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The present comment concerns the correct presentation of an algorithm proposed in the above paper for the glow-curve deconvolution in the case of continuous distribution of trapping states. Since most researchers would use directly the proposed algorithm as published, they should be notified of its correct formulation during the fitting of TL glow curves of materials with continuous trap distribution using this Equation. [ABSTRACT FROM AUTHOR]

• Mathematical and physical analyses of the introduced problem. • Reporting a serious error in an important dimensionless parameter. • Indicating that the reported numerical results are completely erroneous. This is a comment on the paper [Optics and Laser Technology 128 (2020) 106233; https://doi.org/10.1016/j.optlastec.2020.106233 ] titled "Exact coupled solution for photothermal semiconducting beams using a refined multi-phase-lag theory". Herein, we report a serious error in an important dimensionless parameter employed in the problem, revealing that the defined parameter is dimensional and wrong. Accordingly, all given numerical results are based on this serious mistake, and are completely erroneous. [ABSTRACT FROM AUTHOR]

We would like to present the ideas of Makoto Matsumoto and András Rapcsák in the projective theory of Finsler spaces. Finally, we give some remarks using of Matsumoto–Rapcsák Theorem. [ABSTRACT FROM AUTHOR]

Abstract: The study used the simulated e-paper to investigate how the bending radius of curvature (−10cm, plane, and 10cm) and 12 text/background color-combinations of e-paper affect subjects’ visual performance and subjective preference under various ambient illuminance conditions (200 and 500lx). Analysis results indicated that the bending curvature and ambient illuminance did not significantly affect subjects’ visual performance. However, subjects visual performance differed significantly for different text/background color combinations of the simulated e-paper. When the background color of the simulated e-paper was set to yellow-like condition and the luminance of the text was low (2.2 and 4.6cd/m2), subjects’ visual performance was best. Regarding the subjective preferences of subjects, the results of this research also demonstrated that the bending curvature, text/background color combinations and ambient illuminance all significantly affected the subjective preferences of subjects. Subjects exhibited the best preference under the following settings: bending curvature of the simulated e-paper set to plane; background color of the simulated e-paper set to yellow-like condition and low text luminance (2.2 or 4.6cd/m2); high ambient illuminance (500lx). [Copyright &y& Elsevier]

Abstract: In the present paper we studied the Voronovskaya type theorem for modified Gamma operators presented by A. İzgi in the paper “Voronovskaya type asymptotic approximation by modified Gamma operators” [Applied Mathematics and Computation 217 (2011) 8061–8067]. We show that this theorem is not true. We present a correct form of this theorem and its proof. Furthermore, we obtain an error estimate for modified Gamma operators. [Copyright &y& Elsevier]

Abstract: Comment on the paper “A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications” in Applied Mathematics and Computation 174 (2006) 1169–1180. The paper considered a class of two-point boundary-value problems of the form where f(x) and g(x) are continuous on [a, b], and A i and B i (i =1,2) are finite real constants. Here we correct some mistake in derivation of non-polynomial spline, boundary formulas, truncation errors, convergence analysis and computational experiments. [Copyright &y& Elsevier]

Abstract: In this paper, we determine the modularities of asymptotically optimal towers found by Maharaj and Wulftange in 2005. This is also a continuation of the work of Elkies in 2002. [Copyright &y& Elsevier]

Abstract: In this paper, we establish new Lyapunov-type inequalities for two classes of one-dimensional quasilinear elliptic systems of resonant type, which improve the recent results of Tang and He [X.H. Tang, X. He, Lower bounds for generalized eigenvalues of the quasilinear systems, J. Math. Anal. Appl. 385 (2012) 72–85] when 1< p i <2 for i =1,2,…, n. [Copyright &y& Elsevier]

Abstract: In this paper, some sufficient conditions are established for the oscillation of second-order neutral differential equations where and . On the other hand, some new oscillation criteria are established for the second-order nonlinear neutral delay differential equations where . The results obtained here complement and correct some known results in . Some examples are given to illustrate the main results. [Copyright &y& Elsevier]

