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This study aims to develop a compartmental epidemiological model for the co-infection of COVID-19 and tuberculosis, incorporating a Holling type II treatment rate for individuals with tuberculosis, COVID-19, and dual infections while considering incomplete treatment in some TB cases. The model analysis examines the sub-models for COVID-19, TB, and the combined co-infection model. Using the fixed-point method, the research investigates the existence and uniqueness of solutions for the proposed model. It also explores a stability analysis to evaluate Ulam-Hyer’s reliability. Furthermore, it discusses and validates Lagrange’s interpolation polynomial through a specific case study to numerically compare different fractal and fractional orders.

Some new uniqueness theorems are proposed and a flexible, efficient numerical algorithm is formulated and analysed for convergence and numerically verified for nonlinear fractal-fractional differential equations with Mittag-Leffler kernel. Under some generalized conditions which admit a wider class of functions than the standard Lipschitz condition, the uniqueness of solution is established. By linearly interpolating between grid points, we design a numerical algorithm. Unlike existing methods, our constructed method avoids any form of grid restriction, uses minimal computation of special functions and is second order accurate under appropriate smoothness conditions. The convergence of the method is fully analysed, and numerical test cases are presented to verify the convergence result.

We consider the dynamics of an elastic continuum under large deformation but small strain. Such systems can be described by the equations of geometrically nonlinear elastodynamics in combination with the St. Venant-Kirchhoff material law. The velocity-stress formulation of the problem turns out to have a formal port-Hamiltonian structure. In contrast to the linear case, the operators of the problem are modulated by the displacement field which can be handled as a passive variable and integrated along with the velocities. A weak formulation of the problem is derived and essential boundary conditions are incorporated via Lagrange multipliers. This variational formulation explicitly encodes the transfer between kinetic and potential energy in the interior as well as across the boundary, thus leading to a global power balance and ensuring passivity of the system. The particular geometric structure of the weak formulation can be preserved under Galerkin approximation via appropriate mixed finite elements. In addition, a fully discrete power balance can be obtained by appropriate time discretization. The main properties of the system and its discretization are shown theoretically and demonstrated by numerical tests.

This study presents a methodology for decomposing time series data into trend, seasonal, and cyclical components using the moving linear model approach by Kyo and Kitagawa (Journal of Business Cycle Research, 19(3): 373-397, 2023). Our approach integrates seasonal adjustment and decomposition into a single framework. We evaluated our approach with two case studies: examining daily COVID-19 case data and the Index of Industrial Production (IIP) in Japan, comparing the results to seasonally adjusted IIP data. Performance metrics included the discrimination power index and the variance of the adjusted cyclical component. Our findings show that our method effectively extracts business cycle information, achieving higher discrimination power and greater adjusted variance compared to seasonally adjusted IIP data, highlighting the superior performance of our integrated seasonal adjustment method. We compared the proposed approach with a state-space modelling method by introducing an overall stability as a new indicator. The results demonstrated the stability of the estimations obtained with our proposed method.

We introduce and study an infinite family of graceful graphs, which we call kites. The kites are graphs where a path is joined with a graph "forming" a kite. We study and characterize three classes of the kites: kites formed by cycles known to be graceful, fan kites and lantern kites. Beside showing in a transparent way that all these graphs are graceful, we provide characterizations of these graphs among all simple graphs via three tools: via Sheppard's labelling sequences introduced in the 1970s and via labelling relations and graph chessboards. The latter are relatively new tools for the study of graceful graphs introduced by Haviar and Iva\v ska in 2015. The labelling relations are closely related to Sheppard's labelling sequences while the graph chessboards provide a~nice visualization of the graceful labellings.

We extend results of Vidaux and Videla concerning the set of Julia Robinson numbers.

This study extensively investigates a specific category of Kirchhoff-Schrödinger systems in fractional Sobolev space with Dirichlet boundary conditions. The main focus is on exploring the existence and multiplicity of non-negative solutions. The non-linearity of the problem generally exhibits singularity. By employing minimization arguments involving the Nehari manifold and a variational approach, we establish the existence and multiplicity of positive solutions for our problem with respect to the parameters \(\eta\) and \(\zeta\) in suitable fractional Sobolev spaces. Our key findings are novel and contribute significantly to the literature on coupled systems of Kirchhoff-Schrödinger system with Dirichlet boundary conditions.

In 2019, Bagul et al. posed two open problems dealing with inequalities involving trigonometric and hyperbolic functions and an adjustable parameter. This article is an attempt to solve these open problems. The results are supported by three-dimensional graphics, taking into account the variation of the parameter involved.

