Zero‐coupon bond prices in the Vasicek and CIR models: Their computation as group‐invariant solutions

We compute prices of zero‐coupon bonds in the Vasicek and Cox–Ingersoll–Ross interest rate models as group‐invariant solutions. Firstly, we determine the symmetries of the valuation partial differential equation that are compatible with the terminal condition and then seek the desired solution among the invariant solutions arising from these symmetries. We also point to other possible studies on these models using the symmetries admitted by the valuation partial differential equations. Copyright © 2007 John Wiley & Sons, Ltd.     

Periodic solutions of the Navier–Stokes equations in a perturbed half‐space and an aperture domain

We shall construct a periodic strong solution of the Navier–Stokes equations for some periodic external force in a perturbed half‐space and an aperture domain of the dimension n?3. Our proof is based on L^p–L^q estimates of the Stokes semigroup. We apply L^p–L^q estimates to the integral equation which is transformed from the original equation. As a result, we obtain the existence and uniqueness of periodic strong solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

Assessment and propagation of input uncertainty in tree‐based option pricing models

This paper aims to provide a practical example of assessment and propagation of input uncertainty for option pricing when using tree‐based methods. Input uncertainty is propagated into output uncertainty, reflecting that option prices are as unknown as the inputs they are based on. Option pricing formulas are tools whose validity is conditional not only on how close the model represents reality, but also on the quality of the inputs they use, and those inputs are usually not observable. We show three different approaches to integrating out the model nuisance parameters and show how this translates into model uncertainty in the tree model space for the theoretical option prices. We compare our method with classical calibration‐based results assuming that there is no options market established and no statistical model linking inputs and outputs. These methods can be applied to pricing of instruments for which there is no options market, as well as a methodological tool to account for parameter and model uncertainty in theoretical option pricing. Copyright © 2008 John Wiley & Sons, Ltd.     

On a class of PDEs with nonlinear distributed in space and time state‐dependent delay terms

A new class of nonlinear partial differential equations with distributed in space and time state‐dependent delay is investigated. We find appropriate assumptions on the kernel function which represents the state‐dependent delay and discuss advantages of this class. Local and long‐time asymptotic properties, including the existence of global attractor and a principle of linearized stability, are studied. Copyright © 2008 John Wiley & Sons, Ltd.     

Multifunctional land‐use value mapping and space type classification: A case study of Puge County,China

Land exhibits diverse functions under the combined influence of natural and human forces. A production–living–ecology functional classification system was constructed by integrating land, ecosystem, and landscape functions. The land functional value was calculated by systematically integrating ecosystem service value assessments. The primary and secondary functions, as well as combinations of different land‐use types, were determined using vertical and horizontal comparison methods. The production–living–ecology ranges were then delineated in Puge County, which is a typical mountain county in China. The production–living–ecology functions identified were well connected with the current land‐use types. The “production–living–ecology” space in Puge County showed obvious multifunctionality and agglomeration. The function identification system proposed in this paper integrated multiple methods, overcame the difficulty of direct quantitative identification of land functions. The methods used to map and quantify land function will enhance our ability to understand and model land system changes and adequately inform policies and planning. Summary for Managers

• The function valuation method constructed in this paper could be used to reflect the multifunctionality and importance of land use and provide guidance and a quantitative basis for regional development planning.
• The spatial classification results provided in this paper could offer a valuable reference for the land management department to scientifically formulate land use planning.
• Under the goal of creating a group‐type urban development pattern and constructing an ecological protection pattern in Puge County, the hotspot analysis results of this paper can provide decision‐making tools and alternative spatial plans.

     

Well‐posedness of a 1D transport equation with nonlocal velocity in the Lei–Lin space

In this paper, we consider the well‐posedness of a one‐dimensional transport equation with nonlocal velocity in the Lei–Lin space . We first modify the product estimate and then establish the global existence of solutions to the Cauchy problem with small enough initial data. Finally, we discuss the stability of the global solution. Copyright © 2016 John Wiley & Sons, Ltd.     

Evolution in spatial predator–prey models and the “prudent predator”: The inadequacy of steady‐state organism fitness and the concept of individual and group selection

We review recent research which reveals: (1) how spatially distributed populations avoid overexploiting resources due to the local extinction of over‐exploitative variants, and (2) how the conventional understanding of evolutionary processes is violated by spatial populations so that basic concepts, including fitness assignment to individual organisms, are not applicable, and even kin and group selection are unable to describe the mechanism by which exploitative behavior is bounded. To understand these evolutionary processes, a broader view is needed of the properties of multiscale spatiotemporal patterns in organism–environment interactions. We discuss measures that quantify the effects of these interactions on the evolution of a population, including multigenerational fitness and the heritability of the environment. © 2008 Wiley Periodicals, Inc. Complexity, 2008.     

