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

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

Abstract: 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: 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]

• 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]

• 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]

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]

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]

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

Abstract In this paper, we numerically investigate a nanoscale plasmonic biosensor based on Mach-Zehnder interferometry. The operation of Mach-Zehnder interferometer (MZI) biosensor is examined based on two methods. In the first method, in which the transmission of surface plasmon polariton (SPP) modes is investigated under different refractive indices of sample medium as well as different dimensions, the best transmission rate achieved about 56.6% which is resulted by refractive index variation about 0.045 for the length 12 μm and width 80 nm of the gold layer. Also, the sensitivity, figure of merit (FOM) and quality factor (Q-factor) of MZI are examined for different geometries by utilizing the alternative method. It is realized that for the constant length, increasing the thickness of gold layer has significantly led to increased Q-factor and FOM. On the other hand, considering fixed thickness of the Au layer and three different lengths, the major outcome is that as the length of biosensor increases, the sensitivity, Q-factor as well as FOM follow an upward trend. Finally, inserting two distinct additional gold layers on top of the main gold layer, resulted in an extreme increase for the sensitivity and FOM of the plasmonic MZI biosensors with respect to the MZI biosensor without additional layer. Highlights • In this paper, we numerically investigate a nanoscale plasmonic biosensor based on Mach-Zehnder interferometry. • Considering fixed thickness of Au layer, as the length of biosensor increases, the sensitivity, Q-factor and FOM escalate. • The sensitivity and FOM of the plasmonic MZI biosensors including additional layers have extremely increased. • These outcomes are in line with experimental implementations of the MZI biosensor. [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 • This paper investigates crane scheduling problems for a new terminal system. • The new terminal system is based on multi-storey frame bridges. • Mathematical models are proposed for the two scheduling problems. • Meta-heuristics are developed to solve the models. Abstract This paper investigates crane scheduling problems for a new type of automated container terminal system, which is based on multi-storey frame bridges. For the new design concept, this paper studies how to schedule two types of cranes, i.e., quay cranes and bridge cranes that transfer containers between different storeys. The schedules of these two types of cranes impact the operation efficiency of the terminal system. Mathematical models are proposed for the two scheduling problems. Meta-heuristics are developed to solve them. Numerical experiments are conducted to validate the effectiveness of the proposed models and the efficiency of the proposed solution method. [ABSTRACT FROM AUTHOR]

As a type of uncertain differential equations, uncertain spring vibration equation is driven by Liu process. This paper proposes a concept of α -path, and shows that the solution of an uncertain spring vibration equation can be expressed by a family of solutions of second-order ordinary differential equations. This paper also proves that the inverse uncertainty distribution of solution of uncertain spring vibration equation is just the α -path of uncertain spring vibration equation, and a numerical algorithm is designed. Moreover, a formula to calculate the expected value of solution of uncertain spring vibration equation is derived. Finally, several numerical examples are provided to illustrate the efficiency of the numerical method. [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]

Abstract This paper presents three different necessary and sufficient conditions for the admissibility and robust stabilization of singular fractional order systems (FOS) with the fractional order α : 0 < α < 1 case. Two results are obtained in terms of strict linear matrix inequalities (LMIs) without equality constraint. The system uncertainties considered are norm bounded instead of interval uncertainties. The equivalence between quadratic admissibility and general quadric stability for FOS are derived. A condition is not only strict LMI condition without quality constraint but also avoid a singularity trouble caused by the superfluous solved variable. When α = 1 and E = I , the three results reduce to the conditions of stability and robust stabilization of normal integer order systems. Numerical examples are given to verify the effectiveness of the criteria. With the approaches proposed in this technical note, we can analyze and design singular fractional order systems with similar way to the normal integer order systems. Highlights • This paper presents three necessary and sufficient conditions for the admissibility and robust stabilization of singular FOS. • Two results are obtained in terms of strict LMIs. The system uncertainties considered are norm bounded uncertainties. • The strict LMI approaches have been developed to both judge admissibility and design robust stabilizing controller. • The electrical circuit on Fig. 1 with R , capacitances are the α order derivative i C (t) = C d α u C (t) dt α which is clear real-world example in fact. • It is worth noting that the criteria obtained in this technical note can be regarded as a natural extension of Lyapunov stability. [ABSTRACT FROM AUTHOR]

