Search

In this paper, we develop and analyze a mathematical model for spreading malaria, including treatment with transmission‐blocking drugs (TBDs). The paper's main aim is to demonstrate the impact the chosen model for demographic growth has on the disease's transmission and the effect of its treatment with TBDs. We calculate the model's control reproduction number and equilibria and perform a global stability analysis of the disease‐free equilibrium point. The mathematical analysis reveals that, depending on the model's demography, the model can exhibit forward, backward, and even some unconventional types of bifurcation, where disease elimination can occur for both small and large values of the reproduction number. We also conduct a numerical analysis to explore the short‐time behavior of the model. A key finding is that for one type of demographic growth, the population experienced a significantly higher disease burden than the others, and when exposed to high levels of treatment with TBDs, only this population succeeded in effectively eliminating the disease within a reasonable timeframe. [ABSTRACT FROM AUTHOR]

Summary: This survey paper studies deterministic control systems that integrate three of the most active research areas during the last years: (1) online learning control systems, (2) distributed control of networked multiagent systems, and (3) hybrid dynamical systems (HDSs). The interest for these types of systems has been motivated mainly by two reasons: First, the development of cheap massive computational power and advanced communication technologies, which allows to carry out large computations in complex networked systems, and second, the recent development of a comprehensive theory for HDSs that allows to integrate continuous‐time dynamical systems and discrete‐time dynamical systems in a unified manner, thus providing a unifying modeling language for complex learning‐based control systems. In this paper, we aim to give a comprehensive survey of the current state of the art in the area of online learning control in multiagent systems, presenting an overview of the different types of problems that can be addressed, as well as the most representative control architectures found in the literature. These control architectures are modeled as HDSs, which include as special subsets continuous‐time dynamical systems and discrete‐time dynamical systems. We highlight the different advantages and limitations of the existing results as well as some interesting potential future directions and open problems. [ABSTRACT FROM AUTHOR]

This paper proposes a new semi‐parametric identification and estimation approach to multinomial choice models in a panel data setting with individual fixed effects. Our approach is based on cyclic monotonicity, which is a defining convex‐analytic feature of the random utility framework underlying multinomial choice models. From the cyclic monotonicity property, we derive identifying inequalities without requiring any shape restrictions for the distribution of the random utility shocks. These inequalities point identify model parameters under straightforward assumptions on the covariates. We propose a consistent estimator based on these inequalities. [ABSTRACT FROM AUTHOR]

The inflammatory phase is an important event in the skin wound healing process. The deposition of granulation tissue in the wound bed and the rebuilding of the vascular network occur as inflammation diminishes. An angiogenic component in the formation of granulation tissue is the secretion of vascular endothelial growth factor, which assists in the chemotaxis, proliferation, and replication of fibroblasts. In this paper, we develop a mathematical model of skin wound healing angiogenic factors based on inflammatory cells (macrophages and neutrophils) and mediators (interleukin 6 and interleukin 10). We highlight the importance of this process in vascular endothelial growth factor release and in the formation of new capillary tips. We used a mathematical model of partial differential equations based on the reaction‐diffusion‐advection equations. In order to calibrate the parameters, we considered an in vivo model composed by four treatments: hydroalcoholic extract and oil‐resin of Copaifera langsdorffii at 10% concentration, collagenase, and Lanette cream. Using the laboratory data for the wound edge, our mathematical model estimated the values of vascular endothelial growth factor concentration, and tips density in the center of the wound with a maximum error of 2.9%, and predicted healing time required for each treatment. The region of viability for the parameters, in the proposed model, was found through numerical simulations from the Interleukin 6 and 10 dysregulation and we obtained that, among the parameters analyzed, the greatest influencer in the dynamics of the system is the one, which represents the production of Interleukin 10 during phagocytosis. [ABSTRACT FROM AUTHOR]

In this paper, output regulation for linear delta operator systems subject to actuator saturation is investigated by state feedback. The relation between the regulatable regions and the null controllable region is described in this paper. A set of all initial conditions of a plant and a exosystem is called asymptotically regulatable region for which output regulation is possible. An asymptotically regulatable region is characterized according to a null controllable region of an anti-stable subsystem of the plant. Feedback laws are constructed to solve the problems on output regulation. A numerical example is given to illustrate the effectiveness and potential for the developed techniques. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the problem of opportunistic spectrum sharing for the next generation of wireless systems empowered by the cloud radio access network (C‐RAN) is studied. More precisely, low‐priority users employ cooperative spectrum sensing to detect a vacant portion of the spectrum that is not currently used by high‐priority users. The authors' aim is to maximize the overall throughput of the low‐priority users while guaranteeing the quality of service of the high‐priority users. This objective is attained by optimally adjusting spectrum sensing time, with respect to target probabilities of detection and false alarm, as well as dynamically allocating C‐RAN resources, that is, powers, sub‐carriers, remote radio heads, and base‐band units. To solve this problem, which is non‐convex and NP‐hard, a low‐complex iterative solution is proposed. Numerical results demonstrate the necessity of sensing time adjustment as well as effectiveness of the proposed solution. [ABSTRACT FROM AUTHOR]

