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The intention of this work is to study a mathematical model for fractal-fractional tuberculosis and COVID-19 co-infection under the Atangana-Baleanu fractal-fractional operator. Firstly, we formulate the tuberculosis and COVID-19 co-infection model by considering the tuberculosis recovery individuals, the COVID-19 recovery individuals, and both disease recovery compartment in the proposed model. The fixed point approach is utilized to explore the existence and uniqueness of the solution in the suggested model. The stability analysis related to solve the Ulam-Hyers stability is also investigated. This paper is based on Lagrange's interpolation polynomial in the numerical scheme, which is validated through a specific case with a comparative numerical analysis for different values of the fractional and fractal orders. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is the numerical analysis of a class of mathematical models that describe the contact between a thermo-piezoelectric body and a conductive foundation. Under the assumption of a static process, the material's behavior is modeled with a linear thermo-electro-elastic constitutive law and the frictional contact with Signorini's and Tresca's laws. A variational problem is derived and the existence of a unique weak solution is proved by combining arguments from the theory of variational inequalities with linear strongly monotone Lipschitz continuous operators. A successive iteration technique to linearize the problem by transforming it into an incremental recursive form is proposed, and its convergence is established. An Augmented Lagrangian variant, known as the Alternating Direction Multiplier Method (ADMM), is employed to split the original problem into two subproblems, resolve them sequentially, as well as update the dual variables at each iteration. To illustrate the performance of the proposed approach, several numerical simulations on two-dimensional test problems are carried out. [ABSTRACT FROM AUTHOR]

A mathematical model is presented in this paper to investigate the effects of time delay in vaccine production on COVID-19 spread. The model is analyzed qualitatively and numerically. The qualitative analysis indicates that the system variables are non-negative, bounded, and biologically meaningful. Moreover, the model has produced two equilibrium points: the free equilibrium point, which can exist without conditions, and the endemic equilibrium point, which can exist if the control reproduction number, R c , is not less than one. In addition, the local stability of the equilibrium points is investigated and agrees with the numerical analysis results. Finally, a sensitivity analysis is conducted for R c . In particular, we examine the effect of the vaccine's time delay, vaccine rate, and vaccine efficiency on the model dynamics. [ABSTRACT FROM AUTHOR]

In this paper, a multi-echelon, multi-period, decentralized supply chain (SC) with a single manufacturer, single distributor and single retailer is considered. For this setting, a two-phase planning approach combining centralized and decentralized decision-making processes is proposed, in which the first-phase planning is a coordinated centralized controlled, and the second-phase planning is viewed as independent decentralized decision-making for individual entities. This research focuses on the independence and equally powerful behavior of the individual entities with the aim of achieving the maximum profit for each stage. A mathematical model for total SC coordination as a first-phase planning problem and separate ones for each of the independent members with their individual objectives and constraints as second-phase planning problems are developed. We introduce a new solution approach using a goal programming technique in which a target or goal value is set for each independent decision problem to ensure that it obtains a near value for its individual optimum profit, with a numerical analysis presented to explain the results. Moreover, the proposed two-phase model is compared with a single-phase approach in which all stages are considered dependent on each other as parts of a centralized SC. The results prove that the combined two-phase planning method for a decentralized SC network is more realistic and effective than a traditional single-phase one. [ABSTRACT FROM AUTHOR]

This article examines the research of Louis J. Mordell on the Diophantine equation y 2 - k = x 3 as it appeared in one of his first papers, published in 1914. After presenting a number of elements relating to Mordell's mathematical youth and his (problematic) writing, we analyze the 1914 paper by following the three approaches he developed therein, respectively, based on the quadratic reciprocity law, on ideal numbers, and on binary cubic forms. This analysis allows us to describe many of the difficulties in reading and understanding Mordell's proofs, difficulties which we make explicit and comment on in depth. [ABSTRACT FROM AUTHOR]