Multi-product pipelines usually transport several products in batches to respective delivery stations. As for a multi-product pipeline with multiple pump stations, this paper develops a continuous-time mixed-integer linear programming (MILP) model based on flowrate database to optimize its detailed scheduling. In the proposed model, various unit pump cost and flowrate constraints, which strongly depend on pump operation schemes, are introduced for the economy and safety of solved scheduling plans. Moreover, this paper considers the actual field processing constraints which vary with batch interface migration and rarely considered in previous work. And a novel method of historical flowrate database preprocessing is presented to enhance solving efficiency. Finally, through comparing with three real-world cases solved by another two available models, the proposed one performs the best in scheduling optimization as well as substantial reduction of pump cost. [ABSTRACT FROM AUTHOR]

This paper presents an optimization model of inspection and replacement planning for a refinery plant under the consideration of corrosion in terms of cost. The management of corrosion is an essential task for processes that operate over several years without a shutdown. This is because corrosion can cause severe failures by thinning the wall thickness and eventually cause pipes or equipment to burst. However, required safety measures, such as the corrosion management, involve costly inspection and replacement. Therefore, a cost-effective safety-action strategy is proposed in this paper. The developed model presents an optimal combination of steel grade, design wall thickness, inspection number, and inspection timing under a given corrosion rate to minimize the cost of design, inspection, replacement, and failure. Three case studies using sensitivity analyses are applied to three major processes in a refinery plant: a crude distillation unit, visbreaker, and hydrocracker. [ABSTRACT FROM AUTHOR]

In this paper, the time discrete higher order projection method is proposed and analyzed for the time-dependent viscoelastic flow problem. Our numerical method is based on the time iterative discrete schemes. By the projection method, the considered problem is decoupled into two linear subproblems: One is for the velocity and the other is for the pressure. Unconditional stability of the numerical schemes is established. Convergence results for the velocity and pressure are also derived. Our main results of this paper are that the convergence analysis for the velocity is weakly second order and for the pressure is weakly first order. Finally, some numerical examples are provided to confirm the performances of the developed numerical algorithms. [ABSTRACT FROM AUTHOR]

Direct bonding is based on molecular adhesion. This bonding technique consists to join two surfaces into direct contact without the use of any adhesives or additional material. This process requires clean surfaces with a nanometric roughness, sufficiently close together to initiate bonding. Mechanical characterization of this type of assembly with classical mechanical test as for instance wedge test, cleavage test or double shear test present a highly scattering on mechanical results. This paper presents the Flexible Initiation Test (FIT test), an original test designed to characterize fracture initiation in mode I, and to decrease scattering in fracture initiation load measurements, in particular for adhesive with brittle behavior. This new test has to take into account the industrial framework: to be easy to manufacture, easy to execute repeatedly and efficient to provide experimental data for numerical models (stress criteria applications for instance). The paper proceeds first with an explanation of the main initial ideas to introduce the concept of this new test. Next, a numerical analysis is proposed to validate the concept and to determine the optimal geometry of the tests. Then the experimental device is set up and the concept is validated on three different adhesives with the same substrate (a brittle cyanoacrylate adhesive, a ductile and a brittle epoxy adhesives). To conclude, the FIT test is applied on direct bonded samples (an extreme case nanometric interface and very brittle behavior) to determine the fracture initiation load and to compare scattering of measurements. [ABSTRACT FROM AUTHOR]

Generalized/extended finite element methods (GFEM/XFEM) for an interface problem are generally enriched by a distance function to the interface to handle discontinuities across the interface. Evaluations of the distance function and its gradients are needed for assembling stiffness matrices, which requires certain computational geometry algorithms. The computational complexity grows if the number of integration points is increased. Besides, the mathematical analysis on the effect of numerical integration has not been established in the field of GFEM/XFEM yet. This study designs an improved enriched function for a stable GFEM (SGFEM, a stable version of GFEM) based on the distance function, which only requires evaluating the distance function at nodes of elements that interact the interface (the gradients of distance function are not needed). The optimal convergence order (in the energy norm) of the SGFEM with such an improved enriched function is proven. In turn, we propose a perturbed variational formula, which can be integrated exactly by simple Gaussian rules designed in this paper. We prove that the SGFEM based on the improved enriched function and the perturbed variational formula (exactly integrated by the numerical integration) achieves the optimal convergence order for the interface problem. Namely, we develop a numerical integration rule for the SGFEM such that the optimal convergence order of SGFEM is maintained for the interface problem. The theoretical achievements are verified by numerical experiments. [ABSTRACT FROM AUTHOR]

