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This paper focuses on the complex version of the Cahn-Hilliard-Oono equation with Neumann boundary conditions, which is used to capture long-range nonlocal interactions in the phase separation process. The first part of the paper establishes the well-posedness of the corresponding stationary problem associated with the equation. Subsequently, a numerical model is constructed using a finite element discretization in space and a backward Euler scheme in time. We demonstrate the existence of a unique solution to the stationary problem and obtain error estimates for the numerical solution. This, in turn, serves as proof of the convergence of the semi-discrete scheme to the continuous problem. Finally, we establish the convergence of the fully discrete problem to the semi-discrete formulation. [ABSTRACT FROM AUTHOR]

This paper investigates consensus control in heterogeneous and uncertain multiple autonomous underwater vehicle (AUV) systems under implicit reduced visibility conditions. We address challenges such as environmental uncertainties and system nonlinearity by utilizing a unified connectivity approach to model low-visibility interactions and heterogeneous multi-AUV dynamics. Our main contributions include developing a feedback linearization model for heterogeneous multi-AUV systems that accounts for uncertainties, introducing an adaptive consensus controller based on relative positioning that effectively manages implicit visual interaction limitations and validating our strategies through stability analysis and numerical simulations. Our simulations demonstrate approximately a 60% improvement in accuracy compared to previous algorithms, highlighting the practical value of our approach in AUV recovery operations. These advancements provide a robust solution for consensus control in complex underwater environments. [ABSTRACT FROM AUTHOR]

This work explores a well-established eighth-algebraic-order numerical method belonging to the explicit Numerov-type family. To enhance its efficiency, we integrated a cost-effective algorithm for adjusting the step size. After each step, the algorithm either maintains the current step length, halves it, or doubles it. Any off-step points required by this technique are calculated using a local interpolation function. Numerical tests involving diverse problems demonstrate the significant efficiency improvements achieved through this approach. The method is particularly effective for solving differential equations with oscillatory behavior, showcasing its ability to maintain high accuracy with fewer function evaluations. This advancement is crucial for applications requiring precise solutions over long intervals, such as in physics and engineering. Additionally, the paper provides a comprehensive MATLAB-R2018a implementation, facilitating ease of use and further research in the field. By addressing both computational efficiency and accuracy, this study contributes a valuable tool for the numerical analysis community. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid Halpern-based extragradient algorithm for finding a common solution of a pseudomonotone equilibrium problem and a fixed point problem of a nonexpansive mapping. We prove the strong convergence of the proposed algorithm under some mixed conditions. Some numerical examples are provided to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Entropy-regularized quadratic optimization problems are a special class of optimization problems with wide applications in various fields, such as transportation and machine learning. In this paper, we apply the augmented Lagrangian method to this problem with its subproblem solved by the block coordinate descent method. Under certain mild conditions, we analyze the global convergence of this algorithm. Numerical experiments demonstrate the effectiveness of this algorithm. [ABSTRACT FROM AUTHOR]

This contribution discusses the influence of different barrier update strategies on the performance and robustness of an interior point algorithm for single-crystal plasticity at small strains. To this end, single-crystal plasticity is first briefly presented in the framework of a primal-dual interior point algorithm to outline the general algorithmic structure. The manner in which the barrier parameter is modified within the interior point method, steering the penalization of constraints, plays a crucial role for the robustness and efficiency of the overall algorithm. In this paper, we compare and analyze different strategies in the framework of crystal plasticity. In a thorough analysis of a numerical example covering a broad range of settings in monocrystals, we investigate robust hyperparameter ranges and identify the most efficient and robust barrier parameter update strategies. [ABSTRACT FROM AUTHOR]

In this paper, a two-stage robust optimisation is presented for an uncapacitated hub location problem in which demand is uncertain and the level of conservatism is controlled by an uncertainty budget. In the first stage, locations for establishing hub facilities were determined, and allocation decisions were made in the second stage. An accelerated Benders decomposition algorithm was used to solve the problem. Computational experiments showed better results in terms of number of iterations and computation time for Benders decomposition with Pareto-optimal cuts in comparison with the classical Benders decomposition algorithm. According to numerical analysis, it was concluded that increasing the uncertainty budget also increased total costs for more established hubs. To determine the uncertainty budget in an appropriate manner, a new expected aggregate function was introduced. The numerical studies demonstrated the usefulness of the proposed method in defining the appropriate uncertainty budget in the presence of uncertainty. [ABSTRACT FROM AUTHOR]

In this paper-series, we investigate the performance of 12 explicit non-conventional algorithms. All of them have the convex combination property, thus they are unconditionally stable and preserve the positivity of the solution when they applied to the heat equation. In this part of the series, we construct several 2D systems to find how the errors depend on the time step size. Sweeps for other key parameters will be presented in the next part of the series. [ABSTRACT FROM AUTHOR]