Abstract: In this short note an addition to the paper [A.G. Bratsos, M. Ehrhardt, I.Th. Famelis, A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations, Appl. Math. Comput. 197(1) (2008) 190–205] using the modulus of the terms evaluated from the Adomian decomposition method on p. 194 and their relation to the convergence of the resulting series is presented. Conclusions for the accuracy of the approximated solution are derived. [Copyright &y& Elsevier]

Abstract: A generalization of two sharp inequalities in a recent paper by N. Ujević is established. Applications in numerical integration are also given and the results of N. Ujević are revised and improved. [Copyright &y& Elsevier]

Abstract: In this note, we point out an error in the recently published article [R.K. Mohanty, M.K. Jain, D. Dhall, A cubic spline approximation and application of TAGE iterative method for the solution of two-point boundary value problems with forcing function in integral form, Appl. Math. Model. 35 (2011) 3036–3047] and then correct it. [Copyright &y& Elsevier]

Abstract: The aim of this note is to show that the optimization algorithm proposed in may not lead to the optimal solution in some cases. In fact, the optimization problem remains open if we do not apply the branch-and-bound method to solve it or compute all the objective values of minimal solutions of the feasible domain. [Copyright &y& Elsevier]

Abstract: A counterexample is provided in this short note to show that some of local convergence theorems established in [D.K.R. Babajee, M.Z. Dauhoo, An analysis of the properties of the variants of Newton’s method with third order convergence, Appl. Math. Comput. 183 (2006) 659–684] are not always true. Some mistakes in the proofs of these theorems are pointed out. [Copyright &y& Elsevier]

Abstract: In this technical note, we give a short extension application for nonlinear sum of ratios problem (P) considered in [Y.J. Wang, K.C. Zhang, Global optimization of nonlinear sum of ratios problem, Applied Mathematics and Computation 158 (2004) 319–330]. Actually our result is slightly more general, since we do not specify additional positive coefficient for each ratio. In this note, we use different equivalent problem as done in Wang and Zhang (2004). Our method introduce p variables less than other method (Wang and Zhang, 2004), and our approach need not additional special program to obtain the upper and lower bound of numerator and denominator for each ratio in the objective function. [Copyright &y& Elsevier]

Abstract: We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials. [Copyright &y& Elsevier]

This paper enriches a pre-existing decision algorithm, which in turn augmented a fragment of Tarski's elementary algebra with one-argument real functions endowed with a continuous first derivative. In its present (still quantifier-free) version, our decidable language embodies the addition of functions and multiplication of functions by scalars; the issue we address is the one of satisfiability. As regards real numbers, individual variables and constructs designating the basic arithmetic operations are available, along with comparison relators. As regards functions, we have variables of another sort, out of which compound terms are formed by means of constructs designating addition and differentiation. An array of predicates designates various relationships between functions, as well as function properties, that may hold over intervals of the real line; those are: function comparisons, strict and non-strict monotonicity / convexity / concavity, comparisons between the derivative of a function and a real-valued term. Our decision method consists in preprocessing the given formula into an equi-satisfiable quantifier-free formula of the elementary algebra of real numbers, whose satisfiability can then be checked by means of Tarski's decision method. No direct reference to functions will appear in the target formula, each function variable having been superseded by a collection of stub real variables; hence, in order to prove that the proposed translation is satisfiability-preserving, we must figure out a flexible-enough family of interpolating C 1 functions that can accommodate a model for the source formula whenever the target formula turns out to be satisfiable. With respect to the results announced in earlier papers of the same stream, a significant effort went into designing the family of interpolating functions so that it could meet the new constraints stemming from the presence of function addition (along with differentiation) among the constructs of our fragment of mathematical analysis. • A formal language RDF* concerned with differentiable real functions is proposed. • The class of differentiable functions treated is closed under addition. • The expressive power of RDF* is illustrated through a gallery of examples. • A satisfiability-preserving algorithm reducing RDF* formulas into an existential sentence of Tarskian algebra is presented. • The correctness of the reduction algorithm is reported. [ABSTRACT FROM AUTHOR]

