Information technology and systems

Book Review Editorial

Information technology and systems     

Variational discretization for parabolic optimal control problems with control constraints

This paper studies variational discretization for the optimal control problem governed by parabolic equations with control constraints.First of all,the authors derive a priori error estimates where |||u-U₍h|||_L∞（J;L²（Ω））=O（h²+k）.It is much better than a priori error estimates of standard finite element and backward Euler method where |||μ-U_h|||₍L∞（J;L²（Ω））=O（h+ k）.Secondly,the authors obtain a posteriori error estimates of residual type.Finally,the authors present some numerical algorithms for the optimal control problem and do some numerical experiments to illustrate their theoretical results.     

均衡函数及其在变权综合中的应用

进一步研究了均衡函数，改进了［４］中公理化体系，获得了两大数均衡函数及相应的变权模式并分析了这些模式之间的关系。     

Control and Stabilization of the Rosenau Equation Posed on a Periodic Domain

This paper considers the Rosenau equation with a moving control?t u + ?_t?_x~4 u + ?_xu + u?x u = a(x + ct)h(x, t), c = 0, x ∈ T = R/(2πZ), t 0.The authors prove that the Rosenau equation with a moving control is locally exact controllable in Hs(T) with s ≥ 0 and globally exponential stable in H~s(T) with s ≥ 2. The two results nontrivially extend the work of(Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.     

A general iterative method of fixed points for equilibrium problems and optimization problems

The purpose of this paper is to present a general iterative scheme as below:

Primality Testing for Numbers of the Form h·2~n± 1

This paper studies the problem of primality testing for numbers of the form h · 2~n± 1,where h 2~n is odd, and n is a positive integer. The authors describe a Lucasian primality test for these numbers in certain cases, which runs in deterministic quasi-quadratic time. In particular, the authors construct a Lucasian primality test for numbers of the form 3 · 5 · 17 · 2~n± 1, where n is a positive integer, in half of the cases among the congruences of n modulo 12, by means of a Lucasian sequence with a suitable seed not depending on n. The methods of Bosma(1993), Berrizbeitia and Berry(2004), Deng and Huang(2016) can not test the primality of these numbers.     

Two-Weight Norm Inequality for Imaginary Powers of a Laplace Operator

We study two-weight norm inequality for imaginary powers of a Laplace operator in R^n, n ≥ 1, especially from weighted Lebesgue space Lv^p（R^n） to weighted Lebesgue space Lμ^p（R^n）, where 1 〈 p 〈 ∞. We prove that the two-weighted norm inequality holds whenever for some t 〉 1, （μ^t, v^t） ∈ Ap, or if （μ, v） ∈Ap, where μ and v^-1/（p-1） satisfy the growth condition and reverse doubling property.     

Observability Analysis and Navigation Algorithm for Distributed Satellites System Using Relative Range Measurements

The problem of navigation for the distributed satellites system using relative range measurements is investigated. Firstly, observability for every participating satellites is analyzed based on the nonlinear Keplerian model containing J₂ perturbation and the nonlinear measurements. It is proven that the minimum number of tracking satellites to assure the observability of the distributed satellites system is three. Additionally, the analysis shows that the J₂ perturbation and the nonlinearity make little contribution to improve the observability for the navigation. Then, a quasi-consistent extended Kalman filter based navigation algorithm is proposed, which is quasi-consistent and can provide an online evaluation of the navigation precision. The simulation illustrates the feasibility and effectiveness of the proposed navigation algorithm for the distributed satellites system.     

Empirical likelihood for partially linear models under negatively associated errors

This paper proposes to use the blockwise empirical likelihood(EL) method to construct the confidence regions for the regression vector β in a partially linear model under negatively associated errors. It is shown that the blockwise EL ratio statistic for β is asymptotically χ~2 distributed. The result is used to obtain an EL-based confidence region for β. Results of a simulation study on the finite sample performance of the proposed confidence regions are reported.     

A New Algorithm for Computing the Extended Hensel Construction of Multivariate Polynomials

This paper presents a new algorithm for computing the extended Hensel construction(EHC) of multivariate polynomials in main variable x and sub-variables u_1, u_2, ···, u_m over a number field K. This algorithm first constructs a set by using the resultant of two initial coprime factors w.r.t. x, and then obtains the Hensel factors by comparing the coefficients of x~i on both sides of an equation. Since the Hensel factors are polynomials of the main variable with coefficients in fraction field K(u_1, u_2, ···, u_m), the computation cost of handling rational functions can be high. Therefore,the authors use a method which multiplies resultant and removes the denominators of the rational functions. Unlike previously-developed algorithms that use interpolation functions or Gr?bner basis, the algorithm relies little on polynomial division, and avoids multiplying by different factors when removing the denominators of Hensel factors. All algorithms are implemented using Magma, a computational algebra system and experiments indicate that our algorithm is more efficient.     

Scheduling with Rejection and Non-Identical Job Arrivals

In this paper, we address the scheduling problem with rejection and non-identical job arrivals, in which we may choose not to process certain jobs and each rejected job incurs a penalty, Our goal is to minimize the sum of the total penalties of the rejected jobs and the maximum completion time of the processed ones, For the off-line variant, we prove its NP-hardness and present a PTAS, and for the on-line special case with two job arrivals, we design a best possible algorithm with competitive ratio （√5＋1/2） .     