We show that there are finite distributive lattices that are not the congruence lattice of any finite semidistributive lattice. For \(0 \leq k \leq 2\), the distributive lattice \((\mathbf{B}_k)_{++} = \mathbf{2} + \mathbf{B}_k\), where \(\mathbf{B}_k\) denotes the boolean lattice with \(k\) atoms, is not the congruence lattice of any finite semidistributive lattice. Neither can these lattices be a filter in the congruence lattice of a finite semidistributive lattice. However, each \((\mathbf{B}_k)_{++}\) with \(k \geq 3\) is the congruence lattice of a finite semidistributive lattice, say \(\mathbf{L}_k\). These lattices \(\mathbf{L}_k\) cannot be bounded (in the sense of McKenzie), as no \((\mathbf{B}_k)_{++}\) \((k \geq 0)\) is the congruence lattice of a finite bounded lattice. A companion paper shows that every \((\mathbf{B}_k)_{++}\) \((k \geq 0)\) can be represented as the congruence lattice of an infinite semidistributive lattice. We also find sufficient conditions for a finite distributive lattice to be representable as the congruence lattice of a finite bounded (and hence semidistributive) lattice.

In this manuscript, we carried out a thorough analysis of the general SIR model for epidemics. We broadened the model to include vaccination, treatment, and incidence rate. The vaccination rate is a testament to the alternatives made by individuals when it comes to receiving vaccinations and merging with the community of the recovered. The treatment rate measures how often people who have contracted a disease are able to transition into the recovered category. The continuous Galerkin-Petrov method, specifically the cGP(2)-method, is employed to calculate the numerical solutions of the models. The cGP(2)-method imperative to analyse two unknowns over every time interval. The unknowns can be determined by solving a block system of size (2 × 2). This approach demonstrates a strong level of precision throughout the entire time interval, with an impressive rate of convergence at the discrete time points. In addition, the article investigates the concept of the basic reproduction number ([Formula: see text]) and explores the intricacies of conducting sensitivity analysis of the developed system.

To improve the accuracy of predicting the remaining useful life (RUL) of computer numerical control (CNC) machine tool components, this study proposes a novel method. In the method, a condition monitoring platform for components is built to obtain component operation information. The collected information is processed to acquire signal features with better trend. The Weibull model is modified via the fusion of internal signal features and external operating information. Accordingly, a Weibull regression model that fully considers the operating condition information of components is established. The fminsearch function is applied to solve the WRM with complete parameterization, and the optimal parameter estimates of the model are obtained. The RUL prediction method is demonstrated using a specific example. Multiple indexes are used to evaluate the model performance. Furthermore, the validity of the model is verified by comparison. The proposed method can obtain more accurate RUL prediction results of the components. It is of great significance to the health operation of CNC machine tools.

Transmission expansion planning (TEP) is known as long-term study, which is related to the generation expansion pattern, i.e. where and how many new generation facilities will be constructed. Recently, some researchers have paid special attention to network reliability and maintainability in TEP design. As such, the uncertainty of generation expansion planning (GEP) can alter the results of TEP. Therefore, the robustness of TEP to the uncertainty of GEP should be investigated in TEP process. This paper aims to define the robustness of TEP to the long-term uncertainties mathematically. To do so, a simple TEP problem is first proposed and then the uncertainty of GEP is applied to the problem by developing a novel uncertainty-oriented TEP objective function as multi-objective optimization. Two objectives of this model are the conventional TEP costs and minimum changes. Then, the model is implemented on the IEEE 24-bus reliability test system (IEEE RTS) for two main items in order to assess the applicability of the proposed method. Furthermore, the effect of the method on undoing the uncertainty of generation mixture is investigated at the plan horizon in TEP. As TEP planning is NP-hard, genetic algorithm (GA) is utilized along with fminc optimization function in MATLAB, where the lower levels are resolved using the quadprog function in MATLAB. Afterwards, Pareto front of the solutions is analyzed to choose the most possible and economical solution between them. It can be concluded that the uncertain generation expansion would result in drastic economic losses both in the operation stage and in investment cost waste. Eventually, the obtained results confirm the applicability of the proposed model and solution method.

Making accurate predictions of the construction cost is essential for ensuring the smooth implementation of projects and guaranteeing economic benefits. The problem to be studied in this article is how to predict construction project costs accurately. The related factors affecting construction project costs are briefly introduced in this paper. A back-propagation neural network (BPNN) was proposed to predict construction engineering costs, and the AdaBoost algorithm was used to improve it. Then, simulation experiments were carried out. It was found that the Adaboost-BPNN algorithm converged to stability faster, and the mean square error was smaller (10-5) when it was stable. Compared with the support vector machine and traditional BPNN algorithms, the AdaBoost-BPNN algorithm had better goodness of fit (0.787) and provided more accurate prediction results for construction engineering costs (mean average error: 0.467, root-mean-square error: 1.118). The novelty of this article lies in utilizing AdaBoost to combine multiple weak predictors into a strong predictor, thereby enhancing the performance of the BPNN algorithm. The contribution lies in improving the predictive performance of the BPNN through the combination principle of AdaBoost, providing an effective reference for accurate cost prediction in construction engineering.