In the internet of battlefield things, ammunition is becoming networked and intelligent, which depends on location information. Therefore, this paper focuses on the self-organized network collaborative localization of munitions with an aerial three-dimensional (3D) highly-dynamic topographic structure under a satellite denied environment. As for aerial networked munitions, the measurement of munitions is objectively incomplete due to the degenerated and interrupted link of munitions. For this reason, a cluster-oriented collaborative localization method is put forward in this paper. Multidimensional scaling (MDS) was first integrated with a trilateration localization method (TLM) to construct a relative localization algorithm for determining the relative location of a mobile cluster network. The information related to relative velocity was then combined into a collaborative localization framework to devise a TLM-vMDS algorithm. Finally, an iterative refinement algorithm based on scaling by majorizing a complicated function (SMACOF) was employed to effectively eliminate the influence of incomplete link observation on localization accuracy. Compared with the currently available advanced algorithms, the proposed TLM-vMDS algorithm achieves higher localization accuracy and faster convergence for a cluster of extensively networked munitions, and also offers better numerical stability and robustness for highspeed motion models. [ABSTRACT FROM AUTHOR]

Two-dimensional tomographic forward modeling based on first arrivals requires the calculation of the minimum travel times of multiple emission points in a single iteration. The conventional method, which calculates each emission point one by one, produces many unuseful calculations and has low computational efficiency. To solve this problem, given the characteristic that the velocity distribution of a model does not change during a single iteration of forward modeling, an improved algorithm was proposed based on the reciprocity principle and Fermat's principle. The ray tracing results of a small number of emission points were used to constrain the calculation area of other emission points, which reduced the number of unuseful calculations and improved the calculation efficiency of a single-iteration tomographic forward modeling simulation. Theoretical analysis and numerical examples showed that for a homogeneous model, when the transmitting and receiving points were located on two long sides, three adjacent sides (i.e., two long sides and one short side), and four sides, the computational efficiency of the improved algorithm was about 2 times, 2 times, and 1.5 times, respectively, that of the conventional method. For heterogeneous models, the computational efficiency of the improved algorithm was usually more significant. [ABSTRACT FROM AUTHOR]

This paper proposes an L1/LDG algorithm for a time–space fractional convection equation on a bounded rectangular domain Ω⊂ℝ2$$ \Omega \subset {\mathrm{\mathbb{R}}}^2 $$. Here, the temporal partial derivative is in the sense of Caputo with order α∈(0,1)$$ \alpha \in \left(0,1\right) $$, and the spatial partial derivatives are of Riesz type with orders β,γ∈(0,1)$$ \beta, \gamma \in \left(0,1\right) $$ in x$$ x $$‐ and y$$ y $$‐directions, respectively. L1 approximation is utilized to evaluate the temporal Caputo derivative, while the local discontinuous Galerkin (LDG) method is adopted to deal with the spatial Riesz derivative. The rigorous numerical stability analysis and error estimate are presented which are supported by illustrative numerical examples. [ABSTRACT FROM AUTHOR]

In this paper-series, we investigate the performance of 12 explicit non-conventional algorithms in several 2D systems. All of them have the convex combination property, thus they are unconditionally stable and preserve the positivity of the solution when they are applied to the heat equation. In the first part of the series, we examined how the errors depend on the time step size and running times. Now we present additional numerical test results, where sweeps for parameters such as the stiffness and the wavelength of the initial function will be performed. [ABSTRACT FROM AUTHOR]

We study hedonic editing principles that aim to find individuals' maximum utility when confronted with multiple outcomes Thaler (Mark Sci 4:199–214, 1985). These principles have been primarily defined and studied for only two outcomes. However, when dealing with more than two outcomes, the principles become more ambiguous, and some of them may not continue to be valid. To address this, we present an algorithm designed to find the best solution over a partition set of a given vector of n outcomes. We demonstrate that this algorithm identifies the best-majorized vector for up to four outcomes and establish the conditions under which this vector is optimal for n outcomes. Our algorithm is fast since it requires at most n - 1 steps. We provide a detailed analysis of the algorithm's performance, characterizing the conditions that guarantee the optimal solution and identifying cases where the algorithm may not converge to the optimal solution. Nevertheless, in these cases, we demonstrate through numerical analysis that it can find the optimal solution with a high accuracy rate in most 'practical' instances, making it a reliable tool for solving hedonic editing problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose two new hybrid methods for solving nonlinear equations, utilizing the advantages of classical methods (bisection, trisection, and modified false position), i.e., bisection-modified false position (Bi-MFP) and trisection-modified false position (Tri-MFP). We implemented the proposed algorithms for several benchmark problems. We discuss the graphical analysis of these problems with respect to the number of iterations and the average CPU time. [ABSTRACT FROM AUTHOR]

