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This paper illustrates the use of curriculum mapping as a process that can support productive boundary encounters between lecturers in an initial teacher education (ITE) programme as part of curriculum review. Using mathematics as the context, lecturers in a 1-year primary graduate ITE programme developed a curriculum map to identify the mathematical thinking opportunities available to their pre-service teachers in their courses and across the programme. The coordinated approach to curriculum analysis/mapping expanded lecturers' definition of mathematical skills and reasoning and their awareness of opportunities their students had to engage with mathematical ideas. The mapping process included collaborative discussions, document analysis and iterative development of a curriculum map. In an overcrowded curriculum, which responds to government policies and university initiatives such as embedding critical literacy, mathematical foundations and cross-disciplinary study, the mapping process has potential to meet multiple demands and agendas. In our study, the mapping process and the map offered purposeful and productive grounds for learning and development. They were central to facilitating dialogic boundary encounters between programme lecturers resulting in the re-conceptualisation of course and programme curriculum boundaries. We expect study findings will be of interest to programme leaders, lecturers and researchers facing the challenge of identifying and supporting the development of competencies and multi-literacies that span courses and programmes. [ABSTRACT FROM AUTHOR]

This paper delves into fixed point findings within a complete partially ordered b-metric space, focusing on mappings that adhere to weakly contractive conditions in the presence of essential topological characteristics. These findings represent modifications of established results and further extend analogous outcomes in the existing literature. The conclusions are substantiated by illustrative examples that strengthen the conclusion of the paper. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to compare the proof of the existence and uniqueness of fixed points for T -contractive mappings in various metric spaces and different distances regarding some techniques in mathematical analysis. Also, several comparisons to show the efficiency of the obtained result will be considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a regularized iterative scheme for solving the split common fixed point problem of asymptotically demicontractive and demimetric mappings in real Banach spaces. We then prove that the iterative scheme converges strongly to a solution to the problem, which is also a solution to a variational inequality problem. A split feasibility problem is also considered with the aid of our scheme. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new classes of mixed (S,T)-α-admissible mappings and interspersed (S, g,T)-α-admissible mappings and study the sufficient conditions for the existence and uniqueness of a common fixed point of generalized (αs, ξ, ħ, τ)-Geraghty contractive mapping in the framework of partial b-metric spaces. We also provide two examples to show the applicability and validity of our results. Moreover, we present an application to the existence of solutions to an integral equation by means of one of our results. [ABSTRACT FROM AUTHOR]

This paper aims to give an extended class of contractive mappings combining types of Suzuki contractions α-admissible mapping and Wardowski F-contractions in b-metric-like spaces. Our results cover and generalize many of the recent advanced results on the existence and uniqueness of fixed points and fulfill the Suzuki-type nonlinear hybrid contractions on various generalized metrics. [ABSTRACT FROM AUTHOR]

This paper presents the stability theorem for the T-Picard iteration scheme and establishes the existence and uniqueness theorem for fixed points concerning T-mean nonexpansive mappings within b-metric-like spaces. The outcome of our fixed point theorem substantiated the existence and uniqueness of solutions to the Fredholm-Hammerstein integral equations defined on time scales. Additionally, we provided two numerical examples from distinct time scales to support our findings empirically. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide examples to illustrate our findings and also apply these results to the ordinary differential equation to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

This article is devoted to the study of mappings with bounded and finite distortion defined in some domain of the Euclidean space. We consider mappings that satisfy some upper estimates for the distortion of the modulus of families of paths, where the order of the modulus equals to p, n - 1 < p ⩽ n. The main problem studied in the manuscript is the investigation of the boundary behavior of such mappings, more precisely, the distortion of the distance under mappings near boundary points. The publication is primarily devoted to definition domains with "bad boundaries", in which the mappings not even have a continuous extension to the boundary in the Euclidean sense. However, we introduce the concept of a quasiconformal regular domain in which the specified continuous extension is valid and the corresponding distance distortion estimates are satisfied; however, both must be understood in the sense of the socalled prime ends. More precisely, such estimates hold in the case when the mapping acts from a quasiconformal regular domain to an Ahlfors regular domain with the Poincar'e inequality. The consideration of domains that are Ahlfors regular and satisfy the Poincar'e inequality is due to the fact that, lower estimates for the modulus of families of paths through the diameter of the corresponding sets hold in these domains. (There are the so-called Loewner-type estimates). We consider homeomorphisms and mappings with branching separately. The main analytical condition under which the results of the paper were obtained is the finiteness of the integral averages of some majorant involved in the defining modulus inequality under infinitesimal balls. This condition includes the situation of quasiconformal and quasiregular mappings, because for them the specified majorant is itself bounded in a definition domain. Also, the results of the article are valid for more general classes for which Poletsky-type upper moduli inequalities are satisfied, for example, for mappings with finite length distortion. [ABSTRACT FROM AUTHOR]