While the handling for temporally-varying linear equation (TVLE) has received extensive attention, most methods focused on trading off the conflict between computational precision and convergence rate. Different from previous studies, this paper proposes two complete adaptive zeroing neural dynamics (ZND) schemes, including a novel adaptive continuous ZND (ACZND) model, two general variable time discretization techniques, and two resultant adaptive discrete ZND (ADZND) algorithms, to essentially eliminate the conflict. Specifically, an error-related varying-parameter ACZND model with global and exponential convergence is first designed and proposed. To further adapt to the digital hardware, two novel variable time discretization techniques are proposed to discretize the ACZND model into two ADZND algorithms. The convergence properties with respect to the convergence rate and precision of ADZND algorithms are proved via rigorous mathematical analyses. By comparing with the traditional discrete ZND (TDZND) algorithms, the superiority of ADZND algorithms in convergence rate and computational precision is shown theoretically and experimentally. Finally, simulative experiments, including numerical experiments on a specific TVLE solving as well as four application experiments on arm path following and target motion positioning are successfully conducted to substantiate the efficacy, superiority, and practicability of ADZND algorithms. [ABSTRACT FROM AUTHOR]

Isothermal surfaces within the device [Display omitted] This paper presents a computational model of molecular diffusion through the interfollicular stratum corneum. Specifically, it extends an earlier two-dimensional microscopic model for the permeability in two ways: (1) a microporous leakage pathway through the intercellular lipid lamellae allows slow permeation of highly hydrophilic permeants through the tissue; and (2) the model yields explicit predictions of both lateral ( D ‾ ‖ sc ) and transdermal ( D ‾ ⊥ sc ) effective (average, homogenized) diffusivities of solutes within the tissue. We present here the mathematical framework for the analysis and a comparison of the predictions with experimental data on desorption of both hydrophilic and lipophilic solutes from human stratum corneum in vitro. Diffusion in the lipid lamellae is found to make the effective diffusivity highly anisotropic, with the predicted ratio D ‾ ‖ sc / D ‾ ⊥ sc ranging from 34 to 39 for fully hydrated skin and 150 to more than 1000 for partially hydrated skin. The diffusivities and their ratio are in accord with both experimental data and the results of mathematical analyses performed by others. [ABSTRACT FROM AUTHOR]

Abstract: In this short note we point to an error in the proof of a theorem stated in [L. Balková, E. Pelantová, Š. Starosta, On Brlek-Reutenauer conjecture, Theoret. Comput. Sci. 412 (2011) 5649–5655]. By constructing a counterexample, we show that the assertion of the theorem is actually incorrect. Although this theorem is of a technical character, it was used in an argument leading to a corollary of a general interest to the Brlek-Reutenauer conjecture, and thus as a consequence of this note we have that the proof of the mentioned corollary is also flawed. [Copyright &y& Elsevier]

Abstract: In this note, we will modify several gaps in Gurudwan and Sharma [N. Gurudwan, B.K. Sharma, Convergence theorem for the common solution for a finite family of -strongly accretive operator equations, Appl. Math. Comput. 217 (2011) 6748–6754]. [Copyright &y& Elsevier]

Abstract: This special issue contains the revised and extended versions of three papers presented in the 4th Workshop on Advances in Model-Based Testing (A-MOST 2008). In addition to an executive summary of these three papers, this preface briefly reviews the papers published in the four editions of the A-MOST workshop. We hope that the reader will find this special issue interesting and informative. [Copyright &y& Elsevier]