In this paper, we have considered a deterministic mathematical model to analyze effective interventions for meningitis and pneumonia coinfection as well as to make a rational recommendation to public healthy, policy or decision makers and programs implementers. We have introduced the epidemiology of infectious diseases, the epidemiology of meningitis, the epidemiology of pneumonia, and the epidemiology of infection of meningitis and pneumonia. The positivity and boundedness of the sated model was shown. Our model elucidate that, the disease free equilibrium points of each model are locally asymptotically stable if the corresponding reproduction numbers are less than one and globally asymptotically stable if the corresponding reproduction numbers are greater than one. Additionally, we have analyzed the existence and uniqueness of the endemic equilibrium point of each sub models, local stability and global stability of the endemic equilibrium points for each model. By using standard values of parameters we have obtained from different studies, we found that the effective reproduction numbers of meningitis R e f f (m) = 9 and effective reproduction numbers of pneumonia R e f f (p) = 11 that lead us to the effective reproduction number of the meningitis and pneumonia co-infected model is m a x R e f f m , R e f f (p) = 9 . Applying sensitivity analysis, we identified the most influential parameters that can change the behavior of the solution of the meningitis pneumonia coinfection dynamical system are α 1 , α 2 and π . Biologically, decrease in α 1 and increasing in π is a possible intervention strategy to reduce the infectious from communities. Finally, our numerical simulation has shown that vaccination against those diseases, reducing contact with infectious persons and treatment have the great effect on reduction of these silent killer diseases from the communities. [ABSTRACT FROM AUTHOR]

In this paper we study the mathematical model of auxiliary (or coupled) reactions, a mechanism which describes several chemical reactions. In order to apply singular perturbation techniques, we determine an appropriate perturbation parameter ϵ (which is related to the kinetic constants and initial conditions of the model), the inner and outer solutions and the matched expansions of the solutions, up to the first order in ϵ , in the total quasi-steady-state approximation (tQSSA) framework. The contribution of these expansions can be useful for the estimation of the kinetic parameters of the reaction by means of the interpolation of experimental data with the explicit approximations of the solutions. Some numerical results are discussed, showing the high reliability of the tQSSA with respect to the standard QSSA. [ABSTRACT FROM AUTHOR]

The mathematical P2D model is a system of strongly coupled nonlinear parabolic-elliptic equations that describes the electrodynamics of lithium-ion batteries. In this paper, we present the numerical analysis of a finite element-implicit Euler scheme for such a model. We obtain error estimates for both the spatially semidiscrete and the fully discrete systems of equations, and establish the existence and uniqueness of the fully discrete solution. [ABSTRACT FROM AUTHOR]

Published in 1999, Christodoulou proved that the naked singularities of a self-gravitating scalar field are not stable in spherical symmetry and therefore the cosmic censorship conjecture is true in this context. The original proof is by contradiction and sharp estimates are obtained strictly depending on spherical symmetry. In this paper, appropriate a priori estimates for the solution are obtained. These estimates are more relaxed but sufficient for giving another robust argument in proving the instability, in particular not by contradiction. In a companion paper, we are able to prove certain instability theorems of the spherically symmetric naked singularities of a scalar field under gravitational perturbations without symmetries. The argument given in this paper plays a central role. [ABSTRACT FROM AUTHOR]

This paper which depended on the foundation of back strip method has established mathematic model to simulate stratum burial history, which considered the computation of stratum skeleton depth based on max depth and the equation-depth point on the procedure to recover stratum by stripping each layer, and put forward the enhanced restoration method taking layers group as studying object. Finally, the method has been applied to build the computer model and program automatic back strip algorithm successfully. Experiments have proved that the method is accurate, applicable, and extensible under the conditions of various complex strata. [ABSTRACT FROM AUTHOR]

In this paper, we derive closed-form formulas for moments of the asset price in the Barndorff-Nielsen and Shephard (BN-S) stochastic volatility model. We also present similar results where the market is driven by a BN-S-type stochastic process. It is shown that in both cases the results depend on the cumulant transform of the background driving Lévy process for the models. In this paper, we have also obtain various approximate expressions for the expected value of the square-root process for the shifted asset price with respect to the BN-S model. [ABSTRACT FROM AUTHOR]

This paper aims to study two-factor uncertain term structure model where the volatility of the uncertain interest rate is driven by another uncertain differential equation. In order to solve this model, the nested uncertain differential equation method is employed. This paper is also devoted to the study of the numerical solutions for the proposed nested uncertain differential equation using the α-path methods. We also use the built two-factor term structure model to value the bond price with the help of proposed numerical method. Finally, we give a numerical example where the price of a zero-coupon bond is calculated based on the α-path methods. [ABSTRACT FROM AUTHOR]

