Categorical approach to modelling and to coupling of models

Solution of any engineering problem starts with a modelling process, which typically involves a choice among different kinds of models. To create a realistic model, one has to think carefully about the modelling process. Particularly in the case of coupled problems when several models are coupled together to represent a given physical phenomenon. This paper presents an approach based on the category theory that allows to describe this modelling process on a more abstract level. Using the advantages of abstract level, one can describe the coupling process in a concise way and introduce certain criteria to check consistency of a coupled model. The main idea of the proposed approach is to introduce a structure in the modelling process, which allows to see how different models interact without a precise look into them. Copyright © 2016 John Wiley & Sons, Ltd.     

升值之言该如何听

自今年6月中国暗示将松动人民币汇率以来,人民币升值幅度仅为0．4％,这大大低于华盛顿的期待,因此,中美两国的关系日益紧张起来。随着失业率的膨胀,以及选举年即将到来,美国国会再一次将人民币汇率摆上了议事日程：9月6日,华盛顿两位高官为缓和中美关系前往北京,就人民币及其他重要问题进行高峰会晤,以期达成共识。     

Correction to a proposition related to ergodicity of Markov chains

Proposition 5.5.6 (ii) in the book Markov Chains and Stochastic Stability (2nd ed, Cambridge Univ. Press, 2009) has been used in the proof of a theorem about ergodicity of Markov chains. Unfortunately, an example in this paper shows that this proposition is not always true. Thus, a correction of this proposition is provided.     

Comparison of decay of solutions to two compressible approximations to Navier-Stokes equations

In this article, we use the decay character of initial data to compare the energy decay rates of solutions to different compressible approximations to the Navier- Stokes equations.We show that the system having a nonlinear damping term has slower decay than its counterpart with an advection-like term. Moreover, me characterize a set of initial data for which the decay of the first system is driven by the difference between the full solution and the solution to the linear part, while for the second system the linear part provides the decay rate.     

From A to B to Z

Semigroup Forum - The variety generated by the Brandt semigroup $$B_2$$ can be defined within the variety generated by the semigroup $$A_2$$ by the single identity $$x^2y^2\approx y^2x^2$$ . Edmond...     

An approach to predictive-reactive scheduling of parallel machines subject to disruptions

In this paper, a new predictive-reactive approach to a parallel machine scheduling problem in the presence of uncertain disruptions is presented. The approach developed is based on generating a predictive schedule that absorbs the effects of possible uncertain disruptions through adding idle times to the job processing times. The uncertain disruption considered is material shortage, described by the number of disruption occurrences and disruption repair period. These parameters are specified imprecisely and modelled using fuzzy sets. If the impact of a disruption is too high to be absorbed by the predictive schedule, a rescheduling action is carried out. This approach has been applied to solving a real-life scheduling problem of a pottery company.     

The location of public facilities intermediate to the journey to work

Location—allocation models typically locate facilities with respect to points to be served, for example to the homes of potential patrons. Certain types of facility, however, are employed by persons who travel to the facility from their homes and continue their journey to another location. Child care facilities are an example of this pattern of patronage, with parents dropping children off at a centre en route to work. The paper presents a discrete-space location—allocation model minimizing the diversion of patrons' journeys to work. The problem reduces to the structure and combinatorial dimensions of the simple P-median problem. The model is applied to the transit worktrip patterns of single parents in Edmonton, Canada. The facilities generated by the model tend to central locations in the city where workplaces are concentrated and transit connections are efficient. The model provides a compromise between ones minimizing home-facility travel times and facility-workplace travel times.     

Differentiability with respect to parameters of solutions to convex programming problems

We consider a family of convex programming problems that depend on a vector parameter, characterizing those values of parameters at which solutions and associated Lagrange multipliers are Gâteaux differentiable.These results are specialized to the problem of the metric projection onto a convex set. At those points where the projection mapping is not differentiable the form of Clarke's generalized derivative of this mapping is derived.     

Convergence to steady states of solutions to nonlinear integral evolution equations

We prove that any global bounded solution of the nonlinear evolutionary integral equation $$\dot{u}(t) + \int\limits_0^t a(t-s)\mathcal{E}'(u(s))ds =f(t), \quad t >0 $$ tends to a single equilibrium state for long time (i.e., ${\mathcal{E}'(\vartheta)=0}$ where ${\vartheta= \lim_{t \rightarrow \infty} u(t)}$ on a real Hilbert space), where ${\mathcal{E}'}$ is the Fréchet derivative of a functional ${\mathcal{E}}$ , which satisfies the ?ojasiewicz?CSimon inequality near ${\vartheta}$ . The vector-valued function f and the scalar kernel a satisfy suitable conditions.     

Random allocation of particles to cells corresponding to the Polya distribution

A generalized scheme of particle allocation to cells corresponding to the multivariate Polya distribution is considered. Theorems are derived describing the limiting behavior of the number of particles in a wide range of parameters. The results are extended to the case of jointly distributed random variables.Translated from Statisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 88–94, 1986.     

On differentiability with respect to parameter of solutions to convex optimal control problems subject to state space constraints

A family of convex optimal control problems that depend on a real parameterh is considered. The optimal control problems are subject to state space constraints.It is shown that under some regularity conditions on data the solutions of these problems as well as the associated Lagrange multipliers are directionally-differentiable functions of the parameter.The respective right-derivatives are given as the solution and respective Lagrange multipliers for an auxiliary quadratic optimal control problem subject to linear state space constraints.If a condition of strict complementarity type holds, then directional derivatives become continuous ones.     

根据人体的手部数据推断性别的研究

本文对18对男女的手长、手宽、掌长、掌宽数据,应用两总体线性判别分析方法得到推断性别的判别函数及判别临界值,经检验证明,准确率很好.     

A counter-example to the boundary regularity of solutions to elliptic quasilinear systems

It is shown that solutions to the Dirichlet problem for quasilinear elliptic systems in a domain ofR ⁿ n3 with smooth boundary datum can be singular at the boundary.     

Using MACBETH to determine utilities of governments to parties in coalition formation

In the paper, we present an application of the MACBETH approach to a certain model of coalition formation. We apply the MACBETH technique to quantify the attractiveness and repulsiveness of possible governments to parties. We use this method to calculate the utilities of governments to parties. Based on these utilities, stable governments are determined. In the paper, an adequate example is presented.     

利用人的手部数据推断身高的研究

利用男性(52例)成人人体手部的有关数据(手长、手宽、掌长、掌宽、拇指长、食指长、中指长、环指长、小指长)与身高数据应用多元线性回归统计数值计算软件系统,得出上述9个指标值推断身高的回归方法,经过结果分析,有其应用价值。