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The stochastic approximation (SA) method stands as the foundational mathematical tool for modern large-scale optimization and machine learning. Therefore, gaining a theoretical understanding of SA algorithms is of fundamental interest. In their paper titled "A Lyapunov Theory for Finite-Sample Guarantees of Markovian Stochastic Approximation," Chen et al. present a unified Lyapunov framework for the finite-sample analysis of a Markovian SA algorithm under a contractive operator with respect to an arbitrary norm. The key novelty lies in the construction of a smooth Lyapunov function called the generalized Moreau envelope. The authors demonstrate the effectiveness of their SA results in the context of reinforcement learning (RL), specifically through popular algorithms such as variants of temporal difference (TD) learning and Q-learning. As byproducts, the results provide theoretical insights into the efficiency of bootstrapping in TD learning with eligibility traces and the bias-variance tradeoff in off-policy learning. This paper develops a unified Lyapunov framework for finite-sample analysis of a Markovian stochastic approximation (SA) algorithm under a contraction operator with respect to an arbitrary norm. The main novelty lies in the construction of a valid Lyapunov function called the generalized Moreau envelope. The smoothness and an approximation property of the generalized Moreau envelope enable us to derive a one-step Lyapunov drift inequality, which is the key to establishing the finite-sample bounds. Our SA result has wide applications, especially in the context of reinforcement learning (RL). Specifically, we show that a large class of value-based RL algorithms can be modeled in the exact form of our Markovian SA algorithm. Therefore, our SA results immediately imply finite-sample guarantees for popular RL algorithms such as n-step temporal difference (TD) learning, TD (λ) , off-policy V-trace, and Q-learning. As byproducts, by analyzing the convergence bounds of n-step TD and TD (λ) , we provide theoretical insight into the problem about the efficiency of bootstrapping. Moreover, our finite-sample bounds of off-policy V-trace explicitly capture the tradeoff between the variance of the stochastic iterates and the bias in the limit. Funding: This work was supported by RTX, the National Science Foundation [Grants 2019844, 2107037, 211247, 2112533, 2144316, and 2240982], and the Machine Learning Laboratory at University of Texas at Austin. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.0249. [ABSTRACT FROM AUTHOR]

Two of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to some interesting subclasses of those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs. [ABSTRACT FROM AUTHOR]

In this paper, we study a type of nonlinear hybrid Δ-difference equations of fractional-order. The main objective is to establish some stability criteria including the Ulam–Hyers stability, generalized Ulam–Hyers stability together with the Mittag-Leffler–Ulam–Hyers stability for the addressed problem. Prior to the stabilization processes, solvability criteria for the existence and uniqueness of solutions are considered. For this purpose, a hybrid fixed point theorem for triple operators and the Banach contraction mapping principle are applied, respectively. For the sake of illustrating the practical impact of the proposed theoretical criteria, we finish the paper with particular examples. [ABSTRACT FROM AUTHOR]

In this paper we investigate the existence of a solution of Integral equations of fractional order via Hadamard's fractional integral by reducing the research to the search of the existence of fixed points of appropriate operators. The nonlinear alternative fixed point theorem for the sum of a completely continuous operator and a contraction one in Frechet spaces due to Avraniescu and a fractional version of Pachpatte's inequality are the main tools in this study. We demonstrate the existence of a solution with a suitable illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new mapping namely L-contraction for fixed function and we also prove a novel fixed function theorem using L-contraction mapping. Moreover, we apply our result to solve integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the following integral system u i (x) = ∫ ℝ n u i + 1 p i + 1 (y) | x − y | n − α d y , i = 1 , 2 , ... , m − 1 , u m (x) = ∫ ℝ n u 1 p 1 (y) | x − y | n − α d y , m ≥ 1 , n ≥ 1 , where u i > 0 , 0 < α < n , and p i > 1 (i = 1 , 2 , ... , m). When m ∈ { 1 , 2 } , such an integral system is associated with the best constants of the Hardy–Littlewood–Sobolev inequality. Chen, Li and their cooperators obtained optimal integrability intervals of the finite energy solutions by an argument of contraction and shrinking operators. This result is helpful to well understand the classification of the extremal functions of the Hardy–Littlewood–Sobolev inequality. The critical condition plays a key role in their work. In this paper, we study optimal integrability intervals when the positive solutions have some initial integrability. Now, the critical condition is not necessary, and we apply a weaker condition, the Serrin-type condition, to establish some important relations of exponents which come into play to lift the regularity. In addition, we also generalize this result to the case of m ∈ ℤ + . [ABSTRACT FROM AUTHOR]