In this paper, we present a calcium dynamics model that firmly orchestrates exchanges of calcium flux through intracellular/extracellular sources of calcium to investigate cellular activities and calcium homeostasis. The generalized two-dimensional space-time reaction-diffusion model is formulated and analyzed for a wide range of calcium flux. The analytical technique is applied to solve the model by use of the fractional integral transform and some special functions. The existence and uniqueness of the proposed model are discussed. Finally, the obtained results are presented graphically to show the significance of calcium flux by amalgamating the memory of cells and prove the efficiency of the method. • We developed a calcium dynamics model to investigate the interplay of calcium flux based on a reaction-diffusion equation. • We present the computational technique to derive the model's solution using integral transform and special functions. • The existence and uniqueness of the calcium dynamics model are discussed. • We estimated the concentration profile in the presence/absence of VGCC, ER leak, SERCA pump, NCX, and mitochondrial flux. • The modulation of calcium flux provides a noteworthy effect due to the intermediate memory of cells. [ABSTRACT FROM AUTHOR]

• The functional relationship between the heat transport coefficients is explored. • The well-posedness of the Guyer–Krumhansl equation is proved. • The uniform stabilization property is proved. • The results are supported by a numerical demonstration. The Guyer–Krumhansl heat equation has numerous important practical applications in heat conduction problems. In recent years, it turned out that the Guyer–Krumhansl model can effectively describe the thermal behavior of macroscale heterogeneous materials. Thus, the Guyer–Krumhansl equation is a promising candidate to be the next standard model in engineering. However, to support the Guyer–Krumhansl equation's introduction into the engineering practice, its mathematical properties must be thoroughly investigated and understood. In the present paper, we show the basic structure of this particular heat equation, focusing on the differences in comparison to the Fourier heat equation obtained when (τ q , μ 2) → (0 , 0). Additionally, we prove the well-posedness of a particular, practically significant initial and boundary value problem. The stability of the solution is also investigated in the discrete space using a finite difference approach. [ABSTRACT FROM AUTHOR]

This paper aims to explore the accurate control of hole shape for AWJ hole-making of C f / SiC based on experimental and mathematical analysis methods, and the influence mechanism involved is emphatically analyzed. The results reveal that D difference is most influenced by the standoff distance, followed by the traverse speed, while it is less influenced by the pressure and the abrasive flow rate. The traverse speed, pressure and abrasive flow rate affect the D difference by changing the total energy of the jet; while the standoff distance mainly affects the D difference by changing the effective impact area, which is fundamentally different from other process parameters. In terms of interaction effects, decreasing the traverse speed and increasing the waterjet pressure can amplify the effect of interaction with the involvement of the standoff distance on the D difference. Based on the established D difference model and D offset model, a control method that can gain acquired hole shape is finally obtained for selecting the process parameters of AWJ machining. [ABSTRACT FROM AUTHOR]

The benefits of using crossover in crossing fitness gaps have been studied extensively in evolutionary computation. Recent runtime results show that majority-vote crossover is particularly efficient at optimizing the well-known Jump benchmark function that includes a fitness gap next to the global optimum. Also estimation-of-distribution algorithms (EDAs), which use an implicit crossover, are much more efficient on Jump than typical mutation-based algorithms. However, the allowed gap size for polynomial runtimes with EDAs is at most logarithmic in the problem dimension n. In this paper, we investigate variants of the Jump function where the gap is shifted and appears in the middle of the typical search trajectory. Such gaps can still be overcome efficiently in time O (n log ⁡ n) by majority-vote crossover and an estimation-of-distribution algorithm, even for gap sizes almost n. However, if the global optimum is located in the gap instead of the usual all-ones string, majority-vote crossover would nevertheless approach the all-ones string and be highly inefficient. In sharp contrast, an EDA can still find such a shifted optimum efficiently. Thanks to a general property called fair sampling , the EDA will with high probability sample from almost every fitness level of the function, including levels in the gap, and sample the global optimum even though the overall search trajectory points towards the all-ones string. Finally, we derive limits on the gap size allowing efficient runtimes for the EDA. • We study 2 algorithms using majority-vote crossover and an estimation-of-distribution algorithm on modified jump functions. • We derive theorems on the algorithms' runtime using rigorous mathematical analyses. • All 3 algorithms can overcome the fitness gap of the jump functions efficiently for moderate sizes of the gap. • All but the estimation-of-distribution algorithm usually fail to find an optimum located within the gap. • The estimation-of-distribution is efficient since it samples fairly on all fitness levels towards the optimum. [ABSTRACT FROM AUTHOR]

