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Abstract: A left canonical factorization theorem for rational matrix functions relative to the unit circle is presented. The result is a time invariant version of a recent strict LU factorization theorem for certain semi-separable operators, due to Dewilde (2012) [6]. Explicit formulas for the factors are also given. The theorem is proved, first by using the state space method of Dewilde (2012) [6], and next by using an operator theory approach. In both cases the main part of the proof concerns rational matrix functions that are unitary on the unit circle. [Copyright &y& Elsevier]

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]

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: 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: 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: 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]

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: 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]

Abstract: A lemma presented by Matkowski requires a proof. [Copyright &y& Elsevier]

Abstract: We recall some bibliography on fast polynomial multiplication related to the recent progress in the paper by Cenk and Ozbudak of 2011. [Copyright &y& Elsevier]

The integration of multiterminal hybrid HVDC grids connecting LCC- and VSC-based networks faces several technical challenges such as DC fault isolation, ensuring multi-vendor interoperability, managing high DC voltage levels, and facilitating high-speed power reversal without interruptions. The two-stage DC-DC converter emerges as a key solution to address these challenges. By implementing the modular multilevel converter (MMC) structure, the converter's basic topology includes half-bridge sub-modules on the VSC side and full-bridge sub-modules on the LCC side. However, while this topology has been discussed in the literature, its connection to an LCC-based network with controlled current magnitude lacks detailed analysis regarding operational challenges, control strategies under various scenarios, and design considerations. This paper fills this gap by providing comprehensive mathematical analysis, design insights, and control strategies for the modular DC-DC converter to regulate DC voltage on the LCC-HVDC side. Additionally, the proposed control scheme minimizes the interfacing inductor between the two bridges, ensuring uninterrupted power flow during reversal and effective handling of DC faults. Validation through Control-Hardware-in-the-Loop testing across diverse operational and fault scenarios, along with a comparative analysis of different converters, further strengthens the findings. © 2017 Elsevier Inc. All rights reserved. [ABSTRACT FROM AUTHOR]

The rapid growth in HVDC grids is becoming inevitable for long-distance power transmission. Therefore, the idea of interconnection between the point-to-point links becomes essential. However, these point-to-point connections face several challenges such as the requirement of DC fault blocking capability, interfacing of different grounding schemes, offering multi-vendor interoperability, and difficulty to achieve high DC voltage stepping. DC-DC converters are considered the optimum solution to tackle these challenges in DC grids interconnection. In this paper, a new hybrid modular DC-DC converter is proposed that achieves a low number of semiconductors, low losses, and cost in comparison to other DC-DC converters due to the utilization of thyristors. The new DC-DC converter consists of two hybrid MMC bridges connected through an isolating transformer. Each MMC bridge is comprised of half bridge submodules and bidirectional thyristors. Detailed mathematical analysis, design, and control are illustrated. A comparison is carried out between different topologies in terms of semiconductor count, power loss, and cost. Also, both simulation model and experimental test rig are built to validate the proposed hybrid modular DC-DC converter under different scenarios. Finally, another variant of the hybrid-thyristor based converter (version two) is proposed for multiport DC-Hub application to achieve DC fault blocking without turning off all connected bridges. [ABSTRACT FROM AUTHOR]

Investigating the effects of periodic magnetic field and triple diffusion on bioconvection flow through a rotating cone populated by oxytactic bacteria and an Eyring-Powell fluid is innovative and significant. The magneto-bioconvection flow of an Eyring-Powell multi-diffusive fluid across a spinning cone is investigated in this paper, considering the effect of oxytactic microorganisms. The non-similar technique is used in the mathematical analysis of the flow over a spinning cone. The flow under consideration contains two diffusive species: liquid hydrogen and liquid oxygen. In light of the periodic magnetic field, the surface gradients, notably skin friction, exhibit wavy effects in the boundary layer domain. The governing equations for the fluid flow in the current flow problem, accompanied by heat diffusion, species diffusion, rotation, bioconvection, and periodic magnetic, are highly coupled nonlinear PDEs dependent on the proper initial and boundary conditions. Mangler's transformations convert them into non-dimensional forms, and numerical non-similar solutions are produced using implicit finite difference approximation and quasi-linearisation. The enriching values of bioconvective Rayleigh number Rb decline the velocity F, as a result, lessen the friction between the surrounding fluid and the cone's surface. The improving Peclet number Pe and microbial density difference σ reduced the microorganism density profile and heightened the microorganism density number R e - 1 / 2 N n. [ABSTRACT FROM AUTHOR]

