Numerical Analysis and Computational Mathematics

This review delves into the latest advancements in quantum-secure cryptography, focusing on the Quantum Permutation Pad (QPP), a pivotal innovation proposed by Kuang et al. QPP harnesses the non-commutativity and generalized uncertainty derived from the Galois permutation group, making it highly suitable for cryptographic applications. The review underscores QPP's versatility across both symmetric and asymmetric cryptography through three core representations: matrix-based for classical encryption, quantum gates for quantum-native encryption, and arithmetic-based for multivariate public key systems such as Merkle-Hellman cryptosystems, Multivariate Public Key Cryptography (MPKC), and the most recent Homomorphic Polynomial Public Key (HPPK). In particular, QPP strengthens the security of HPPK's Key Encapsulation Mechanism (KEM) and Digital Signature (DS) schemes, offering robust quantum resistance.This work further examines QPP's integration with various encryption techniques, enhancing resilience against quantum attacks. By addressing challenges in cryptographic complexity, key size optimization, and security enhancement, the review presents a thorough evaluation of QPP's role in fortifying cryptographic protocols, ensuring strong security foundations in the quantum computing era.

In this paper, we present a deterministic mathematical model for the study of overweight, and obesity in a population and its impact on the growth of the number of diabetics. For the construction of the model, we take into account social factors and the interactions between the elements of society. We find the basic reproduction number and prove the global stability of the disease-free equilibrium point. We present theoretical results and find the sensitivity indices to characterize the impact of parameters associated with overweight, obesity and diagnosed diabetes on the basic reproduction number. To validate the model, we perform computational simulations and study the basic reproduction number and compartments. We present the behavior of the compartments for a scenario and study the impact of the variation of parameters associated with overweight by social pressure and diabetes due to causes other than obesity.

The cubic convergence of a method inspired by a Hummel and Seebeck for solving variational inclusions, has been showed when the second order Fréchet derivative of some function f satisfies a Lipschitz condition. Here, we prove the superquadratic convergence of this method whenever this second order Fréchet derivative satisfies a Hölder condition.

In this paper we investigate the existence of a sequence (xk) satisfying 0 ∈ f(xk)+∇f(xk)(xk+1 −xk)+ 1 2 ∇ 2 f(xk)(xk+1 −xk) 2 +G(xk+1) and converging to a solution xof the generalized equation 0 ∈ f(x)+G(x); wheref is a function and G is a set-valued map acting in Banach spaces. We show that the previous sequence is locally cubic convergent to xwhenever the set-valued map (f(x � ) + ∇f(x � )(� − x � ) + 1 2 ∇ 2 f(x � )(� − x � ) 2 +G(� )) 1 is M-pseudo-Lipschitz around (0,x � ).

Dedicated to Francis Buekenhout on the occasion of his 65th birthday Abstract. The fundamental theorem of projective geometry is generalized for projective spaces over rings. Let RM and SN be modules. Provided some weak conditions are satisfied, a mor-phism g:PðMÞnE!PðNÞ between the associated projective spaces can be induced by a semilinear map f: M! N. These conditions are satisfied for instance if S is a left Ore domain and if the image of g contains three independent free points. No assumptions are made on the module M, and both modules may have some torsion.

Error estimates for midpoint, trapezoid, Simpson’s, Maclaurin’s, 3/8-Simpson’s and Boole’s type rules are obtained. Some related inequalities of Ostrowski’s type are pointed out. These results are obtained for mappings of bounded variation, Lipschitzian, and absolutely continuous mappings whose first derivatives are belong to Lp[a, b] (1 ≤ p ≤ ∞). Applications to numerical integration are provided.

In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary described by the Clarke generalized gradient of a locally Lipschitz function. First, we prove a new existence result for the inequality employing the theory of pseudomonotone operators. Next, we give a result on comparison of solutions, and provide sufficient conditions that guarantee the asymptotic behavior of solution, when the heat transfer coefficient tends to infinity. Further, we show a result on the continuous dependence of solution on the internal energy and heat flux. Finally, some examples of convex and nonconvex potentials illustrate our hypotheses.