Parkinson’s patients experience severe pathological tremors because of abnormality of central oscillator that entrains the corticothalamic system and the basal ganglia. Normally, medications are used to decrease involuntary antagonistic muscle contraction can affect life, therefore, safe treatment methods have attention. The mechanical vibration absorber is an outstanding method, and can be used as an alternative treatment. Based on the biodynamics of the human arm, the objective of this study is to provide the performance of Parkinson’s patients and to design a model-free control to suppress their pathological tremor, called an active dynamic vibration absorber system (DVAs). An active DVA with model-free control inside can handle the complex system, disturbances, complicated working behavior, and so forth. Frequency of resting tremor as resonance frequencies of shoulder and elbow muscle is activation operating. The response of the active DVAs is studied in the case that it is attached to the arm and compared to the passive DVA with excitation frequencies in the previous study. The results verify the effectiveness of active DVA with controller inside, which can reduce the pathological tremor in amplitude feature in Parkinson's patient’s arm.

The classical transportation problem (CTP) is a particular kind of optimization problem. It involves determining the most cost-effective way to transport a uniform product from several suppliers (sources) to several consumers (destinations). In the real-world scenario, transportation of goods often involves fulfilling the demand of multiple destinations from a single source. However, a source can fulfill the demand of multiple destinations, which is known as bulk transportation problem. Sometimes, the shipment of these goods involves some fixed cost along with a variable cost. Generally, in logistics and transportation, a fixed charge denotes an unchanging expense incurred each time a shipment is sent from one location to another, irrespective of the shipment's volume. Fixed charges can include costs such as setup costs, handling costs, loading or unloading costs or any other costs that remain constant regardless of shipment volume. This fixed cost was earlier in-curred in the context of classical transportation problems only. In literature, the fixed cost was not introduced in the bulk transportation problem (BTP) which should be an essential part of the BTP in the current scenario. Considering this gap, the fixed cost is taken as a step function, which uses some fixed costs for each route and keeps them constant until a particular number of quantities is reached after which it increases in multiple. The branching method in modified form is used to solve the numerical problem, which then converges upon the optimal solution.

Recommender systems are widely used in today’s world as they narrow down a huge number of options for a user in various fields. These recommender systems can also be significantly used by cab drivers also, since they can recommend the nearest location of passengers waiting for a cab. For the system to perform better, cluster formation is an essential step to be performed using the pick-up locations of the cab provided in the historical data. The recommendation is highly dependent on various other parameters also like timestamp, density of the area, clustering technique used, etc. This research paper aims to analyze the impact of varying minimum density of the pick-up data points on the accuracy of the recommendations by Clustering Based Cab Recommender System (CBCRS). Therefore, the research paper has a threefold objective: Firstly, to identify different clustering techniques for clustering the pickup locations. Secondly, the research paper proposes the design and development of a framework for CBCRS to cluster the cab pick-up data points along with recommending the nearest pick-up location of passengers to the cab drivers. Finally, the paper analyzes and evaluates the accuracy of CBCRS recommendation across varying densities of the pick-up data points as compared to the Partition-based Clustering Method, Density-based Clustering Method and Hierarchical Clustering Methods.

An online distributed system which is helpful for users to contribute their surplus resources to handle the wide range of tasks is called volunteer computing. In Volunteer Computing System (VCS) technology, there exists heterogeneous devices which vary in terms of processing power, latency, cost, and energy efficiency. VCS is heterogeneous in nature so, it is essential to utilize all the resources to provide high Quality of Service (QoS), innovation and cost effectiveness for all requests. The dynamism and heterogeneity of VCS makes it essential to utilize all the resources for providing excellent Quality of Service(QoS). This innovation is also cost effective for all the requests. Task scheduling problems that are classified as NP-hard are very challenging in heterogeneous VCS environments. Therefore, two scheduling algorithms Min-CCV and Min-V are proposed for volunteer computing systems. The primary objective of the proposed algorithms is to improve network performance and also enhance the QoS by reducing the computational, communicational, and violational costs for various Internet of Things (IoT) based applications which in turn improves the quality of life. A task scheduler module allocates tasks Ti as a group of n jobs that are identified T1, T2, T3,…….,Tn for a volunteer computing system. These tasks have specific attributes like memory requirement, input and output file sizes, QoS requirements, etc. The outcome of the simulator describes that the proposed algorithm can allocate tasks in a more efficient way to the volunteer fog-cloud environment in comparison to existing methods. As compared to the generic-based algorithms, the proposed Min-CCV and Min-V algorithms enhance the deadline satisfaction rate to approximately 99.5% and decrease the costs incurred by 15 to 53%. The comprehensive simulation results give the better outcome of proposed work as compared to existing practices.