The paper proposes an ameliorated methodology to minimize the effect of charge injection over a wide input common-mode range. Instead of a conventional single dummy switch compensation [1] , the multi-dummy switches are proposed and employed to eradicate the injected charge on to the sampling capacitor. A detailed methodology is presented to compensate the charge injection in a MOS switch. The closed-form equations are derived mathematically to substantiate the proposed technique. For the proof-of-concept, a track-and-hold (T/H) stage has been simulated in 0. 18 μ m CMOS technology with the proposed technique for a 10-bit resolution. The proposed technique based T/H stage exhibits the spurious free dynamic range (SFDR) of 62.6 dB, effective number of bits (ENOB) of 9.36, peak input-referred third-order intercept point (IIP3) of 13.02 dBm and an input-referred 1 dB compression point (P 1dB) of 3.8 dBm at 1.074 MHz input frequency, sampled at 100 MSa/s. The performance of the proposed method is compared with the existing single dummy switch compensation method where our technique shows 88.8% compensation in minimizing the charge injection error and 272% improvement in dynamic linearity. Moreover, the presented technique quantifies 9 × improvement in mean percentage error (MPE) when simulated across the various process corners and rail-to-rail input common-mode voltage. • The paper presents a multi-dummy switch technique to minimize the charge injection error in a MOS switch. • Mathematical analysis has been carried out to validate the concept. • A design methodology is proposed to limit the charge injection error within ±0.5 LSB for 10-bit track-and-hold circuit. • The presented method is compared with existing single dummy switch compensation technique and the results depict 272% improvement in dynamic linearity. • The proposed method provides 9X improvement in the mean percentage error over the existing method. • The design is simulated in CMOS 180 nm technology and the post-layout simulation results are reported in the paper. [ABSTRACT FROM AUTHOR]

• Detailed modeling of CIGRE-14 bus standard test system along with inverter control scheme (with and without grid code) and protection system is done in PSCAD environment. • The performance of directional relaying schemes (32Q and 67pos,67neg,67zero) are evaluated in the presence of inverter-interfaced renewable energy resources. A comparative study on the performance of the relays is done in the presence of inverter-interfaced renewable energy resources for different fault types and fault resistances. • The interdependencies between the inverter control scheme used and performance of relaying schemes have been analyzed through mathematical analysis and circuit realization of the inverter-interfaced renewable energy resources. • Based on the mathematical analysis and circuit realization, the probable causes of relay failures in the presence of inverter-interfaced renewable energy resources are detailed. • The impact analysis of the dynamic response of the controller on the protective relay settings from the perspective of protection operation time-frame has been attempted. The potential impacts of the inverter-interfaced renewable energy resources (IIRERs) on the performance of sequence-based directional relaying schemes (SBDRS) have been investigated in this paper. The directional overcurrent relays such as 67 POS , 67 NEG , 67 ZERO and 32Q have been considered for the investigation. CIGRE-14 bus system with IIRERs along with detailed modeling of inverter control scheme (with and without grid codes) and SBDRS have been done in the PSCAD environment. The mathematical analysis and circuit realization of the IIRERs have been attempted in the paper. The exclusive fault characteristics exhibited by IIRERs cause the conventional SBDRS to mal-operate. Significant change in levels of sequence currents and angular relationships between sequence voltages and currents during faults contributes to relay's unpredictable behavior. The comparative study based on different fault types, fault resistances and interconnecting transformer connections have also been done. The study reveals the impact of non-generalized angular differences between positive sequence voltage and current at the inverter terminal on performance of 67 POS. It is found that 67 NEG and 32Q mal-operated for all types of unbalanced faults while the 67 ZERO can be utilized for grounded fault with delta-star grounded connection of interconnecting transformer. [ABSTRACT FROM AUTHOR]