Tumor growth models have proved as an important tool to produce an engineering background for cancer therapy either by designing therapeutic procedures combined with control engineering or by using the models for simulations and evaluation of treatment procedures. Mathematical modeling has been critical for the description of tumor growth, which is a highly complex process, as a finely chiseled tumor growth model always outlines the measurements and the physiological processes of the tumors. Therefore, a mathematical model involving partial differential equations for the growth of tumor have been studied, modified and developed in this paper. It is based on the deterministic model of an avascular tumor growth which is framed in a system of nonlinear coupled PDEs, describing the proliferating, quiescent, necrotic, and surrounding cells densities, accompanied by a supply of the nutrients. These equations are explained numerically by the Finite Difference Method. Furthermore, the simulations are carried out by introducing the Gompertz growth rate function for mitosis rate function g(c) of proliferating cells in the model. The discretization forms a system of coupled nonlinear difference equations which are solved at each iteration. The algorithm is implemented sequentially in MATLAB 2018a and numerical results suggest that the employed model is an authentic tool for analyzing the dynamics of tumor. [ABSTRACT FROM AUTHOR]

This paper presents computer-based design and analysis of control systems for centrifugal compressors when the operating fluid is supercritical CO 2 . It reports a non-linear dynamic model including a main forward compression line and two different configurations for the recycle antisurge line. Disturbance scenarios are proposed for testing the configurations and performance indicators are suggested to evaluate control performance and power consumption of the compression system. The paper demonstrates that compared to the hot recycle, the process configuration including a cold gas recycle has better overall stability, but higher power consumption and lower values for the control performance indicators. Based on the previous considerations, the paper gives suggestions regarding the choice of the recycle configuration. Moreover it compares subcritical and supercritical compression during surge prevention and highlights the importance of the selection of the gas recycle configuration when full recycle is needed. [ABSTRACT FROM AUTHOR]

In this paper, a new interference-tolerant fast convergence zeroing neural network (ITFCZNN) using a novel activation function (NAF) for solving dynamic matrix inversion (DMI) is presented and investigated. Compared with the original zeroing neural network (OZNN) models, the proposed ITFCZNN not only has the ability to converge to 0 within a fixed-time, but also resist different types of interference and noises in solving DMI problems. Besides, detailed mathematical analysis of convergence and robustness of the ITFCZNN are provided. Comparative numerical simulation verifications of the new ITFCZNN and the OZNN activated by other commonly used activation functions (AF) are also provided to demonstrate the better robustness, effectiveness and fixed-time convergence of the ITFCZNN. In addition, a mobile manipulator path tracking application example is given to verify the applicability and feasibility of the ITFCZNN with interference and noises. Both of the theoretical analysis and numerical simulation results verify the effectiveness and robustness of the ITFCZNN model. [ABSTRACT FROM AUTHOR]

Non-standard fuzzy sets play a significant role in uncertainty modeling. In addition to membership and non-membership degree, how to handle the hesitant degree is the key issue in the uncertain information process. In this paper, we model the Pythagorean fuzzy set (PFS) under the belief structure and measure its uncertainty based on fractal-based belief (FB) entropy. A novel fuzzy entropy for PFS called belief structure-based Pythagorean fuzzy (BSPF) entropy is proposed, whose effectiveness and advantages are proven based on mathematical analysis and numerical examples. A comparative analysis between BSPF entropy and other methods shows that BSPF entropy can obtain more reasonable results. Besides, a BSPF entropy-based multi-criteria decision-making (MCDM) method and a classification method are designed to solve practical problems. The experimental results demonstrate the effectiveness of these two proposed methods in solving real-world problems of decision-making and classification. • A novel entropy measure for PFSs was defined and proposed. • Comparisons made with other state-of-art approaches. • The TOPSIS method with the presented entropy measure was applied to fault diagnosis. • Medical diagnoses were more reasonable by reassigning the hesitation degree. • Performance of the classification improved with the presented entropy measure. [ABSTRACT FROM AUTHOR]