Integration algorithm is an important mean to solve the discrete time equations of structural dynamics in earthquake engineering. In this paper, a new model‐based explicit integration algorithm, featured by optimization‐based integration parameter updating, is developed for a more accurate and efficient solution of structural dynamic problems. The new integration algorithm is designed to yield minimum error and controllable numerical dispersion under the premise of stability by defining objective functions and constraints. Numerical properties of the new integration algorithm are investigated in details using the amplification matrix method for a linear elastic single degree‐of‐freedom system. Meanwhile, representative numerical examples and complex structure examples are analyzed and compared with other representative algorithms. As a result, the proposed algorithm yields comparable numerical characteristics with other methods, but exhibits pronounced superiority in controllable algorithmic dissipation, higher precision, and better efficiency. Therefore, the new integration algorithm possesses extensive application prospect in solving complicated linear and nonlinear structural dynamic problems. [ABSTRACT FROM AUTHOR]

Fractional calculus serves as a versatile and potent tool for the modeling and control of intricate systems. This discussion debates the system of DFDEs with two regimes; theoretically and numerically. For theoretical analysis, we have established the EUE by leveraging the definition of Hilfer (α,β)-framework. Our investigation involved the examination of the possessions of the FRD, FCD, and FHD, utilizing their forcefulness and qualifications to convert the concerning delay system into an equivalent one of fractional DVIEs. By employing the CMT, we have successfully demonstrated the prescribed requirements. For numerical analysis, the Galerkin algorithm was implemented by leveraging OSLPs as a base function. This algorithm allows us to estimate the solution to the concerning system by transforming it into a series of algebraic equations. By employing the software MATHEMATICA 11, we have effortlessly demonstrated the requirements estimation of the nodal values. One of the key advantages of the deployed algorithm is its ability to achieve accurate results with fewer iterations compared to alternative methods. To validate the effectiveness and precision of our analysis, we conducted a comprehensive evaluation through various linear and nonlinear numerical applications. The results of these tests, accompanied by figures and tables, further support the superiority of our algorithm. Finally, an analysis of the numerical algorithm employed was provided along with insightful suggestions for potential future research directions. [ABSTRACT FROM AUTHOR]

We propose and study a weakly convergent variant of the forward-backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector, providing additional degrees of freedom. The only requirement on the deviation vector to guarantee convergence is that its norm is bounded by a quantity that can be computed online. This approach offers great flexibility and paves the way for the design of new forward-backward-based algorithms, while still retaining global convergence guarantees. These guarantees include linear convergence under a metric subregularity assumption. Choosing suitable monotone operators enables the incorporation of deviations into other algorithms, such as the Chambolle-Pock method and Krasnosel'skĭı--Mann iterations. We propose a novel inertial primal-dual algorithm by selecting the deviations along a momentum direction and deciding their size by using the norm condition. Numerical experiments validate our convergence claims and demonstrate that even this simple choice of a deviation vector can enhance the performance compared to, for instance, the standard Chambolle--Pock algorithm. [ABSTRACT FROM AUTHOR]

This paper proposed an efficient and adaptive frequency sampling algorithm for frequency response analysis using dynamic condensation-based reduced-order modeling. For the degree of freedom-based model reduction method, the reduced-order basis becomes a frequency-dependent matrix since the relationship between master and slave degrees of freedom stems from partial equations of a second-order dynamical system. Such frequency-dependency makes the analysis inefficient for investigating the frequency response of the system. Considering that the coverage of a local reduced-order basis at a single frequency varies depending on the frequency, a new frequency sampling algorithm was proposed with a strategy of constructing multiple local reduced-order models (ROMs) at sample frequencies. For adaptive sampling, the frequency range of a local ROM was evaluated, and a new sample was added if there was a gap between two adjacent ROMs. As a result, the accuracy of the local ROM can be estimated, and the efficiency in the online stage was greatly enhanced. The proposed method was verified by performing frequency response analysis with several numerical examples, including a large-scale structural and dynamic system. [ABSTRACT FROM AUTHOR]

An intelligent assembly method was designed to realize the intelligent assembly of the profiled thermal battery pack and improve its assembly accuracy. Firstly, as the number and size of different monomer batteries vary, this paper takes the monomer thermal battery assembly as the object, with a common shape circle assembly screw arrangement and an established process model. Then, the assembly also has an improved differential evolution algorithm for assembly arrangement and process on the number, location, tightening of the screw assembly, torque, and the order of solutions. According to this scheme, the assembly and the flatness test were carried out. The results showed that the bottom plate of the assembly frame was "concave in the middle and warped around", and the flatness error was large. The scheme was optimized by numerical simulation analysis. After optimization, the average offset of the floor plane was 0.04 mm, and the offset accounted for 0.028% of the overall height; the maximum offset was 0.094 mm and the offset was reduced by 0.312%. [ABSTRACT FROM AUTHOR]

In this paper we revisit some classical queueing systems such as the M $^b$ /E $_k$ /1/ m and E $_k$ /M $^b$ /1/ m queues, for which fast numerical and recursive methods exist to study their main performance measures. We present simple explicit results for the loss probability and queue length distribution of these queueing systems as well as for some related queues such as the M $^b$ /D/1/ m queue, the D/M $^b$ /1/ m queue, and fluid versions thereof. In order to establish these results we first present a simple analytical solution for the invariant measure of the M/E $_k$ /1 queue that appears to be new. [ABSTRACT FROM AUTHOR]