Chaos synchronization of a fractional‐order modified Van der Pol–Duffing system via new linear control,backstepping control and Takagi–Sugeno fuzzy approaches

In this article, based on the stability theory of fractional‐order systems, chaos synchronization is achieved in the fractional‐order modified Van der Pol–Duffing system via a new linear control approach. A fractional backstepping controller is also designed to achieve chaos synchronization in the proposed system. Takagi‐Sugeno fuzzy models‐based are also presented to achieve chaos synchronization in the fractional‐order modified Van der Pol–Duffing system via linear control technique. Numerical simulations are used to verify the effectiveness of the synchronization schemes. © 2015 Wiley Periodicals, Inc. Complexity 21: 116–124, 2016     

On the optimal focusing of solitons and breathers in long‐wave models

Conditions of optimal (synchronized) collisions of any number of solitons and breathers are studied within the framework of the Gardner equation (GE) with positive cubic nonlinearity, which in the limits of small and large amplitudes tends to other long‐wave models, the classic and the modified Korteweg–de Vries equations. The local solution for an isolated soliton or breather within the GE is obtained. The wave amplitude in the focal point is calculated exactly. It exhibits a linear superposition of partial amplitudes of the solitons and breathers. The crucial role of the choice of proper soliton polarities and breather phases on the cumulative wave amplitude in the focal point is demonstrated. Solitons are most synchronized when they have alternating polarities. The straightforward link to the problem of synchronization of envelope solitons and breathers in the focusing nonlinear Schrödinger equation is discussed (then breathers correspond to envelope solitons propagating above a condensate).     

Bayesian‐type count data models with varying coefficients: estimation and testing in the presence of overdispersion

In this paper we study varying‐coefficient models for count data. A Bayesian approach is taken to model the variability of the regression parameters. Based on a Kalman filter procedure the varying coefficients are estimated as the mode of the posterior distribution. All hyperparameters, including an overdispersion parameter in the negative binomial varying‐coefficient model (NBVC), are estimated as ML‐estimators using an EM‐type algorithm. A bootstrapping test of the fixed‐coefficient hypothesis against a varying‐coefficient alternative is proposed, which is evaluated running a simulation study. The study shows that the choice of a suitable count data model is of special importance in the framework of varying‐coefficient models. The methodology is illustrated analysing the determinants of the number of individual doctor visits. Copyright © 2001 John Wiley & Sons, Ltd.     

Self‐organization of genic and intergenic sequence lengths in genomes: Statistical properties and linguistic coherence

In a genome, genes (coding constituents) are interrupted by intergenic regions (noncoding constituents). This study provides a general picture of the large‐scale self‐organization of coding, noncoding, and total constituent lengths in genomes. Ten model genomes were examined and strong correlations between the number of genomic constituents and the constituent lengths were observed. The analysis was carried out by adopting a linguistic distribution model and a structural analogy between linguistic and genomic constructs. The proposed linguistic‐based statistical analysis may provide a fundamental basis for both understanding the linear structural formation of genomic constituents and developing insightful strategies to figure out the function of genic and intergenic regions in genomic sequences. © 2014 Wiley Periodicals, Inc. Complexity 21: 268–282, 2015     

Finite‐volume schemes for Friedrichs systems in multiple space dimensions: A priori and a posteriori error estimates

We consider a class of finite‐volume schemes on unstructured meshes for symmetric hyperbolic linear systems of balance laws in two and three space dimensions. This class of schemes has been introduced and analyzed by Vila and Villedieu ( 5 ). They have proven an a priori error estimate for approximations of smooth solutions. We extend the results to weak solutions. This is the base to derive an a posteriori error estimate for finite‐volume approximations of weak solutions. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

Bogdanov‐Takens bifurcations of codimensions 2 and 3 in a Leslie‐Gower predator‐prey model with Michaelis‐Menten–type prey harvesting

The Bogdanov‐Takens bifurcations of a Leslie‐Gower predator‐prey model with Michaelis‐Menten–type prey harvesting were studied. In the paper “Diff. Equ. Dyn. Syst. 20(2012), 339‐366,” Gupta et al proved that the Leslie‐Gower predator‐prey model with Michaelis‐Menten–type prey harvesting has rich dynamics. Some equilibria of codimension 1 and their bifurcations were discussed. In this paper, we find that the model has an equilibrium of codimensions 2 and 3. We also prove analytically that the model undergoes Bogdanov‐Takens bifurcations (cusp cases) of codimensions 2 and 3. Hence, the model can have 2 limit cycles, coexistence of a stable homoclinic loop and an unstable limit cycle, supercritical and subcritical Hopf bifurcations, and homoclinic bifurcation of codimension 1 as the values of parameters vary. Moreover, several numerical simulations are conducted to illustrate the validity of our results.     

Asymptotic dynamics of a deterministic and stochastic predator–prey model with disease in the prey species

In this paper, we discuss a predator–prey model with the Beddington–DeAngelis functional response of predators and a disease in the prey species. At first we study permanence and global stability of a positive equilibrium for the deterministic version of the model. Then we include a stochastic perturbation of the white noise type. We analyse the influence of this stochastic perturbation on the systems and prove that the positive equilibrium is also globally asymptotically stable in this case. The key point of our analysis is to choose appropriate Lyapunov functionals. We point out the differences between the deterministic and stochastic versions of the model. Copyright © 2013 John Wiley & Sons, Ltd.