The unique solvability of the inverse problem of recovering the source function in a nonuniformly parabolic equation with many independent variables in a bounded domain is proved. As an additional condition, the integral observation condition is given. The unknown source function can be found by iteration from the operator equation with contraction operator. An example of an the inverse problem for which the results proved in this paper are applicable is presented. The results obtained for the inverse problem are based on the preliminary study of the unique solvability of the corresponding direct problem, which is also of interest in itself. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a novel fixed point iterative scheme based on Green's function, called the Picard–Ishikawa–Green's iterative scheme and use it in approximating the solution of boundary value problems (BVPs). It is proved that Picard–Ishikawa–Green's scheme converges strongly for an integral operator which represents the solution of BVP and the scheme is stable. Moreover, we prove that the integral operator is a contraction. Furthermore, it is shown that the novel scheme converges faster than all of Ishikawa–Green's, Khan–Green's, and Mann–Green's schemes. Finally, numerical examples are given to substantiate the validity of our results for third‐order BVPs. Our results extend and generalize several other results in literature. [ABSTRACT FROM AUTHOR]

Telecommunications companies are constantly chasing continuous technological advances with their management methods of Operations & Maintenance (O&M) that still struggle to turn their eye toward innovation and simplification of processes. In a future that aims at fully fiber-optic networks, the objective of the research is to propose guidelines and provide data to support the Wholesale Operator for the definition of the acceptable attenuation threshold on the Passive Optical Network Fiber-To-The-Home (PON FTTH) infrastructure to determine the Service Level Agreements (SLA) to be contracted with Retail Operators. Following exceeding the threshold, the Retail Operator has the right to open a Trouble Ticket to request the resolution of the anomaly. Consequently, the definition of the attenuation threshold strongly affects the number of Trouble Tickets to be managed and the related costs the Wholesale Operator bears. This paper analyzes a specific case of the PON FTTH network of the Italian wholesale operator Open Fiber. The studied infrastructure, with a length of 11 km, allows a maximum attenuation of 37 dB without degrading the service. An economic model has been proposed to assess the cost impact of moving the attenuation threshold in the SLA. [ABSTRACT FROM AUTHOR]

In this paper, a generalization of the fixed point theorem of the Reichtype mapping on a complete metric space (X,d) Xd is given. Continuous, injective and sub-sequentially convergent mapping T was used, as well as it is taken that function f is from the class Θ continuous monotonically nondecreasing functions: [0,+∞) f: [0,+∞) such that f-1(0)={0}, where it is additionally assumed that it is subadditive, i.e. f (x + y) ≤ f (x) + f (y), for each x, y ∊ [0,+∞). [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with the optimal integrability, regularity and symmetry of integrable solutions for the following Wolff type integral systems: (1.1) { u (x) = R 1 (x) W β , γ (v q) (x) , u (x) > 0 , x ∈ R N , v (x) = R 2 (x) W β , γ (u p) (x) , v (x) > 0 , x ∈ R N , where γ > 2 , β > 0 , β γ < N , p , q > γ − 1 with γ − 1 p + γ − 1 + γ − 1 q + γ − 1 = N − β γ N , R 1 , R 2 are double bounded in R N and W β , γ (h) (x) : = ∫ 0 ∞ [ ∫ B t (x) h (y) d y t N − β γ ] 1 γ − 1 d t t. Firstly, we prove the optimal integrability and boundedness of solutions (u , v) ∈ L p + γ − 1 (R N) × L q + γ − 1 (R N) for system (1.1) , by constructing a nonlinear, contracting operator and applying the regularity lifting lemma of C. Ma, W. Chen and C. Li (2011) [21]. Moreover, we exploit the general regularity lifting theorem to derive the Lipschitz continuity of u and v when R 1 ≡ R 2 ≡ 1 in R N. These extend the above important results of C. Ma, W. Chen and C. Li to γ > 2. We also prove that u and v vanish at infinity. As the corollaries of the above results, we obtain the optimal integrability, boundedness and the property of vanishing at infinity of integrable solutions for the corresponding γ -Laplace and k -Hessian systems. Secondly, we use the method of moving planes in integral forms to prove the symmetry and monotonicity of solutions (u , v) ∈ L p + γ − 1 (R N) × L q + γ − 1 (R N) for system (1.1) when R 1 ≡ R 2 ≡ 1 in R N , which extends the useful result of W. Chen and C. Li (2011) [5] to γ > 2. In comparison with the above two papers, Minkowski's inequality is crucial in our proofs. We believe that our arguments can be used to prove similar results for other Wolff type integral systems when γ > 2. [ABSTRACT FROM AUTHOR]

