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This paper derives well-posedness and asymptotic results that provide qualitative information about the behavior, mechanism and strategies used by living organisms to navigate their biological networks. Chemical driven swimming is a captivating phenomenon that is observed in various living organisms like bacteria and protozoa but the problem in weighted networks is more complex, since the equations of parabolic-parabolic Keller-Segel model coupled with incompressible Navier-Stokes equations must be reformulated in a discrete setting. The starting point is to transpose the coupled system from the Euclidean case to the connected networks with certain network-theoretic simplified approaches, which yields fruitful key results. These results not only enable the construction of global solutions but also serve as a foundation for determining information about the stability and large time behavior of the system. Then, decay rates are well established to predict important features, such as how quickly weak solutions at a given point decrease over time due to dissipative processes. Additionally, the L 1 - convergence of cell densities towards the self-similar Gaussian solution of the heat equation is well proved by time dependent scaling, which shows that the solution maintains its shape and only scales in time and space as time evolves. Finally, this paper includes many numerical tests through a recent robust numerical scheme to illustrate the theoretical results and to develop computational control and prediction of living organisms' trajectories around central nodes in networked flows. [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 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]

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]

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]

[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]

• 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]

• A new DC-hub is proposed for interconnection of VSC-based HVDC ports based on thyristor device. • Zero-reactive power control across the common AC link is proposed to achieve reduced RMS current. • Comprehensive mathematical analysis is illustrated for circuit design parameters for the DC-Hub under study. • Transformation from Sinusoidal to Quasi-Trapezoidal to accommodate the utilization of thyristor based DC-Hub. • Small scale hardware setup is built to test the proposed DC-Hub under different healthy and unhealthy scenarios of power flow. The promising features of HVDC technology have led to the possibility of numerous renewable resources integration and enormous DC grids interconnection. In spite of the obstacles, these interconnections encounter such as the necessity to block DC faults, achieving isolation between different schemes, the ability to maintain power flow throughout different power flow profiles, and the interfacing with various infrastructures, the DC-Hub arises to overcome these interconnection obstacles being the excellent approach to enhance the DC grid capabilities. This paper proposes a new monolithic modular thyristor-based multilevel converter, which serves as the fundamental building block of the DC-Hub, offering advantages such as lower switch count, bidirectional power flow, and DC fault blocking capability. Moreover, a control algorithm, for zero reactive power circulation in the DC-Hub, is introduced. The proposed algorithm successfully mitigates the circulation of reactive power throughout the entire range of power flow. A comprehensive mathematical analysis, optimum design of converter parameters, and the proposed control technique, which suppress the circulating reactive power at full range of power flow, are illustrated. Finally, simulation modelling and hardware test rig are established to validate the claims of the DC-Hub at different normal and faulty scenarios. [ABSTRACT FROM AUTHOR]

Multiphysics processes are common in nature and can occur in conjuction with intense strains. When strain softening is also present, the original uniform strain distribution is lost and strain localization occurs. In a classical continuum strain localization happens on a mathematical plane (i.e shear band of zero thickness). This leads to mesh dependent numerical analyses, in which strain localizes on the smallest mesh length. In this paper we investigate under which conditions multiphysics processes regularize the problem of strain localization. We study, for the first time, the influence of all the different coupling terms present in the original coupled multiphysics balance equations on the strain localization profile. We also consider the influence of viscosity and inertia effects. We show that the multiphysics processes do not always lead to mesh independent results. Furthermore, our rigorous mathematical analysis provides bounds for the different coupling parameters, for which multiphysics processes lead to strain regularization and mesh independent numerical results. Finally, we corroborate our mathematical findings, applying them to a numerical example of a coupled hydro-mechanical system of a fault under shear. [Display omitted] • The hypothesis that multiphysics couplings alleviate mesh dependence is tested. • All mechanisms of the multiphysics coupling are considered. • The influence of viscosity and inertia is investigated. • Bounds are given for the different coupling parameters for strain regularization. • A numerical example of the hydro-mechanical system of a fault under shear is shown. [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]

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]