This paper studies the partial consensus problem for identical feedforward dynamic systems with input saturations. We construct two consensus protocols using the partial-state information and full-state information, respectively. Applying a change of coordinates, feedforward system is transformed into the block diagonal form. Then, by utilizing the bounded real lemma and small gain theorem, we solve the partial consensus problem, and the existence of each protocol is derived. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new model reference control architecture to effectively suppress system uncertainties and achieve a guaranteed transient and steady-state system performance. Unlike traditional robust control frameworks, only a parameterization of the system uncertainty given by unknown weights with known conservative bounds is needed to stabilize uncertain dynamical systems with predictable system performance. In addition, the proposed architecture's performance is not dependent on the level of conservatism of the bounds of system uncertainty. Following the same train of thought as adaptive controllers that modify a given reference system to improve system performance, the proposed method is inspired by a recently developed command governor theory that minimizes the effect of system uncertainty by augmenting the input signal of the uncertain dynamical and reference systems. Specifically, a dynamical system, called a command governor, is designed such that its output is used to modify the input of both the controlled uncertain dynamical and reference systems. It is theoretically shown that if the command governor design parameter is judiciously selected, then the controlled system approximates the given original, unmodified reference system. The proposed approach is advantageous over model reference adaptive control approaches because linearity of the uncertain dynamical system is preserved through linear control laws, and hence, the closed-loop performance is predictable for different command spectrums. Additionally, it is shown that the architecture can be modified for robustness improvements with respect to high frequency content due to, for example, measurement noise. Modifications can also be made in order to accommodate actuator dynamics and retain closed-loop stability and predictable performance. The main contribution of this paper is the rigorous analysis of the stability and performance of a system utilizing the command governor framework. A numerical example is provided to illustrate the effectiveness of the proposed architecture. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Dynamic two-phase interaction of soil can be modelled by a displacement-based, two-phase formulation. The finite element method together with a semi-implicit Euler-Cromer time-stepping scheme renders a discrete equation that can be solved by recursion. By experience, it is found that the CFL stability condition for undrained wave propagation is not sufficient for the considered two-phase formulation to be numerically stable at low values of permeability. Because the stability analysis of the two-phase formulation is onerous, an analysis is performed on a simplified two-phase formulation that is derived by assuming an incompressible pore fluid. The deformation of saturated porous media is now captured in a single, second-order partial differential equation, where the energy dissipation associated with the flow of the fluid relative to the soil skeleton is represented by a damping term. The paper focuses on the different options to discretize the damping term and its effect on the stability criterion. Based on the eigenvalue analyses of a single element, it is observed that in addition to the CFL stability condition, the influence of the permeability must be included. This paper introduces a permeability-dependent stability criterion. The findings are illustrated and validated with an example for the dynamic response of a sand deposit. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Threshold noise reduction methods of vibration signals have been widely researched and used. However, these methods are less efficient in such situation, including requiring a time-consuming and subjective to manual editing because different degree of noise signal requires selecting different characterization for filtering. In this paper, an efficient denoising method based on PDE for mechanical vibration signals time-frequency distribution is investigated, in which, a one-dimensional vibration signal is transformed into 2D time-frequency domain by using Gabor transform. This enables (i) simultaneously utilize both time and frequency characteristic for effectively multiple dimension signal denosing and (ii) isotropic and anisotropic characteristics to be imposed by employing PDE, which explicitly fit with the local structure of time-frequency signal. This paper analyzes the basic methods of isotropic and anisotropic diffusion filtering, investigates the anisotropic diffusion method based on local feature structure of 2D information, and conducts a set of comparative tests. Experiments show that this proposed method has a better performance of denoising than that of thresholding. At the same time, it is more handy than that of other methods, such as independent component analysis. Finally, problems and ways of improving the PDE-based filter method are analyzed in this paper. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The main motivation of the TP model transformation is that modern identification and control analysis, along with design methodologies, are based on various kinds of different representations that have different benefits and drawbacks in terms of identification and modeling effort and structure, however, the link between these representations is in many cases difficult to establish, especially if the model components are not given by closed formulae but rather by various soft-computing-based or black box models. This paper shows that the TP model transformation can serve as a gateway between different representations by bridging to a widely adopted polytopic representation. Further, it is capable of readily manipulating the resulting polytopic representation for further design requirements, which in many cases has a strong effect on the resulting control performance and the conservativeness of the solution. The paper discusses how the TP model transformation can be used as a final step of modeling and, at the same time, as a preprocessing step in polytopic model based design approaches. The paper introduces the generalized TP model transformation, which is a tractable, non-heuristic numerical tool that can be executed on sets of functions. Different manipulation techniques are investigated to show the benefits of the generalized TP model transformation. Finally, a stability verification technique is proposed for cases where system components are available in different representations. [ABSTRACT FROM AUTHOR]