In this paper, we extend and improve a common fixed point theorem of G. Jungck. We utilize the notions of weakly commuting and compatible mappings in probabilistic Banach spaces to prove some common fixed point theorems for improved type Jungck contractions. In addition, we present some examples which support our theorems. [ABSTRACT FROM AUTHOR]

The interval Newton method, which combines the Newton method with the interval arithmetic and branch-and-prune algorithm, has been applied to the problem of finding all direct current operating points of nonlinear circuits. The modified linear programming narrowing technique has also been proposed to improve the computational efficiency of the interval Newton method when applying to a circuit whose nonlinear elements are only diodes and bipolar junction transistors. In this paper, a contraction operator based on interval linearization has been applied to further improve the performances. In addition, the application of the proposed method to circuits containing MOSFET is presented. The numerical experimental results on some test nonlinear circuits indicate that the proposed method can further reduce the number of search boxes and improve the computation time. [ABSTRACT FROM AUTHOR]

In open quantum systems, the quantum Zeno effect consists in frequent applications of a given quantum operation, e.g., a measurement, used to restrict the time evolution (due, for example, to decoherence) to states that are invariant under the quantum operation. In an abstract setting, the Zeno sequence is an alternating concatenation of a contraction operator (quantum operation) and a C 0 -contraction semigroup (time evolution) on a Banach space. In this paper, we prove the optimal convergence rate O (1 n) of the Zeno sequence by proving explicit error bounds. For that, we derive a new Chernoff-type n -Lemma, which we believe to be of independent interest. Moreover, we generalize the convergence result for the Zeno effect in two directions: We weaken the assumptions on the generator, inducing the Zeno dynamics generated by an unbounded generator, and we improve the convergence to the uniform topology. Finally, we provide a large class of examples arising from our assumptions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an orthogonal L ⋆ -contraction map concept and prove the fixed-point theorem in an orthogonal complete Branciari metric space (OCBMS). We also provide illustrative examples to support our theorems. We demonstrated the existence of a uniqueness solution to the fourth-order differential equation using a more orthogonal L ⋆ contraction operator in OCBMS as an application of the main results. [ABSTRACT FROM AUTHOR]

In this paper we investigate AGM belief contraction operators by using the tools of algebraic logic. We generalize the notion of contraction to arbitrary finitary propositional logics, and we show how to switch from a syntactic-based approach to a semantic one. This allows to build a solid bridge between the validity of AGM postulates in a propositional logic and specific algebraic properties of its intended algebraic counterpart. Such a connection deserves particular attention when we deal with maxichoice contractions, as studied in the final part of the paper. [ABSTRACT FROM AUTHOR]

Discussions of the issue of iterated belief revision are commonly accompanied by the presentation of three "concrete" operators: natural, restrained and lexicographic. This raises a natural question: What is so distinctive about these three particular methods? Indeed, the common axiomatic ground for work on iterated revision, the AGM and Darwiche-Pearl postulates, leaves open a whole range of alternative proposals. In this paper, we show that it is satisfaction of an additional principle of "Independence of Irrelevant Alternatives", inspired by the literature on Social Choice, that unites and sets apart our three "elementary" revision operators. A parallel treatment of iterated belief contraction is also given, yielding a family of elementary contraction operators that includes, besides the well-known "conservative" and "moderate" operators, a new contraction operator that is related to restrained revision. [ABSTRACT FROM AUTHOR]

This paper introduces a new iteration process for the approximation of fixed points of contraction mapping. We prove the comparison theorem to indicate that our iteration process converges faster than the other iteration processes and also prove data dependence, stability. and convergence results. Moreover, we give numerical examples to check the performance of our algorithm over the Piri, SM, CR, and K* iterations process for different types of functions. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a common fixed point theory for a pair of multivalued operators in complete metric spaces. Existence and stability results for the common fixed point problem will be discussed. The approach is based on some fixed point results for multivalued graphical contractions and for multivalued operators of Feng-Liu type. Our results extend to the multivalued case some recent results in the literature. [ABSTRACT FROM AUTHOR]