This paper introduces the innovative concept of (τ, α)-weak contractive mappings. We establish several fixed point results without relying on conditions essential in prior works. Examples are presented to showcase our key findings, particularly in scenarios where earlier research outcomes are not applicable. Furthermore, we provide an application of our obtained results to fractional differential equations involving non-singular and non-local kernels. [ABSTRACT FROM AUTHOR]

We explore the intermixed method for finding a common element of the intersection of the solution set of a mixed variational inequality and the fixed point set of a nonexpansive mapping. We point out that Khuangsatung and Kangtunyakarn's statement [J. Inequal. Appl. 2023:1, 2023] regarding the resolvent utilized in their paper is not correct. To resolve this gap, we employ the epigraphical projection and the product space approach. In particular, we obtain a strong convergence theorem with a weaker assumption. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notion of (incident) higher-order generalized epiderivative for a set-valued map and obtain a crucial result of the epiderivative. Then we use this result to establish the higher-order sufficient and necessary optimality conditions of a constrained set-valued optimization problem. By virtue of the epiderivatives and the optimality conditions, we establish the higher-order mixed duality problem for the set-valued optimization problem and obtain the corresponding duality theorems. [ABSTRACT FROM AUTHOR]

In this paper, we consider a faster iterative method for approximating the fixed points of generalized α -nonexpansive mappings. We prove several weak and strong convergence theorems of the considered method in mild conditions within the control parameters. In order to validate our findings, we present some nontrivial examples of the considered mappings. Furthermore, we show that the class of mappings considered is more general than some nonexpansive-type mappings. Also, we show numerically that the method studied in our article is more efficient than several existing methods. Lastly, we use our main results to approximate the solution of a delay fractional differential equation in the Caputo sense. Our results generalize and improve many well-known existing results. [ABSTRACT FROM AUTHOR]

This paper delves into an inquiry that centers on the exploration of fractional adaptations of Milne-type inequalities by employing the framework of twice-differentiable convex mappings. Leveraging the fundamental tenets of convexity, Hölder's inequality, and the power-mean inequality, a series of novel inequalities are deduced. These newly acquired inequalities are fortified through insightful illustrative examples, bolstered by rigorous proofs. Furthermore, to lend visual validation, graphical representations are meticulously crafted for the showcased examples. [ABSTRACT FROM AUTHOR]

This paper studies λ-constacyclic codes and skew λ-constacyclic codes over the finite commutative non-chain ring R = Z4 + uZ4 + u²Z4 with u3 = 0 for λ = (1 + 2u + 2u²) and (3 + 2u + 2u²). We introduce distinct Gray maps and show that the Gray images of λ-constacyclic codes are cyclic, quasi-cyclic, and permutation equivalent to quasi-cyclic codes over Z4. It is also shown that the Gray images of skew λ-constacyclic codes are quasi-cyclic codes of length 2n and index 2 over Z4. Moreover, the structure of λ-constacyclic codes of odd length n over the ring R is determined and give some suitable examples. [ABSTRACT FROM AUTHOR]

The main aim of our manuscript is to present common fixed point solution for Urysohn integral equation 41, Our paper divided in to two folds, Firstly with the help of class function we established fixed point results for two pair of weakly compatible mapping satisfying the contractive condition of rational type in CVMS our work inspired from [15]. Secondly Common solution to the integral equation, .... [ABSTRACT FROM AUTHOR]