Summary: In this paper, optimal control for a novel nonlinear mathematical model of tumor under immune suppression is presented. The proposed model is governed by a system of fractional differential equations, where the fractional derivative is defined in the Caputo sense. Modified parameters are introduced to account for the fractional order. Necessary and sufficient conditions that guarantee the existence and the uniqueness of the solution of the control problem are given. Two control variables are proposed to minimize the cost of interventions. Two simple numerical methods are used to study the nonlinear fractional optimal control problem. The methods are the generalized Euler method and the nonstandard generalized Euler method. The stability analysis and the truncation error of the nonstandard generalized Euler method are given. Comparative studies are implemented. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we develop new governing equations for thermo‐gradient‐dependent theory of plasticity. They include the coupled effects of thermal elastic‐plastic theory, including balance and constitutive equations. To demonstrate the salient feature of the gradient‐dependent model of plasticity, particular attention is addressed to isotropic hardening with second sound effects to eliminate the paradox of infinite speed of thermal signals. The resulting system of partial differential equations formally describes the coupled thermomechanical behavior of the gradient‐dependent elasto‐plastic system. Then, we develop an appropriate state‐space form and, by using the semigroup theory, we prove the well‐posedness and the exponential stability of the thermo‐gradient‐dependent elasto‐plastic one‐dimensional problem. Finally, we perform numerical simulations to validate the proposed model and to show its capability. [ABSTRACT FROM AUTHOR]

In this paper, we consider the almost periodic dynamics of an impulsive multispecies Lotka-Volterra competition system with time delays on time scales. By establishing some comparison theorems of dynamic equations with impulses and delays on time scales, a permanence result for the model is obtained. Furthermore, based on the permanence result, by studying the Lyapunov stability theory of impulsive dynamic equations on time scales, we establish the existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results, and our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new even if for both the case of the time scale [ABSTRACT FROM AUTHOR]