In recent years, sparse recovery-based space-time adaptive processing (SR-STAP) technique has exhibited excellent performance with insufficient samples. Sparse Bayesian learning algorithms have received considerable attention for their remarkable and reliable performance. Its implementation in large-scale radar systems is however hindered by the overwhelming computational load and slow convergence speed. This paper aims to address these drawbacks by proposing an improved iterative reweighted sparse Bayesian learning algorithm based on expansion-compression variance-components (ExCoV-IIR-MSBL). Firstly, a modified Bayesian probabilistic model for SR-STAP is introduced. Exploiting the intrinsic sparsity prior of the clutter, we divide the space-time coefficients into two parts: the significant part with nontrivial coefficients and the irrelevant part with small or zero coefficients. Meanwhile, we only assign independent hyperparameters to the coefficients in the significant part, while the remaining coefficients share a common hyperparameter. Then the generalized maximum likelihood (GML) criterion is adopted to classify the coefficients, ensuring both accuracy and efficiency. Hence, the parameter space in Bayesian inference will be significantly reduced, and the computational efficiency can be considerably promoted. Both theoretical analysis and numerical experiments validate that the proposed algorithm achieves superior performance with considerably improved computational efficiency in sample shortage scenarios. [ABSTRACT FROM AUTHOR]

This paper is devoted to the construction of certain polynomials related to Lucas polynomials, namely, modified Lucas polynomials. The constructed modified Lucas polynomials are utilized as basis functions for the numerical treatment of the linear and non-linear second-order boundary value problems (BVPs) involving some specific important problems such as singular and Bratu-type equations. To derive our proposed algorithms, the operational matrix of derivatives of the modified Lucas polynomials is established by expressing the first-order derivative of these polynomials in terms of their original ones. The convergence analysis of the modified Lucas polynomials is deeply discussed by establishing some inequalities concerned with these modified polynomials. Some numerical experiments accompanied by comparisons with some other articles in the literature are presented to demonstrate the applicability and accuracy of the presented algorithms. [ABSTRACT FROM AUTHOR]

In this paper, the 2D incompressible Navier-Stokes (INS) equations in terms of vorticity and stream function are considered. These equations describe the physics of many phenomena of scientific and engineering. By combining monotone upwind methods and weighted essentially non-oscillatory (WENO) procedures, a new numerical algorithm is proposed to approximate the solution of INS equations. To design this algorithm, after obtaining an optimal polynomial, it is rewritten as a convex combination of second-order modified ENO polynomials. Following the methodology of the traditional WENO procedure, the new non-linear weights are calculated. The performance of the new scheme on a number of numerical examples is illustrated. [ABSTRACT FROM AUTHOR]

The volumetric accuracy of a machine tool generally changes with time. Its periodic check, performed at a user's site in a semi-automated manner, can be a key to ensure a sufficient volumetric accuracy in the long term. A laser interferometer can only measure the linear positioning error motion of a linear axis. This paper proposes a scheme to identify all the two-dimensional (2D) error motions of two linear axes in a plane based on a set of distance measurements using only a laser interferometer. Unlike conventional tracking interferometers, the proposed scheme requires only a numerically controlled rotary table on which a laser interferometer is mounted. It regulates the laser beam direction based on the command target position in an open-loop control manner. This paper presents an algorithm to identify 2D error motions of two linear axes by performing only a single tracking test, in addition to the direct measurement of linear positioning error motions of two linear axes. The experimental comparison of the estimated error motions with their direct measurements is presented. The uncertainty analysis is also presented. [ABSTRACT FROM AUTHOR]

Confronting the challenges provided by jumbo container vessels, managers of world-class seaports must take into consideration water depths-related constraints when making the vessel berthing decisions. That is, when the water depths satisfy the requirement of jumbo vessels' drafts, these vessels are allowed to sail through the navigation channel. In this paper, we study a tactical berth allocation problem under the consideration of time-varying water depths. For the resolution, we propose an integer programming model, a set partitioning formulation and an improved differential evolutionary algorithm. Computational experiments demonstrate that the set partitioning formulation outperforms the integer programming model and can be applied to solve small- and medium-sized problems. The improved differential evolutionary algorithm is recommended for large-sized problems. [ABSTRACT FROM AUTHOR]

This article investigates a particular version of the cutting angle method for finding the global minimizer of sub-topical (increasing and plus sub-homogeneous) functions over a simplex. The algorithm is based on the abstract convexity of sub-topical functions. Furthermore, we discuss the proof of convergence of the algorithm and provide results from numerical experiments. [ABSTRACT FROM AUTHOR]