The development of efficient methods for detecting quasiperiodic oscillations and computing the corresponding invariant tori is a subject of great importance in dynamical systems and their applications in science and engineering. In this paper, we prove the convergence of a new Newton-like method for computing quasiperiodic normally hyperbolic invariant tori carrying quasiperiodic motion in smooth families of real-analytic dynamical systems. The main result is stated as an a posteriori KAM-like theorem that allows controlling the inner dynamics on the torus with appropriate detuning parameters, in order to obtain a prescribed quasiperiodic motion. The Newton-like method leads to several fast and efficient computational algorithms, which are discussed and tested in a companion paper (Canadell and Haro in J Nonlinear Sci, 2017. doi:), in which new mechanisms of breakdown are presented. [ABSTRACT FROM AUTHOR]

In their 2010 (Erkenntnis 73:393-412) paper, Dizadji-Bahmani, Frigg, and Hartmann (henceforth 'DFH') argue that the generalized version of the Nagel-Schaffner model that they have developed (henceforth 'the GNS') is the right one for intertheoretic reduction, i.e. the kind of reduction that involves theories with largely overlapping domains of application. Drawing on the GNS, DFH (Synthese 179:321-338, 2011) presented a Bayesian analysis of the confirmatory relation between the reducing theory and the reduced theory and argued that, post-reduction, evidence confirming the reducing theory also confirms the reduced theory and evidence confirming the reduced theory also confirms the reducing theory, which meets the expectations one has about theories with largely overlapping domains. In this paper, I argue that the Bayesian analysis presented by DFH (Synthese 179:321-338, 2011) faces difficulties. In particular, I argue that the conditional probabilities that DFH introduce to model the bridge law entail consequences that run against the GNS. However, I also argue that, given slight modifications of the analysis that are in agreement with the GNS, one is able to account for these difficulties and, moreover, one is able to more rigorously analyse the confirmatory relation between the reducing and the reduced theory. [ABSTRACT FROM AUTHOR]

In this paper, we present a parallel cloth simulation with an efficient collision detection algorithm for interactive AR applications. In the first step of the proposed method, a set of sphere colliders is automatically defined for the 3D moving object colliding with a cloth model for the effective collision detection even on low-end devices. In the second step, the collision detection and handling between a set of sphere colliders and a cloth model are performed in parallel. We propose an efficient collision handling method based on a sphere to prevent the penetration of cloth into the object which can be happened due to the low mesh resolution of the cloth model. The proposed method was implemented as a plugin for Unity which is widely used for the real-time game development. Comparative experimental tests with the cloth object basically provided by Unity was performed in order to analyze the performance of the proposed method. As a result, we confirmed that the proposed method can reduce the cumbersome work to manually build colliders on a 3D model, and can effectively express more accurate and plausible behavior of the cloth that collides with the object. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new technique for the asymmetric approximation of discrete functions arising in seasonal customer demand extrapolation. We adapt the technique for two different settings, the so-called pull and push models. Our main goal here is to find effectively extrapolations minimizing the loss. For bothmodels, we discuss several features related to sampling, approximation, and extrapolation. [ABSTRACT FROM AUTHOR]

Comprehending life history of migratory fish, onset of migration in particular, is a key biological and ecological research topic that still has not been clarified. In this paper, we propose a simple mathematical model for the onset of fish migration in the context of a stochastic optimal stopping theory, which is a new attempt to our knowledge. Finding the criteria of the onset of migration reduces to solving a variational inequality of a degenerate elliptic type. As a first step of the new mathematical modeling, mathematical and numerical analyses with particular emphasis on whether the model is consistent with the past observation results of fish migration are examined, demonstrating reasonable agreement between the theory and observation results. The present mathematical model thus potentially serves as a simple basis for analyzing onset of fish migration. [ABSTRACT FROM AUTHOR]

This paper investigates a class of non-autonomous cellular neural networks with mixed delays. Based on the basic theory of the weighted pseudo-almost periodic functions, several sufficient conditions are established to ensure that every solution of the addressed model exponentially tends to a weighted pseudo-almost periodic solution as t→+∞, which generalize some existing ones. In particular, some numerical examples are also given. [ABSTRACT FROM AUTHOR]

