Abstract. The increased deployment of Internet of Things (IoT) has revolutionized global connectivity through applications such as smart cities, smart industries, healthcare systems, and industrial automation. However, resource-constrained IoT devices face severe security challenges, particularly in device authentication. Traditional authentication mechanisms based on symmetric and asymmetric cryptography introduce excessive communication and computation overhead, making them unsuitable for constrained IoT environments. In this paper, we propose a secure and lightweight device authentication mechanism based on digital certificates from a global stochastic perspective. The proposed framework considers the dynamic and uncertain behavior of IoT networks while ensuring secure identification and communication. The protocol employs asymmetric cryptography, hash functions, nonces, and timestamps to prevent impersonation, replay, and device capture attacks. The security properties of the proposed protocol are formally verified using the AVISPA tool under the Dolev-Yao attacker model. Performance evaluation demonstrates low communication, storage, and computational overhead, making the proposed mechanism suitable for Industrial IoT, smart cities, defense systems, and other mission-critical IoT applications.

In his notebooks, Ramanujan noted various degrees of appealing Eisenstein series relations.In addition, Shaun Cooper mentioned a number of identities involving theta functions and Eisenstein series in his work.This work establishes certain differential identities involving Eisenstein series of various levels, eta-functions, and series identities.Additionally, the Eisenstein series of levels 5 and 7 is being used to evaluate the convolution sum.

Currently, the development of the theory of Haar interpolations of financial markets with the use of martingale measures continues. The existence of martingale measures of discounted stock prices means that this kind of interpolation can only be used in arbitrage-free markets (c.f. the survey [1]). However, real financial markets often contain elements of arbitrage opportunities. Therefore, it is important to develop techniques for interpolating processes that do not admit martingale measures. The work [2] is devoted to just this problem, where signed martingale measures serve as the main interpolation tool. In this paper, we proceed to consider admissible signed martingale deformations (in particular, their existence). Various other facts about processes on deform structures are contained in the works [3]–[13]).

This paper suggests a novel method for acceptance sampling that integrates fuzzy logic with the negative binomial distribution. In quality control and reliability assessment, acceptance sampling plans play a crucial role in decision-making under uncertainty. Traditional sampling plans often rely on precise information and fixed parameters, which may not reflect real-world vagueness and imprecision. This paper introduces a Fuzzy Acceptance Sampling Plan (FASP) based on the Negative Binomial Distribution (NBD), providing a more flexible and realistic framework for dealing with over-dispersed count data and uncertainty in quality inspection. By incorporating fuzzy set theory, key parameters such as the acceptance number, lot quality, and inspection risks are modeled as fuzzy numbers. The plan allows for soft decision boundaries, enhancing the responsiveness to varying production conditions. Analytical expressions for the operating characteristic (OC) function, the average sample number (ASN) and average outgoing quality (AOQ) are derived in the fuzzy environment using membership functions. Numerical examples illustrate the application and advantages of the proposed plan over classical approaches, particularly in handling uncertain or imprecise inspection data. The proposed FASP-NBD model is especially useful in industries where defective items occur in clusters, and precise parameter estimation is difficult.

We propose a new topological index for graphs, referred to as the second neighborhood stress index, which is defined based on the neighborhood stresses of individual vertices.Various inequalities involving this index are derived, and some results are proven. Additionally, the second neighborhood stress index values are calculated for certain well-known graphs. This study further explores the chemical relevance of the second neighborhood stress index by applying regression analysis to a dataset of 22 benzenoid hydrocarbons. Through power regression models, we assess the relationship between the second neighborhood stress index and multiple physicochemical properties of these hydrocarbons.

This study investigates the behavior of incompressible flow over a permeable stretched sheet, considering the effects of viscous dissipation and Joule heating in a constant two-dimensional electrically conducting, thermally radiant Williamson Nanofluid.Employing suitable transformation equations reduces the governing partial differential equations to a set of nonlinear ordinary differential equations.These equations are subsequently solved numerically using the standard fourth-order Runge-Kutta method in conjunction with the shooting technique.The results are presented graphically, illustrating the flow, temperature, and nanoparticle volume fraction profiles.The research examines how various physical characteristics influence heat and mass transfer rates, including temperature, velocity, skin friction coefficient, and nanoparticle volume percentage.

We study nonlinear Hammerstein/Urysohn integral inclusions with set-valued inputs on = (; ), < < , of the form + () where () = {(): (), () (, (); ( ))}.Under Carathodory/u.s.c.structure with convex compact values for the multivalued Nemytskii map , measurability of the input multifunction (), and compact or Kuratowski-condensing properties of the linear integral operator K, we perform a Lyapunov-Schmidt reduction at the Fredholm linear part = - (index 0 ) to obtain a finite-dimensional reduced multimap : on = .Using multivalued fixed-point index/degree, we prove set-valued Fredholm alternatives: either the homogeneous inclusion has a nontrivial solution, or for every satisfying the classical compatibility conditions with the cokernel * = * , the inhomogeneous inclusion admits solutions; in the compact case the solution set is nonempty, compact, and acyclic, and in the condensing case it is bounded and closed.We further establish Hausdorff-Lipschitz stability of solution sets with respect to perturbations of the input multifunction and, for Volterra kernels, deliver the necessary a priori bounds via Grnwall-Bihari inequalities, thereby closing all hypotheses in a broad causal class.

Today's growing awareness of environmental preservation and social responsibilities, the idea of sustainability is evolving into a fundamental guiding principle for many industrial sectors.The value of the green supply chain (GSC) can be maximised through supplier selection (SS) to keep the business sustainable and profitable.A multi-criteria decision-making (MCDM) is the most desirable technique for choosing electric vehicle from a variety of options.The objective of this study is to create the testing process correlate with the analytical hierarchy process (AHP) and the technique for ordering performance by similarity to ideal solution (TOPSIS) that will be useful for performers in the vehicle company select the best electric vehicle in fuzzy surroundings where, subjectivity and ambiguity are handled by Parameterized triangular fuzzy numbers for linguistic values.The electric vehicle selection problem's structure is analysed using the AHP, and the weights criteria are determined.The fuzzy TOPSIS approach is then used to calculate the resultant ranking.

To analyze the performance of various estimators, this paper compares Bayesian and classical estimate approaches across a variety of loss functions. The work focuses on informative versus non-informative priors in Bayesian estimation. The calculations are based on a number of loss functions, including the Square Error Loss Function (SELF), Quadratic Loss Function (QLF), Precautionary Loss Function (PLF), and Entropy Loss Function (ELF). The methodology uses simulation techniques as well as real-world datasets to test the performance and robustness of the proposed estimators. The Bayesian estimators, classical estimators, and related Bayes hazards using empirical analysis and extensive simulations to computed. The findings show that the Minimum Mean Square Error estimator (MiniMSE) is more accurate and reliable than other estimators in a variety of settings. Furthermore, for both types of priors, it is demonstrated that the Bayes risk under the Quadratic Loss Function (QLF) is the lowest among all loss functions considered, including SELF, PLF, and ELF. This suggests that, when compared to other loss functions, QLF is a more effective and balanced criterion for making estimation decisions. The study’s findings provide vital new insights into how to choose the optimum estimate techniques and loss functions for statistical decision theory and practical data processing.