A newly developed method in the mixed space–wavenumber domain is proposed for 3D DC resistivity modeling in anisotropic structures. Unlike the traditional method for numerical simulation of DC resistivity, this method performs a 2D Fourier transform directly on the partial differential equation of DC abnormal potential along the horizontal direction, so that the horizontal direction is converted into the wavenumber domain while the vertical direction remains in the spatial domain. In this way, the 3D partial differential equation in the spatial domain is transformed into a 1D ordinary differential equation in different wave numbers. Therefore, a large-scale 3D numerical simulation problem is decomposed into many 1D numerical simulation problems. The 1D finite element method is used to solve the equations, and a contraction operator is used for iterative calculation to obtain a highly accurate solution. The accuracy of the algorithm is verified by comparison with the goal-oriented adaptive finite element method. Compared with the COMSOL Multiphysics commercial finite element simulation software, the algorithm in this paper has high computational efficiency. To identify the electrical anisotropy, we propose a new measurement and then use it to study the response characteristics of a half-space model with two prisms. The test results show that this measurement can accurately reflect the underground electrical anisotropy. Finally, the code is applied to the numerical simulation of a vertical-borehole survey and shows that the significant information on the hydraulically induced fracturing system can be reflected well by the electric anisotropy. [ABSTRACT FROM AUTHOR]

The bounded linear operators T on a Hilbert space which have 2-isometric liftings S on are investigated in this paper. We refer to the structure of those operators in the case of general liftings, as well as for a more special type of such liftings S, namely for which is invariant to the orthogonal projection onto the kernel of S∗S − I. In this special case we describe the canonical triangulation of T induced by S, with entries expressed by operators close to contractions or isometries. Also, in this case we refer to some asymptotic properties of T and of its adjoint T∗ obtained by means of asymptotic limits associated to T∗ and T, relative to a lifting S for T. The canonical triangulations of T in this setting are described in detail, and as an application, the Wold type decomposition of a concave operator is obtained. [ABSTRACT FROM AUTHOR]

Nowadays, the issue of traffic flow assignment has become an interdisciplinary topic that concerns multiple research areas and branches of science. This work is focussed on the mathematical and computational aspects of the equilibrium traffic assignment problem in the case when route flows are considered to be decision variables. Firstly, we obtain a fixed-point mapping with the explicit contraction operator, which is proven to equilibrate the journey times on feasible routes between a single origin-destination pair of nodes with the quadratic rate. Remarkable that from mathematical perspectives, the developed operator generalizes most path-equilibration operators already exploited by researchers. Secondly, we use the obtained fixed-point procedure to run the sequential path-equilibration algorithm for traffic flow assignment on well-known test urban road networks with arc-additive travel time functions. Our computational results appear to demonstrate higher accuracy of user-equilibrium traffic assignment solutions than the best ones known to us. In other words, developed within this paper sequential path-equilibration algorithm leads to solutions with less goal function values compared to the best solutions for today, according to our knowledge. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce a new three-step fixed point iteration called SNIA-iteration (Naveen et al. iteration) which converges faster than the original iteration. It is possible by introducing a contraction operator on the existing iteration algorithm where the coefficients of the new iterative process are chosen in (1 2 , 1) instead of [0, 1]. The strong convergence result for the SNIA-iteration method is also proved by showing the convergence of this iteration method towards its fixed point. Further, the coefficients involved in SNIA-iteration have been interchanged, and then the result is compared with the original iteration. It is found that the new result is better than the previous one in the sense of its rate of convergence for contraction mappings. [ABSTRACT FROM AUTHOR]

This paper proves a new q-Hermite-Hadamard inequality for convex functions using quantum integrals. We also prove some new midpoint-type inequalities for q-differentiable convex functions. Moreover, we present some examples to illustrate our established results, supplemented with graphs. [ABSTRACT FROM AUTHOR]

In this paper, some sufficient conditions for the oscillation of all solutions of second order dynamic equations with a negative sub-linear neutral term are established. The obtained results provide a unified platform that adequately covers both discrete and continuous equations. Furthermore, it covers a wide range of equations by utilizing different time scales. Illustrative examples are provided. [ABSTRACT FROM AUTHOR]

In this research paper, we investigate some new identifies for Sarıkaya fractional integrals which introduced by Sarıkaya and Ertugral in [20]. The fractional integral operators also have been applied to Hermite-Hadamard type integral inequalities to provide their generalized properties. Furthermore, as special cases of our main results, we present several known inequalities such as Simpson, Bullen, trapezoid for convex functions. [ABSTRACT FROM AUTHOR]