In this paper, we study properties of functions and sequences with a semi-heavy tail, that is, functions and sequences of the form w(x) = e−βxf(x), β > 0, resp., wn = cnfn, 0 < c < 1, where the function f(x), resp., the sequence (fn), is regularly varying. Among others, we give a representation theorem and study convolution properties. The paper includes several examples and applications in probability theory. [ABSTRACT FROM AUTHOR]

In this paper, we consider a risk model by introducing a temporal dependence between the claim numbers under periodic environment, which generalizes several discrete-time risk models. The model proposed is based on the Poisson INAR(1) process with periodic structure. We study the moment-generating function of the aggregate claims. The distribution of the aggregate claims is discussed when the individual claim size is exponentially distributed. [ABSTRACT FROM AUTHOR]

In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. This series formula is obtained from the Mellin-Barnes representation of the option price with help of residue summation in ℂ2. We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions. [ABSTRACT FROM AUTHOR]

Fast estimation of thermal transmittance based on temperature measurements is uncertain, and the obtained results can be burdened with a large error. Nevertheless, such attempts should be undertaken merely due to the fact that a precise measurement by means of heat flux measurements is not always possible in field conditions (resentment of the residents during the measurements carried out inside their living quarters), and the calculation methods do not allow for the nonlinearity of thermal insulation, heat bridges or other fragments of building envelope of diversified thermal conductivity. The present paper offers the estimation of thermal transmittance and internal surface resistance with the use of temperature measurements (in particular with the use of thermovision). The proposed method has been verified through tests carried out on a laboratory test stand built in the open space, subjected to the influence of real meteorological conditions. The present elaboration involves the estimation of thermal transmittance by means of temperature measurements. Basing on the mentioned estimation, the authors present correction coefficients which have impact on the estimation accuracy. Furthermore, in the final part of the paper, various types of disturbance were allowed for using perturbation numbers, and the introduced by the authors “credibility area of thermal transmittance estimation” was determined. [ABSTRACT FROM AUTHOR]

In the majority of the existing preventive optimization models only costs related to maintenance actions are accounted for, while breakdown and operational costs are usually ignored. Liao et al. (J Intell Manuf 21(6):875-884, 2010) proposed a preventive maintenance model to deal with this shortcoming. In the present paper, we revisit and discuss the results provided in Liao et al. (2010) and point out some inconsistencies in the maintenance optimization model proposed therein. Accordingly, we develop a new maintenance optimization model and discuss some of its main cost components. Furthermore, optimality conditions are also formally investigated and a solution method is provided. Numerical experiments are conducted to illustrate the validity of the proposed approach and results are compared with those provided in the original paper by Liao et al. (2010). [ABSTRACT FROM AUTHOR]

This paper addresses the problem of exponential stability and stabilization for a class of delayed distributed parameter systems, which is modeled by partial integro-differential equations (PIDEs). By employing the vector-valued Wirtinger's inequality, the sufficient condition of exponential stability of the PIDE system with a given decay rate is investigated. The condition is presented by linear matrix inequality (LMIs). After that, we develop a spatial proportional-integral-derivative state-feedback controller that ensures the exponential stabilization of the PIDE system in terms of LMIs. Finally, numerical examples are presented to verify the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we study the global properties of a computer virus propagation model. It is, interesting to note that the classical method of Lyapunov functions combined with the Volterra-Lyapunov matrix properties, can lead to the proof of the endemic global stability of the dynamical model characterizing the spread of computer viruses over the Internet. The analysis and results presented in this paper make building blocks towards a comprehensive study and deeper understanding of the fundamental mechanism in computer virus propagation model. A numerical study of the model is also carried out to investigate the analytical results. [ABSTRACT FROM AUTHOR]

Drift rate is a very important parameter in the evolution of stock price, which has significant impact on the corresponding option pricing. This paper deals with an inverse problem of recovering the drift function by current market prices of options. Different from the usual inverse volatility problem, our mathematical model does not tend to zero at infinity, which may bring great trouble to theoretical analysis and numerical calculation. To overcome this difficulty, we use an artificial boundary and homogenization technique to transform the original problem into a homogeneous initial boundary value problem on a bounded domain. Then, based on the optimal control framework, we construct the corresponding optimization problem and strictly prove the well-posedness of the minimizer. Finally, we design an iterative algorithm to obtain the numerical solution. We give some typical examples to verify the validity of our method. [ABSTRACT FROM AUTHOR]