We consider one-dimensional two-phase Stefan problems for a finite substance with different boundary conditions at the fixed faces. The goal of this paper is to determine the behavior of the free boundary and the temperature when the thermal coefficients of the material change. We obtain properties of monotony with respect to the latent heat, the common mass density, the specific heat of each phase and the thermal conductivity of the liquid phase. We show that the solution is not monotone with respect to the thermal conductivity of solid phase, in some cases, by computing a numerical solution through a finite difference scheme. The results obtained are important in technological applications as the climate of buildings, the storage of energy in satellites and clothes and the transport of biological substances and telecommunications.

Technological metal forming processes of extrusion, forging and rolling with imposed cyclic torsion or shear deformation have been recently studied in view of their ad-vantages with respect to monotonic loading processes, cf. Bochniak and Korbel [2-4]. The present work is aimed to analyze such process in the case of simple tension or compression of a cylindrical tube with imposed cyclic torsional deformation. The material element response is assumed as rigid-perfectly plastic or elastic-perfectly plastic. For these models, the analytical solutions can be provided for the steady cyclic responses and the effect of two process parameters, namely the ratio of shear and axial strain rates η and the amplitude of shear strain γ m , can be clearly demon-strated. Three different regimes of cyclic response can be visualized in the plane η, γ m . The cyclic response of a cylinder under combined axial compression and cyclic torsion is predicted by considering a simplified model of a set of conc...

The problem of calculating future capacity of a projected port involves several uncertainties, which means that it is not possible to find a single formula that considers the interaction of the different variables affecting the port’s operational performance, particularly considering that many of these variables are related to stochastic distributions and restrictions in shared resources. Only a simulation model can consider all the variables and produce a reliable projection of the port’s future behavior. It is very important to precisely estimate the figures because the demurrage costs grows exponentially as the port’s occupancy moves toward 100%, which directly affects the project’s feasibility.

Recency, Frequency and Monetary (RFM) analysis is a popular marketing technique that seeks to classify customers according to the frequency and value of their transactions. This article provides an introduction to the RFM analysis process and how it is used to gather crucial information for developing targeted marketing strategies. By using the RFM analysis on our catalogue and analysing sales data, we gain significant insights into the performance of particular products. According to the demand, the Recency dimension reveals which items are selling swiftly or slowly. Frequency dimension shows how well-liked particular goods are. The financial component, sheds information on viability and worth of any offering. RFM analysis gives marketers an opportunity to pinpoint various consumer categories with varied degree of loyalty, engagement and profitability. RFM analysis enables marketers to group customers into categories, like high-value, at-risk or dormant, using a combination of statistical methodologies and data mining. With a deep understanding of catalogue and sales data, we can make better choices on the products for customers. By emphasising top-selling items on the home-page, we may captivate customers and instantly pique their curiosity. In order to increase consumer involvement, we might simultaneously prepare to promote slower moving products with targeted incentives. The messaging, promotions and customer interactions can be modified for specific preferences of each group. High value customers can receive exclusive incentives to strengthen loyalty, and at risk customers receive re-engagement initiatives. By using RFM framework, businesses may develop targeted marketing strategies, enhance client interaction and boost marketing return-on-investment.

In the challenging environment of the construction industry and especially after the Corona pandemic crisis in Iran, supply chains (SCs) needed to adopt a new management model to continue the activity. Among the investigated approaches, the four sustainable, anti-fragile, agile and lean (SAAL) approaches were given more attention. The main objective of this paper is to draw a conceptual model for SAAL SCs with the aim of improving their operational, economic and environmental performance. For this purpose, several performance measures have been proposed. This concept is drawn based on the literature review of four supply chain management (SCM) approaches and their performance measurement system. Among the measures proposed by SAAL, which affect SC performance, are just-in-time relationships as well as supplier relationships (modular suppliers) and creating anti-fragile infrastructure.