In this manuscript, we are going to study a novel model of the dynamics of alcohol consumption under induced complications. The mentioned model is considered under the concept of conformable fractional order derivative (CFOD). Currently, most of real-world problems are considered under fractional order derivatives because of their stable and global behavior. First, we will investigate the model for qualitative theory including existence and uniqueness of solution and Ulam-Hyers stability. For qualitative theory, we will use fixed point theory. In addition, we use a numerical method to find the approximate solution of the proposed model. In the final part of the paper, we give a detailed discussion of its numerical results and its graphical presentation. [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]

[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]

Abstract: Two-dimensional axially moving materials have a wide range of industrial applications such as papers, plastics and composites in producing lines, power transmission and conveyor belts, etc. In many of these instances, the moving material is not isotropic, but is a single-layer orthotropic material or consists of several orthotropic layers. In this article, free vibration of axially moving symmetrically laminated plates subjected to in-plan forces is studied by classical plate theory. This category includes symmetric cross-ply and angle-ply laminates and anisotropic plates. Firstly, an exact method is developed to analyze vibration of multi-span traveling cross-ply laminates, and then a semi-analytical finite strip method is extended for moving symmetric laminated plates in general, with arbitrary boundary conditions. By the finite strip method intermediate elastic or rigid supports can also be added to the model of the moving plate. The supports may be in the form of point, line or local distributed supports. [Copyright &y& Elsevier]

Abstract: In the present paper, a description and mathematical analysis of a simple model of nonlinear pattern formation is given. The model is based on the so-called activator-inhibitor system proposed by Thomas. We introduce time delay into the reaction term and focus on its influence on morphogenesis and pattern formation. Numerical simulations are presented and compared for both cases without and with delay. [Copyright &y& Elsevier]

In this paper, the consensus tracking problem for the linear and nonlinear partial difference multi-agent systems with switching communication topology and control delay is investigated. Based on relative local measurements of neighboring followers, while considering spatio-temporal discretization and initial state deviation, a discrete distributed consensus protocol with initial value learning is designed for each agent via D-type iterative learning approach. Through rigorous mathematical theoretical analysis, the necessary and sufficient conditions are obtained. Under the switching of the communication topology, these conditions ensure that the consensus tracking control of the MASs can be solved. After applying the designed protocol, in the sense of the L 2 norm and along the positive direction of the iteration axis, the consensus tracking error between any two agents can converge to zero. Finally, some simulation examples are used to demonstrate the validity of the protocol and theoretical results. • A novel partial difference MASs dynamic model is established to describe the discrete spatio-temporal evolution behavior. • A new distributed iterative learning approach with initial value learning for partial difference MASs is given. • The proposed control approach can solve the problem of switching topology and control delay simultaneously. [ABSTRACT FROM AUTHOR]

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]