In this paper, we introduce triple θ-centralizers and weak triple θ-centralizers on an algebra A, where θ: A → A is a triple homomorphism. Some observations concerning triple θ-centralizers, weak triple θ-centralizers and approximate weak triple θ-centralizers are given. [ABSTRACT FROM AUTHOR]

In this paper, we consider some numerical aspects of branched continued fractions as special families of functions to represent and expand analytical functions of several complex variables, including generalizations of hypergeometric functions. The backward recurrence algorithm is one of the basic tools of computation approximants of branched continued fractions. Like most recursive processes, it is susceptible to error growth. Each cycle of the recursive process not only generates its own rounding errors but also inherits the rounding errors committed in all the previous cycles. On the other hand, in general, branched continued fractions are a non-linear object of study (the sum of two fractional-linear mappings is not always a fractional-linear mapping). In this work, we are dealing with a confluent branched continued fraction, which is a continued fraction in its form. The essential difference here is that the approximants of the continued fraction are the so-called figure approximants of the branched continued fraction. An estimate of the relative rounding error, produced by the backward recurrence algorithm in calculating an nth approximant of the branched continued fraction expansion of Horn's hypergeometric function H4, is established. The derivation uses the methods of the theory of branched continued fractions, which are essential in developing convergence criteria. The numerical examples illustrate the numerical stability of the backward recurrence algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized weakly contractive type multi-valued mapping with respect to a single-valued mapping and prove the existence of PPF dependent coincidence points in Banach spaces. Further, we introduce the notion of generalized weakly contractive type multivalued mappings for a pair of multi-valued mappings and prove the existence of PPF dependent common fixed points in Banach spaces. We draw some corollaries and provide nontrivial examples to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence and uniqueness of solutions for the following nonlinear multi-order fractional differential equation with integral boundary conditions { (C D 0 + α u) (t) + ∑ i = 1 m λ i (t) (C D 0 + α i u) (t) + ∑ j = 1 n μ j (t) (C D 0 + β j u) (t) + ∑ k = 1 p ξ k (t) (C D 0 + γ k u) (t) + ∑ l = 1 q ω l (t) (C D 0 + δ l u) (t) + σ (t) u (t) + f (t , u (t)) = 0 , t ∈ [ 0 , 1 ] , u ″ (0) = u ‴ (0) = 0 , u ′ (0) = η 1 ∫ 0 1 u (s) d s , u (1) = η 2 ∫ 0 1 u (s) d s , where 0 < δ 1 < δ 2 < ⋯ < δ q < 1 < γ 1 < γ 2 < ⋯ < γ p < 2 < β 1 < β 2 < ⋯ < β n < 3 < α 1 < α 2 < ⋯ < α m < α < 4 and η 1 + 2 (1 − η 2) ≠ 0 . Using a fixed point theorem and Banach contractive mapping principle, we obtain some existence and uniqueness results. [ABSTRACT FROM AUTHOR]

It is known that a strict contraction on a complete metric space with a graph possesses a fixed point. In the present paper, we show that this property holds for single valued and set-valued self-mappings of metric spaces with graphs that are of the contractive type. We also show the convergence of iterates of these mappings to fixed points. In particular, our results are true for metric spaces with symmetric graphs. [ABSTRACT FROM AUTHOR]

In the year 2016, Pragadeeswarar et al. [V. Pragadeeswarar, M. Marudai, P. Kumam, J. Nonlinear Sci. Appl., 9 (2016), 1911-1921] considered a special class of multi-valued mappings and investigated the existence of best proximity points for such class of mappings which generalizes the fixed point result established by Choudhury et al. [B. S. Choudhury, N. Metiya, Arab J. Math. Sci., 17 (2011), 135-151] in the context of partially ordered metric spaces. In this note, we have showed that the best proximity point result is a direct consequence of the corresponding fixed point result. In the last part of this note, we applied our result in [V. Pragadeeswarar, M. Marudai, P. Kumam, J. Nonlinear Sci. Appl., 9 (2016), 1911-1921, Example 2.2] to validate our claim. [ABSTRACT FROM AUTHOR]

Let X be a continuum. A mean is a continuous function m: X ×X → X such that m(x,x) = x and m(x,y)=m(y,x) for every x,y ∈ X. In this note we give an example to respond negatively a question that appears in [3] and observe that using a theorem that appears in [1], two other questions posed in [3] are answered. [ABSTRACT FROM AUTHOR]