• According to the comparative small-signal analysis of GCC adopting PLL and RPS, it is demonstrated that the current information introduced by the RPS is equivalent to adding a positive real part to its open-loop transfer function, which improves the stability of the GCC system. • Based on the admittance model developed in this paper, it is revealed that RPS can effectively reduce the negative resistance area and reduce the frequency coupling effect. Then the stability of GCC in a weak grid is improved. However, the specific mechanistic analysis cannot be easily carried out on the unified admittance model. • Finally, a SISO model is derived to intuitively visualize the mechanism of instability for GCC adopting PLL in a weak grid, which can be attributed to the gain spike and phase jump. RPS with a lower-order structure can effectively avoid the above two shortcomings, which achieves the same dynamic performance as PLL. For grid-connected converters (GCC), the synchronization unit (SU) is indispensable for the vector current control (VCC). Usually, the phase-locked loop (PLL) is employed as SU. However, PLL could introduce negative resistance contributing to potential instability issues. Thus, the second-order generalized integrator PLL (SOGI-PLL) and the reactive power-based synchronization method (RPS) are proposed to enhance the stability. Nevertheless, the intrinsic reason why RPS enhances stability is not clear. Therefore, a detailed comparative analysis among PLL, SOGI-PLL, and RPS is presented in this paper to reveal the mechanism of this stability enhancement. Firstly, an admittance model is derived to analyze the differences between these three synchronization methods. However, it is not intuitive enough to explain the detailed mechanism. Then, a SISO model containing the current controller, physical circuit, and synchronization unit is developed, which is established on the relationship between power and angle. According to this SISO model, it is revealed that the presence of the gain spike introduced by PLL and SOGI-PLL leads to instability. RPS avoids these issues due to its introducing current information for phase margin enhancement and its lower-order structure. Finally, the validity of the mathematical analysis and derived models are verified by experimental results. [ABSTRACT FROM AUTHOR]

The Hybrid Event-B framework was introduced to add continuously varying behaviour to the discrete changes of state characteristic of the well established Event-B method. This is made necessary by the needs of verifying the hybrid and cyber-physical systems that are increasingly prevalent today. The semantic foundation of Hybrid Event-B rests on piecewise absolutely continuous functions of time. This enables unproblematic modelling of all classical physical phenomena, as well as the specification of conventional discrete changes of state, regardless of whether these arise in the physical arena or as abstractions of computational behaviour. In this paper, the large gap between arbitrary piecewise absolutely continuous functions, and what can be reasoned about mechanically/symbolically, is addressed. First, piecewise absolutely continuous real functions are restricted to piecewise complex analytic functions, real and without singularities on a semi-infinite portion of the real axis. This class has good properties with respect to symbolic manipulation and thus provides a good foundation for an approach to system verification that avoids dealing with the interleaved quantifiers of mathematical analysis, thus reducing the verification of the proof obligations of Hybrid Event-B to calculational checks. The individual proof obligations, whose discharge assures the correctness of a Hybrid Event-B machine, are examined, and results establishing sufficient conditions for their successful discharge via calculation are given. A small scale case study illustrates the verification process in this setting. • The paper considers in detail the reasoning processes that formal verification of Hybrid Event-B machines would require. • It presents a series of results concerning how such reasoning could be reduced to symbolic manipulation. • Thereby, individual Hybrid Event-B events can be proved correct, leading to correctness of the machine as a whole. [ABSTRACT FROM AUTHOR]