[Display omitted] • The counties with high abandonment rates are close to 30%, while those with low rates are between 0 and 2%. • The abandoned farmland in Chongqing expanded from the northeast to the whole area. • Wild boar invasion has become the leading factor of farmland abandonment. • Ecological restoration and land abandonment are a vicious cycle of mutual causality. • A vicious cycle of farmland abandonment, mainly by wild boars, has emerged. Farmland abandonment reflects the decline of rural areas, resulting in a series of vicious chain reactions, hindering the promotion of the comprehensive rural revitalization strategy. From the perspective of ecological restoration, this paper integrated multi-source data such as Landsat, GF-1, and Google Earth images and household survey data, aiming to reveal the spatiotemporal pattern, attribution, and mechanism of farmland abandonment in typical mountainous areas over the past 20 years by employing spatial analysis and mathematical models and to promote comprehensive management of abandoned farmland. The results are as follows. (1) The scope of abandoned farmland in Chongqing has been expanding, with the abandoned area growing from 142,385.8 hm2 to 345,778.4 hm2 from 2000 to 2020, with the initially abandoned farmland mostly concentrated in the northeastern areas, such as Chengkou, with an abandonment rate of 21.8%, and thereafter, spreading in all directions; In the end, abandoned farmland was concentrated in northeastern and southeastern Chongqing, such as Wuxi and Youyang, with abandonment rates of approximately 25.1% and 20%, respectively. (2) The attribution of farmland abandonment mainly includes wild boar damage, labour shortage, and natural conditions, among which wild boar proliferation has become an important factor under the background of ecological restoration. (3) Ecological restoration has produced a counter-servicing effect of the ecosystem on human beings, forming a vicious circle in the mountainous countryside where ecological restoration continues to aggravate farmland abandonment. The contribution of this study is to investigate the pattern of farmland abandonment from both macroscopic and microscopic perspectives. At the same time, this paper explores the intrinsic mechanism between ecological restoration and farmland abandonment and proposes scientific countermeasures to break the vicious cycle of ecological restoration that continues to exacerbate farmland abandonment in mountainous areas. [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 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]

• 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]

In this paper, a fractional-order Hantavirus infection model incorporating harvesting is formulated and investigated. The populations are divided into susceptible mice, infected mice and alien species. Mathematical analysis and numerical simulations are performed to clarify the characteristics of the proposed fractional-order Hantavirus infection model. The existence, uniqueness, non-negativity and boundedness of the solutions are examined. The local stability of the equilibrium points of the fractional-order model is studied. The mathematical proof of the existence of transcritical bifurcation is given by using Sotomayor's theorem. The theoretical findings are illustrated by numerical simulations. The impact of fractional-order, competitive effect of alien species on mice, competitive effect of mice on alien species, carrying capacity and harvesting efforts on the stability of the Hantavirus infection model are studied. The basin of attraction regions is also illustrated. [ABSTRACT FROM AUTHOR]

This paper introduces a new low-voltage, low-power FVF current mirror circuit. The bulk-driven (BD) technique is employed to achieve extended input voltage swing and low supply voltage. Besides, the quasi-floating gate (QFG) is used to achieve high frequency performance. The merging of (BD) and (QFG) appear as a good and attractive solution to improve the circuit performance with reduced supply voltage. Benefiting from the interesting properties of (BD-QFG) MOSFET (MOST) technique, the proposed FVF current mirror circuit exhibits superior performance compared to other previously reported works. The workability of the proposed circuit has been verified through ELDO simulator based on a 0.18 μm USMC process. It achieves an enhanced bandwidth (2.7 GHz), low power consumption (79.33 μW), a low input impedance (130 Ω), and high output impedance (9.5 G Ω) from a low supply voltage (0.8 V). Monte Carlo simulation is also carried out, which proves the robust performance of the proposed circuit against mismatches. An application of the proposed current mirror is presented in the form of the current comparator to ensure the workability of the proposed BD-QFG current mirror. • A new CMOS of a FVF current mirror based on BD-QFG technique is presented. • It is operated at a low supply voltage of 0.8 V with a small power consumption of 79.33 µW and large bandwidth of 2.7 GHz. • Various simulation results and mathematical analysis are presented in the paper to verify circuit performance. • An application example is presented to prove the workability of the BD-QFG current mirror. [ABSTRACT FROM AUTHOR]

• Fractional calculus is a fast growing field in mathematics, science and engineering. • This is a bibliographic analysis of 351 articles that use Atangana-Baleanu operators • Articles grow by 80.25% yearly from all countries, especially developing countries. • This shows the influence of this rapidly growing field of applied mathematics. Fractional calculus is a branch of mathematical analysis that studies the several different possibilities of defining real number powers or complex number powers of the differentiation and integration operators. Recently, Atangana and Baleanu proposed operators based on generalized Mittag-Leffler functions to solve fractional integrals and derivatives. These contributions have set off an explosion of new research in fractional calculus, and this paper present a comprehensive bibliometric analysis of the peer-reviewed papers inspired by Atangana and Baleanu. In total, 351 papers in the Scopus database have used Atangana-Baleanu operators and this number is growing at 80.25% each year since 2016. These papers were written by 343 authors, predominantly from Mexico, Saudi Arabia and India. Although these data show that Atangana-Baleanu operators support global and fast growing scientific research, the field is dominated statistically by a few productive individuals. I present citation network of the most prolific authors and show collaboration and citation networks. Finally, I present a thematic analysis of the papers applying Atanagana-Baleanu operators and show how research forms clusters based on: analytical solutions, numerical simulations or applications in science and engineering. [ABSTRACT FROM AUTHOR]