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

For biomimetic robots to be used in the real world, it is very important to have animal-like turning motion. Excellent turning ability can help quadruped robots navigate more complex obstacle terrain. To solve this problem, we conducted the corresponding study by collecting multiple sets of data on different movements of Marinua dogs. First, we extracted the key movement joints of dogs and captured the motion trajectories of the key joints by a reduced order model. Then, on the basis of systematic analysis and mathematical modeling of the experimental dog's turning motion, we propose an N -step turning strategy to enable the quadruped robot to realize a wide range of multi-angle movements. Meanwhile, based on the extracted joint trajectory and considering the influence of the actual turning speed, radius and stability of the quadruped robot, the more reasonable biomimetic turning trajectory is obtained through optimization. In terms of motion control, we propose a virtual spine control method to realize turning motion, and plan the foothold adjustment according to different speeds. Finally, experiments show that the proposed method can effectively realize multi-angle turning and U-turn and O-circle turning motion of quadruped robot, which proves the effectiveness of the proposed method. At the same time, the biomimetic turning control method proposed in this paper can be easily extended to other biomimetic robot movements inspired by other organisms. • The turning ability help quadruped robot pass through various complex obstacles. • The key movement joints extraction method can identify important biomimetic joints. • N-step turning strategy and biomimetic turning trajectory are proposed. • The virtual spine control method can reduce freedoms in turning motion. • The effectiveness of this method is verified by the multi-angle turning motion. [ABSTRACT FROM AUTHOR]

This paper deals with the approximation of discrete probability measure-valued data by a new subdivision scheme. Its construction relies on a coupling between linear subdivision and optimal transport. A mathematical analysis is performed to study its convergence. Two test cases are finally described to emphasize its capability: the first one is related to point cloud interpolation while the second one is a first attempt in the framework of image approximation. [ABSTRACT FROM AUTHOR]

As one of the most commonly used energy-saving methods in buildings, thermal insulation layer is widely used in building façade and it also endangers the human safety in buildings due to its combustibility. U-shaped facade is a commonly used structure in high-rise buildings since it could improve both the light and ventilation conditions indoors. This paper investigated the flame acceleration over the thermal insulation in u-shaped building facade fires. It was found that the flame spread rate over u-shaped facade had an exponential growth with time as the direction of preheating zone location is the same direction of the heat transfer from the pyrolysis zone. The air entrainment and the upward induced airflow played an important role in the acceleration. As the side wall length increased or the back wall length decreased, the flame spread rate accelerated more rapidly. Furthermore, a mathematical prediction model of the unsteady flame spread rate over u-shaped structure façade was established and validated through experiments. This study provides technical guidance for the fire safety design of building facade. [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]

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]

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]

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]

This paper investigates the connection between non-prehensile manipulation, specifically juggling, and legged locomotion, focusing on biped robots. In this direction, the hybrid nature of juggler robot dynamics and biped robots, the zero moment point stability, and the non-prehensile dynamic grasping conditions are provided and analysed. The similarities between juggling actions and bipedal robot locomotion are discussed. The descriptive and mathematical analysis demonstrates many similitudes between juggler systems with cubic objects and flat-feet biped robots in throwing, catching, and stabilization phases, and between juggler actions with impact and point-feet legged robots in their switching (hybrid) dynamic behaviours. Finally, a common control framework based on the zero dynamic concept and integral sliding mode approach is proposed, and it applies to both classes of non-prehensile juggler systems and biped robots. To test the performance of the devised control system, a three-degrees-of-freedom juggler robot and a two-link walker are selected as case studies, whose simulation results demonstrate the effectiveness and feasibility of the proposed unified control framework for both systems. [ABSTRACT FROM AUTHOR]

In this paper, it is addressed by mathematical analysis how network-oriented modeling relates to the dynamical systems perspective on mental processes. It has been mathematically proven that any dynamical system can be modeled as a temporal-causal network model and that any adaptive dynamical system (of any order) can be modeled by a self-modeling network (of the same order). [ABSTRACT FROM AUTHOR]

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]