With an increasing prominence of electric vehicles (EVs) in sustainable transportation, it demands a robust and steady charging infrastructure. The widespread adoption of EVs into the transportation ecosystem hinges on continuous and reliable operation of charging stations (CSs). This paper delves its focus on reliability and resilience of EV chargers using various fault-tolerant (FT) techniques. It also analyzes the EV chargers’ failure scenarios such as hardware malfunctions and power outages which can disrupt the charging process. To evaluate these strategies, advanced FT algorithms and system reconfiguration protocols has been analyzed. Also, Total Harmonic Distortion (THD) act as key performance indicator which indicates the reduction from 60% to -40% with diminished current and voltage variations and enhanced grid stability. The extensive real-world research and simulations on charging scenarios reflects the key performance metrics with 95% charging efficiency and fault recovery times of 0.8 seconds at 180 Volts. This research evaluates the compatibility and cost-effectiveness of these strategies with diverse EV models. Ultimately, the findings highlight the effectiveness and practicality of FT techniques for EV chargers providing valuable insights for infrastructure developers and ensures a reliable EV charging fostering consumer trust and accelerating the global transition to electric mobility.

Negabent functions play a vital role in the field of cryptography and coding theory for designing secure cryptosystems. In this article, we investigate the various properties of 2q-nega-Hadamard transform (2q-NHT) of the functions from Z_q^n to Z_2q with q≥2 is a positive integer. We discuss the 2q-NHT of the derivative of these functions and develop a connection between 2q-walsh-Hadamard transform (2q-WHT) and 2q-NHT for the derivative of these functions. Also, we show that the dual g ̃ of g∈B_(n,q) is 2q-bent if N_g (ϑ)=ω^(g ̃(ϑ)) for all ϑ∈Z_q^n. The 2q-nega convolution transform theorem for the current setup is obtained. Further, we have obtained the 2q-NHT of composition of generalized vectorial function and generalized function.

Manufacturing plays a crucial role in robust economies, and effective optimization of manufacturing processes ensures competitive viability. Multi-hole drilling is a fundamental process in manufacturing, especially in the mass production of boilerplates, food processing separators, drum and trammel screens, and printed circuit boards, where optimizing drill tool paths is crucial for cost competitiveness. Multi-hole drill tool path sequencing is often framed as Traveling Salesman Problems, known for their NP-hard complexity. Researchers employed evolutionary algorithms to tackle the challenges associated with these NP-hard complexities. The recently proposed Discrete Teaching Learning Based Optimization (DTLBO) can address the intricacies of multi-hole drill tool path sequencing. This study proposes the use of DTLBO for multi-hole drill tool path sequencing optimization and highlights the critical distinctions between Canonical and Non-Canonical approaches of the DTLBO. Further, it assesses their performances through a comparative analysis using test problems, investigating the merits and demerits of these approaches. The findings of this investigation provide a foundation for refining the algorithms and improving their practical effectiveness, which will be pursued as future research. Notably, no prior research in the literature has undertaken such a comprehensive comparison.

In retail transactions, mobile payment services (MPS) can potentially replace cash, particularly in developing nations that lack card-swipe machines. Due to the concern that currency notes could spread diseases during the COVID-19 outbreak, digital payments saw a rise in popularity as a practical payment alternative. The extended period of the pandemic resulted in an extended period of continued usage, even for new users. Despite having a lengthy trial period, user-friendly interfaces, and greater fungibility than cash, MPS did not find widespread acceptance, and cash still predominates in retail transactions. There is a lot of research on technology adoption, however there is considerably less on usage retention. While there is some literature on continued use of technology, the main factor for discontinuation or reduction of usage is the lack of satisfaction. With MPS, satisfaction is rarely an issue, yet users limit the extent of their usage. In the context of retail transactions, this research explicitly examines continued usage following extensive initial use. The Gioia method of grounded theory was used to investigate the factors preventing continued use of MPS for retail transactions. The qualitative interviews were carried out among users in an emerging economy that is a leader in MPS adoption and use. To explain the barriers to the continued use of beneficial technology, this study proposes a conceptualization of consumer decision inertia with three dimensions categorized as deep-rooted habits, vicarious indifference, and kairotic uncertainty. This insight would be beneficial to MPS organizations not just in developing countries but even for developed economies. The conceptualization of consumer decision inertia also offers insights that can be applied in the context of sustained usage of other consumer-facing technologies.

With an increase in market competition, the association between marketing and inventory management has become more important. The commercial activities are more rapid through social media, and advertising has played a crucial role in reaching the product to the consumers before it hits the market. It has thus become normal in an oligopolistic marketing system to increase sales through advertising effort and gain more profit from potential market. It is challenging, nevertheless, to calculate demand and costs related to advertising efforts. As a result, the purpose of this study is to identify the best advertising approach and its potential impact on demand in order to optimize the firm's overall profit. In this paper, we develop an inventory model for deteriorating items to obtain an optimal advertising and inventory strategy, where the consumer demand rate depends on advertising effort and inventory of the items displayed in the store. We have formulated two optimal control problems with the assumption that the replenishment cycle is longer than the fresh product time or not. It is assumed that products do not decay within the fresh product time interval, and inventory decreases due to consumer demand. Next, items will deteriorate and inventory level decreases because of the combined effects of customer demand and deterioration. The analytical solution for the optimal dynamic advertising effort strategies obtained by applying Pontryagin’s maximum principle to maximize overall profit over the planning period. The efficiency of the proposed model is demonstrated by numerical examples. A parameter sensitivity analysis is also performed, providing suggestions for enhancing the firm's profitability when dealing with deteriorating products.