Modern modeling languages for general physical systems, such as Modelica, Amesim, or Simscape, rely on Differential Algebraic Equations (DAEs), i.e., constraints of the form f (x ′ , x , u) = 0. This drastically facilitates modeling from first principles of the physics, as well as the reuse of models. In this paper, we develop the mathematical theory needed to establish the development of compilers and tools for DAE-based physical modeling languages on solid mathematical bases. Unlike Ordinary Differential Equations (ODEs, of the form x ′ = g (x , u)), DAEs exhibit subtle issues because of the notion of differentiation index and related latent equations —ODEs are DAEs of index zero, for which no latent equation needs to be considered. Prior to generating execution code and calling solvers, the compilation of such languages requires a nontrivial structural analysis step that reduces the differentiation index to a level acceptable by DAE solvers. The models supported by tools of the Modelica class involve multiple modes, with mode-dependent DAE-based dynamics and state-dependent mode switching. However, multimode DAEs are much more difficult to handle than DAEs, especially because of the events of mode change. Unfortunately, the large literature devoted to the mathematical analysis of DAEs does not cover the multimode case, typically saying nothing about mode changes. This lack of foundations causes numerous difficulties to the existing modeling tools. Some models are well handled, others are not, with no clear boundary between the two classes. In this paper, we develop a comprehensive mathematical approach supporting compilation and code generation for this class of languages. Its core is the structural analysis of multimode DAE systems. As a byproduct of this structural analysis, we propose sound criteria for accepting or rejecting multimode models. Our mathematical development relies on nonstandard analysis , which allows us to cast hybrid system dynamics to discrete-time dynamics with infinitesimal step size, thus providing a uniform framework for handling both continuous dynamics and mode change events. [ABSTRACT FROM AUTHOR]

With an increase in the number of internet users and the need to secure internet traffic, the IPv4 protocol has been replaced by a more secure protocol, namely IPv6. The IPv6 protocol does not allow intermediate routers to fragment the on-going packets. Moreover, due to IP tunneling, some extra headers are added to the IPv6 packet, exceeding the packet size, resulting in increased packet drops due to lower path mtu. One probable solution is to use Path MTU Discovery (PMTUD) to know the path mtu using ICMP packets. Due to dependency on ICMP error messages, this method faces security and failure issues. In this paper, we propose a Dynamic MTU (DMTU) scheme, which tries to handle the packet drops in IPv6 network, by dynamically adjusting the MTU of each link depending upon the incoming packet size, thereby reducing the number of packet drops by a significant amount. Unlike PMTUD, the algorithm works on intermediate node level which is further optimised by assigning specific phases for validation and then, for processing. The method has ability to work in standalone and in parallel with PMTUD. Using mathematical and graphical analysis, our scheme proves to be much more efficient than the state-of-the-art PMTUD scheme. [ABSTRACT FROM AUTHOR]

This paper studies the underwater glider trajectory tracking in currents field. The objective is to ensure that trajectories fit to the straight target track. The underwater glider model is introduced to demonstrate the vehicle dynamic properties. Considering currents disturbance as well as the uncertain status of the glider controlled by complicated roll policies, the trajectory tracking task can be classified into the model-free optimization. Such problem is difficult to solve with mathematical analysis. This work transfers the underwater glider trajectory tracking into a Markov Decision Process by specifying the actions and observations as well as rewards. On this basis, a neural network controls framework called experience breeding actor-critic is proposed to handle the trajectory tracking. The EBAC enhances the explorations to the potentially high reward area. And it steers glider heading meticulously so as to counteract the currents influence. Through simulation results, the EBAC shows a desired performance in controlling the gliders to accurately fit the target track • The underwater glider simulator is established to develop algorithms and evaluate the effectiveness. • The novel experience breeding actor-critic algorithm is applied for underwater gliders trajectory tracking. • The optimizing framework of glider trajectory tracking from the Markov decision process perspective is proposed. • The proposed method enhance the tracking accuracy compared with PID and SMC with the LOS guidance. [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]