This paper addresses the design of synergetic control (SC) for synchronizing two chaos systems represented by Takagi-Sugeno (T-S) fuzzy models. Unlike many works published, the present paper provides a new synchronization algorithm of two different hyperchaotic systems which corroborate the given analytical stability proof of the closed-loop systems. The main idea is to represent the chaos systems as an aggregated fuzzy model which compromises a set of linear models in the first place. Afterwards, the synergistic controller is applied to synchronize a nonlinear hyperchaotic (slave) system with another hyperchaotic (master) system. The proposed approach achieves hyperchaos synchronization such that it has a simple structure leading to an easy implementation. Then, theoretical analysis and numerical simulation results are compared to those obtained with a conventional sliding mode (SMC) approach clearly showing the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

The problem of interest in this paper is the mathematical and numerical analysis of a new non-variational model based on a high order non-linear PDE system resulting from image denoising. This model is motivated by involving the decomposition approach of H − 1 norm suggested by Guo et al. [1,2] which is more appropriate to represent the small details in the textured image. Our model is based on a diffusion tensor that improves the behavior of the Perona-Malik diffusion directions in homogeneous regions and the Weickert model near tiny edges with a high diffusion order. A rigorous analysis of the existence and uniqueness of the weak solution of the proposed reaction-diffusion model is cheked in a suitable functional framework, using the Schauder fixed point theorem. Finally, we carry out a numerical result to show the effectiveness of our model by comparing the results obtained with some competitive models. [ABSTRACT FROM AUTHOR]

The " fast iterative shrinkage-thresholding algorithm " (FISTA) is one of the most famous first order optimization schemes, and the stepsize, which plays an important role in theoretical analysis and numerical experiment, is always determined by a constant relating to the Lipschitz constant or by a backtracking strategy. In this paper, we design a new adaptive non-monotone stepsize strategy (NMS), which allows the stepsize to increase monotonically after finite iterations. It is remarkable that NMS can be successfully implemented without knowing the Lipschitz constant or without backtracking. And the additional cost of NMS is less than the cost of some existing backtracking strategies. For using NMS to the original FISTA (FISTA_NMS) and the modified FISTA (MFISTA_NMS), we show that the convergence results stay the same. Moreover, under the error bound condition, we show that FISTA_NMS achieves the rate of convergence to o 1 k 6 and MFISTA_NMS enjoys the convergence rate related to the value of parameter of t k , that is o 1 k 2 a + 1 ; and the iterates generated by the above two algorithms are convergent. In addition, by taking advantage of the restart technique to accelerate the above two methods, we establish the linear convergences of the function values and iterates under the error bound condition. We conduct some numerical experiments to examine the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we consider an accelerated shrinking projection based parallel hybrid algorithm to study the split null point problem (SNPP) associated with the maximal monotone operators in Hilbert spaces. The analysis of the proposed algorithm provides strong convergence results under suitable set of control conditions as well as viability with the help of a numerical experiment. The results presented in this paper improve various existing results in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we study a Bregman proximal point algorithm (BPPA) for convex optimization problems. Though the convergence and sublinear convergence rate for BPPA are well-understand, the linear convergence rate for BPPA has yet been thoroughly studied in the literature. In this paper, we analyze the linear convergence rate of BPPA. Under the assumption that the objective function is strongly convex relative to a Legendre function, we establish the linear convergence for the function values sequence. Moreover, if the Legendre function is strongly convex and smooth, the linear convergence for the iterative sequence of BPPA is obtained. [ABSTRACT FROM AUTHOR]

In order to meet the edge services placement demand for multiobjective optimization of Power Internet of Things, an edge services placement strategy based on an improved strength Pareto evolutionary algorithm (SPEA2) is proposed in this paper. Firstly, we model the delay, resource utilization, and energy consumption. Then, a multiobjective optimization is proposed. Finally, an enhanced genetic algorithm is used to derive the decision candidate set. Moreover, the optimal solution in the candidate set is selected to be utilized in the iteration of the multicriteria decision and the superior-inferior solution distance method. Numerical results and analysis show that the proposed strategy is more effective in reducing system delay, improving resource utilization, and saving energy consumption than the other two benchmark algorithms. [ABSTRACT FROM AUTHOR]

The principal objective of the current paper is to propose a numerical algorithm for treating the linearized time-fractional KdV equation based on selecting two different sets of basis functions. The members of the first set are selected to be suitable combinations of the Chebyshev polynomials of the second kind and also to be compatible with the governing boundary conditions of the problem, while the members of the second set are selected to be the shifted second-kind Chebyshev polynomials. After expressing the approximate solutions as a double expansion of the two selected basis functions, the spectral tau method is applied to convert the equation with its underlying conditions into a linear system of algebraic equations that can be treated numerically with suitable standard procedures. The convergence analysis of the double series solution is carefully tested. Some numerical examples accompanied with comparisons with some other methods in the literature are displayed aiming to demonstrate the applicability and accuracy of the presented algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in finding a numerical solution of a linear BVP for a Fredholm IDE with a degenerate kernel subjected to impulsive actions. By Dzumabaev's parametrization method the original problem is reduced to a multipoint BVP for the system of Fredholm IDEs with additional parameters. For fixed parameters, the special Cauchy problem for the system of FIDEs on subintervals is obtained and by using a solution to this problem, a system of algebraic equations in parameters is constructed. An algorithm for solving the BVP and its computational implementation is developed. In the algorithm, Cauchy problems for ODEs and the calculation of definite integrals are the main auxiliary problems. By using various numerical methods for solving these auxiliary problems, the proposed algorithm can be implemented in different ways. The program codes were written to solve the problem and all calculations are performed on the Matlab 2018 software platform. [ABSTRACT FROM AUTHOR]