In this paper, three conservative finite volume element schemes are proposed and compared for the modif ied Korteweg-de Vries equation, especially with regard to their accuracy and conservative properties. The schemes are constructed basing on the discrete variational derivative method and the finite volume element method to inherit the properties of the original equation. The theoretical analysis show that three schemes are conservative under suitable boundary conditions as well as unconditionally linear stability. Numerical experiments are given to confirm the theoretical results and the capacity of the proposed methods for capturing the solitary wave phenomena. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the issue of stability of multi-group coupled systems on networks with multi-diffusion (MCSNMs) is mainly analyzed. Utilizing graph theory, a novel and practical method of constructing a proper Lyapunov function for the MCSNMs is presented. Furthermore, based on the graph-theoretic approach and the proposed Lyapunov function, sufficient criteria, in the term of Lyapunov function and coefficients of the system, respectively, are derived to ensure the stability of the MCSNMs. Apart from accessibility to checking, the proposed results can generalize the corresponding results published in a previous time. Finally, the effectiveness and feasibility of the obtained results are demonstrated by a numerical example. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we investigate with a time fractional‐order derivative in a three‐species predator‐prey model with the presence of prey social behavior. A new approximation for predator‐prey interaction in the presence of prey social behavior has been considered. For the model analysis, the study has been divided into two principal parts. First of all, we study the local stability of the equilibria and the existence of Hopf bifurcation. Then, for the numerical analysis, the Caputo fractional derivative operator is utilized to approximate the numerical solution of the model. An excellent agreement is seen between the numerical results and the theoretical predictions. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of static anti-windup design for uncertain continuous-time Markovian jump systems with partially unknown transition rates in the face of actuator saturation. The underlying system is subject to time-varying and norm-bounded parameter uncertainties in both the state and input matrices. It is assumed that a set of stabilizing dynamic output-feedback controllers have been designed for the system in the absence of control saturation. The objective is to design anti-windup compensation gains for the given controllers such that the system can still be stabilized, irrespective of whether actuator saturation appears or not. To obtain a maximum estimation of the domain of attraction of the resulting closed-loop system, a convex optimization problem in the linear matrix inequality framework is formulated. Furthermore, the results are extended to the cases of the systems with completely known transition rates and with completely unknown transition rates. Finally, the usefulness of the developed method is demonstrated through simulation examples. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we present the modeling and local equilibrium controllability analysis of a spherical robot. The robot consists of a spherical shell that is internally actuated by a pendulum mechanism. The rolling motion of the sphere manifests itself as a nonholonomic constraint in the modeling. We derive the dynamic model of the system using Lagrangian reduction and the variational principle. We first compute the Lagrangian and identify the symmetry with respect to a group action. The system Lagrangian and the rolling constraint are invariant with respect to the group isotropy and hence permit a reduced dynamic formulation termed as the nonholonomic 'Euler-Poincaré' equation with advected dynamics. Using Lie brackets and symmetric products of the potential and control vector fields, local configuration accessibility and local (fiber) equilibrium controllability are presented. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this article, we employ the complex method to obtain all meromorphic exact solutions of complex Klein-Gordon (KG) equation, modified Korteweg-de Vries (mKdV) equation, and the generalized Boussinesq (gB) equation at first, then find all exact solutions of the Equations KG, mKdV, and gB. The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic solutions are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutions w2r,2(z) and simply periodic solutions w1s,2(z),w2s,1(z) in these equations such that they are not only new but also not degenerated successively by the elliptic function solutions. We have also given some computer simulations to illustrate our main results. [ABSTRACT FROM AUTHOR]

This paper is concerned with a periodic two-component μ-Hunter-Saxton system. We prove that the solution map of the Cauchy problem of the μ-Hunter-Saxton system is not uniformly continuous in Hs.S/, s > 5=2. [ABSTRACT FROM AUTHOR]

This paper examines some of the recent literature on the estimation of production functions. We focus on techniques suggested in two recent papers, Olley and Pakes (1996) and Levinsohn and Petrin (2003). While there are some solid and intuitive identification ideas in these papers, we argue that the techniques can suffer from functional dependence problems. We suggest an alternative approach that is based on the ideas in these papers, but does not suffer from the functional dependence problems and produces consistent estimates under alternative data generating processes for which the original procedures do not. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new Lyapunov-type inequalities for a class of even-order linear differential equations, the results are new and generalize and improve some early results in this field. [ABSTRACT FROM AUTHOR]

This paper is concerned with a class of fourth-order nonlinear difference equations. By using the critical point theory, we establish various sets of sufficient conditions of the nonexistence and existence of solutions for Dirichlet boundary value problems and give some new results. Our results successfully complement the existing ones. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, the cobweb model is reformulated in terms of fractional‐order derivatives. In particular, we describe linear cobweb models in continuous time by using conformable fractional‐order derivatives. Then, the general solutions as well as stability criteria for the proposed models are given. Moreover, the developed models are illustrated with some examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider sequences of polynomials that satisfy certain recurrences. Our interest is motivated by the fact that polynomials satisfying such recurrences frequently appear as generating polynomials of integer valued random variables that are of interest in discrete mathematics. In particular, we will use our approach to show that the number of diagonal boxes in symmetric tree‐like tableaux is asymptotically normal. This extends earlier results of Aval, Boussicault and Nadeau, who found the asymptotics of the expected number of diagonal boxes. Through our discussion, we establish a general framework to approach such recurrences and prompt a generalization of the probabilistic consequences of them. [ABSTRACT FROM AUTHOR]

Let S=K[x1,...,xn] denote the polynomial ring in n variables over a field K with each degxi=1 and let I⊂S be a homogeneous ideal of S with dimS/I=d. The Hilbert series of S/I is of the form hS/I(λ)/(1−λ)d, where hS/I(λ)=h0+h1λ+h2λ2+⋯+hsλs with hs≠0 is the h‐polynomial of S/I. It is known that, when S/I is Cohen–Macaulay, one has reg(S/I)=deghS/I(λ), where reg(S/I) is the (Castelnuovo–Mumford) regularity of S/I. In the present paper, given arbitrary integers r and s with r≥1 and s≥1, a monomial ideal I of S=K[x1,...,xn] with n≫0 for which reg(S/I)=r and deghS/I(λ)=s will be constructed. Furthermore, we give a class of edge ideals I⊂S of Cameron–Walker graphs with reg(S/I)=deghS/I(λ) for which S/I is not Cohen–Macaulay. [ABSTRACT FROM AUTHOR]