This paper proposes an extended state observer (ESO) based data-driven set-point learning control (DDSPLC) scheme for a class of nonlinear batch processes with a priori P-type feedback control structure subject to nonrepetitive uncertainties, by only using the process input and output data available in practice. Firstly, the unknown process dynamics is equivalently transformed into an iterative dynamic linearization data model (IDLDM) with a residual term. A radial basis function neural network is adopted to estimate the pseudo partial derivative information related to IDLDM, and meanwhile, a data-driven iterative ESO is constructed to estimate the unknown residual term along the batch direction. Then, an adaptive set-point learning control law is designed to merely regulate the set-point command of the closed-loop control structure for realizing batch optimization. Robust convergence of the output tracking error along the batch direction is rigorously analyzed by using the contraction mapping approach and mathematical induction. Finally, two illustrative examples from the literature are used to validate the effectiveness and advantage of the proposed design. • Novel extended state observer (ESO) based data-driven set-point learning control (DDSPLC). • Iterative dynamic linearized data model (IDLDM) for nonlinear batch processes. • Use the radial basis function neural network (RBFNN) to approximate pseudo partial derivative. • Set-point learning law with an adaptive learning gain for a priori P-type feedback structure. • Robust convergence of the resulting ILC system along the batch direction is rigorously analyzed. [ABSTRACT FROM AUTHOR]

It is known that a strict contraction on complete metric spaces with graphs possesses a fixed point. In the present paper we show that this property holds for mappings on complete metric spaces with graphs which are merely contractive. We also obtain some stability results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of analyzing the performance of 3D face alignment (3DFA), or facial landmark localization. This task is usually supervised, based on annotated datasets. Nevertheless, in the particular case of 3DFA, the annotation process is rarely error-free, which strongly biases the results. Alternatively, unsupervised performance analysis (UPA) is investigated. The core ingredient of the proposed methodology is the robust estimation of the rigid transformation between predicted landmarks and model landmarks. It is shown that the rigid mapping thus computed is affected neither by non-rigid facial deformations, due to variabilities in expression and in identity, nor by landmark localization errors, due to various perturbations. The guiding idea is to apply the estimated rotation, translation and scale to a set of predicted landmarks in order to map them onto a mathematical home for the shape embedded in these landmarks (including possible errors). UPA proceeds as follows: (i) 3D landmarks are extracted from a 2D face using the 3DFA method under investigation; (ii) these landmarks are rigidly mapped onto a canonical (frontal) pose, and (iii) a statistically-robust confidence score is computed for each landmark. This allows to assess whether the mapped landmarks lie inside (inliers) or outside (outliers) a confidence volume. An experimental evaluation protocol, that uses publicly available datasets and several 3DFA software packages associated with published articles, is described in detail. The results show that the proposed analysis is consistent with supervised metrics and that it can be used to measure the accuracy of both predicted landmarks and of automatically annotated 3DFA datasets, to detect errors and to eliminate them. Source code and supplemental materials for this paper are publicly available at https://team.inria.fr/robotlearn/upa3dfa/. [ABSTRACT FROM AUTHOR]

The Topographic Chart of the Kingdom of Poland (pol. Topograficzna Karta Królestwa Polskiego, commonly referred to as 'the Quartermaster's Map', hereinafter: TKKP) is the first Polish modern topographic map of Poland (1:126,000, 1843). Cartographic historians acclaim its conception by the General Quartermaster of the Polish Army, noting its editorial principles and technical execution as exemplars of the early 19th-century cartographic standards. Today, it stands as a national heritage relic, furnishing invaluable insights into the former Polish Kingdom's topography. Although extensively utilised in geographical and historical inquiries, the TKKP has yet to undergo a comprehensive geomatic investigation and publication as spatial data services. Primarily, this delay stems from the challenges of mosaicking and georeferencing its 60 constituent sheets, owing to the uncertain mathematical framework and irregular sheet cuts. In 2023, the authors embarked on rectifying this by creating a unified TKKP mosaic and georeferencing the map to contemporary reference data benchmarks. This endeavour involved scrutinising the map's mathematical accuracy and verifying prior findings. The resultant product is accessible via the 'Maps with the Past' platform, developed by the Institute of History of the Polish Academy of Sciences The dissemination of raster data services adhering to OGC standards such as WMTS (Web Map Tile Service), ECW (Enhanced Compression Wavelet), and COG (Cloud Optimized GeoTIFF) facilitates the swift and seamless integration of the generated data into web and GIS tools. The digital edition of the TKKP emerges as a pivotal resource for investigations spanning natural and anthropogenic environmental transformations, sustainable development, and cultural heritage studies. [ABSTRACT FROM AUTHOR]