Image encryption has been an attractive research filed in recent years. In this paper, we propose a novel hyperchaotic encryption algorithm for color image utilizing DNA dynamic encoding and self-adapting permutation. Firstly, A new 4-dimensional hyperchaotic system is designed, and the detailed dynamic analysis shows that the system has strong pseudo-randomness and a large range of chaotic parameters. Secondly, based on the new 4-D hyperchaotic system, we devise the methods of DNA dynamic encoding, DNA dynamic calculation and DNA dynamic decoding in the image encryption algorithm, and the sequences generated by the hyperchaotic control these coding rules dynamically to make the results of operation more unpredictable. Moreover, the initial keystream is designed dependent upon the plaintext image, and the method of plaintext-related self-adapting permutation is proposed at the bit level and DNA level of the image respectively, which enhances the sensitivity of the algorithm to plaintext image and key. The theoretical analysis and numerical simulation show that the image algorithm has good security and can resist various attacks. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce a new three-step iteration procedure for fixed points of generalized hybrid operators. Weak and strong convergence results are obtained. The stability and the data dependence are also obtained for quasi-strictly contractive operators. The split feasibility problem, the problem of maximizing the modulus of a complex polynomial, and the reconstruction of signals using the compressive sensing technique are numerically addressed. Examples are presented to show the efficiency of the iteration procedure. [ABSTRACT FROM AUTHOR]

In comparison with integer-order chaotic systems, fractional-order chaotic systems exhibit more complex dynamics. In recent years, research into fractional chaotic systems for the utilization of image cryptosystems has become increasingly highlighted. This paper describes the development, testing, numerical analysis, and electronic realization of a fractional-order memcapacitor. Then, a new four-dimensional (4D) fractional-order memcapacitive hyperchaotic system is suggested based on this memcapacitor. Analytically and numerically, the nonlinear dynamic properties of the hyperchaotic system have been explored, where various methods, including equilibrium points, phase portraits of chaotic attractors, bifurcation diagrams, and the Lyapunov exponent, are considered to demonstrate the chaos behaviour of this new hyperchaotic system. Consequently, an encryption cryptosystem algorithm is used for colour image encryption based on the chaotic behaviour of the memcapacitive model, where every pixel value of the original image is incorporated in the secret key to strengthen the encryption algorithm pirate anti-attack robustness. For generating the keyspace of that employed cryptosystem, the initial condition values, parameters, and fractional-order derivative value(s) (q) of the memcapacitive chaotic system are utilized. The common cryptanalysis metrics are verified in detail by histogram, keyspace, key sensitivity, correlation coefficient values, entropy, time efficiency, and comparisons with other recent related fieldwork in order to demonstrate the security level of the proposed cryptosystem approach. Finally, images of various sizes were encrypted and recovered to ensure that the utilized cryptosystem approach is capable of encrypting/decrypting images of various sizes. The obtained experimental results and security metrics analyses illustrate the excellent accuracy, high security, and perfect time efficiency of the utilized cryptosystem, which is highly resistant to various forms of pirate attacks. [ABSTRACT FROM AUTHOR]

The article describes the Usage of fractional order PI λ D μ controller as AQM algorithm. The alternative, integer-based calculation process for PI λ D μ controller is proposed and tested in numerical analysis, simulation environment, and Linux-based testbed environment with real-life devices. The FPGA design for the calculation process is presented. Experimental evaluation and setup process for AQM in the network is presented. [ABSTRACT FROM AUTHOR]

This paper proposes a novel crosstalk prediction method between the triple-twisted strand (uniform and non-uniform) and the signal wire, that is, using back-propagation neural network optimized by the beetle antennae search algorithm based on chaotic disturbance mechanism (CDBAS-BPNN) to extract the per unit length (p.u.l) parameter matrix, and combined with the chain parameter method to obtain crosstalk. Firstly, the geometric model and cross-sectional model between the uniform triple-twisted strand and the signal wire are established, and the corresponding model between the non-uniform triple-twisted strand and the signal wire is obtained by the Monte Carlo (MC) method. Then, the beetle antennae search algorithm based on chaotic disturbance mechanism (CDBAS) and backpropagation neural network (BPNN) are combined to construct a new extraction network of the p.u.l parameter matrix, and the chain parameter method is combined to predict crosstalk. Finally, in the verification and analysis part of the numerical experiments, comparing the crosstalk results of CDBAS-BPNN, BAS-BPNN and Transmission Line Matrix (TLM) algorithms, it is verified that the proposed method has better accuracy for the prediction of the model. [ABSTRACT FROM AUTHOR]