In this paper, our focus is to acquaint with the Suzuki-type mappings to establish some fixed point results using the new w-interpolative approach. We present some results for interpolative contraction operators via the w-admissible maps which satisfy the Kannan, Ćirić–Reich–Rus, and Hardy–Rogers contractions in quasi-partial b-metric space. Further, the outcomes so obtained are affirmed with relevant examples. [ABSTRACT FROM AUTHOR]

Automatic text processing is now a mature discipline in computer science, and so attempts at advancements using quantum computation have emerged as the new frontier, often under the term of quantum natural language processing. The main challenges consist in finding the most adequate ways of encoding words and their interactions on a quantum computer, considering hardware constraints, as well as building algorithms that take advantage of quantum architectures, so as to show improvement on the performance of natural language tasks. In this paper, we introduce a new framework that starts from a grammar that can be interpreted by means of tensor contraction, to build word representations as quantum states that serve as input to a quantum algorithm. We start by introducing an operator measurement to contract the representations of words, resulting in the representation of larger fragments of text. We then go on to develop pipelines for the tasks of sentence meaning disambiguation and question answering that take advantage of quantum features. For the first task, we show that our contraction scheme deals with syntactically ambiguous phrases storing the various different meanings in quantum superposition, a solution not available on a classical setting. For the second task, we obtain a question representation that contains all possible answers in equal quantum superposition, and we implement Grover's quantum search algorithm to find the correct answer, agnostic to the specific question, an implementation with the potential of delivering a result with quadratic speedup. [ABSTRACT FROM AUTHOR]

This paper consists of Hankel results of ω-order reversing partial contraction as a semigroup of linear operator. Spectral mapping theorem was investigated and it was established that ω-order reversing partial contraction mapping is an eventually uniform continuous semigroup in which we showed that the proof of the extension of T(t) to a C0-semigroup ˆ T(t) on a space ˆX containing X isometrically bounded. The space is constructed in such a way that the spectrum of the generator A of T(t) coincides with the spectrum of the generator Aˆ of Tˆ(t) and the approximate point spectrum of A coincides with the point spectrum of Aˆ. [ABSTRACT FROM AUTHOR]

In this paper, we introduce some common fixed point theorems for interpolative contraction operators using Perov operator which satisfy Suzuki type mappings. Further, some results are given. These results generalize several new results present in the literature. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of impulsive stochastic partial integrodifferential equations (ISPIEs) with delays and Poisson jumps. First, using the resolvent operator technique and contraction mapping principle, we can directly prove the existence and uniqueness of the mild solution for the system mentioned above. Then we develop a new impulsive integral inequality to obtain the global, both pth moment exponential stability and almost surely exponential stability of the mild solution is established with sufficient conditions. Also, a numerical example is provided to validate the theoretical result. [ABSTRACT FROM AUTHOR]

Two interesting extensions of Banach contraction principle to mappings that do not to be continuous, are Kannan and Chatterjea's theorems. Before this, in the cyclical form, extensions of these two theorems and Banach contraction principle were produced. But so far, these theorems have not been studied in the noncyclical form. In this paper, we answer the question whether there are versions of these theorems for non-cyclic mappings, also we give generalizations of existing results. For this purpose, in the setting of metric spaces we introduce the notions of cyclic and noncyclic contraction of Fisher type. We establish the existence of fixed points for these mappings and iterative algorithms are furnished to determine such fixed points. As a result of our results we give new theorems for cyclic orbital contractions. [ABSTRACT FROM AUTHOR]

In this paper, the notion of fuzzy (θ,L)-weak contraction in G--metric space is introduced, and sufficient conditions for the existence of fuzzy fixed points for such mappings are investigated. Relevant illustrative examples are constructed to support the assumptions of our established theorems. It is observed that the principal ideas obtained herein extend and subsume some well-known results in the corresponding literature. A few of these special cases of our results are noted and discussed as corollaries. [ABSTRACT FROM AUTHOR]