ABSTRACT Many studies demonstrate that inference for the parameters arising in portfolio optimization often fails. The recent literature shows that this phenomenon is mainly due to a high-dimensional asset universe. Typically, such a universe refers to the asymptotics that the sample size n + 1 and the sample dimension d both go to infinity while d ∕ n → c ∈ (0,1). In this paper, we analyze the estimators for the excess returns' mean and variance, the weights and the Sharpe ratio of the global minimum variance portfolio under these asymptotics concerning consistency and asymptotic distribution. Problems for stating hypotheses in high dimension are also discussed. The applicability of the results is demonstrated by an empirical study. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: This paper makes a review of current raw material criticality assessment methodologies and proposes a new approach based on the second law of thermodynamics. This is because conventional methods mostly focus on supply risk and economic importance leaving behind relevant factors, such as the physical quality of substances. The new approach is proposed as an additional dimension for the criticality assessment of raw materials through a variable denoted “thermodynamic rarity,” which accounts for the exergy cost required to obtain a mineral commodity from bare rock, using prevailing technology. Accordingly, a given raw material will be thermodynamically rare if it is: (1) currently energy intensive to obtain and (2) scarce in nature. If a given commodity presents a high risk in two of the three dimensions (economic importance, supply risk, and thermodynamic rarity), it is proposed to be critical. As a result, a new critical material list is presented, adding to the 2014 criticality list of the European Commission (EC) Li, Ta, Te, V, and Mo. With this new list and using Sankey diagrams, a material flow analysis has been carried out for Europe (EU‐28) for 2014, comparing the results when using tonnage and thermodynamic rarity as units of measure. Through the latter, one can put emphasis on the quality and not only on the quantity of minerals traded and domestically produced in the region, thereby providing a tool for improving resource management. [ABSTRACT FROM AUTHOR]

Because of the finiteness of the life span and boundedness of the physical space, the more reasonable or physical choice is the tempered power‐law instead of pure power‐law for the CTRW model in characterizing the waiting time and jump length of the motion of particles. This paper focuses on providing the variational formulation and efficient implementation for solving the corresponding deterministic/macroscopic models, including the space tempered fractional equation and time tempered fractional equation. The convergence, numerical stability, and a series of variational equalities are theoretically proved. And the theoretical results are confirmed by numerical experiments. [ABSTRACT FROM AUTHOR]

Abstract: This paper re‐evaluates previous records and adds new data to the relative sea level (RSL; namely the sea level related to the level of the national terrestrial datum) reconstruction in Israel from the last 2400 years based on ancient coastal water wells. Different methods for obtaining the most accurate modern offset between coastal groundwater level and mean sea level are also tested, since this is a crucial component for using wells as reliable sea‐level indicators in the Mediterranean and beyond. Very few, if any, sea‐level studies outside of Israel use coastal wells as RSL indicators; refinements to the methods associated with this indicator type will facilitate their use in other regions. Coastal wells in the study are located within 200 m of the present‐day coastline. The functional age range for the wells is based on site stratigraphy, artifacts, historical records, and the coastal water well typology. These archaeological indicators rely on finding the vertical offset between present‐day coastal groundwater and sea level, and applying it to ancient times. The current study explores two methods to calculate accurate vertical offsets: a) modern averages of the upper aquifer groundwater elevation in the vicinity of ancient wells, which are calculated from 60 years of measurements by the Israeli Hydrological Service; and b) a hydrological model where groundwater elevation is a function of distance from the modern coastline. The model uses a simulation of the coastal aquifer with a two‐dimensional, vertical cross‐section. The modeled approach is found to be preferable. The results show that sea level in Roman times (1st century CE) was similar to present‐day, slightly higher in the Byzantine period (4th to 7th centuries CE), and lower in part of the Early Islamic period (9th to 10th centuries CE). For the later Fatimid/Ayyubid and Crusader periods (11th to 13th centuries CE), RSL reaches its lowest elevations (of about −0.5 m) as previously found. Following these low levels, sea level rose going into the 18th and 19th centuries CE. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study the essential spectrum of the operator L A u ( x ) = − ( A ( x ) u ′ ( x ) ) ′ + u ( x )where A ( x ) is a positive absolutely continuous function on (0, 1) that resembles x 2 α for some α ≥ 1. We prove that the essential spectrum of L A coincides with the essential spectrum of the operator L α u ( x ) : = − ( x 2 α u ′ ( x ) ) ′ + u ( x ). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce iterative algorithm which is a combination of hybrid viscosity approximation method and the hybrid steepest-descent method for solving proximal split feasibility problems and obtain the strong convergence of the sequences generated by the iterative scheme under certain weaker conditions in Hilbert spaces. Our results improve many recent results on the topic in the literature. Several numerical experiments are presented to illustrate the effectiveness of our proposed algorithm, and these numerical results show that our result is computationally easier and faster than previously known results on proximal split feasibility problem. [ABSTRACT FROM AUTHOR]