In this paper we study and obtain the existence of a positive almost periodic solution to the nonlinear differential equation with delays that describes the so-called hematopoiesis model. The main tool utilized to establish our existence result consists of the fixed-point theorem in a cone. Two examples are given at the end of the paper to illustrate our main result. [ABSTRACT FROM AUTHOR]

This paper deals with the attitude determination algorithm for the satellite with an attitude measurement unit that is comprised of one gyroscope and two star trackers installed perpendicularly. Since the data updating rate of star trackers is typically lower than that of the gyro and filter, appropriate compensation is made for star sensors, but this results in more difficulties of determining the performed noise level. A fuzzy adaptive tuning method is used to help tuning, and with modified Rodrigues parameters and rotation vector to represent attitude error, a fuzzy adaptive unscented Kalman filter with minimal skew sampling method is realized, which works as a sub-system and estimates sub-optimal attitude states and gyro bias. Two such sub-systems are federated into the framework of Covariance Intersection algorithm to achieve data fusion for an optimal attitude and gyro bias estimation in system level. Simulation is performed to verify the attitude determination algorithm presented in this paper. [ABSTRACT FROM AUTHOR]

This paper aims at desensitizing the optimal trajectory for landing on the small bodies with reduced landing error in the presence of initial state error, parameters uncertainties of the target body (the gravity and the body's rotation rate) and thrust error (the error in thrust magnitude and direction). The motion of the lander is expressed in the body-fixed coordinate frame, and the thruster is considered to be variable. Instead of directly optimizing the landing trajectory, this paper propagates the linear covariance of the stochastic landing dynamics equations, and minimizes the fuel consumption as well as the covariance. Firstly, the stochastic state equations including the effects of these uncertainties are constructed. The rotation rate is augmented as the new state of the state equations, and the uncertainties in gravity and thruster are modeled as the stochastic process noise acting on the lander. Then, the closed-loop linear covariance is derived and optimized with the fuel consumption performance index as a penalty factor. Finally, several sets of simulations are performed in the scenarios of Eros 433 and Vesta. The open-loop trajectory is firstly performed in the scenario of Eros 433 and the result shows that these uncertainties contribute greatly to the trajectory dispersions. The 3 σ trajectory dispersions for tracking the optimal and desensitized optimal trajectory show that the desensitized approach reduces the landing error effectively. And the statistic landing velocities show that the desensitized approach meets the requirement of soft and stable landing on small bodies. To especially discuss the fuel consumption of optimal and desensitized optimal trajectory, the simulation in the scenario of Vesta is performed. The results show that the desensitized optimal approach takes only about 1.01 kg more fuel for the lander of 800 kg size. And the landing error of desensitized trajectory is reduced significantly compared to that of the optimal trajectory. The total simulations in the scenario of Eros 433 and Vesta indicate that the desensitized approach is fuel-saving, and can reduce the landing error effectively for landing on small bodies. [ABSTRACT FROM AUTHOR]

Rosenbrock–Wanner methods usually have order reduction if they are applied to stiff ordinary differential or differential algebraic equations. Therefore, in several papers further order conditions are derived to reduce this effect. In Rang (2014) the example of Prothero and Robinson (1974) is analysed to find further order conditions. In this paper we consider traditional ROW methods such as ROS3P (Lang and Verwer, 2001), ROS3Pw (Rang and Angermann, 2005), ROS3PL (Lang and Teleaga, 2008), and RODASP (Steinebach, 1995) and improve these methods such that these further order conditions are satisfied. Numerical examples show the advantages of the new methods. [ABSTRACT FROM AUTHOR]