Securing the information from the attackers is a crucial aspect of modern digital life. Numerous cryptographic algorithms are employed to provide security for data transmission. Among these, the International Data Encryption Algorithm (IDEA) stands out as a widely utilized algorithm for enhancing security. However, the IDEA algorithm has a notable drawback due to its relatively large number of weak keys. This susceptibility stems from the fixed 25-bit circular left shift during each key generation round. It is made weakens the regular key generation process of the IDEA algorithm. To address these concerns, this research work introduces a Modified International Data Encryption Algorithm (MIDEA) using a key size of 1024 bits. The method suggests a novel approach for the circular left shift by employing different bits that effectively overcome the limitations of fixed bits of the circular left shift. Additionally, this work presented innovative encryption and decryption techniques using a key size of 1024 bits. A comprehensive comparison is conducted between the IDEA and the MIDEA algorithm based on time complexity and security. Furthermore, this work provides a novel phishing attack detection framework using the suggested MIDEA technique. This framework is used for securely sharing patient data in the healthcare sector. The results of the proposed work indicate that encryption time varied from 20.08930 to 494.18258 seconds across file sizes from 0.97 to 40.8 megabytes. The experimental results demonstrate that the MIDEA algorithm exhibits significant performance enhancements with encryption speed improved by 60.67 percent and decryption robustness by 63.24 percent.

The aim of the current study is to investigate the stability analysis in case of the linear as well as nonlinear of a thermo-solutal chemically reactive couple stress fluid under uniform magnetic field convection. Investigations have been conducted on the impact of chemical reaction and external vertical magnetic field on the commencement of double diffusive convection in couple stress fluid between infinite horizontal parallel plates. Darcy's modified law governs the flow in porous media and the Oberbeck-Boussinesq approximation is accurate. For modelling the momentum equation, the modified Darcy equation with the time derivative and inertia terms is utilized. Expressions for the Rayleigh numbers with finite amplitude, oscillatory, and stationary states are found in accordance with the regulating factors. Graphics are used to illustrate how the couple-stress parameter, solute Rayleigh number, Vadasz number and diffusivity ratio affect stationary, oscillatory and finite-amplitude convection. Stationary, oscillatory and finite-amplitude convection are found to be stabilized by the couple-stress parameter and the solute Rayleigh number. The normal mode analysis method is utilized to look into the linear stability of flow dynamics after the nonlinear mathematical problem has been linearized. When stationary and finite-amplitude modes are present, the diffusivity ratio has a destabilizing effect; when oscillatory convection is present, it has a dual effect. Oscillatory convection develops earlier when the Vadasz number is higher. The couple-stress parameter and diffusivity ratio both increase with increasing solute Rayleigh number values, but the heat and mass transfer decreases as these values rise. Using double Fourier series, a generalized weakly nonlinear stability analysis is done. The research illustrates how various regulating parameters support and destabilize the flow dynamics. The influence of finite-amplitude convection on stability is also examined. Furthermore, the best conditions for stationary and oscillatory convection are based on altering the couple stress flow stability by controlling the applied magnetic field.

Underwater environments, especially the coral reefs, are the habitat of many critically endangered species. Extensive monitoring of these aquatic ecosystems is essential for conserving and deep understanding of these vulnerable habitats. Monitoring by extracting details from underwater images of turbid, hazy marine environments is extremely challenging. In this work, a novel annotated dataset is created for three classes of objects in the images of coral reef environment considering fish, rock/coral and background for the Fish4Knowledge dataset, a benchmark dataset primarily for binary segmentation. This work also proposes a multiclass ResUnet based image segmentation model for the newly created multiclass annotations. Various encoder-decoder convolutional architectures were analysed and found that ResUnet exhibits better robustness. The performance of the multiclass ResUnet model is also analysed by optimizing with different cost functions. Various underwater noisy conditions are simulated in the test images to find the robustness of the model, and observed that the proposed model optimised with Jaccard loss performs better even in extremely noisy scenarios.

In order to make the constructed investment portfolio model better adapt to the actual securities market, this paper incorporates the multifractal correlations into the portfolio model of multi-risk assets optimization. On the basis of using variable detrended covariance to measure multifractal correlations, the variable detrended covariance is embedded into the reward-risk criterion, the mean multifractal detrended cross correlation analysis portfolio (M-D) model of multi-risk assets is constructed, and the analytical solution of the M-D model of multi-risk assets is given. The empirical analysis shows that the M-D model not only can improve investment performance but also meet the return-risk criterion much more, reaching the goal of optimizing the multi-risk asset portfolio model.