Hybrid manufacturing systems that use both raw materials and returned products as a supply for their production process are considered. Specifically, the system under study contains two machines: one uses raw materials for manufacturing, while another utilises end-of-life products returned from the market for remanufacturing. Machines are failure-prone, demand and return rates fluctuate in time reflecting market behaviour due to economical, seasonal and environmental changes. The system performance is characterised by a long-term discounted cost that integrates several partial costs (those of manufacturing, remanufacturing, disposal, holding costs in serviceable and return inventories). Optimisation of the hybrid system behaviour requires to determine the combined manufacturing, remanufactruring and disposal policy, withstanding machine failures under dynamic market conditions. Optimality conditions in the form of Hamilton-Jacoby-Bellman equations are obtained and a novel numerical approach, based on the estimation of value function timederivative, is proposed in order to deal with demand and return variations. Extensive simulations are performed to address the numerous scenarios corresponding to evolving relationship between manufacturing capacities and varying demand and return levels. Simulation results show that the optimal policies have an important property of anticipating the future changes in the demand and return, and making the timely decisions relevant to these changes. [ABSTRACT FROM AUTHOR]

Selecting financial products is one of the most fundamental investment activities to both individuals and companies, and therefore it is very important to establish an efficient and practical method for financial products selection. To address the challenge of the complicated decision-making environment and decision makers' expression habits for the selection of financial products, this paper develops the incomplete additive probabilistic linguistic preference relation to depict decision makers' preferences. Considering that, when decision makers express their opinions using probabilistic linguistic preference relation, it is possible that the sum of the value of the probability information is more than 1, this paper also extends the concepts of probabilistic linguistic term set, additive probabilistic linguistic preference relation and incomplete additive probabilistic linguistic preference relation to improve and ensure their practicability. Moreover, an "inverse prospect theory-based" algorithm is proposed to choose proper financial products. The algorithm processes the original incomplete additive probabilistic linguistic preference relation by using the inverse functions of the prospect theory at first. Then, a priority weights deriving model is established based on the extended concepts. Finally, the numerical case and analysis is presented as the evidences to the conclusion that the proposed algorithm is practical and robust. [ABSTRACT FROM AUTHOR]

This paper presents a new numerical method to solve the non-linear constitutive equations of viscoelastic string with variable fractional order model. Firstly, the non-linear constitutive equation of the string is established based on the variable fractional viscoelastic model. Secondly, non-linear constitutive equation of the string is transformed into a matrix equation by using Bernstein polynomials, which can greatly simplify the solving process. Then the matrix equation is discretized and solved to obtain the numerical solutions. Finally, numerical results of viscoelastic string show the effect of the axial tension and axial velocity on its displacement, velocity and acceleration. It also indicates that how dynamic behaviours are affected by external force excitation. In addition, the proposed algorithm shows enormous potentials for solving the problem of high precision dynamics with the variable fractional order model. [ABSTRACT FROM AUTHOR]

In this paper, an efficient numerical algorithm is proposed for the valuation of unilateral American better-of options with two underlying assets. The pricing model can be described as a backward parabolic variational inequality with variable coefficients on a two-dimensional unbounded domain. It can be transformed into a one-dimensional bounded free boundary problem by some conventional transformations and the far-field truncation technique. With appropriate boundary conditions on the free boundary, a bounded linear complementary problem corresponding to the option pricing is established. Furthermore, the full discretization scheme is obtained by applying the backward Euler method and the finite element method in temporal and spatial directions, respectively. Based on the symmetric positive definite property of the discretized matrix, the value of the option and the free boundary are obtained simultaneously by the primal-dual active-set method. The error estimation is established by the variational theory. Numerical experiments are carried out to verify the efficiency of our method at the end. [ABSTRACT FROM AUTHOR]

Due to the fact that many classical numerical methods have not yet mature quantum counterparts, quantum circuit design is very important in quantum image processing. In this paper, using the novel enhanced quantum representation (NEQR) model, an image encryption algorithm based on Feistel structure is carried out in quantum computer by giving the encryption quantum circuits. First, the modified Feistel structure for image encryption is proposed. It is a 128-bit block cipher and requires 16-bit subkeys to encrypt the image, and it is a mixture of Feistel and substitution–permutation network; then, the detailed quantum circuits design of the encryption algorithm are given. Through numerical simulation and analysis, it is verified that the proposed quantum image encryption algorithm is effective and can resist statistical attacks effectively. [ABSTRACT FROM AUTHOR]