• Based on the derivation method, a new derived grey multi-parameter prediction model (DMGM (1, n)) is proposed. • The mathematical analysis is used to discuss the main reason why DMGM (1, n) is superior to GMC (1, n). • DMGM (1, n) outperforms the other grey multivariable models by comparing the results of these models in three cases. In this study, in order to reduce the morbidity and improve the structural stability of the existing grey multivariable convolution forecasting model, a new derived multivariable grey model based on the derivation method, abbreviated as DMGM (1, n), is presented. Firstly, the time response formula of DMGM (1, n) is deduced by derivation method, which can avoid solving the inverse matrix so as to reduce the morbidity of the model. Secondly, the parameter identification of the model is given based on the least-squares method. Then, it is proved theoretically that DMGM (1, n) is superior to GMC (1, n) because the solution of the former overcomes the shortcoming of the latter that the original model does not take full advantage of all the information from the raw data for modeling. Finally, three real cases with different variables were performed. The fitting and prediction results indicate that DMGM (1, n) is better than GMC (1, n) and the other multivariate grey prediction models in these cases, which also demonstrates that this novel model outperforms the other grey models in this paper. [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]

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]

Abstract Many of our cognitive capacities are shaped by enculturation. Enculturation is the acquisition of cognitive practices such as symbol-based mathematical practices, reading, and writing during ontogeny. Enculturation is associated with significant changes to the organization and connectivity of the brain and to the functional profiles of embodied actions and motor programs. Furthermore, it relies on scaffolded cultural learning in the cognitive niche. The purpose of this paper is to explore the components of symbol-based mathematical practices. Phylogenetically, these practices are the result of concerted organism-niche interactions that have led from approximate number estimations to the emergence of discrete, symbol-based mathematical operations. Ontogenetically, symbol-based mathematical practices are associated with plastic changes to neural circuitry, action schemata, and motor programs. It will be suggested that these practices rely on previously acquired capacities such as subitizing and counting. With these considerations in place, I will argue that computations, understood in the sense of Turing (1936), are a specific kind of symbol-based mathematical practices that can be realized by human organisms, machines, or by hybrid organism-machine systems. In sum, this paper suggests a new way to think about mathematical cognition and computation. [ABSTRACT FROM AUTHOR]

This paper presents a comparison between three different controller methods added to a cracked beam under the action of a harmonic excitation. Those three controllers are Positive Position Feedback (PPF), Integral Resonant Control (IRC) and Nonlinear Integral Positive Position Feedback (NIPPF) which be added to the measured system. The multiple scales method (MSM) is applied for getting the approximate solution on behalf of measured design. This method is effective to solve the major equations of measured system. Stability and effect of different coefficients of the system are demonstrated. The approximate solution response is established via numerical simulation outcome. NIPPF controller is the best one gives better results compared to the other two controllers in decreasing the high amplitude of the system. Comparison between mathematical solution and numerical simulation are considered. Relationship of formerly available papers is considered. [ABSTRACT FROM AUTHOR]

This paper constructs an evolutionary game model of haze cooperative control between the heterogeneity governments, which is used to analyze the dynamic evolution path of game system as well as evolutionarily stable strategy under the three different conditions: no constraint, the introduction of compensation mechanisms and the introduction of punishment mechanism. The results show that, due to the heterogeneity of governments, the stable model of cooperation cannot be formed between heterogeneous governments spontaneously, so the superior government should impose administrative penalties on the uncooperative governments to promote the formation and stability of cooperation control model. The conclusion of this paper can provide reference for the Chinese government to formulate environmental policies. [ABSTRACT FROM AUTHOR]

This paper considers the usual compound matrix, the additive compound matrix, and the discriminant matrix. An investigation of the Jordan structure of discriminant matrices is initiated. The primary objective of the paper is the determination of the Jordan form of the discriminant of one Jordan block. This Jordan form has a very simple pattern. A number of related results are obtained. The main results are facilitated by the new precedence relation ordering and the block-persymmetric property of the matrices. Examples of the discriminant matrices and Jordan forms are provided. [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]

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]