• A coupling mechanism model of an FSDB unit is developed and verified. • Mathematical analysis is explored to reveal the coupling mechanism of an FSDB system. • Rigid and elastic motions of disk and cyclic blades induce diagonal and cross-coupling terms. • The motion patterns of cyclic blades are classified and clarified. • Effects of motion patterns of cyclic blades on NFs and CSs are applied to interpret and validate the dynamic coupling. This paper focuses on the influence mechanism of cyclic blades on the dynamic coupling of a flexible shaft-disk-blade (FSDB) system through mathematical analysis and numerical simulation. Firstly, a coupling mechanism model of an FSDB unit is developed through a Lagrange method and the assumed mode method (AMM), after considering the coupling behavior among shaft bending, shaft torsion, disk vibration, and blade bending. The modal comparison results between the proposed model and FEM affirm the validity of the model. Then the analytical interpretation is explored by decomposing and discussing the diagonal coupling and cross-coupling matrices of the FSDB system. The mechanism discussion reveals that the coupling matrices originate from the rigid and elastic motions of flexible disk and cyclic blades, indicating that the motions of cyclic blades play an important role in dynamic coupling. Therefore, the motions of cyclic blades are classified and analyzed, and their effects on natural frequencies (NFs) and critical speeds (CSs) are applied to further interpret and validate the dynamic coupling through numerical simulation. The numerical results indicate that motions of cyclic blades can increase, decrease, and eliminate the magnitude of dynamic coupling significantly. [ABSTRACT FROM AUTHOR]

The highly reliable nanosatellite platforms have broad application prospects in the construction of satellite Internet. Obtaining accurate attitude information is crucial to enhance the reliability of nanosatellite platforms. However, the traditional attitude sensors are not suitable for nanosatellite and attitude sensor faults are the main ones in space field. Therefore, sensor fault detection and fault-tolerant processing are essential to improve the reliability of platforms. In this paper, the distributed fusion fault-tolerant attitude estimation (FTAE) problems for nanosatellite with commercial off-the-shelf (COTS) sensors are investigated. Considering the low development cost of nanosatellite platforms, a FTAE scheme using COTS sensors is developed, which can acquire high-precision attitude information and improve the fault tolerance of nanosatellite platforms. Moreover, a novel fault detection method is designed and strict mathematical analysis is applied to fault threshold in FTAE scheme, which can significantly reduce complicated debugging work in engineering application and improve the design efficiency of FTAE scheme. Some case studies are given to illustrate the efficacy of the designed distributed fusion FTAE scheme. [ABSTRACT FROM AUTHOR]

This work is devoted to the mathematical analysis of an inverse source problem governed by a time-fractional diffusion equation. The aims of this paper are to identify the source function from additional data based on a regularized optimal control approach, and to determine the regularization parameters using bi-level optimization. To do this, firstly we formulate our inverse problem to an optimal control one with two types of fidelity terms, which are the Least-Squares fitting and L 1 norm. Secondly, we establish the existence of the minimizer for the optimal control problem corresponding to the L 1 cost function, since it is the general case. Thirdly, we present some numerical results for the different cases of the cost function. These results are based on solving the optimal control model by gradient method for the L 2 case and the primal-dual method for non-smooth L 1 norm. Finally, we propose an adaptive selection strategy for the regularization parameter based on the bi-level optimization method, and we give some numerical results to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

[Display omitted] • This article proposes a new robust nonlinear controller that stabilizes a chaotic finance system in a finite-time without cancellation of the spacecraft's nonlinear terms, it improves the efficiency of the closed-loop. • It accomplishes an oscillation-free faster convergence of the perturbed state variables to the desired steady-state. • The proposed controller is insensitive to the parameter uncertainties of the nonlinear terms and exogenous disturbances. • The paper performs a comparative study to verify the performance and efficiency of the proposed controller. Robust, stable financial systems significantly improve the growth of an economic system. The stabilization of financial systems poses the following challenges. The state variables' trajectories (i) lie outside the basin of attraction, (ii) have high oscillations, and (iii) converge to the equilibrium state slowly. This paper aims to design a controller that develops a robust, stable financial closed-loop system to address the challenges above by (i) attracting all state variables to the origin, (ii) reducing the oscillations, and (iii) increasing the gradient of the convergence. This paper proposes a detailed mathematical analysis of the steady-state stability, dissipative characteristics, the Lyapunov exponents, bifurcation phenomena, and Poincare maps of chaotic financial dynamic systems. The proposed controller does not cancel the nonlinear terms appearing in the closed-loop. This structure is robust to the smoothly varying system parameters and improves closed-loop efficiency. Further, the controller eradicates the effects of inevitable exogenous disturbances and accomplishes a faster, oscillation-free convergence of the perturbed state variables to the desired steady-state within a finite time. The Lyapunov stability analysis proves the closed-loop global stability. The paper also discusses finite-time stability analysis and describes the controller parameters' effects on the convergence rates. Computer-based simulations endorse the theoretical findings, and the comparative study highlights the benefits. Theoretical analysis proofs and computer simulation results verify that the proposed controller compels the state trajectories, including trajectories outside the basin of attraction, to the origin within finite time without oscillations while being faster than the other controllers discussed in the comparative study section. This article proposes a novel robust, nonlinear finite-time controller for the robust stabilization of the chaotic finance model. It provides an in-depth analysis based on the Lyapunov stability theory and computer simulation results to verify the robust convergence of the state variables to the origin. [ABSTRACT FROM AUTHOR]