• The paper examines how transit authorities may influence traffic safety through requirements set in the contracts with bus companies. • Transit authorities may have direct influence on traffic safety, especially if they set requirements that exceeds (inter) national legislation. • Indirect impact on traffic safety through contracts is related to requirements for punctuality and regularity, which we find to be related to drivers' stress, driving style and accident involvement. • Environmental concerns also influence traffic safety indirectly, as it influences the use of large buses in narrow streets, to maintain and increase a high passenger capacity. The main objective of the study is to evaluate direct and indirect traffic safety consequences of the requirements that Norway's largest transit authority (Ruter) sets in the contracts with bus companies. To assess the representativity of Ruter's requirements and its consequences, the data focuses both on Ruter and transit authorities from other areas in Norway, serving a mix of urban and rural areas. The study is based on qualitative interviews (N = 18), a workshop, reviews of documents and a quantitative survey (N = 1012). The study indicates that transit authorities may have direct influence on traffic safety, especially if they set requirements that exceeds (inter) national legislation. Ruter does that when it comes to driver collision protection and blind zone warning systems. We also find indications of indirect impact on traffic safety through the contracts. This is firstly related to the requirements for punctuality and regularity, which we find to be related to drivers' stress, driving style and accident involvement in our quantitative analysis. It is secondly related to environmental concerns, which motivate maintaining (and increasing) a high level of passengers. Interviewees said that this influences the types of buses specified in contracts (e.g. large high capacity buses), and their routes (e.g. in narrow streets, "where people live"). They also emphasized that roads and infrastructure, for example in Oslo, are poorly adapted to bus transport. In our quantitative analysis, we found that buses that are poorly adapted to the roads they are used on, and roads that are poorly adapted to bus transport were related to bus drivers' reported stress and time pressure, which were related to risky driving style, which in turn was related to accidents. Based on the study, we developed several policy implications, that we believe also can be relevant for, and inspire other transit authorities. Ruter has applied several of these changes after our study (e.g. requiring ISO:39001 certification from the bus operators in the contracts, starting to develop a system to learn from accidents), and may thus stand out as a transit authority that other may learn from when it comes to management of traffic safety. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains the classes of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskii iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problem is solved. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. Cluj- Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. 2010 Mathematics Subject Classification: 47H10, 47H09, 34K05, 34K12, 45D05, 45G10, [ABSTRACT FROM AUTHOR]

In the digital world today, cellular networks and their operators play a competitive and important role in communications. The bases of the competition of operators are the quality of provided services and the coverage level of their antennas, thereby attract customers. This paper studies cellular networks with two old and new operators and under the influence of government intervention in one area. Due to the high cost of building an antenna, the new operator participates in the cost of the infrastructure of the old operator to use the services of these antennas for their customers. On the other hand, the government considers incentive schemes to support mobile operators. The government plans to take part in the infrastructure costs of the old operator, and will receive the income tax from it. Hence, the new operator will go off from paying tax. The government subsidy contract with the old operator is based on the coverage level of the antenna and supports the operator to increase the coverage level. By doing so, the quality level of services and coverage development rate for the old operator increases, leading to increased demand and increased profits for this operator. On the other hand, as government support increases the demand for the old operator, the demand for the new operator decreases and the profit of the new operator decreases. Some numerical examples for Iranian telecommunication companies are applied to examine the applicability of the proposed models. Finally, sensitivity analysis on the main parameters is analyzed in-depth to extract some managerial implications. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new concepts that relates to soft space based on work that was previously presented by researchers in this regard. First we give the definition of Soft Contraction Operator and some examples. After that we introduce the concepts of soft Picard iteration and soft Mann iteration processes. We also give some examples to illustrate them. Many concepts in normed spaces have been generalized in soft normed spaces. One of the important concepts is the concept of stability of soft iteration in soft normed spaces. We discuss this concept by giving some lemmas that are used to prove some theorems about stability of soft iteration processes (with soft contraction operator) with soft Picard iteration procedure as well as soft Mann iteration procedure. [ABSTRACT FROM AUTHOR]

European Institutions and scholars are reflecting upon the nature of the requirements that are or can be used to implement sustainability through Public Procurement. As far as public organisations are concerned, the Portuguese government's actions are in the same wavelength as the European guidelines on the matter. Public procurement involves economic operators. Thus, it is important to try to understand if the European Union proposal for a directive on "Corporate Sustainability Due Diligence" is an interesting tool in the discussion. Recently, the Portuguese Council of Ministers issued Resolution no. 132/2023, of 25 October, defining the ecological criteria applicable to certain kinds of contracts and products, goods and services concerning some administrative bodies, a Resolution which, nevertheless, is prone to criticism. May the shift of the European Union Public Procurement paradigm help implement Sustainable Public Procurement through mandatory requirements? Can the future Directive help economic operators align with contracting authorities to implement Sustainable Public Procurement? Might the obligation to include environmental factors help fulfil the Directive's due diligence obligations? And, lastly, has Portugal taken the right step with the issuance of Resolution no. 132/2023? [ABSTRACT FROM AUTHOR]