When experimental resources are significantly constrained, resolution V fractional factorial designs are often prohibitively large for experiments with 6 or more factors. Resolution IV designs may also be cost prohibitive, as additional experimentation may be required to de-alias active 2-factor interactions (2FI). This paper introduces 20-run no-confounding screening designs for 6 to 12 factors as alternatives to resolution IV designs. No-confounding designs have orthogonal main effects, and since no 2FI is completely confounded with another main effects or 2FI, the experimental results can be analyzed without follow-on experimentation. The paper concludes with the results of a Monte Carlo simulation used to assess the model-fitting accuracy of the recommended designs. [ABSTRACT FROM AUTHOR]

In this paper, we present the approximate solution of damped Boussinesq equation using extended Raviart-Thomas mixed finite element method. In this method, the numerical solution of this equation is obtained using triangular meshes. Also, for discretization in time direction, we use an implicit finite difference scheme. In addition, error estimation and stability analysis of both methods are shown. Finally, some numerical examples are considered to confirm the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we have studied a prey-predator model living in a habitat that divided into two regions: an unreserved region and a reserved (refuge) region. The migration between these two regions is allowed. The interaction between unreserved prey and predator is Crowley-Martin-type functional response. The local and global stability of the system is discussed. Further, the system is extended to incorporate the effect of time delay. Then the dynamical behavior of the system is analyzed, taking delay as a bifurcation parameter. The direction of Hopf bifurcation and the stability of the bifurcated periodic solution are determined with the help of normal form theory and centre manifold theorem. We have also discussed the influence of prey refuge on densities of prey and predator species. The analytical results are supplemented with numerical simulations. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The shock instability phenomenon is a well-known problem for hypersonic flow computation by the shock-capturing Roe scheme. The pressure checkerboard is another well-known problem for low-Mach-number flow computation. The momentum interpolation method (MIM) is necessary for low-Mach-number flows to suppress the pressure checkerboard problem, and the pressure-difference-driven modification for cell face velocity can be regarded as a version of the MIM by subdividing the numerical dissipation of the Roe scheme. In this paper, MIM has been discovered through analysis and numerical tests to have the most important function in shock instability. MIM should be completely removed for nonlinear flows. However, the unexpected MIM is activated on the cell face nearly parallel to the flow for the high-Mach-number flows or low-Mach-number cells in numerical shock. Therefore, MIM should be retained for low-Mach-number flows and be completely removed for high-Mach-number flows and low-Mach-number cells in numerical shock. For such conditions, two coefficients are designed on the basis of the local Mach number and a shock detector. Thereafter, the improved Roe scheme is proposed. This scheme considers the requirement of MIM for incompressible and compressible flows, and is validated for good performance of numerical tests. An acceptable result can also be obtained with only the Mach number coefficient for general practical computation. Therefore, the objective of decreasing rather than increasing numerical dissipation to cure shock instability can be achieved with simple modification. Moreover, the mechanism of shock instability has been profoundly understood, in which MIM plays the most important role, although it is not the only factor. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An Euler tour of a hypergraph (also called a rank-2 universal cycle or 1-overlap cycle in the context of designs) is a closed walk that traverses every edge exactly once. In this paper, using a graph-theoretic approach, we prove that every triple system with at least two triples is eulerian, that is, it admits an Euler tour. Horan and Hurlbert have previously shown that for every admissible order >3, there exists a Steiner triple system with an Euler tour, while Dewar and Stevens have proved that every cyclic Steiner triple system of order >3 and every cyclic twofold triple system admits an Euler tour. [ABSTRACT FROM AUTHOR]