In this paper, we develop algorithms to independently draw from a family of conjugate posterior distributions over the structural parameterization when sign and zero restrictions are used to identify structural vector autoregressions (SVARs). We call this family of conjugate posteriors normal‐generalized‐normal. Our algorithms draw from a conjugate uniform‐normal‐inverse‐Wishart posterior over the orthogonal reduced‐form parameterization and transform the draws into the structural parameterization; this transformation induces a normal‐generalized‐normal posterior over the structural parameterization. The uniform‐normal‐inverse‐Wishart posterior over the orthogonal reduced‐form parameterization has been prominent after the work of Uhlig (2005). We use Beaudry, Nam, and Wang's (2011) work on the relevance of optimism shocks to show the dangers of using alternative approaches to implementing sign and zero restrictions to identify SVARs like the penalty function approach. In particular, we analytically show that the penalty function approach adds restrictions to the ones described in the identification scheme. [ABSTRACT FROM AUTHOR]

Tempered fractional Laplacian is the generator of the tempered isotropic Lévy process. This paper provides the finite difference discretization for the two-dimensional tempered fractional Laplacian by using the weighted trapezoidal rule and the bilinear interpolation. Then it is used to solve the tempered fractional Poisson equation with homogeneous Dirichlet boundary condition and the error estimate is also derived. Numerical experiments verify the predicted convergence rates and effectiveness of the schemes. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive generalised function projective synchronisation scheme of fractional-order chaotic systems with different dimensions and orders and fully unknown parameters is presented. On the basis of the Lyapunov method of fractional-order systems, a stability theorem of the fractional-order system with non-identical orders is proven. Using the fractional-order controller and adaptive control theory, sufficient conditions for synchronisation and unknown parameters update rules are obtained. Theoretical analysis and numerical simulations are provided to verify the validity of the proposed scheme. Moreover, synchronisation results are applied to secure communication via modified chaotic masking (MCM) method. The unpredictability of the scaling function matrix and the use of fractional-order systems with different orders can increase the security of the cryptosystem. The security analysis shows that the introduced algorithm has large key space, high sensitivity to encryption keys, higher security and the acceptable encryption speed. [ABSTRACT FROM AUTHOR]

The dynamics of the particle size distribution (PSD) of polydispersed fuel spray is important in the evaluation of the combustion process. A better understanding of the dynamics can provide a tool for selecting a PSD that will more effectively meet the needs of the system. In this paper, we present an efficient and elegant method for evaluating the dynamics of the PSD. New insights into the behaviour of polydispersed fuel spray were obtained. A simplified theoretical model was applied to the experimental data and a known approximation of the polydispersed fuel spray. This model can be applied to any distribution, not necessarily an experimental distribution or approximation, and involves a time-dependent function of the PSD. Such simplified models are particularly helpful in qualitatively understanding the effects of various sub-processes. Our main results show that during the self-ignition process, the radii of the droplets decreased as expected, and the number of smaller droplets increased in inverse proportion to the radius. An important novel result (visualised by graphs) demonstrates that the mean radius of the droplets initially increases for a relatively short period of time, which is followed by the expected decrease. Our modified algorithm is superior to the well-known 'parcel' approach because it is much more compact; it permits analytical study because the right-hand sides of the mathematical model are smooth, and thus eliminates the need for a numerical algorithm to transition from one parcel to another. Moreover, the method can provide droplet radii resolution dynamics because it can use step functions that accurately describe the evolution of the radii of the droplets. The method explained herein can be applied to any approximation of the PSD, and involves a comparatively negligible computation time. [ABSTRACT FROM AUTHOR]

Oblivious routing is a static algorithm for routing arbitrary user demands with the property that the competitive ratio, the proportion of the maximum congestion to the best possible congestion, is minimal. Oblivious routing turned out surprisingly efficient in this worst-case sense: in undirected graphs, we pay only a logarithmic performance penalty, and this penalty is usually smaller than 2 in directed graphs as well. However, compared to an optimal adaptive algorithm, which never causes congestion when subjected to a routable demand, oblivious routing surely has congestion. The open question is of how often is the network in a congested state. In this paper, we study two performance measures naturally arising in this context: the probability of congestion and the expected value of congestion. Our main result is the finding that, in certain directed graphs on n nodes, the probability of congestion approaches 1 in some undirected graphs, despite the competitive ratio being O (1) . [ABSTRACT FROM AUTHOR]

Privacy-preserving empirical risk minimization model is crucial for the increasingly frequent setting of analyzing personal data, such as medical records, financial records, etc. Due to its advantage of a rigorous mathematical definition, differential privacy has been widely used in privacy protection and has received much attention in recent years of privacy protection. With the advantages of iterative algorithms in solving a variety of problems, like empirical risk minimization, there have been various works in the literature that target differentially private iteration algorithms, especially the adaptive iterative algorithm. However, the solution of the final model parameters is imprecise because of the vast privacy budget spending on the step size search. In this paper, we first proposed a novel adaptive differential privacy algorithm that does not require the privacy budget for step size determination. Then, through the theoretical analyses, we prove that our proposed algorithm satisfies differential privacy, and their solutions achieve sufficient accuracy by infinite steps. Furthermore, numerical analysis is performed based on real-world databases. The results indicate that our proposed algorithm outperforms existing algorithms for model fitting in terms of accuracy. [ABSTRACT FROM AUTHOR]