The Riemann problem for the pressure-gradient system in three pieces

The Riemann problem for a two-dimensional pressure-gradient system is considered. The initial data are three constants in three fan domains forming different angles. Under the assumption that only a rarefaction wave, shock wave or contact discontinuity connects two neighboring constant initial states, it is proved that the cases involving three rarefaction waves are impossible. For the cases involving one shock (rarefaction) wave and two rarefaction (shock) waves, only the combinations when the three elementary waves have the same sign are possible (impossible).     

On the Riemann problem for 2D compressible Euler equations in three pieces

The Riemann problem for two-dimensional isentropic Euler equations is considered. The initial data are three constants in three fan domains forming different angles. Under the assumption that only a rarefaction wave, shock wave or contact discontinuity connects two neighboring constant initial states, it is proved that the cases involving three shock or rarefaction waves are impossible. For the cases involving one rarefaction (shock) wave and two shock (rarefaction) waves, only the combinations when the three elementary waves have the same sign are possible (impossible).     

Advection-mediated competition in general environments

We consider a reaction–diffusion–advection system of two competing species with one of the species dispersing by random diffusion as well as a biased movement upward along resource gradient, while the other species by random diffusion only. It has been shown that, under some non-degeneracy conditions on the environment function, the two species always coexist when the advection is strong. In this paper, we show that for general smooth environment function, in contrast to what is known, there can be competitive exclusion when the advection is strong, and, we give a sharp criterion for coexistence that includes all previously considered cases. Moreover, when the domain is one-dimensional, we derive in the strong advection limit a system of two equations defined on different domains. Uniqueness of steady states of this non-standard system is obtained when one of the diffusion rates is large.     

On the Computational Homogenization of Transient Diffusion Problems

In this contribution, we address the computational treatment of transient diffusion problems with heterogeneous microstructures using first-order homogenization. There, we treat two different cases, firstly, when the transient part at the microscale can be neglected due to the vanishingly small size of the representative volume element (RVE) and secondly, when no steady state is reached at the microscale. This is the case when dealing with a relaxed version of the scale separation condition. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rank 4 groups with a 3-transitive suborbit

Rank 4 groups with a 3-transitive suborbit such that the graph constructed with respect to this suborbit is connected and has no quadrangles are investigated. Two cases are considered on the 2-transitive representations of an edge stabilizer on the two sets of vertices adjacent to that edge, viz., when these representations are equivalent, and when they are inequivalent and have different permutation characters. The connection between the latter case and the point-line incidence graphs of desarguesian projective planes is also investigated.     

Competitive exclusion in a discrete juvenile–adult model with continuous and seasonal reproduction

We develop a general discrete juvenile–adult population model that describes two competing species. We consider species in which the juveniles only compete with other juveniles, and the adults only compete with other adults, i.e. juveniles and adults of either species do not compete. This is typical of amphibians where juveniles (tadpoles) live in water and adults (frogs) live on land. Assuming competition efficiencies of the two species are similar, we analyse the cases where reproduction is either continuous or seasonal. In both cases, we develop conditions on the invasion net reproductive numbers of the two species that will lead to competitive exclusion. We show using numerical simulations that coexistence and bistability are possible outcomes when competition efficiencies of the two species are different.     

Economic order and production quantity models without constraint on the percentage of defective items

The paper deals with a version of the economic order and production quantity models when the fraction of defective items is probability variable that either may vary from cycle to cycle, or remains the same as it was in the first period. We drop the well-known assumption intended to avoid shortages, and two lot sizing rules are derived. Relationships between the new and known lot sizing rules are analyzed and cases are identified when lot sizing rules give significantly different results.     

Multiprocessor systems with reserves and preferences

Two models involving multiprocessor systems with two different groups of processors are examined. In the first model, the processors which are in use break down from time to time; one of the two groups is used only when the other one is entirely inoperative. In the second model, the breakdowns are replaced by a Poisson stream of jobs. Again, one group of processors is used in preference to the other one. In both cases, the analysis is based on finding a polynomial in two variables which satisfies a partial differential-functional equation. Exact solutions are obtained.     

Neural network-based state fusion and adaptive tracking for maneuvering targets

An adaptive algorithm for tracking maneuvering targets is proposed. This algorithm is implemented with two filters and a multilayer feedforward neural network using state fusion, together with the current statistic model and adaptive filtering. The neural network fuses automatically all the state information of the two filters and tunes adaptively the system variance for one of the two filters to adapt to different target maneuvers when the two filters track the same maneuvering target in parallel. Simulation results show that the adaptive algorithm tracks very well maneuvering targets over a wide range of maneuvers with high precision, in both one and three-dimensional cases.     