It is well-known that analysis of incomplete Cholesky and LU decompositions with a general dropping is very difficult and of limited applicability, see, for example, the results on modified decompositions (Dupont et al., 1968; Gustafsson, 1978; Bern et al., 2006) and later results based on similar concepts. This is true not only for the dropping based on magnitude of entries but it also applies to algorithms that use a prescribed sparsity pattern. This paper deals with dropping strategies for a class of AINV-type incomplete decompositions (Benzi et al., 1996) that are based on the generalized Gram–Schmidt process. Its behavior in finite precision arithmetic has been discussed in Rozložník et al. (2012). This analysis enables better understanding of the incomplete process, and the main goal of the paper is to propose a new adaptive dropping strategy and to illustrate its efficiency for problems in structural mechanics. In addition, we add a brief comparison with another approximate inverse preconditioning strategy that is based on different principles and used in engineering applications. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with linear neutral systems with unstable difference operators. All the unstable characteristic roots of the linear neutral systems are located in a bounded half circular region. Then, based on the argument principle, a computable stability criterion is derived which is necessary and sufficient for asymptotic stability of the neutral systems. Furthermore, the number of the unstable characteristic roots is given. The main results of the present paper extend those in literature. Numerical experiments are provided to illustrate the main results. [Copyright &y& Elsevier]

A graph H has the hourglass property if in every induced hourglass S (the unique simple graph with the degree sequence (4, 2, 2, 2, 2)), there are two non-adjacent vertices which have a common neighbor in H-(S). Let G be a claw-free simple graph and k a positive integer. In this paper, we prove that if either G is hourglass-free or G has the hourglass property and δ(G) ≥ 4, then G has a 2-factor with at most k components if and only if it has an even factor with at most k components. We provide some of its applications: combining the result (the case when k=1) with Jaeger (1979) and Chen et al. (2006), we obtain that every 4-edge-connected claw-free graph with the hourglass property is hamiltonian and that every essentially 4-edge-connected claw-free hourglass-free graph of minimum degree at least three is hamiltonian, thereby generalizing the main result in Kaiser et al. (2005) and the result in Broersma et al. (2001) respectively in which the conditions on the vertex-connectivity are replaced by the condition of (essential) 4-edge-connectivity. Combining our result with Catlin and Lai (1990), Lai et al. (2010) and Paulraja (1987), we also obtain several other results on the existence of a hamiltonian cycle in claw-free graphs in this paper. [ABSTRACT FROM AUTHOR]

The paper presents a new semi-analytic numerical method for solving multi-point boundary value problems with linear and nonlinear equations of the second and higher orders. The method is based on the use of the particular solutions of the linearized equation. Presented in the paper examples include the solution of equations with differential operators of the second, third and fourth orders. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we obtain some Lyapunov-type inequalities for a class of higher-order linear differential equations. The results of this paper generalize and improve some earlier results on this topic. [Copyright &y& Elsevier]

Abstract: This paper elaborates a global error estimation and control mechanism in explicit two-step peer methods. These recently designed methods exhibit their high efficiency even in comparison to the best explicit Runge–Kutta pairs. More precisely, we form here triples of the so-called superconvergent explicit peer schemes and show that they are cheap and able to achieve preassigned accuracy conditions in automatic mode. For comparison, we present also numerical data derived by built-in explicit Matlab ODE solvers implemented with only local error control. Especially, we point out that a scaled global error is computed and regulated in this paper in contrast to the earlier published results where the absolute values of the global error have been utilized. [Copyright &y& Elsevier]

Abstract: In this paper, we apply a complete pivoting strategy to compute the left-looking version of AINV preconditioner for linear systems. As the preprocessing, the MultiLevel Nested Dissection reordering has also been applied. We have used this preconditioner as the right preconditioner for several linear systems where the coefficient matrices have been downloaded from the University of Florida Sparse Matrix Collection. Numerical experiments presented in this paper indicate the effectiveness of such a complete pivoting on the quality of left-looking version of AINV preconditioner. [Copyright &y& Elsevier]

Abstract: One of the most interesting new developments in hypergraph colourings in the last few years has been Voloshin’s notion of colourings of mixed hypergraphs. In this paper we shall study a specific instance of Voloshin’s idea: a non-monochromatic non-rainbow (NMNR) colouring of a hypergraph is a colouring of its vertices such that every edge has at least two vertices coloured with different colours (non-monochromatic) and no edge has all of its vertices coloured with distinct colours (non-rainbow). Perhaps the most intriguing phenomenon of such colourings is that a hypergraph can have gaps in its NMNR spectrum, that is, for some , the hypergraph is NMNR colourable with and with colours but not with colours. Several beautiful examples have been constructed of NMNR colourings of hypergraphs exhibiting phenomena not seen in classical colourings. Many of these examples are either ad hoc or else are based on designs. The latter are difficult to construct and they generally give uniform -hypergraphs only for low values of , generally . In this paper we shall study the NMNR colourings of a type of -uniform hypergraph which we call -hypergraphs. The attractive feature of these -hypergraphs is that they are easy to define, even for large , and that, by suitable modifications of their parameters, they can give families of hypergraphs which are guaranteed to have NMNR spectra with gaps or NMNR spectra without gaps. These -hypergraphs also team up very well with the notion of colour-bounded hypergraphs recently introduced by Bujtás and Tuza to give further control on the appearance of gaps and perhaps explain better the existence of gaps in the colouring of mixed hypergraphs. [Copyright &y& Elsevier]