Introduces a series of papers related to mathematical techniques, modeling, numerical simulations, atmospheric and oceanic processes and field experiments conducted to gain insight into the weather and climate system. Application of the "splitting methods" of numerical modeling to a high resolution model of the Indian Ocean; Numerical experiments designed to determine the fidelity of predictions of major features of the Indian monsoon season; Analysis of the 2002 Colorado drought.

Many applications have a mixed-criticality nature. They contain tasks with a different criticality, meaning that a task with a lower criticality can be skipped if a task with a higher criticality needs more time to be executed. This paper deals with a mixed-criticality scheduling problem where each task has a criticality given by a positive integer number. The exact processing time of the task is not known. Instead, we use different upper bounds of the processing time for different criticality levels of the schedule. A schedule with different criticality levels is generated off-line, but its on-line execution switches among the criticality levels depending on the actual values of the processing times. The advantage is that after the transient prolongation of a higher criticality task, the system is able to match up with the schedule on a lower criticality level. While using this model, we achieve significant schedule efficiency (assuming that the prolongation of the higher criticality task rarely occurs), and at the same time, we are able to grant a sufficient amount of time to higher criticality tasks (in such cases, some of the lower criticality tasks may be skipped). This paper shows a motivation for the non-preemptive mixed-criticality match-up scheduling problem arising from the area of the communication protocols. Using a polynomial reduction from the 3-partition problem, we prove the problem to be $$\mathcal {NP}$$ -hard in the strong sense even when the release dates and deadlines are dropped and only two criticality levels are considered. [ABSTRACT FROM AUTHOR]

Conventional data envelopment analysis (DEA) models make the assumption of non-negativity and real values in the input and output of the systems that are under study. This paper combines these two interrelated ideas. One is the non-radial measurement of efficiency by establishing an aggregate directional distance formulation of the DEA model (ADDM). Another is the introduction of an integer directional distance function. Usually, directional distance formulations of DEA and ADDM projections of efficient targets for inefficient decision making units (DMUs) have non-integer values. In this paper directional distance function is modified and a mixed integer directional distance formulation of DEA is proposed. This model guarantees integer targets for inefficient DMUs and is applicable to measure efficiency even when input and output variables are negative integer values. [ABSTRACT FROM AUTHOR]

When a tsunami occurred on a sea area, prediction of its arrival time is critical for evacuating people from the coastal area. There are many problems related to tsunami to be solved for reducing negative effects of this serious disaster. Numerical modeling of tsunami wave propagation is a computationally intensive problem which needs to accelerate its calculations by parallel processing. The method of splitting tsunami (MOST) is one of the well-known numerical solvers for tsunami modeling. We have developed a tsunami propagation code based on MOST algorithm and implemented different parallel optimizations for GPU and FPGA. In the latest study, we have the best performance of OpenCL kernel which is implemented tsunami simulation on AMD Radeon 280X GPU. This paper targets on design and evaluation on FPGA using OpenCL. The performance on FPGA design generated automatically by Altera offline compiler follows the results of GPU by several kernel modifications. [ABSTRACT FROM AUTHOR]

The paper is motivated by a model for the injection of air into a porous medium that contains a solid fuel. In previous work, a system of three evolutionary partial differential equations that models combustion of light porous foam under air injection was considered. The existence and uniqueness of traveling waves were studied and the wave sequences appearing in Riemann solutions were identified. This analysis was done under assumption that the combustion wave velocity is positive. In the present work, this hypothesis was neglected and the results generalized including the case of negative combustion wave speed. The existence of such waves was proved and the uniqueness investigated for some particular cases using Melnikov’s integral. The wave sequences appearing in Riemann solutions were identified and the numerical examples using finite difference scheme were presented. [ABSTRACT FROM AUTHOR]