Berth allocation with time-dependent physical limitations on vessels

We consider a berth allocation problem in container terminals in which the assignment of vessels to berths is limited by water depth and tidal condition. We model the problem as a parallel-machine scheduling problem with inclusive processing set restrictions, where the time horizon is divided into two periods and the processing sets in these two periods are different. We consider both the static and dynamic cases of the problem. In the static case all of the vessels are ready for service at time zero, while in the dynamic case the vessels may have nonzero arrival times. We analyze the computational complexity and develop efficient heuristics for these two cases. Computational experiments are performed to test the effectiveness of the heuristics and to evaluate the benefits of taking tidal condition into consideration when making berth allocation decisions.     

A remark on the ODE with two discrete delays

The aim of this paper is to outline a formal framework for the analytical analysis of the Hopf bifurcations in the delay differential equations with two independent time delays. Some results for the differential-difference equations with two delays, when the both of the coefficients of linearized equation are negative were obtained in [X. Li, S. Ruan, J. Wei, Stability and bifurcation in delay-differential equations with two delays, J. Math. Anal. Appl. 236 (1999) 254-280]. In the paper we present some remarks on the case studied in [X. Li, S. Ruan, J. Wei, Stability and bifurcation in delay-differential equations with two delays, J. Math. Anal. Appl. 236 (1999) 254-280] and also two other cases, namely when the coefficients of linearized equation have different signs and when coefficients are both positive.     

Nonuniqueness for the vanishing viscosity solution with fixed initial condition in a nonstrictly hyperbolic system of conservation laws

We consider the Riemann problem for a system of two decoupled, nonstrictly hyperbolic, Burgers-like conservation equations with added artificial viscosity. We analytically establish two different vanishing viscosity limits for the solution of this system, which correspond to the two cases where one of the viscosities vanishes much faster than the other. This is done without altering the initial condition as is necessary with travelling wave methods. Numerical evidence is then provided to show that when the two viscosities vanish at the same rate, the solution converges to a limit that lies strictly between the two previously established limits. Finally, we use control theory to explain the mechanism behind this nonuniqueness behavior, which indicates other systems of nonstrictly hyperbolic conservation laws where nonuniqueness will occur.     

时滞种群模型的正周期解对所有正解的吸引性

建立了对数种群模型Ｎ′（ｔ）＝Ｎ（ｔ）｛ｒ（ｔ）－ａ１（ｔ）ｌｎ［Ｎ（ｔ）］－ａ２（ｔ）ｌｎ［Ｎ（ｔ－τ（ｔ））］｝的周期正解的存在性，并得到了正周期解对所有正解的吸引性．     

Linear Gaussian affine term structure models with unobservable factors: Calibration and yield forecasting

This paper provides a significant numerical evidence for out-of-sample forecasting ability of linear Gaussian interest rate models with unobservable underlying factors. We calibrate one, two and three factor linear Gaussian models using the Kalman filter on two different bond yield data sets and compare their out-of-sample forecasting performance. One-step ahead as well as four-step ahead out-of-sample forecasts are analyzed based on the weekly data. When evaluating the one-step ahead forecasts, it is shown that a one factor model may be adequate when only the short-dated or only the long-dated yields are considered, but two and three factor models performs significantly better when the entire yield spectrum is considered. Furthermore, the results demonstrate that the predictive ability of multi-factor models remains intact far ahead out-of-sample, with accurate predictions available up to one year after the last calibration for one data set and up to three months after the last calibration for the second, more volatile data set. The experimental data denotes two different periods with different yield volatilities, and the stability of model parameters after calibration in both the cases is deemed to be both significant and practically useful. When it comes to four-step ahead predictions, the quality of forecasts deteriorates for all models, as can be expected, but the advantage of using a multi-factor model as compared to a one factor model is still significant.     

Shield versus sword resource distribution in K-round duels

The paper considers optimal resource distribution between offense and defense in a duel. In each round of the duel two actors exchange attacks distributing the offense resources equally across K rounds. The offense resources are expendable (e.g. missiles), whereas the defense resources are not expendable (e.g. bunkers). The outcomes of each round are determined by a contest success functions which depend on the offensive and defensive resources. The game ends when at least one target is destroyed or after K rounds. We show that when each actor maximizes its own survivability, then both actors allocate all their resources defensively. Conversely, when each actor minimizes the survivability of the other actor, then both actors allocate all their resources offensively. We then consider two cases of battle for a single target in which one of the actors minimizes the survivability of its counterpart whereas the counterpart maximizes its own survivability. It is shown that in these two cases the minmax survivabilities of the two actors are the same, and the sum of their resource fractions allocated to offense is equal to 1. However, their resource distributions are different. In the symmetric situation when the actors are equally resourceful and the two contest intensities are equal, then the actor that fights for the destruction of its counterpart allocates more resources to offense. We demonstrate a methodology of game analysis by illustrating how the resources, contest intensities and number of rounds in the duels impact the survivabilities and resource distributions.     