灰色系统关联度之分辨系数的研究

本文讨论了灰关联度ｒｉ中分辨系数ρ的实质意义，研究了ρ与ｒｉ的关系，分析了在不同的系统观测信息下，ρ的取值对关联度的影响，提出了ρ的取值准则并给出了应用实例.     

On-Line Scheduling with Rejection on Identical Parallel Machines

In this paper, we consider the on-line scheduling of unit time jobs with rejection on rn identical parallel machines. The objective is to minimize the total completion time of the accepted jobs plus the total penalty of the rejected jobs. We give an on-line algorithm for the problem with competitive ratio 1/2 （2 ＋√3） ≈ 1.86602.     

Polynomial dynamic programming algorithms for lot sizing models with bounded inventory and stockout and/or backlogging

This paper addresses a dynamic lot sizing problem with bounded inventory and stockout where both no backlogging and backlogging allowed cases are considered. The stockout option means that there is outsourcing in a period only when the inventory level at that period is non-positive. The production capacity is unlimited and production cost functions are linear but with fixed charges. The problem is that of satisfying all demands in the planning horizon at minimal total cost. We show that the no backlogging case can be solved in ) O(T ²) time with general concave inventory holding and outsourcing cost functions where T is the length of the planning horizon. The complexity can be reduced to O(T) when the inventory holding cost functions are also linear and have some realistic properties, even if the outsourcing cost functions remain general concave functions. When the inventory holding and outsourcing cost functions are linear, the backlogging case can be solved in O(T ³logT) time whether the outsourcing level at each period is bounded by the sum of the demand of that period and backlogging level from previous periods, or only by the demand of that period.     

Forced Oscillations of a Class of Nonlinear Dispersive Wave Equations and their Stability

It has been observed in laboratory experiments that when nonlinear dispersive waves are forced periodically from one end of undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. The observation has been confirmed mathematically in the context of the damped Korteweg-de Vries （KdV） equation and the damped Benjamin-Bona-Mahony （BBM） equation. In this paper we intend to show the same results hold for the pure KdV equation （without the damping terms） posed on a finite domain. Consideration is given to the initial-boundary-value problem {ut＋ux＋uux＋uxxx=0, u（x,0）=φ（x）, 0〈x〈1, t〉0,u（0,t）=h（t）, u（1,t） = 0, ux（1,t） = 0, t〉0.It is shown that if the boundary forcing h is periodic with small ampitude, then the small amplitude solution u of （＊） becomes eventually time-periodic. Viewing （＊） （without the initial condition） as an infinite-dimensional dynamical system in the Hilbert space L^2（0, 1）, we also demonstrate that for a given periodic boundary forcing with small amplitude, the system （＊） admits a （locally） unique limit cycle, or forced oscillation, which is locally exponentially stable. A list of open problems are included for the interested readers to conduct further investigations.     

A Maturing of Systems Thinking? Evidence from Three Perspectives

This paper reviews trends in systems theory/thinking from the 1970s to the early 2000s. It proposes a maturation of the field based on certain conceptual and methodological advances that have sought to liberate systems thinking from earlier strictures. An edited dialogue among three prominent systems thinkers from different systems schools—Merrelyn Emery, Bob Flood, and Eric Wolstenholme—provides evidence. Similarities and differences are identified, complementarities among the schools are derived and analyzed, and trajectories for future research are indicated.     

Further study strong consistency of M estimator in linear model for \tilde \rho-mixing random samples

The strong consistency of M estimators of the regression parameters in linear models for $\tilde \rho$ -mixing random errors under some mild conditions is established, which is an essential improvement over the relevant results in the literature on the moment conditions and mixing errors. Especially, Theorem of Wu (2005) is improved essentially on the moment conditions.     

Pricing and inventory control strategy for a periodic-review energy buy-back system

Along with the rapid development of economics and enhancement of industrialization, the power demand keeps rising and frequently creates mismatch between demand and supply in electricity. This provides miscellaneous energy buy-back programs with great opportunities. Such programs, when activated, offer certain amount of financial compensations to participants for reducing their energy consumption during peak time. They aim at encouraging participants to shift their electricity usage from peak to non-peak time, and thereby release the demand pressure during peak time. This paper considers a periodic-review joint pricing and inventory decision model under an energy buy-back program over finite planning horizons, in which the compensation levels, setup cost and additive random demand function are incorporated. The objective is to maximize a manufacturer’s expected total profit. By using Veinott’s conditions, it is shown that the manufacturer’s optimal decision is a state dependent (s, S, P) policy under a peak market condition, or partly an (s, S, A, P) policy under the normal market condition.     

Automobile Dominance and the Tragedy of the Land-Use/Transport System: Some Critical Issues

Although the automobile is the least energy-efficient, the least space-efficient, and one of the most expensive of the transport modes to operate, it has dominated our cities for the last 50 years and impaired their quality in fundamental ways. Increasing dependence on the automobile has led to such problems as severe traffic congestion, widespread air and noise pollution, increased fuel consumption, steeper infrastructure costs, and higher accident rates. Through an insidious process, this automobile domination has also encouraged the widespread development of sprawling suburbs that are the most uneconomical, environmentally degrading, and socially deplorable patterns of residential land-use development. It is demonstrated that these adverse consequences, created as a direct or indirect result of the automobile, have impaired the systemicity of the land-use/transport system, representing a modern-day example of the tragedy of the commons. To demonstrate whether the systemicity of land-use/transport systems can be appraised, a methodology is outlined for helping planning organizations to become cognizant of these problems and to spur major technological, policy, and behavioral changes.