In this paper, we consider a general class of external cusps defined by linking appropriate collections of John domains. For that class, weighted Korn inequalities are proved by means of rather elementary arguments. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Concrete-faced rockfill dam (CFRD) is a popular alternative to traditional dam types in the last two decades. The modelling of CFRD involves complex multi-body contact and strong geometry and material nonlinearities. We present a numerical approach for the modelling of CFRDs in this paper. Based on the dual-mortar finite element method, the presented approach considers different parts of rockfill and all concrete slabs as independent deformable continuum. The multi-body contacts are modelled using Lagrange multipliers with a weak form segment-to-segment contact strategy. To alleviate instability induced by strong geometry nonlinearity in the slab-slab contact, we propose a mixed type of constraints for the tangential contact. A general transformation scheme is introduced to simplify the implementation of contact constraints. Three-dimensional analysis of Tianshengqiao-1 CFRD is performed. The nonlinear and time-dependent deformation of the rockfill is considered. We study the influence of the rockfill deformation on the reliability of the concrete face. Three major concerns of the face, that is, the axial compression, the slab-slab separation and the face-rockfill separation, are discussed in detail. The numerical results are compared with data from in-situ observation. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The problem of robust optimal Robin boundary control for a parabolic partial differential equation with uncertain input data is considered. As a measure of robustness, the variance of the random system response is included in two different cost functionals. Uncertainties in both the underlying state equation and the control variable are quantified through random fields. The paper is mainly concerned with the numerical resolution of the problem. To this end, a gradient-based method is proposed considering different functional costs to achieve the robustness of the system. An adaptive anisotropic sparse grid stochastic collocation method is used for the numerical resolution of the associated state and adjoint state equations. The different functional costs are analysed in terms of computational efficiency and its capability to provide robust solutions. Two numerical experiments illustrate the performance of the algorithm. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Various analytical theories of consolidation for soils with vertical drains have been proposed in the past. Most conventional theories are based on a cylindrical unit cell that contains only a single vertical drain. This paper described a new analytical model where a vertical drain located at the centre (the 'inner vertical drain') and is surrounded by two or three vertical drains (the 'outer vertical drains'), the number of which depends on whether the configuration is triangular or rectangular. Both types of drains are combined into a cylindrical unit cell, and the water is assumed to flow both inwards to the inner vertical drain and outwards to the outer vertical drains distributed around the circumference. The outer radial boundary of the unit cell is regarded as a permeable boundary, with a drainage capacity of two or three separate vertical drains for triangular and rectangular configurations, respectively. The smear effects and the drainage resistances for both the inner and outer vertical drains are considered in the analysis as well. In this way, the equations governing the consolidation process with multiple vertical drains are derived, and the corresponding analytical solutions are obtained for instantaneously loading, ramp loading and multi-stage of instantaneously loading and multi-stage of ramp loading. The present solutions are finally compared with several conventional solutions for a single vertical drain in the literature. The results show that the present model predicts the same average degree of consolidation as conventional models do, which verifies the correctness of this new model. Finally, the settlement predicted by the present solution is compared with the measured settlement from a field test at the Port of Brisbane, Australia, which shows a good agreement between them. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, a novel robust sliding mode learning control scheme is developed for a class of non-minimum phase nonlinear systems with uncertain dynamics. It is shown that the proposed sliding mode learning controller, designed based on the most recent information of the stability status of the closed-loop system, is capable of adjusting the control signal to drive the sliding variable to reach the sliding surface in finite time and remain on it thereafter. The closed-loop dynamics including both observable and non-observable ones are then guaranteed to asymptotically converge to zero in the sliding mode. The developed learning control method possesses many appealing features including chattering-free characteristic, strong robustness with respect to uncertainties. More importantly, the prior information of the bounds of uncertainties is no longer required in designing the controller. Numerical examples are presented in comparison with the conventional sliding mode control and backstepping control approaches to illustrate the effectiveness of the proposed control methodology. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of designing robust linear quadratic regulators for uncertain polytopic continuous-time systems over networks subject to delays. The main contribution is to provide a procedure to determine a discrete-time representation of the weighting matrices associated to the quadratic criterion and an accurate discretized model, in such a way that a robust state feedback gain computed in the discrete-time domain assures a guaranteed quadratic cost to the closed-loop continuous-time system. The obtained discretized model has matrices with polynomial dependence on the uncertain parameters and an additive norm-bounded term representing the approximation residual error. A strategy based on linear matrix inequality relaxations is proposed to synthesize, in the discrete-time domain, a digital robust state feedback control law that stabilizes the original continuous-time system assuring an upper bound to the quadratic cost of the closed-loop system. The applicability of the proposed design method is illustrated through a numerical experiment. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we discuss Airy solutions of the second Painlevé equation (PII) and two related equations, the Painlevé XXXIV equation ( [ABSTRACT FROM AUTHOR]