Periodic motions of a class of forced infinite lattices with nearest neighbor interaction

In this paper, by using a priori bounds, topological degree and limiting arguments, we study the existence of periodic solutions of a class of one-dimensional chain of particles periodically perturbed and with nearest neighbor interaction between particles. We study the necessary and sufficient conditions for the existence of periodic solutions in two cases when the number of particles is finite and infinite and obtain different results.     

Breakdowns and stagnation in iterative methods

One of the disadvantages of Krylov subspace iterative methods is the possibility of breakdown. This occurs when it is impossible to get the next approximation of the solution to the linear system of equationsAu=f. There are two different situations: lucky breakdown, when we have found the solution and hard breakdown, when the next Krylov subspace cannot be generated and/or the next approximate solution (iterate) cannot be computed. We show that some breakdowns depend on the chosen method of generating the basis vectors. Another undesirable feature of the iterative methods is stagnation. This occurs when the error does not change for several iterative steps. We investigate when iterative methods can stagnate and describe conditions which characterize stagnation. We show that in some cases stagnation can imply breakdown.     

基于马尔柯夫机制转换模型的中国出口集装箱运价指数波动研究

时间序列的显著变化可视为时间序列的内在生成机制从一种机制向另外一种机制的转换。如果机制转换的时间点已知,则可以用著名的邹氏检验来确定已知的时间点是否发生结构变化。但在很多时候,人们并不知道转折点在哪里,在哪一点模型的参数就已经发生了变化,因此有时就需要去推断转折点和参数的变化。马尔柯夫机制转换模型将这种机制的转换作为一个内生变量,认为机制转换是随机的,从而实现用一个统一的模型对显著的结构变化进行刻画,有利于对未来进行推断。文章利用二状态马尔柯夫机制转换模型对1998年1月至2006年12月中国出口集装箱运价指数的变动进行刻画,研究结果表明各状态之间存在不同的转换概率,且每一种状态的平均持续期分别为2.9个月、2.65个月。     

Propagating waves in elastic material with voids subjected to electro-magnetic interactions

Constitutive relations and field equations are developed for an elastic solid with voids subjected to electro-magnetic field. The linearized form of the relations and equations are presented separately when medium is subjected to a large magnetic field and when it is subjected to a large electric field. The possibility of propagation of time harmonic plane waves in an infinite elastic solid with voids has been explored. It is found that when the medium is subjected to large magnetic field, there exist two coupled longitudinal waves propagating with distinct speeds and a transverse wave mode. However, when the medium is subjected to a large electric field, there may propagate five basic waves comprising of four coupled longitudinal waves propagating with distinct speeds and a lone transverse wave. The effects of magnetic and electric fields are observed on the propagation characteristics of the existing waves. Under the limiting cases of frequency and for different electric conductive materials, the speeds of various waves are investigated. The phase speeds of different waves and their corresponding attenuations have been computed against the frequency parameter and depicted graphically for a specific material.     

Simulation of Multiphase Flows with Strong Shocks and Density Variations

The system of extended Euler type hyperbolic equations is considered to describe a two-phase compressible flow. A numerical scheme for computing multi-component flows is then examined. The numerical approach is based on the mathematical model that considers interfaces between fluids as numerically diffused zones. The hyperbolic problem is tackled using a high resolution HLLC scheme on a fixed Eulerian mesh. The global set of conservative equations (mass, momentum and energy) for each phase is closed with a general two parameters equation of state for each constituent. The performance of various variants of a diffuse interface method is carefully verified against a comprehensive suite of numerical benchmark test cases in one and two space dimensions. The studied benchmark cases are divided into two categories: idealized tests for which exact solutions can be generated and tests for which the equivalent numerical results could be obtained using different approaches. The ability to simulate the Richtmyer-Meshkov instabilities, which are generated when a shock wave impacts an interface between two different fluids, is considered as a major challenge for the present numerical techniques. The study presents the effect of density ratio of constituent fluids on the resolution of an interface and the ability to simulate Richtmyer-Meshkov instabilities by various variants of diffuse interface methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)