Early estimation of biological growth of organisms is an indispensable task in ecology and related research areas. The biological growth is always time-continuous, while our observations of the phenomenon are time-discrete in practice. The formalism of the discrete costly observation (DCO) enables us to mathematically bridge the two qualitatively different processes. This formalism is still germinating, and its practical applications have not been carried out. This paper presents a first application of the DCO formalism to a cost-effective early estimation problem of the biological growth, and its mathematical and numerical analysis. Growth dynamics of organisms, which are fishery resources in this paper, is governed by a stochastic differential equation whose solution is observed discretely. The optimality equation to be solved for finding the most cost-effective observation policy is derived as a fixed point problem based on degenerate parabolic partial differential equations. The fixed point problem turns out to be uniquely solvable. A recursive approximation of the fixed point problem is presented and its solvability in a viscosity sense is discussed. A finite different scheme is then employed to fully-discretize the recursive equations. The present model is finally applied to a problem of Japanese smelt Plecoglossus altivelis altivelis (Ayu): an important inland fishery resource in Japan. [ABSTRACT FROM AUTHOR]

Abstract Szlachányi showed that bialgebroids can be characterised using skew monoidal categories. The characterisation reduces the amount of data, structure, and properties required to define them. Lack and Street provide a bicategorical account of that same fact; they characterise quantum categories in terms of skew monoidal structures internal to a monoidal bicategory. A quantum category is an opmonoidal monad on an enveloping monoidale R ∘ ⊗ R in a monoidal bicategory. In a previous paper, we characterised opmonoidal arrows on enveloping monoidales as a simpler structure called oplax action. This is the second paper based on the author's PhD thesis. Here, motivated by the fact that opmonoidal monads are monads in the bicategory of monoidales, opmonoidal arrows, and opmonoidal cells; we prove that right skew monoidales are "monads of oplax actions". To do so, we arrange oplax actions as the 1-simplices of a simplicial object in Cat. In nice cases this simplicial object is ought to be thought as a bicategory whose arrows are oplax actions, that is to say, it is weakly equivalent to a nerve of a bicategory. We define monads of oplax actions as simplicial maps out of the Catalan simplicial set and prove that these are in bijective correspondence with right skew monoidales whose unit has a right adjoint, no assumptions required on the ambient monoidal bicategory. [ABSTRACT FROM AUTHOR]

This paper addresses the importance of the alignment of an acoustic Doppler current profiler (ADCP) with a global positioning system (GPS) in moving-boat streamflow measurements. It presents a mathematical analysis of the discharge bias induced by a misalignment angle. A small misalignment angle may cause a significant bias in a transect discharge. The bias consists of non-directional and direction components. The directional bias is proportional to the ratio between boat velocity and water velocity. In a normal condition of ADCP streamflow measurements, however, the directional bias in transect discharges can be approximately cancelled in the average discharge of reciprocal transects, even if heading-dependent errors are involved in the misalignment. This paper also presents a trial-and-error method for estimating the misalignment angle. We analyzed the transect discharge data obtained from a field measurement on the Yangtze River at the Huangling Temple hydrology station located about 5 km downstream from the Three Gorges Dam to gain insights on the effect of misalignment. Results of this case study suggest that the data for transect discharges must be processed to remove directional bias prior to the Type A evaluation of the random uncertainty of the measured discharge. Otherwise, the estimated Type A uncertainty would be false and misleading. • A small misalignment angle may cause a significant directional bias in transect discharges. • Directional bias can be approximately cancelled in reciprocal transects. • Misalignment angle can be estimated with the proposed trial-and-error method. • Directional bias must be removed from transect discharges prior to uncertainty analysis. [ABSTRACT FROM AUTHOR]