In this paper, we address shortcomings of themethod of exponential basis functions by extending it to general linear and non-linear problems. In linear problems, the solution is approximated using a linear combination of exponential functions. The coefficients are calculated such that the homogenous form of equation is satisfied on some grid. To solve non-linear problems, they are converted to into a succession of linear ones using a Newton-Kantorovich approach. The generalized exponential basis functions (GEBF) method developed can be implemented with greater ease compared with exponential basis functions, as all calculations can be performed using real numbers and no characteristic equation is needed. The details of an optimized implementation are described. We compare GEBF on some benchmark problems with methods in the literature, such as variants of the boundary element method, where GEBF shows a good performance. Also, in a 3D problem, we report the run time of the proposed method compared with that of Kratos, a parallel, highly optimized finite element code. The results show that in this example, to obtain the same level of error, much less computational effort is needed in the proposed method. Practical limitations might be encountered, however, for large problems because of dense matrix operations involved. [ABSTRACT FROM AUTHOR]

This paper analyzes a sequential search model with adverse selection. We study information aggregation by the price-how close the equilibrium prices are to the full-information prices-when search frictions are small. We identify circumstances under which prices fail to aggregate information well even when search frictions are small. We trace this to a strong form of the winner's curse that is present in the sequential search model. The failure of information aggregation may result in inefficient allocations. [ABSTRACT FROM AUTHOR]

In this paper we compute the motivic Chern classes and homology Hirzebruch characteristic classes of (possibly singular) toric varieties, which in the context of complete toric varieties fit nicely with a generalized Hirzebruch-Riemann-Roch theorem. As important special cases, we obtain new (or recover well-known) formulae for the Baum-Fulton-MacPherson Todd (or MacPherson's Chern) classes of toric varieties, as well as for the Thom-Milnor L-classes of simplicial projective toric varieties. We present two different perspectives for the computation of these characteristic classes of toric varieties. First, we take advantage of the torus-orbit decomposition and the motivic properties of the motivic Chern and respectively homology Hirzebruch classes to express the latter in terms of dualizing sheaves and respectively the (dual) Todd classes of closures of orbits. This method even applies to torus-invariant subspaces of a given toric variety. The obtained formula is then applied to weighted lattice-point counting in lattice polytopes and their subcomplexes, yielding generalized Pick-type formulae. Second, in the case of simplicial toric varieties, we compute our characteristic classes by using the Lefschetz-Riemann-Roch theorem of Edidin-Graham in the context of the geometric quotient description of such varieties. In this setting, we define mock Hirzebruch classes of simplicial toric varieties (which specialize to the mock Chern, mock Todd, and mock L-classes of such varieties) and investigate the difference between the (actual) homology Hirzebruch class and the mock Hirzebruch class. We show that this difference is localized on the singular locus, and we obtain a formula for it in which the contribution of each singular cone is identified explicitly. Finally, the two methods of computing characteristic classes are combined for proving several characteristic class formulae originally obtained by Cappell and Shaneson in the early 1990s.© 2015 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]

In this paper, we prove two blow-up criteria of smooth solution: one for the generalized incompressible Oldroyd model with fractional Laplacian velocity dissipation (-Δ)αu in the space Rn, n = 2, 3 and one for the inviscid Oldroyd model. Assume that (u(t, x), F(t, x)) is a smooth solution to the generalized Oldroyd model in [0, t); then, the solution (u(t, x), F(t, x)) does not develop singularity until t = T provided ▿ u ϵ L1 (0, T; B0 ∞,∞). For the ideal impressible viscoelastic flow, it is shown that the smooth solution (u, F) can be extended beyond T if (▿ u, ▿F) ϵ L1 (0, T; B0 ∞,∞), which is an improvement of the result given by Hu and Hynd (A blowup criterion for ideal viscoelastic flow, J. Math. Fluid Mech., 15(2013), 431-437). [ABSTRACT FROM AUTHOR]

In this paper, a time-delayed free boundary problem for tumor growth under the action of external inhibitors is studied. It is assumed that the process of proliferation is delayed compared with apoptosis. By Lp theory of parabolic equations, the Banach fixed point theorem and the continuation theorem, the existence and uniqueness of a global solution is proved. The asymptotic behavior of the solution is also studied. The proof uses the comparison principle and the iteration method. [ABSTRACT FROM AUTHOR]