We study the uniqueness and explicit derivation of the relaxed optimal solutions, corresponding to the minimization of weighted sum of potential energies for a mixture of two isotropic conductive materials on an annulus. Recently, it has been shown by Burazin and Vrdoljak that even for multiple-state problems, if the domain is spherically symmetric, then the proper relaxation of the problem by the homogenization method is equivalent to a simpler relaxed problem, stated only in terms of local proportions of given materials. This enabled explicit calculation of a solution on a ball, while problems on an annulus appeared to be more tedious. In this paper, we discuss the uniqueness of a solution of this simpler relaxed problem, when the domain is an annulus and we use the necessary and sufficient conditions of optimality to present a method for explicit calculation of the unique solution of this simpler proper relaxation, which is demonstrated on an example. [ABSTRACT FROM AUTHOR]

Despite the development of sophisticated techniques such as sequential Monte Carlo (Del Moral et al. in J R Stat Soc Ser B 68(3):411-436, 2006), importance sampling (IS) remains an important Monte Carlo method for low dimensional target distributions (Chopin and Ridgway in Leave Pima Indians alone: binary regression as a benchmark for Bayesian computation, 32:64-87, 2017). This paper describes a new technique for constructing proposal distributions for IS, using affine arithmetic (de Figueiredo and Stolfi in Numer Algorithms 37(1-4):147-158, 2004). This work builds on the Moore rejection sampler (Sainudiin in Machine interval experiments, Cornell University, Ithaca, 2005; Sainudiin and York in Algorithms Mol Biol 4(1):1, 2009) to which we provide a comparison. [ABSTRACT FROM AUTHOR]

Transition prediction is of great importance for the design of long distance flying vehicles. It starts from the problem of receptivity, i.e., how external disturbances trigger instability waves in the boundary layer. For super/hypersonic boundary layers, the external disturbances first interact with the shock ahead of the flying vehicles before entering the boundary layer. Since direct numerical simulation (DNS) is the only available tool for its comprehensive and detailed investigation, an important problem arises whether the numerical scheme, especially the shock-capturing method, can faithfully reproduce the interaction of the external disturbances with the shock, which is so far unknown. This paper is aimed to provide the answer. The interaction of weak disturbances with an oblique shock is investigated, which has a known theoretical solution. Numerical simulation using the shock-capturing method is conducted, and results are compared with those given by theoretical analysis, which shows that the adopted numerical method can faithfully reproduce the interaction of weak external disturbances with the shock. [ABSTRACT FROM AUTHOR]

The effect of space inhomogeneities on a diffusing particle is studied in the framework of the 1D random walk. The typical time needed by a particle to cross a one-dimensional finite lane, the so-called residence time, is computed possibly in presence of a drift. A local inhomogeneity is introduced as a single defect site with jumping probabilities differing from those at all the other regular sites of the system. We find complex behaviors in the sense that the residence time is not monotonic as a function of some parameters of the model, such as the position of the defect site. In particular we show that introducing at suitable positions a defect opposing to the motion of the particles decreases the residence time, i.e., favors the flow of faster particles. The problem we study in this paper is strictly connected to the classical gambler's ruin problem, indeed, it can be thought as that problem in which the rules of the game are changed when the gambler's fortune reaches a particular a priori fixed value. The problem is approached both numerically, via Monte Carlo simulations, and analytically with two different techniques yielding different representations of the exact result. [ABSTRACT FROM AUTHOR]

An accurate mathematical model has a vital role in controlling and synchronization of chaotic systems. But generally in real-world problems, parameters are mixed with mismatches and distortions. This paper proposes two simple but effective estimation methods to detect the unknown parameters of chaotic models. These methods focus on improving the performance of a recently proposed evolutionary algorithm called backtracking search optimization algorithm (BSA). In this research firstly, a new operator to generate initial trial population is proposed. Then a group search ability is provided for the BSA by proposing a shuffled BSA (SBSA). Grouping population into several sets can provide a better exploration of search space, and an independent local search of each group increases exploitation ability of the BSA. Also new proposed operator to generate initial trial population, by providing a deep search, increases considerably the quality of solutions. The superiority of the proposed algorithms is investigated on parameter identification of 10 typical chaotic systems. Practical experiences and nonparametric analysis of obtained results show that both of the proposed ideas to improve performance of original BSA are very effective and robust so that the BSA by aforementioned ideas produces similar and promising results over repeated runs. A considerably better performance of proposed algorithms based on average of objective functions demonstrates that the proposed ideas can evolve robustness and consistence of BSA. A comparison of the proposed algorithms in this study with respect to other algorithms reported in the literature confirms a considerably better performance of proposed algorithms. [ABSTRACT FROM AUTHOR]