The automatic control of excavator operation trajectories is a pivotal technology for autonomous excavators, with the essential prerequisite being the real-time measurement of manipulator poses. Given the complexity of the operating environment, traditional sensor-based measurement methods face limitations, whereas visual measurement emerges as a promising technique. Accurately measuring excavator manipulator poses involves a crucial aspect: mapping the relationship between image information and poses. First, to address the significant errors in pose prediction encountered with machine learning techniques like artificial neural networks, this work introduces a mathematical model for mapping this relationship, referred to as the pose mapping mathematical model, which includes calibrating model parameters. Second, to address the sensitivity of initial values in the calibration process, we propose a residual-guided initialization algorithm. This algorithm aims to ensure that initial values closely approximate the ground truth values, thus preventing matrix singularity at the source and avoiding parameter estimation divergence. Third, to tackle challenges such as unstable lighting conditions and discrepancies between the dataset and the mathematical model, we introduce the random sample consensus-driven Levenberg–Marquardt parameter optimization algorithm to enhance parameter estimation accuracy. Experiments with static and dynamic online measurement demonstrate that our method reduces pose measurement errors compared to existing methods. This research lays a solid foundation for developing visual measurement techniques for excavators and automated manipulator control based on visual measurements, also serving as a valuable reference for research on mechanical arms. [ABSTRACT FROM AUTHOR]

We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. We use these results in order to write optimality conditions for a special kind of solutions for set optimization problems. [ABSTRACT FROM AUTHOR]

Discrete chaotic maps are a mathematical basis for many useful applications. One of the most common is chaos-based pseudorandom number generators (PRNGs), which should be computationally cheap and controllable and possess necessary statistical properties, such as mixing and diffusion. However, chaotic PRNGs have several known shortcomings, e.g., being prone to chaos degeneration, falling in short periods, and having a relatively narrow parameter range. Therefore, it is reasonable to design novel simple chaotic maps to overcome these drawbacks. In this study, we propose a novel fractal chaotic tent map, which is a generalization of the well-known tent map with a fractal function introduced into the right-hand side. We construct and investigate a PRNG based on the proposed map, showing its high level of randomness by applying the NIST statistical test suite. The application of the proposed PRNG to the task of generating surrogate data and a surrogate testing procedure is shown. The experimental results demonstrate that our approach possesses superior accuracy in surrogate testing across three distinct signal types—linear, chaotic, and biological signals—compared to the MATLAB built-in randn() function and PRNGs based on the logistic map and the conventional tent map. Along with surrogate testing, the proposed fractal tent map can be efficiently used in chaos-based communications and data encryption tasks. [ABSTRACT FROM AUTHOR]

Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human experts. In particular, we introduce a surrogate model where yield surfaces are expressed in terms of a set of single-variable feature mappings obtained from supervised learning. A post-processing step is then used to re-interpret the set of single-variable neural network mapping functions into mathematical form through symbolic regression. This divide-and-conquer approach provides several important advantages. First, it enables us to overcome the scaling issue of symbolic regression algorithms. From a practical perspective, it enhances the portability of learned models for partial differential equation solvers written in different programming languages. Finally, it enables us to have a concrete understanding of the attributes of the materials, such as convexity and symmetries of models, through automated derivations and reasoning. Numerical examples have been provided, along with an open-source code to enable third-party validation at https://github.com/bbhm-90/SymPolyNN. [ABSTRACT FROM AUTHOR]

This study aims to establish common fixed point theorems for a pair of compatible self-mappings within the framework of extended parametric  S b -metric spaces. To support our assertions, we provide corollaries and examples accompanied with graphical representations. Moreover, we leverage our principal outcome to guarantee the existence of a common solution to a system of integral equations. [ABSTRACT FROM AUTHOR]

