Existence and Multiplicity of Positive Solutions for a Coupled Fourth-Order System of Kirchhoff Type

In this paper,we study a coupled fourth-order system of Kirchhoff type.Under appropriate hypotheses of V_(i)(x)for i=1,2,f and g,we obtained two main existence theorems of weak solutions for the problem by variational methods.Some recent results are extended.

Coupling concepts for simulation:A systematic and comprehensive view and advantages with declarative models

A brief review of the importance of simulation-based engineering and science(including social sciences)is followed by a historic perspective of model-based simulation.Section 2 is on declarative modeling of component systems as well as its advantages for self-documentation and for computer-aided checks and coupling.As an example for declarative modeling,General System Theory(GEST)implementor is given.In Sec.3,basic concepts for coupling of component models,and rules for computer-assisted coupling specification are explained.Section 4 is devoted to possible computerized checks in couplings of declarative models such as:(1)automatic unit checking to avoid meaning-less input/output matching at the time of coupling specification,(2)automatic threshold checking to provide warnings and/or to avoid disasters,and(3)automatic unit conversion for convenience of using library models.Section 5 is about several layers of nested couplings for modeling systems of systems.In Sec.6,two types of variable couplings are discussed:(1)couplings with variable connections(to allow input/output relations of models to depend on time or state conditions)and(2)coupling with variable component models(to allow component(or coupled)models to be switched based on time or state conditions).Section 7 is on the use of multimodels as component models in couplings.Section 8 is on types of inputs and their use in couplings as well as on exter-nal inputs to simulation studies.In Sec.9,conclusions and future work for complex systems are outlined.Especially,the values of simulation systems engineering as well as understanding and avoidance of misunderstanding in cognitive and emotive simulations are stressed.Appendix A is a list of almost 50 types of couplings and Appendix B lists over 50 terms related with couplings in modeling and simulation.To show the richness of“input”concept which is important in specification of input/output relations of component models,Appendix C lists almost 150 types of inputs.Information shared in this article may be useful in developing advanced modeling and simulation software,tools and environments.

Multiply Kink and Anti-Kink Solutions for a Coupled Camassa–Holm Type Equation

This article amis at revealing dynamical behavior of a coupled Camassa–Holm type equation, which was proposed by Geng and Wang based on a 4×4 matrix spectral problem with two potentials. Its kink and anti-kink solutions are presented explicitly. In particular, some exact multi-kink and anti-kink wave solutions are discussed and under some conditions, the kink and anti-kinks look like hat-shape solitons. The dynamic characters of the obtained solutions are investigated by figures. The method used in this paper can be widely applied to looking for the multi-kinks for Camassa–Holm type equations possessing cubic nonlinearity.

Modeling the spatial distribution of urban population during the daytime and at night based on land use： A case study in Beijing, China

Urban population during the daytime and at night and their spatial distribution are important bases for planning urban infrastructure, public services and disaster relief. As current population statistics cannot distinguish urban population during the daytime from that at night, existed research in this field are quite limited. This paper tries to advance studies at this aspect by establishing a relationship model for the three components of ＇population, land use and time （daytime or night）＇ to explore the temporal and spatial characteristics of different types of population, which is aimed to estimate urban population during the daytime and at night and to analyze their spatial characteristics at grid scale. Furthermore, an empirical case study has been carried out at the Haidian District in Beijing, China to test the model. The results are as follows： （1） The spatial structure of urban population during the daytime is significantly different from that at night. The spatial distribution of urban population during the daytime is more extensive and more agglomerated that that at night. （2） Several types of spatial coupling relationship between population during the daytime and that at night have been identified, such as sandwich mode, symmetry mode, convergence mode and single mode, etc. （3） The spatial distribution of daytime and nighttime population also reflects certain factors during the development of China, such as the distribution of old residential areas, the construction of new industrial districts, and the differences between urban and rural areas, which can provide reference points for studies in this field and other regional research.

In Situ Loading of Cu_(2)O Nanoparticles on a Hydroxyl Group Rich TiO_(2) Precursor as an Excellent Catalyst for the Ullmann Reaction

An in situ method has been used to load Cu_(2)O nanoparticles on the surface of a hydroxyl group rich TiO_(2)precursor.Cu_(2)O nanoparticles are formed by in situ reduction of Cu(OH)_(2) with Sn^(2+)ions linked to the surface of the TiO_(2)precursor.The initial Cu_(2)O nanoparticles serve as seeds for subsequent particle growth.The resulting Cu_(2)O nanoparticles are evenly dispersed on the surface of the TiO_(2)precursor,and are heat and air stable.The as-prepared composite is an excellent catalyst for Ullmann type cross coupling reactions of aryl halides with phenol.The composite catalyst also showed good stability,remaining highly active after five consecutive runs.