In this paper, we establish the quantitative mean ergodic theorems for two subclasses of power bounded operators on a fixed noncommutative L p space with 1 < p < ∞ , which mainly concerns power bounded invertible operators and Lamperti contractions. Our approach to the quantitative ergodic theorems relies on noncommutative square function inequalities. The establishment of the latter involves several new ingredients such as the almost orthogonality and Calderón-Zygmund arguments for non-smooth kernels from semi-commutative harmonic analysis, the extension properties of the operators under consideration from operator theory, and a noncommutative version of the classical transference method due to Coifman and Weiss. [ABSTRACT FROM AUTHOR]

Background: Tumor immune microenvironment (TiME) is prognostically instructive in Pancreatic adenocarcinoma (PAAD). However, the potential value of TiME-related genes in the individualized immunotherapy of PAAD has not been clarified. Methods: Correlation between Immune-Related Genes (IRGs) and immunerelated transcription factors (TFs) was performed to prove the immune correlation of selected genes. Immune-related molecular subtypes were identified by consensus clustering. The TiME-score, an immune microenvironment-related prognostic signature for PAAD, was constructed using minimum absolute contraction and selection operator regression (Lasso-Cox). The International Cancer Genome Consortium (ICGC) dataset validated the reliability of TiME-score as external validation. Single-cell samples from GSE197177 confirmed microenvironment differences of TiME-score hub genes between tumor and its paracancer tissues. Then, RARRES3, a hub gene in TiMEscore, was further analyzed about its upstream TP53 mutation and the specific immune landscape of itself in transcriptome and Single-cell level. Eventually, TiME-score were validated in different therapeutic cohorts of PAAD mice models. Results: A 14-genes PAAD immune-related risk signature, TiME-score, was constructed based on IRGs. The differences of TiME-score hub genes in single-cell samples of PAAD cancer tissues and adjacent tissues were consistent with the transcriptome. Single-cell samples of cancer tissues showed more pronounced immune cell infiltration. The upstream mutation factor TP53 of RARRES3 was significantly enriched in immune-related biological processes. High RARRES3 expression was correlated with a worse prognosis and high macrophages M1 infiltration. Additionally, the immunohistochemistry of hub genes AGT, DEFB1, GH1, IL20RB, and TRAF3 in different treatment cohorts of mice PAAD models were consistent with the predicted results. The combination of immunotherapy, chemotherapy and targeted therapy has shown significantly better therapeutic effects than single drug therapy in PAAD. Conclusion: TiME-score, as a prognostic signature related to PAAD-specific immune microenvironment constructed based on RARRES3, has predictive value for prognosis and the potential to guide individualized immunotherapy for PAAD patients. [ABSTRACT FROM AUTHOR]

In this article, we study the dynamics of collective beliefs. As a first step, we formulate David Westlund's Principle of Collective Change (PCC)--a criterion that characterizes the evolution of collective knowledge--in the realm of belief revision. Thereafter, we establish a number of unsatisfiability results pointing out that the widely-accepted revision operators of Alchourrón, Gärdenfors and Makinson, combined with fundamental types of merging operations--including the ones proposed by Konieczny and Pino Pérez as well as Baral et al.--collide with the PCC. These impossibility results essentially extend in the context of belief revision the negative results established by Westlund for the operations of contraction and expansion. At the opposite of the impossibility results, we also establish a number of satisfiability results, proving that, under certain (rather strict) requirements, the PCC is indeed respected for specific merging operators. Overall, it is argued that the PCC is a rather unsuitable property for characterizing the process of collective change. Last but not least, mainly in response to the unsatisfactory situation related to the PCC, we explore some alternative criteria of collective change, and evaluate their compliance with belief revision and belief merging. [ABSTRACT FROM AUTHOR]