A novel all-pass-based infinite impulse response (IIR) digital multiple-notch filter design method is presented in this paper. The proposed method ensures that, for an arbitrary pass-bands ripple value, specifications regarding positions of notch, left- and right-hand cutoff frequencies are exactly met, which leads to symmetric magnitude responses about notch frequencies. Although iterative in its nature, proposed method requires a small number of iterations to find coefficients of the multiple-notch filter, making it very useful for designers. Since the magnitude response of the all-pass-based IIR multiple-notch filter is more sensitive in the stop-bands than in the pass-bands, sensitivity analysis along with simulation in limited word-length environment is performed. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the numerical solution of second-order nonlinear two-point fuzzy boundary value problems (TPFBVP) by combining the finite difference method with Newton’s method. Numerical example using the well-known nonlinear TPFBVP is presented to show the capability of the new method in this regard and the results are satisfied the convex triangular fuzzy number. We also compare the numerical results with the exact solution, and it shows that the proposed method is good approximation for the analytic solution of the given TPFBVP. [ABSTRACT FROM AUTHOR]

The results of testing formula simplification tools are presented in the first part of this paper. In the second part, an algorithm for constructing canonical forms of linear semi-algebraic formulas is described. The main result of the study is the definition of the canonical form of a linear semi-algebraic formula that has the property of uniqueness and other useful properties. An algorithm for constructing such a formula is described. [ABSTRACT FROM AUTHOR]

This paper investigates the increase in the response speed and stability of artificial intelligence systems that control dynamic technical objects. The problem of calculating the optimal time of switching an artificial intelligence system between software classes by the criterion of the rigidity degree of the model of a control object is considered. The solution of this problem is proposed for the general case of the control object dynamics when the rigidity of the mathematical model can significantly change during functioning and it is necessary to dynamically determine the moment of transition from standard methods of numerical integration to specialized numerical methods intended for calculating rigid dynamic models. [ABSTRACT FROM AUTHOR]

In this paper, we study the global existence and decay rates of the solutions near Maxwellian for non-linear Fokker-Planck equations in the whole space. The global existence is proved by combining uniform-in-time energy estimates with local solution constructed by Picard type iteration sequence. The decay rates of the nonlinear model is obtained by using the precise spectral analysis of the linearized Fokker-Planck operator as well as the energy method. The nonlinearity in the model brings new difficulty to the energy estimates, which is resolved by additional tailored weighted-in-v energy estimates suitable for Fokker-Planck operators. [ABSTRACT FROM AUTHOR]

In this paper, we modify the Langevin dynamics associated to the generalized Curie-Weiss model by introducing noisy and dissipative evolution in the interaction potential. We show that, when a zero-mean Gaussian is taken as single-site distribution, the dynamics in the thermodynamic limit can be described by a finite set of ODEs. Depending on the form of the interaction function, the system can have several phase transitions at different critical temperatures. Because of the dissipation effect, not only the magnetization of the systems displays a self-sustained periodic behavior at sufficiently low temperature, but, in certain regimes, any (finite) number of stable limit cycles can exist. We explore some of these peculiarities with explicit examples. [ABSTRACT FROM AUTHOR]

A code for computing the p-variation of a piecewise monotone function is introduced. The code is publicly available in the R environment package under the name pvar. The algorithm is based on some properties of the p-variation of a piecewise monotone function proved in this paper. The mathematical results may have their own interest. [ABSTRACT FROM AUTHOR]

This paper investigates the fixed charge multi-item solid transportation problem, in which the fixed charges, direct costs, transportation capacities, supply and demand are uncertain variables. Based on the uncertainty theory, expected value programming model and chance-constrained programming model for fixed charge multi-item solid transportation problem are constructed, respectively. We can obtain the optimal solution of two models via solving the relevant deterministic models. Finally, a numerical experiment is implemented to illustrate the application of the models. [ABSTRACT FROM AUTHOR]