In this paper, we delve into the intricate properties of degenerate Poisson random variables, exploring their moment generating function, the law of large numbers, and the central limit theorem. Our study into the law of large numbers unveils the convergence patterns of degenerate Poisson random variables, enlightening the stability and predictability of their expected values and variances. Further enriching our study, we extend our focus to the central limit theorem, unravelling the interesting results that emerge as the sample size approaches infinity.

This study introduces a new approach to the development of generalized 1-parameter, 2-variable Hermite–Frobenius–Euler polynomials, which are characterized by their generating functions, series definitions and summation formulae. Additionally, the research utilizes a factorization method to establish recurrence relations, shift operators and various differential equations, including differential, integro-differential and partial differential equations. The framework elucidates the fundamental properties of these polynomials by utilizing generating functions, series definitions and summation formulae. The results of the study contribute to the understanding of the properties of these polynomials and their potential applications.

This research investigates the security challenges posed by worm propagation in wireless sensor networks (WSNs). A novel stochastic susceptible – infectious – vaccination – recovered model is introduced to analyse the dynamics of worm spread. Conditions for the existence of a unique global solution are examined, and necessary conditions for worm eradication are established. By incorporating random environmental fluctuations, the proposed model provides a more precise depiction of propagation dynamics than deterministic models. Empirical findings are presented to validate the model’s predictive accuracy across diverse scenarios, underscoring its robustness. Numerical simulations affirm the effectiveness of the analytical approach in understanding worm propagation within WSNs. The study offers valuable insights into worm dynamics and proposes a methodological framework to enhance network security. The findings underscore the significant role of stochastic systems in modelling and provide strategic perspectives for designing resilient defensive frameworks against worm attacks in WSNs.

Active control in adaptive structures allows for reducing the structural weight of a building and thus to drastically decrease the construction sector’s global impact. For an active control, it is necessary to estimate the state. Especially for large structures, decentralized approaches are particularly advantageous. However, the choice of the individual decentralized models, the substructuring, is important. This work considers decentralized state estimation for different substructure layouts obtained by the Relative Gain Array (RGA) for an adaptive high-rise structure. The estimators are realized using Information Filters (IF) based on reduced models derived from the full model via SEREP-Guyan and modal reduction. Different degrees of interconnection (none, sparse, full) are investigated w. r. t. estimation accuracy and robustness towards communication failure. For more substructures the estimation error increases. Depending on the layout, communicating is beneficial, but a full interconnection is not necessary for a sufficient estimation. In case of a failed information exchange, communicating estimators should adapt to the fault.

In this paper, we focus on multivariate doubly truncated first two moments of generalized skew-elliptical distributions. This class of distributions includes many useful distributions, such as skew-normal, skew Student-[Formula: see text], skew-logistic and skew-Laplace-normal distributions, as special cases. The formulas of multivariate doubly truncated covariance (MDTCov) for generalized skew-elliptical distributions are also given. Further, we compute multivariate doubly truncated expectations (MDTEs) and MDTCovs for [Formula: see text]-variate skew-normal, skew-Student-[Formula: see text], skew-logistic and skew-Laplace-normal distributions, and use Monte-Carlo method to simulate and compare with the above results. As applications, the results of multivariate tail conditional expectation (MTCE) and multivariate tail covariance (MTCov) for generalized skew-elliptical distributions are derived. In addition, an optimal problem involving MDTE and MDTCov risk measures is proposed. Finally, we use real data to fit skew-normal distribution and to discuss MTCEs and MTCovs of logarithm of adjusted prices for two portfolios consisting of three companies from S&P (Standard & Poor’s) sectors.

We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for the truncation procedure. As this process would lead to high computational costs if we perform it for a large number of parameters, we combine this approach with the reduced basis method that determines a reduced representation of the Lyapunov equation solutions for the parameters of interest. Residual-based error estimators are then used to evaluate the quality of the approximations. After introducing the procedure for a general class of differential-algebraic systems, we turn our focus to systems with a specific structure, for which the method can be applied particularly efficiently. We illustrate the efficiency of our approach on several models from fluid dynamics and mechanics.

In this study, the sequential operator of mixed order is analysed on the domain [Formula: see text] with [Formula: see text]. Then, the positivity of the nabla operator is obtained analytically on a finite time scale under some conditions. As a consequence, our analytical results are introduced on a set, named [Formula: see text], on which the monotonicity analysis is obtained. Due to the complicatedness of the set [Formula: see text] several numerical simulations so are applied to estimate the structure of this set and they are provided by means of heat maps.

Assume that [Formula: see text] is a random variable whose moment generating function exists in a neighbourhood of the origin. In this paper, we study the probabilistic degenerate central Bell polynomials associated with [Formula: see text], as probabilistic extension of the degenerate central Bell polynomials. In addition, we investigate the probabilistic degenerate central factorial numbers of the second kind associated with [Formula: see text] and the probabilistic degenerate central Fubini polynomials associated with [Formula: see text]. The aim of this paper is to derive some properties, explicit expressions, certain identities and recurrence relations for those polynomials and numbers.