For this study, we investigate the existence and uniqueness of local solutions and derive a blow-up solution for a quasi-linear bi-hyperbolic equation under dynamic boundary conditions. We utilize the contraction mapping concept to demonstrate the solution's local well-posedness and employ a concavity approach to establish the blow-up result. [ABSTRACT FROM AUTHOR]

The objective of this research is to present new fixed point theorems for two separate families of fuzzy-dominated mappings. These mappings must satisfy a unique locally contraction in a complete b-multiplicative metric space. Also, we have obtained novel results for families of fuzzy-dominated mappings on a closed ball that meet the requirements of a generalized locally contraction. This research introduces new and challenging fixed-point problems for families of ordered fuzzy-dominated mappings in ordered complete b-multiplicative metric spaces. Moreover, we demonstrate a new concept for families of fuzzy graph-dominated mappings on a closed ball in these spaces. Additionally, we present novel findings for graphic contraction endowed with graphic structure. These findings are groundbreaking and provide a strong foundation for future research in this field. To demonstrate the uniqueness of our novel findings, we provide evidence of their applicability in obtaining the common solution of integral and fractional differential equations. Our findings have resulted in modifications to several contemporary and classical results in the research literature. This provides further evidence of the originality and impact of our work. [ABSTRACT FROM AUTHOR]

The object of this study is the process of risk management at enterprises in the metallurgical industry as a subject of foreign economic activity. Under the conditions of an export-oriented economy, it is important to have tools for early response to crises and challenges caused by various factors. Volatility of the market and global and domestic prices for key products and raw materials add uncertainty and encourage management to look for tools to protect their financial income. The construction of a risk map and the use of mathematical tools for forecasting and minimizing the negative consequences of the occurrence of risky events could contribute to making optimal management decisions in operational activities and in the pricing process. Interpretation of the risk management cycle for the needs of enterprises in the metallurgical industry will make it possible to adequately identify the risks inherent in the industry and devise measures for flexible response to crises and challenges. In the course of the study, it was found out that exporting companies need protection, first of all, against price risk, which increases significantly under the conditions of inflation and due to jumps in the consumer price index in a particular country. It is suggested to use hedging as a protection tool. Determining the perimeter of risk hedging by means of a risk-oriented selection of indicators (external and internal, commercial, and non-commercial risks) depending on a certain market situation will make it possible to establish a correlation between key influencing factors. The implementation of the risk-hedging cycle in the practice of the enterprises in the metallurgical industry will make it possible to ensure flexible management of the pricing procedure for metal products both in the domestic market and during foreign trade. [ABSTRACT FROM AUTHOR]

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The efficacious forecasting of single‐station atmospheric temperature profiles can provide essential support for the structural design and flight missions of spacecrafts in near space. However, empirical models and reference atmospheric models most are calculations of the average state of the atmosphere profiles. Numerical assimilation models require expensive computational costs to improve the accuracy for medium and long‐term forecasting. It has been still a challenge to refined predict short‐term temperature profiles of near space at a low‐cost. We present a temperature profile operator method for refined modeling in the stratosphere by fusing the ability of Long Short‐Term Memory (LSTM) networks or its variants‐ bidirectional LSTM (BiLSTM) to exploit time series correlated information and deep operator networks (DeepONets) to approximate the solution operator of temperature profiles. It consists of three subnetworks. The first subnetwork is used to approximate the discrete temperature profile function, the second net is applied to represent the spatial information of pressure heights, and the third branch is utilized to encode the time domain of the temperature profile operator. We first use the hourly low latitude temperature data (20–50 km) from ERA5 for training, verification and iterative testing in the next 48 hr. The results denote that the temperature profile operator network has a stable and low error of cumulative generalization, and the BiLSTM operator significantly outperform the other models. We also apply two scenarios to testing the refined applicability of the high latitude temperature profile operator and the mid latitude wind profile operator in the stratosphere. This work provides a novel perspective for us to study the refined single‐station modeling of the upper and middle atmosphere. Plain Language Summary: The temporal and spatial distribution mechanism of physical parameters in near space is very complex. It is of great significance to carry out fine modeling and forecasting of atmospheric temperature profiles for spacecrafts in near space. In this study, taking a single‐station temperature profile in the stratosphere as the object, the mathematical mapping problem of temperature operator is realized by a new deep learning method (deep operator networks). This provides a new research perspective for fine spatiotemporal modeling of temperature profiles. The proposed temperature operator shows low cumulative error performance in forecasting low latitude temperature profiles, and is also suitable for high latitude temperature profiles and mid latitude wind profiles in the stratosphere. Key Points: A deep neural operator method is utilized to forecast hourly atmospheric temperature profiles in the stratosphereThe temperature profile operator network based on BiLSTM denotes lower cumulative error in multi‐step iterative forecastingThe proposed method exhibits potential performance in different locations and atmospheric variables [ABSTRACT FROM AUTHOR]