Abstract: The goal of this paper is to investigate a backward parabolic equation with time-dependent coefficient by the truncation method (TM). The key point to our paper is that we give an a posteriori choice of regularization parameter for the TM, with which the convergence estimates between the exact solution and the regularized approximation are obtained. Numerical implementation sheds light on the accuracy and efficiency of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper considers the topological classification of non-autonomous dynamic equations on time scales. In this paper we show, by a counterexample, that the trivial solutions of two topologically conjugated systems may not have the same uniform stability. This is contrary to the expectation that two topologically conjugated systems should have the same topological structure and asymptotic behaviors. To counter this mismatch in expectation, we propose a new definition of strong topological conjugacy that guarantees the same topological structure, and in particular the same uniform stability, for the corresponding solutions of two strongly topologically conjugated systems. Based on the new definition, a new version of the generalized Hartman–Grobman theorem is developed. We also include some examples to illustrate the feasibility and effectiveness of the new generalized Hartman–Grobman theorem. [Copyright &y& Elsevier]

Abstract: This paper discusses the dynamics of particles orbiting planetary rings under a general central potential. Starting with the mathematical description of the dynamical system, we analyze the motion of a particle with infinitesimal mass as attracted by a central body surrounded by a homogeneous circular annular disk. Throughout the paper we carry out an analytic search of the most relevant equilibria solutions and, based on that, we investigate numerically the stability matrix of the system to find stability inequalities. In this way, we describe the in-plane and out-of-plane motion by means of the numerical continuation of a wide number of uni-parametric families of planar and spatial periodic orbits. We present a description of the main families of periodic orbits encountered, their bifurcations and linear stability. With the aim of reproducing a more realistic scenario, we analyse different mass proportions between the annulus and the central body, we consider an oblate planet and we also include a composition of rings in the dynamical model. [Copyright &y& Elsevier]

Abstract: In this study, a three dimensional transversely isotropic piezoelectric layered half-space subjected to concentrated loading and electric charge was analyzed. This paper provides an effective analytical methodology to obtain the explicit full-field solutions for this problem. Due to the dissimilar structures of the solutions, the applied loadings are separated into axis-symmetric loadings and non-symmetric loadings. By using the double Fourier transformation technique in conjunction with series expansion, the explicit closed-from solutions for displacements, stresses, and the electric field in the layered half-space are obtained. The analytical solutions are valid for loadings applied either in the interior or at the surface of the structure. It can be seen that the complete solutions obtained by the method used in this study comprise only the fundamental solutions of an infinite space with a concentrated loading. One of the fundamental solutions is the Green's function of an infinite space and the others are solutions induced to satisfy the boundary and interface conditions. The mathematical meaning of the method used in the study is in fact the image method or Mindlin's superposition method. Instead of finding image singularities manually, the intensity and locations of the image singularities are determined automatically from the mathematical technique used in this paper. Taking PZT materials as an example, the numerical computation for the full-field distributions of the displacement and electric field in the layered half-space medium subjected to a point force and a point charge was discussed. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the new notion which is more general than the previous works on the weakly isotone mappings in the case of single valued mappings and multivalued mappings in an ordered Banach space. We also extend some common fixed point theorems of Dhage et al. [4] and give some applications of the main results. Furthermore, at the end of this paper, we give an open problem for further investigation. [Copyright &y& Elsevier]