Turntable ladders are flexible large-scale manipulators, so an active oscillation damping is highly valuable. Aiming to support the development and parametrization of the controller, a precise dynamic model of the vehicle is desired. Previous work considering solely the dynamic oscillations of the ladder parts is extended by a dynamic model of the chassis and support structure that includes flexible deformation of the chassis. All contact forces to the ground are calculated because they provide potential for determining dynamic outreach limits in future. As it can happen in practice, the outriggers are able to become fully unloaded in the simulation model. This behaviour is validated by measurements. A sensitivity analysis is used to establish a suitable approach for identification of model parameters. Dynamical measurements illustrate that the combination of two dynamic models of ladder and chassis improves representation of the dynamic oscillations that are crucial for the active oscillation damping control.

Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for [Formula: see text]-convex function are obtained. By employing well-known inequalities such as Hölder’s and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.

In this paper, we propose competitive predator-prey models with a small immigration into the prey. The dynamics of these models are investigated by addressing the boundedness, coexistence, and extinction conditions, as well as the local and global stability of equilibria. Immigrants stabilize the systems and increase the probability of coexistence. A Hopf bifurcation analysis shows that the model with Holling type II exhibits a Hopf bifurcation with respect to immigration parameter, but there is no bifurcation of the model with Holling type I. The numerical results support the theoretical results. Additionally, incorporating a few immigrants into the prey has a high sensitivity when the dynamic is periodic, but it has a lower sensitivity when the dynamic is stable. The obtained results can be biologically interpreted to improve the survival of species in the environment by adding immigrants. The rescue effect is considered as one of the implications in the real world that interpret the obtained results in this study.

This work contains a generalization of the Szász-Baskakov operators with the help of Fubini polynomials. Firstly, we get the rate of convergence of our new operators and then we find some approximation results. Finally, Voronovskaya-type theorem and error table with comparisons are given.

ABSTRACTRecently, many authors have studied degenerate Bernoulli and degenerate Euler polynomials. Let [Formula: see text] be a random variable whose moment generating function exists in a neighbourhood of the origin. The aim of this paper is to introduce and study the probabilistic extension of degenerate Bernoulli and degenerate Euler polynomials, namely the probabilistic degenerate Bernoulli polynomials associated with [Formula: see text] and the probabilistic degenerate Euler polynomials associated with [Formula: see text]. Also, we intoduce the probabilistic degenerate [Formula: see text]-Stirling numbers of the second associated with [Formula: see text] and the probabilistic degenerate two variable Fubini polynomials associated with [Formula: see text]. We obtain some properties, explicit expressions, recurrence relations and certain identities for those polynomials and numbers. As special cases of [Formula: see text], we treat the gamma random variable with parameters [Formula: see text], the Poisson random variable with parameter [Formula: see text], and the Bernoulli random variable with probability of success [Formula: see text].

Due to the intermittent contact with the wellbore, determining torque and drag for deviated wells is difficult. Most models have ignored drill string stiffness and assumed continual contact to simplify derivation. However, the accuracy of these ‘soft-string’ models is restricted, especially at high dogleg severities. On the other hand, most ‘stiff-string’ models rely on computationally intensive approaches or continuous contact assumptions. To mitigate these issues, a computationally efficient penalty-based wellbore contact algorithm has been developed based on vector calculation, which at most requires two dot products and three arithmetic operations to determine contact locations. This algorithm is incorporated into a 3D multibody dynamics (MBD) model, which utilizes rigid drill-string segments based on the Newton-Euler formulation, connected via axial, shear, torsional, and bending springs to capture drill string flexibility. This model performs simulations faster than real-time and has been validated using surface measurements from a completed well.

ABSTRACTIn the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by individuals going through the different stages. The main objective of this work is to study, from the methodological point of view, the behaviour of solutions of the discrete time SP models without reinfection and with a general incidence function. Besides calculating [Formula: see text], we find bounds for the epidemic final size, characterize the asymptotic behaviour of the infected classes, give results about the final monotonicity of the infected classes, and obtain results regarding the initial dynamics of the prevalence of the disease. Moreover, we incorporate into the model the probability distribution of the number of contacts in order to make the model amenable to study its effect in the dynamics of the disease.

ABSTRACTIn this study, we study a two-strain nonlinear model for the transmission of COVID-19 with a vaccinated class. Here, it is remarkable that the model we consider contains two kinds of viruses known as Omicron and Delta variants denoted by [Formula: see text] and [Formula: see text], respectively. Also, the uninfected population is denoted by [Formula: see text], the vaccinated class by [Formula: see text] and the recovered individuals by [Formula: see text]. In the presented study, we consider the proposed model under conformable fractional order derivatives. The fundamental reproductive number and equilibrium points are computed. Moreover, we determine the existence and uniqueness of the solution to the suggested model using fixed-point theory. Furthermore, we provide a suitable methodology by applying the Euler numerical method to calculate the approximate solution of each compartment of the proposed model. Additionally, using MATLAB-16, we simulate the given results graphically for a variety of fractional orders using some real values of the parameters and initial conditions.