Network function virtualization (NFV) technology deploys network functions as software functions on a generalised hardware platform and provides customised network services in the form of service function chain (SFC), which improves the flexibility and scalability of network services and reduces network service costs. However, irrational resource allocation during service function chain mapping will cause problems such as low resource utilisation, long service request processing time and low mapping rate. To address the unreasonable problem of service mapping resource allocation, an improved service function chain mapping resource allocation method (SA3C) based on the Asynchronous advantageous action evaluation algorithm (A3C) is proposed. This study proposes an SFC mapping model and a mathematical model for joint allocation, which modeled the minimization of processing time as a Markov process. The main network was trained and multiple sub‐networks were generated in parallel using the ternary and deep reinforcement learning algorithm A3C, with the goal of identifying the optimal resource allocation strategy. The experimental simulation results show that compared with the Actor‐Critic (AC) and Policy Gradient (PG) methods, SA3C algorithm can improve the resource utilisation by 9.85%, reduce the total processing time by 10.72%, and improve the mapping rate by 6.72%, by reasonably allocating node computational resources and link bandwidth communication resources. [ABSTRACT FROM AUTHOR]

In the article, we considered the fixed point problem for contractive mappings of integral type in the setting of b-metric spaces for the first time. First, we introduced the concepts of ϑ-weak contraction and ϑ-ψ-weak contraction. Second, the existence and uniqueness of fixed points of contractive mappings of integral type in b-metric spaces were studied. Meanwhile, two examples were given to prove the feasibility of our results. As an application, we proved the solvability of a functional equation arising in dynamic programming. [ABSTRACT FROM AUTHOR]

We develop new tools for the construction of fixed point sets in digital topology. We define excludable points and show that these may be excluded from all freezing sets. We show that articulation points are excludable. We also present results concerning points that must belong to a freezing set and often are easily recognized. These include points of degree 1 and some local extrema. [ABSTRACT FROM AUTHOR]

The aim of this survey article, is to present in one place the recently published results on S JS-metric spaces, their generalizations and applications. We start with S JS-metric spaces and study their properties. Then we deal with abstract S JS-topological spaces induced by S JS-metric and present several classical results including Cantor’s intersection theorem. Next the notion of sequentially compactness on S JS-metric spaces and properties of sequentially compact S JS-metric spaces are studied. Some fixed point theorems are obtained for integral type contractive mappings. Finally we prove several new results on fixed point for rational type contractive mappings, obtain Ekeland’s variational principle on S JS-metric spaces as an application and in the end also present results regarding best S JS-proximity point with application. [ABSTRACT FROM AUTHOR]

In this article, we extend some recently fixed point theorems in the setting of G-fuzzy metric spaces. We introduce some new concepts of contractions called γ-contractions and γ-weak contractions. We prove some fixed point theorems for mappings providing γ-contractions and γ-weak contractions. On the other hand, we consider a more general class of auxiliary functions in the contractivity condition. [ABSTRACT FROM AUTHOR]

The purpose of this study is to explore the existence and uniqueness of the best proximity points for α , Θ -proximal contractions, a novel concept introduced in the context of F -metric spaces. Moreover, we provide an example to show the usability of the obtained results. To broaden the scope of this research area, we leverage our best proximity point results to demonstrate the existence and uniqueness of solutions for differential equations (equation of motion) and also for fractional differential equations. [ABSTRACT FROM AUTHOR]