ⟶ W ̇ M 1 , λ . Those results are generalization of previous work on Euclid spaces. [ABSTRACT FROM AUTHOR]

In this paper, we discuss two variants of the generalized nonlinear vector variational-like inequality problem. We provide their solutions by adopting topological approach. Topological properties such as compactness, closedness, and net theory are used in the proof. The admissibility of the function space topology and KKM-Theorem have played important role in proving the results. [ABSTRACT FROM AUTHOR]

In this article, we consider an extensive class of monotone nonexpansive mappings. We use S -iteration to approximate the fixed point for monotone total asymptotically nonexpansive mappings in the settings of modular function space. [ABSTRACT FROM AUTHOR]

In this paper, we present some properties of integrable distributions which are continuous linear functional on the space of test function D ℝ 2 . Here, it uses two-dimensional Henstock–Kurzweil integral. We discuss integrable distributional solution for Poisson's equation in the upper half space ℝ + 3 with Dirichlet boundary condition. [ABSTRACT FROM AUTHOR]

The article titled "Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model" has been retracted by Hindawi, the publisher, due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, and availability of data, as well as inappropriate citations and incoherent content. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: On Neutrosophic Extension of the Maxwell Model: Properties and Applications" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that their usual quality checks did not identify these issues before publication and has implemented additional measures to safeguard research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: A New Extension of the Exponentiated Weibull Model Mathematical Properties and Modelling" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Positive Weighted Symmetry Function Kernels and Some Related Inequalities for a Generalized Class of Convex Functions" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: On Stackelberg Leader with Min-Max Followers to Solve Fuzzy Continuous Static Games" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Novel Analysis of Fuzzy Fractional Klein-Gordon Model via Semianalytical Method" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Notion of Complex Spherical Fuzzy Graph with Application" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Approximations of Intuitionistic Fuzzy Ideals over Dual Spaces by Soft Binary Relations" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: On Development of Neutrosophic Cubic Graphs with Applications in Decision Sciences" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi cannot vouch for the reliability of the article's content and regrets that these issues were not identified before publication. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Applications of Karry-Kalim-Adnan Transformation (KKAT) to Mechanics and Electrical Circuits" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Multiplicative Topological Properties on Degree Based for Fourth Type of Hex-Derived Networks" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]

The article titled "Retracted: Applications of Hesitant Interval Neutrosophic Linguistic Schweizer-Sklar Power Aggregation Operators to MADM" has been retracted by Hindawi due to evidence of systematic manipulation of the publication process. The investigation revealed discrepancies in scope, description of the research, availability of data, inappropriate citations, incoherent content, and compromised peer review. Hindawi acknowledges that the usual quality checks did not identify these issues before publication and has implemented additional measures to ensure research integrity. The corresponding author has been given the opportunity to respond to the retraction. [Extracted from the article]