Uncertain singular system, described as a multi-dimensional uncertain differential equation, is a kind of singular system disturbed by canonical process. Stability analysis has been widely investigated while nobody has ever considered the stability of uncertain singular systems. In this paper, three different styles of stabilities called stability in mean, stability in measure and almost sure stability of uncertain singular systems are studied. These stabilities can be employed to illustrate the internal character of uncertain singular systems in different aspects. Several sufficient conditions are presented to judge the above stabilities. An example is given to show the effectiveness of the results obtained. [ABSTRACT FROM AUTHOR]

Modified Patankar-Runge-Kutta (MPRK) schemes are numerical methods for the solution of positive and conservative production-destruction systems. They adapt explicit Runge-Kutta schemes to ensure positivity and conservation irrespective of the time step size. The first two members of this class, the first order MPE scheme and the second order MPRK22(1) scheme, have been successfully applied in a large number of applications. Recently, a general definition of MPRK schemes was introduced and necessary as well as sufficient conditions to obtain first and second order MPRK schemes were presented. In this paper we derive necessary and sufficient conditions for third order MPRK schemes and introduce the first family of such schemes. The theoretical results are confirmed by numerical experiments considering linear and nonlinear as well as nonstiff and stiff systems of differential equations. [ABSTRACT FROM AUTHOR]

It is well-known that the degree of saturation is a soil state condition able to represent the hydrological response of a shallow soil to weather conditions. One of the oldest models that referred on the degree of saturation to carry out the slope stability analysis at different scales, was the Shallow Landslide Instability (SLIP) Model. This paper shows how the SLIP model can be used to derive a simplified method to estimate multiple seasonal cycles of the mean degree of saturation of soil and to carry out the time-varying stability analysis of a test site slope. The simplified method to assess the degree of saturation uses easily available climatic data, such as air temperature and rainfall depth, and is validated through the comparison with long-term field measurements on a slope in Canneto Pavese, northern Italy. The SLIP model is also applied to obtain the safety factor of the slope, that was subjected to a rainfall-induced shallow landslide during the field monitoring period. Comparisons between field measurements and model outputs are used to validate the capability of the model of predicting both the mean degree of saturation of the topsoil and the observed unstable condition. [ABSTRACT FROM AUTHOR]

In this paper, we consider the application of the finite difference method for a class of novel multi-term time fractional viscoelastic non-Newtonian fluid models. An important contribution of the work is that the new model not only has a multi-term time derivative, of which the fractional order indices range from 0 to 2, but also possesses a special time fractional operator on the spatial derivative that is challenging to approximate. There appears to be no literature reported on the numerical solution of this type of equation. We derive two new different finite difference schemes to approximate the model. Then we establish the stability and convergence analysis of these schemes based on the discrete H1 norm and prove that their accuracy is of O(τ + h2) and O(τmin{3–γs,2–αq,2–β}+h2), respectively. Finally, we verify our methods using two numerical examples and apply the schemes to simulate an unsteady magnetohydrodynamic (MHD) Couette flow of a generalized Oldroyd-B fluid model. Our methods are effective and can be extended to solve other non-Newtonian fluid models such as the generalized Maxwell fluid model, the generalized second grade fluid model and the generalized Burgers fluid model. [ABSTRACT FROM AUTHOR]

This paper discusses the existence and controllability of a class of fractional order evolution inclusions with time-varying delay. In the weak topology setting we establish the existence of solutions. Then the controllability of this system with a nonlocal condition is established by applying the Glicksberg-Ky Fan fixed point theorem. As an application, nonlocal problems of a fractional reaction-diffusion equation with a discontinuous nonlinear term is examined. [ABSTRACT FROM AUTHOR]

In this paper we present a new algorithmic realization of a projection-based scheme for general convex constrained optimization problem. The general idea is to transform the original optimization problem to a sequence of feasibility problems by iteratively constraining the objective function from above until the feasibility problem is inconsistent. For each of the feasibility problems one may apply any of the existing projection methods for solving it. In particular, the scheme allows the use of subgradient projections and does not require exact projections onto the constraints sets as in existing similar methods. We also apply the newly introduced concept of superiorization to optimization formulation and compare its performance to our scheme. We provide some numerical results for convex quadratic test problems as well as for real-life optimization problems coming from medical treatment planning. [ABSTRACT FROM AUTHOR]