Compared with the two-valued memristor, the three-valued memristor has higher data density, richer dynamic characteristics, and more potential in digital logic and chaotic circuit. The present model of the three-valued memristor has several limitations. It doesn't perform well enough in three-valued applications since its hysteresis loops are linear and asymmetric. The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this research. To further investigate the electrical characteristics of the three-valued memristor, a circuit emulator of the memristor has been constructed with fundamental components. Multisim simulations and hardware experiments demonstrate the emulator's effectiveness. The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics and lays the foundation for future research. • The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this paper. • A circuit emulator of the three-valued memristor is proposed and verified using hardware and software. • The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics. [ABSTRACT FROM AUTHOR]

In this paper, mathematical analysis and numerical methods for Caputo-Hadamard fractional diffusion-wave equations with initial singularity are investigated. By adopting the modified Laplace transform and the well-known finite Fourier sine transform, we obtain the analytical solution. Furthermore, the regularity and logarithmic decay of its solution are researched. Under the singularity hypothesis, the numerical methods for the problems are then studied. The model is first transformed into its equivalent form and then the technic of exponential type meshes is utilized. The fact that the discrete coefficients of Hadamard fractional integral have several graceful properties is crucial in convergence and stability analysis. For the sake of reducing storage and computational cost, the SOE technology is exploited to the new variable t = log ⁡ t n s. On this basis, a fast compact difference scheme and a fast compact ADI method are constructed for the one- and two-dimensional problems, respectively. To illustrate the significance of studying singularity, a Crank-Nicolson difference scheme is proposed. The final result that the error in numerically approximating the solution depends on the parameter γ shows obviously how the regularity of the solution and the exponential type meshes affect the convergence order of the derived scheme. Ultimately, the numerical examples are provided to verify that the fast algorithm effectively reduces the computational cost compared to the direct method. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the stationary problem for a Lotka–Volterra competition system with advection under homogeneous Dirichlet boundary conditions. By using global bifurcation theory, we establish the sufficient conditions on terms of the birth rates of two competing species assuring the existence of positive solutions. Moreover, some sufficient conditions for the nonexistence of positive solutions are also given. These contrast with the mathematical analyses carried out by Kuto and Tsujikawa (2015) and Wang and Yan (2015), where the corresponding Neumann problem is analyzed. [ABSTRACT FROM AUTHOR]

In this article, we consider a 4-dimensional predator–prey chemostat model of nitrogen-phytoplankton-rotifer interactions with staged structure proposed by Blasius et al. (2020). Although it is still difficult to prove the simulation observations in Blasius et al. (2020) by mathematical arguments, we explore the dynamics in order to better understand the dynamical mechanism of cyclic persistence for this model. We firstly investigate the corresponding system without staged structure, i.e., when the juvenile is absent, the asymptotical behavior of the solutions is given. When the juvenile is present, a threshold condition for the uniform persistence of the 4-dimensional system is provided. Finally, by choosing the life development time delay as a bifurcation parameter, we show that the system admits periodic solutions near one semi-equilibrium undergoing Hopf bifurcation. The rigorous theoretical analytic work in this paper provides some helpful transient information between coherent oscillation and non-coherent oscillation described by the experimental data of Blasius et al. (2020). [ABSTRACT FROM AUTHOR]