Abstract: The paper provides a simple analytical tool which can be used to give estimates of the mean value and the standard deviation of the Stokes drift for sea states. This is achieved by providing bivariate distributions of significant wave height with surface Stokes drift as well as with volume Stokes transport. These Stokes drift parameters are defined in terms of significant wave height and characteristic wave periods. Also bivariate distributions of spectral peak period and these two Stokes drift parameters are provided. The paper presents statistical aspects of the Stokes drift parameters, such as the conditional expected values and the conditional variances for given significant wave height, as well as examples of results corresponding to typical field conditions. The present analytical results can be used to make assessment of Stokes drift based on e.g. global wave statistics. [Copyright &y& Elsevier]

Abstract: There is an abundant literature on inequalities for the (Euler’s) Gamma function Γ and its various related functions. Yet, only very recently, several authors began to study inequalities for the (Barnes’) double Gamma function . Here, in this paper, we aim at presenting several two-sided inequalities for the multiple Gamma functions . In our investigation of these two-sided inequalities for the multiple Gamma functions , we employ and extend a method based upon Taylor’s formula and express as series involving the Zeta functions. We also give a more convenient explicit form of the multiple Gamma functions being the set of positive integers. The main two-sided inequalities for the multiple Gamma functions (which we have presented in this paper) are presumably new and their derivations provide a fruitful insight into the corresponding problem for the multiple Gamma functions when . [Copyright &y& Elsevier]

Abstract: The objective of this paper is to obtain some important properties about convex fuzzy mappings based on a linear ordering of fuzzy numbers proposed by Goetschel and Voxman. Firstly, a new kind of fuzzy mapping, termed semistrictly convex fuzzy mapping, is defined through this linear ordering. Note that semistrict convexity does not imply convexity. And the interrelationships among convex, strictly convex and semistrictly convex mappings are established under certain conditions. Furthermore, this paper obtains several characterizations for the above three classes of fuzzy mappings under the conditions of upper or lower semicontinuity. Finally, some further characteristic properties for semistrictly convex fuzzy mappings are derived. [Copyright &y& Elsevier]

Abstract: Two similar stability notions are considered; one is the long established notion of convergent systems, the other is the younger notion of incremental stability. Both notions require that any two solutions of a system converge to each other. Yet these stability concepts are different, in the sense that none implies the other, as is shown in this paper using two examples. It is shown under what additional assumptions one property indeed implies the other. Furthermore, this paper contains necessary and sufficient characterizations of both properties in terms of Lyapunov functions. [Copyright &y& Elsevier]

Abstract: This paper deals with the problem of observer design for a class of implicit nonlinear systems of index one. To solve this problem, an implicit observer which is given by an implicit system is usually used. The implementation of this kind of observer requires an optimization algorithm to solve at each time the algebraic constraints. Alternatively, an explicit observer which is described by an ordinary differential equation can be used. The advantage of this approach is that no optimization algorithm is required. Moreover the observer initialization may be done outside the constraints. In this paper it is shown that, under some conditions, the existence of an implicit observer implies the existence of an explicit one. Then, an explicit observer is given for implicit state affine systems whose dynamic involves an additional nonlinear term depending on the input, the output and the implicit variable. [Copyright &y& Elsevier]

Abstract: An identity by Chaundy and Bullard writes () as a sum of two truncated binomial series. In a paper which appeared in 2008 in Indag. Math. the authors surveyed many aspects of this identity. In the present paper we discuss much earlier occurrences of this identity in works by Hering (1868), de Moivre (1738) and de Montmort (1713). A relationship with Krawtchouk polynomials in work by Greville (1966) is also discussed. [Copyright &y& Elsevier]

Abstract: This paper focuses on two major issues in cellular manufacturing, namely manpower allocation and cell loading. Although significant work has been done in both of these fields, research to minimize the Total Tardiness (TT) within a multi-cell environment has been limited. The methodology adopted in this paper is a two-step one. First, manpower allocation for operations within a cell is determined using mathematical models. This step also includes variations of the mathematical model for sharing of operators between operations and sharing of operators with restrictions. The models with little or no restrictions have found to yield a higher production rate than the model with no operator sharing allowed. The next step involves a mathematical model for cell loading. The performance measure examined in this phase is the total tardiness subject to total Crew Size restriction. The total tardiness is reduced as the total crew size increases. However, it was also found that selection of alternative cell configurations affect the results as well total crew size. [Copyright &y& Elsevier]