The Kompaneets equation governs dynamics of the photon energy spectrum in certain high temperature (or low density) plasmas. We prove several results concerning the long time convergence of solutions to Bose--Einstein equilibria and the failure of photon conservation. In particular, we show the total photon number can decrease with time via an outflux of photons at the zero-energy boundary. The ensuing accumulation of photons at zero energy is analogous to Bose-Einstein condensation. We provide two conditions that guarantee that photon loss occurs, and show that once loss is initiated then it persists forever. We prove that as t → ∞, solutions necessarily converge to equilibrium and we characterize the limit in terms of the total photon loss. Additionally, we provide a few results concerning the behavior of the solution near the zero-energy boundary, an Oleinik inequality, a comparison principle, and show that the solution operator is a contraction in L¹. None of these results impose a boundary condition at the zero-energy boundary. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the relation between shielded base contraction postulates and credibility-limited (CL) base revision postulates. More precisely, we identify (i) the relation between the postulates satisfied by a shielded base contraction operator and the postulates satisfied by the CL base revision operator that is defined from it by means of the consistency-preserving Levi identity and (ii) the relation between the postulates satisfied by a CL base revision operator and the postulates satisfied by the shielded base contraction operator that is defined from it by means of the Harper identity. Furthermore, we show that the consistency-preserving Levi identity and the Harper identity establish a one-to-one correspondence between the twenty classes of shielded base contractions presented in [21] and the twenty classes of credibility-limited base revisions presented in [22]. [ABSTRACT FROM AUTHOR]

Lung adenocarcinoma is still cancer with the highest mortality. Hypoxia and immunity play an essential role in the occurrence and development of tumors. Therefore, this study is mainly to find new early diagnosis and prognosis markers and explore the relationship among the markers and immunity and hypoxia, to improve the prognosis of patients. Firstly, based on the clinical database in TCGA, we determined the most critical clinicopathological parameters affecting the prognosis of patients through a variety of analysis methods. According to pathological parameters, logistic most minor absolute contraction selection operator (lasso), univariate and multivariate regression analysis, the risk genes related to early prognosis were screened, and the risk model was established. Then, in different risk groups, GSEA and CIBERSORT algorithms were used to analyze the distribution and enrichment of the immune cells and hypoxia, to study the effects of early prognostic indicators on hypoxia and immunity. At the same time, we analyzed the different levels of risk genes in normal cells (BSEA-2B) and tumor cells (H1299, A549, PC9, and H1975). Finally, A549 and PC9 cells were induced by CoCl2 to establish a hypoxic environment, and the correlation between risk genes and HIF1A was analyzed. The risk model based on risk genes (CYP4B1, KRT6A, and FAM83A) was accurate and stable for the prognosis of patients. It is closely related to immunity and hypoxia. In BSEA-2B cells, the mRNA and protein expression of CYP4B1 was higher, while the expression of KRT6A and FAM83A was lower. Finally, we found that FAM83A and HIF1A showed a significant positive correlation when A549 and PC9 cells were exposed to hypoxia. The discovery of early diagnostic markers related to immunity, hypoxia, and prognosis, provides a new idea for early screening and prognostic treatment of lung adenocarcinoma. [ABSTRACT FROM AUTHOR]

We consider the non-symmetric coupling of finite and boundary elements to solve second-order nonlinear partial differential equations defined in unbounded domains. We present a novel condition that ensures that the associated semi-linear form induces a strongly monotone operator, keeping track of the dependence on the linear combination of the interior domain equation with the boundary integral one. We show that an optimal ellipticity condition, relating the nonlinear operator to the contraction constant of the shifted double-layer integral operator, is guaranteed by choosing a particular linear combination. These results generalize those obtained by Of and Steinbach [Is the one-equation coupling of finite and boundary element methods always stable?, ZAMM Z. Angew. Math. Mech.93 (2013), 6–7, 476–484] and [On the ellipticity of coupled finite element and one-equation boundary element methods for boundary value problems, Numer. Math.127 (2014), 3, 567–593], and by Steinbach [A note on the stable one-equation coupling of finite and boundary elements, SIAM J. Numer. Anal.49 (2011), 4, 1521–1531], where the simple sum of the two coupling equations has been considered. Numerical examples confirm the theoretical results on the sharpness of the presented estimates. [ABSTRACT FROM AUTHOR]

In this work, we initiate the notion of a fuzzy cyclic (α, β)-admissibility to establish some fixed point results for contraction mappings involving a generalized simulation function in the class of fuzzy b-metric spaces. We give some illustrative examples to validate the new concepts and obtained results. At the end, we present an application on a Fredholm integral equation. [ABSTRACT FROM AUTHOR]

In this manuscript, the concept of rational-type multivalued F-contraction mappings is investigated. In addition, some nice fixed point results are obtained usingthis concept in the setting of MM-spaces and ordered MM-spaces. Our findings extend, unify, and generalize a large body of work along the same lines. Moreover, to support and strengthen our results, non-trivial and extensive examples are presented. Ultimately, the theoretical results are involved in obtaining a positive, definite solution to nonlinear matrix equations as an application. [ABSTRACT FROM AUTHOR]