ABSTRACTThe goal of this study is to model Bass diffusion and its extensions on complex networks, including scale-free networks with arbitrary power-law exponent and assortative degree correlations. For this purpose we employ a combination of the free software packages networkX and NetLogo. Some new results obtained in the agent-based simulations (and differing from those in mean-field approximation) are the following. The introduction of assortative correlations in scale-free networks has the effect of delaying the adoption peak in the Bass model, compared to the uncorrelated case. The peak time depends strongly also on the maximum degree effectively present in the network. For diffusion models with threshold on signed network, a high level of clustering tends to cause adoption blockades. By analysing statistical ensembles of assortative networks generated via Newman rewiring one observes a remarkable strong correlation between the average degree of first neighbours [Formula: see text] and the average clustering coefficient [Formula: see text].

ABSTRACTWe establish new conformable fractional Hermite-Hadamard (H–H) Mercer type inequalities for harmonically convex functions using the concept of support line. We introduce two new conformable fractional auxiliary equalities in the Mercer sense and apply them to differentiable functions with harmonic convexity. We also use Power-mean, Hölder’s and improved Hölder inequality to derive new Mercer type inequalities via conformable fractional integrals. The accuracy and superiority of the offered technique are clearly depicted through impactful visual illustrations. We also use our technique to derive new estimates for hypergeometric functions and special means of real numbers that are more precise than existing ones. Some applications are provided as well. Our results generalize and extend some existing ones in the literature.

ABSTRACTThis study emphasizes the significance of understanding groundwater flow behavior for effective contaminant transport and heat storage. Aquifers, with their irregular shapes and variable permeability, exhibit anisotropic flow resistances that affect mass and heat transfer, posing challenges for modeling. The dual-porosity model is used as a numerical approach to calculate macroscopic heat transfer without explicitly resolving the structure. By solving equations for mobile and immobile phases and coupling relevant equations for heat conservation, this model was applied to transient numerical experiments simulating heat transfer and storage in a desktop model filled with glass beads. Results indicate alignment with experimental and numerical models resolving porous structures on the microstructure scale. This methodology offers a comprehensive digital toolbox for solving large-scale heat storage problems in aquifers, contributing to digital and sustainability transformations with reasonable computational demands.

ABSTRACTSeveral spatiotemporal epidemic models have described how contact and mobility restrictions have a dynamic effect on morbidity and mortality of fast transmitting pathogens in epidemics. Despite this, there have been rather limited contributions looking at policy optimization. This work combines a new spatiotemporal epidemic model of a heterogeneous mixed population located at different places with an optimal control approach to show the effects of contact and mobility restrictions under policy optimization. The objective of optimization not only includes epidemiological but also socio-economic implications of the restrictions. Several scenarios are numerically investigated, and the dependence of the optimal policy on some basic epidemiological parameters is analysed. The results illustrate the strong impact of spatial heterogeneity on optimal policy measures. An analysis of the stability of the disease-free equilibrium of the model is also presented.

ABSTRACTThe authors introduce new classes of analytic function with respect [Formula: see text]-symmetric points subordinate to a domain that is not Carathéodory. To use the existing infrastructure or framework, usually, the study of analytic function have been limited to a differential characterization subordinate to functions which are Carathéodory. Here, we try to obtain various interesting properties of functions which are not Carathéodory. Integral representation, interesting conditions for starlikeness and inclusion relations for functions in these classes are obtained.

ABSTRACTIn this study, we establish a new class of Kantorovich-Stancu type [Formula: see text]Bernstein operators via an adaptation of Bézier bases which are formulated with the inclusion of the shape parameters [Formula: see text], [Formula: see text], and a positive parameter [Formula: see text] First, we present a uniform convergence result for these operators and, subsequently, examine the convergence properties by utilizing the weighted [Formula: see text]-statistical convergence notion. Furthermore, we estimate the rate of the weighted [Formula: see text]-statistical convergence of these operators. We conclude our work by providing a numerical example with explanatory graphs to show their approximation behaviours.

ABSTRACTIn this paper, we investigate a novel class of Hermite-Hadamard inequalities applicable to functions with h-convex absolute derivatives. Graphical representations are provided to bolster the validity of our key findings. Some limiting results of our main findings are discussed as corollaries. Furthermore, we establish error estimates in terms of trapezoid formulae for differences between generalized means.

ABSTRACTA computational technique for analysing coupled system of singularly perturbed convection-diffusion delay differential equations with large delay is presented in this study. We solve this problem using non-polynomial spline technique and arrive at a system that can potentially be solved. To show the theoretical investigation, an example is solved for different perturbation parameter values, and the computational results are shown in tables. The model we have proposed is of first order convergent, and this technique indicated that the acquired findings were more accurate than earlier results.