The aim of this study is to develop new and efficient theories for handling complex and unreliable data in real-world scenarios. The proposed approach integrates two distinct theories: the Bipolar Complex Fuzzy Set (BCFS) and the Soft Set (SS), resulting in a novel and superior method compared to existing solutions. Furthermore, the value of big data analytics cannot be overstated as it provides businesses with the opportunity to use their data to find areas for development and progress. To gain insights from raw data, it must first be collected and organized. Data modeling represents these large, complex data sets in a visual format, such as a chart or diagram. However, the visualization process often results in uncertainties and inaccuracies, highlighting the need for a more robust approach to data analysis. To address this issue, this paper introduces the concept of Bipolar Complex Fuzzy Soft Relations (BCFSRs), a fuzzy decision-making method within a complex bipolar fuzzy environment that can have the advantages of both a Bipolar Complex fuzzy relation and a soft relation at the same time. In BCFSRs, an element can have degrees of membership in both the positive and negative directions, reflecting a more nuanced and versatile representation of uncertainty or ambiguity. These mathematical ideas are explained through the Cartesian product of two Bipolar Complex Fuzzy Soft Sets (BCFSSs) and serve to simplify the decision-making process by presenting the BCFSSs in a clear and concise manner. The inventive notion of the BCFSRs elucidates the combined positive and negative effects of anything with parameterization. To support organizations in making data-driven choices and obtain insights for strategic planning and inventiveness, the analysis of big data is essential in several industries, including financial services, marketing, and medical treatment, among others. To choose the optimal big data analytics for efficient operation, this research presents modeling methodologies based on BCFSRs, including the formulation and analysis of scoring functions. The validity of the proposed work is demonstrated through a comparison study with existing methods, providing valuable insights for effective data analysis. • Bipolar Complex fuzzy and soft sets are presented. • Introduced novel, and effective ideas to manage complex, unreliable data. • Presents modeling methodologies based on Bipolar Complex fuzzy soft information. • Conducted a comparative study of existing techniques. [ABSTRACT FROM AUTHOR]

The holes are very easy to appear delamination and burr during CFRP drilling. The tool geometry has a great impact on the hole making. In this paper, according to the principle of bionics and structural features, a novel bionic drill bit was designed. The mathematical model of the lower incisor teeth occlusal movement was established. The cutting mechanism of the bamboo rat lower incisor on PW-CFRP material was studied. It was found that the curvature of the contour curves of the front cutter faces were constantly changing, which was conducive to the removal of chips. The curvature change of the contour curve of the rear cutter surface is small and the curve is relatively smooth, which is conducive to reducing friction. The mathematical modeling analysis was carried out on the feeding process of bamboo rats, and the mathematical relationship between the bite radius R and the cutting angle θ was obtained. The optimal cutting angle θ = 10° and the corresponding biting radius R = 40 mm were obtained by finite element simulation. The surface cutting quality of bamboo rat's lower incisors is better than that of ordinary cutting tools. The novel bionic tool can effectively reduce the burr and delamination of the exit layer. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple approach to the construction of a general class of L -stable explicit second-order one-step methods for solving stiff problems. These methods are nonlinear and derive from a novel approximation for the right-hand side functions of differential equations inspired by the nonstandard finite difference methodology introduced by Mickens. Through rigorous mathematical analysis, it is proved that the proposed numerical methods are not only explicit and L -stable, but also convergent of order two. Therefore, they are suitable and efficient to solve stiff problems. The proposed numerical methods generalize and improve a nonstandard explicit integration scheme for initial value problems formulated by Ramos (2007). Moreover, the present approach can be extended to construct A -stable and L -stable high-order explicit one-step methods for differential equations. Finally, the theoretical findings and advantages of the developed numerical methods are supported and illustrated by a series of numerical experiments in which stiff problems are considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel model that simulates the spread of the monkeypox virus. The new model takes into account the effect of the interaction between the human and rodent population along with some realistic factors that have not been introduced before such as imperfect vaccination and nonlinear incidence rates. Moreover, the human population is further divided into low-risk and high-risk groups to better reflect recent observations. To understand the dynamics of the new model, the existence, uniqueness, and continuous dependence on initial conditions, as well as its positivity and boundedness of the model are investigated in detail. The obtained solution is proved to be positive and has bounded behavior. Furthermore, the reproduction number R 0 for the proposed system is computed and detailed bifurcation analysis is performed to reveal major qualitative changes in the model's dynamics. In addition, we investigate the influence of key parameters on the basic reproduction number. We also explore and analyze the stability of equilibrium points in the space of parameters. The new findings reveal that the virus is more frequently witnessed among the high-risk group, which may provide some restrictions to stop the spread through social limitations. To validate our theoretical results, we conduct numerical simulations, which provide insights into the behavior of the model under different conditions. The new findings aim in developing preventive control measures to suppress the spread of the virus and to develop effective strategies for controlling and preventing outbreaks, ultimately protecting public health and minimizing the impact of the disease. [ABSTRACT FROM AUTHOR]

Highlights • Composite fin with high thermal conductivity coatings deliver large heat transfer enhancement. • At high Re typical of Engine Section Stator vanes, the coating thickness should be around 100 μm. • Composite vanes would be more effective at low Re, as predicted also for composite fins. • Using the internal web structure of vanes can improve heat transfer in long vanes. Abstract This paper main goal is aimed at a paradigm shift in the enhancement of heat transfer rate between finned surfaces and surrounding fluid by presenting a novel approach in composite fins. This approach consists in using high thermally conductive coatings on top of the finned substrate in order to increase the local temperature along the fin washed surface. In the present paper a high thermal conductivity coating has been applied to an aeroengine vane of different shape and dimensions subject to icing conditions at high Reynolds numbers and where the main aim was to keep the vane warm as to avoid icing in aerospace applications. Numerical simulations have been carried out to ascertain the range of thickness of the coatings to be used to maximise the wanted effect. Both short Engine Section Stator (ESS) and longer fan Outlet Guide Vane (OGV) have been modelled, having different final goals. In the case of longer OGV, an additional novel design modification has been suggested to enhance further the heat transfer along the vane length by the use of the internal webs. The experimental validation also carried out at much higher Reynolds numbers than that reported in Buffone et al. (2005), demonstrate that the novel concept of heat transfer enhancement in composite fins is a simple and yet powerful strategy in a wide range of Reynolds numbers. A fin analysis has been performed of both the present ESS vane the fins tested in Buffone et al. (2005) at much lower Reynolds numbers and shows that the improvement obtained with the coated fins tested in Buffone et al. (2005) is much larger than the coated ESS vanes investigated in the present study. This said, the present study demonstrates that the use of high conductive coatings in composite fins can keep the ESS vanes ice free, something that was not possible with uncoated vanes. It is important to note that the actual optimal thickness of the thermally conductive coatings is a function of Biot number, fin shape, dimensions and thermal conductivities of fin substrate and coating; depending on the application, a proper design of the fin substrate and coating should be carried out. [ABSTRACT FROM AUTHOR]

Highlights • A method for calculating distances between matrix sequences of different length. • The method can be used with a vast variety of calculi, using matrix sequences. • The proposed method is demonstrated with a three cushion billiards example. Abstract This paper introduces a new method for calculating distances between matrix sequences of different length. Matrix sequences are often used in spatiotemporal analysis, a field of research combining topological frameworks and temporal reasoning. The Qualitative Trajectory Calculus, a spatiotemporal calculus using matrix sequences, is used as an example in this paper. Since current approaches for comparing sequences are not suitable to calculate distances between matrix sequences of different length, a new method is proposed. The method is based on sequence alignment and uses the Levenshtein distance metric as starting point. The method is presented in general at first, followed by an application to QTC-matrix sequences and a three cushion billiards movement pattern detection example. Possible applications in expert and intelligent systems are discussed, such as human-robot interaction with multiple robots, and automated traffic analysis of (autonomous) vehicle interactions. The proposed method, however, can be applied in a broad range of domains, whenever distances need to be calculated between matrix sequences of different length. [ABSTRACT FROM AUTHOR]