Boundary controllability for conservative PDEs

Boundary observability and controllability problems for evolution equations governed by PDEs have been greatly studied in the past years. However, the problems were studied on a case-by-case basis, only for some particular types of boundary controls, and, moreover, several unnatural restrictions concerning lower-order terms were used.Our goal here is to give a general approach for boundary controllability problems, which is valid for all evolution PDEs of hyperbolic or ultrahyperbolic type, all boundary controls for which the corresponding homogeneous problem is well-posed, and all well-posedness spaces for the homogeneous problem. The first example of such equations is the class of hyperbolic equations, but valid examples are also equations such as the Schroedinger equation and various models for the plate equation.This work is essentially based on some apriori estimates of Carleman's type obtained by the author in a previous paper [29].This research was partially supported by the National Science Foundation under Grant NSF-DMS-8903747.     

Study of the size-flux relation of pores and spots

Using the vector magnetic field data from the Huairou Solar Observing Station of National Astronomical Observatories, a statistical study on the size-flux relation of photospheric magnetic features without any assumption is given. The selected data here include mature sunspots, as well as protosunspot (with a partial penumbra) and pore. We studied not only their size-flux relations of pore, protosunspot and mature sunspot, but also that of umbra and penumbra of the mature sunspots. The size-flux relationship of mature sunspots and their umbra and penumbra is found to be in different indexes of power-law. No evident relations are found between size and flux of the pores and protosunspots. We found that there is a threshold of 1×1012 Wb or (3-4.03) × 107 km2 for the transition from a pore to a protospot. Such results may be useful for understanding the physical conditions and dynamical processes of magnetic flux tubes in solar plasma during sunspot's formation. In addition, their characteristic size is also given.     

A new multicriteria approach for the analysis of efficiency in the Spanish olive oil sector by modelling decision maker preferences

The efficiency in production is often analysed as technical efficiency using the production frontier function. Efficiency scores are usually based on distance computations to the frontier in an m + s-dimensional space, where m inputs produce s outputs. In addition, efficiency improvements consider the total consumption of each input. However, in many cases, the “consumption” of each input can be divided into input-consumption sections (ICSs), and trade-off among the ICSs is possible. This share framework can be used for computing efficiency. This analysis provides information about both the total optimal consumption of each input, as does data envelopment analysis, and the most efficient allocation of the “consumption” among the ICSs. This paper studies technical efficiency using this approach and applies it to the olive oil sector in Andalusia (Spain). A non-parametrical methodology is presented, and an input-oriented Multi-Criteria Linear Programming model (MLP) is proposed. The analysis is developed at global, input and ICSs levels, defining the extent of satisfaction achieved at all these levels for each company, in accordance with their own preferences. The companies’ preferences are modelled with their utility function and their set of weights. MLP offers more detailed information to assist decision makers than other models previously proposed in the literature. In addition to this application, it is concluded that there is room for improvement in the olive oil sector, particularly in the management of the skilled labour. Additionally, the solutions with two opposite scenarios indicate that the model is suitable for the intended decision making process.     

Moral responsibility for unprevented harm

That we are morally responsible for what we do willingly and knowingly is a commonplace. That our moral responsibility extends as far as to cover at least the intended consequences of our voluntary actions and perhaps also the ones we did not intend, but could or did foresee, is equally beyond dispute. But what about omissions? Are we, or can we be, (equally) morally responsible for the harm that has occured because we did not prevent it, even though we could have done so? Say, for all the enormous suffering, caused daily by famine, deprivation and curable diseases in the Third World countries?Moral intuitions and practices that one could consult in this matter seem to leave us in the dark. We regularly ascribe responsibility to people for harms resulting from their negligence or failure to fulfill professional duties. On the other hand, we tend to think that unless there is some evidence of the causal contribution that agents made to a harmful event and/or state, it is not really fair to blame it on them. And finally, to complicate things even more, most of us deny that omissions could effect anything (any change) in the world and consequently regard them as causally impotent (as well as possibly harmless).Most of the proposed solutions to this perplexing issue simply take negative moral responsibility for granted and then either try to revise our ordinary notion of causation accordingly or, alternatively, weaken the conditions for holding someone morally responsible. In the paper I present and defend the relative merits of the third approach, one sceptical of the notion of moral responsibility for the ‘outcomes’ of omissions. I try to show that for some identifiable core notion of moral responsibility and paradigmatic cases of omissions, the prospects for a happy marriage are rather slim.     

Simple-direct-modules

A right R-module M is called simple-direct-injective if, whenever, A and B are simple submodules of M with A?B, and B?^⊕M, then A?^⊕M. Dually, M is called simple-direct-projective if, whenever, A and B are submodules of M with M∕A?B?^⊕M and B simple, then A?^⊕M. In this paper, we continue our investigation of these classes of modules strengthening many of the established results on the subject. For example, we show that a ring R is uniserial (artinian serial) with J²(R) = 0 iff every simple-direct-projective right R-module is an SSP-module (SIP-module) iff every simple-direct-injective right R-module is an SIP-module (SSP-module).     

Cooperation when some players are incompatible

A situation with incompatibilities is defined to be a TU-game together with a graph whose arcs link pairs of incompatible players. In this paper we introduce an efficient and fair allocation rule which selects a payoff for every possible situation with incompatibilities (when the set of players is fixed), and prove that it is uniquely determined. Besides, we demonstrate that it is stable, study its relationship with the so-calledIR-Shapley value and show that it generalizes an earlier theory for simple games. Finally, the communication situations with incompatibilities are studied.We thank University of Santiago de Compostela and Xunta de Galicia for financial support through projects 60902.25064(5060) and XUGA20701B91.     

D3-Modules

A right R-module M is called a D3-module, if M ₁ and M ₂ are direct summands of M with M = M ₁ + M ₂, then M ₁ ∩ M ₂ is a direct summand of M. Following the work of Bass on projective covers, we introduce the notion of D3-covers and provide new characterizations of several well-known classes of rings in terms of D3-modules and D3-covers.     

Approximately locating an invisible agent in a graph with relative distance queries

In a pursuit evasion game on a finite, simple, undirected, and connected graph $G$, a first player visits vertices $m_1,m_2,\dots$ of $G$, where $m_{i+1}$ is in the closed neighborhood of $m_i$ for every $i$, and a second player probes arbitrary vertices $c_1,c_2,\dots$ of $G$, and learns whether or not the distance between $c_{i+1}$ and $m_{i+1}$ is at most the distance between $c_i$ and $m_i$. Up to what distance $d$ can the second player determine the position of the first? For trees of bounded maximum degree and grids, we show that $d$ is bounded by a constant. We conjecture that $d=O(logn)$ for every graph $G$ of order $n$, and show that $d=0$ if $m_{i+1}$ may differ from $m_i$ only if $i$ is a multiple of some sufficiently large integer.     

小区域科技实力及其评估体系

科技实力是运作主体能够进行并完成科技活动的能力。科技实力是一个评估性概念，它反映了科学技术的创新，发展，转移，推广，储备条件以及管理，效果等不同层面的综合性的特征，科技实力由科技潜在能力（科技势能），科技显现能力（科技动能）构成，它包含了对科技资源及分布状态，科技资源保障能力，科技创新能力，科技开发能力，科技转移能力和科技活动运作能力的综合描述。     

Quenching Versus Blow-up

This paper is concerned with the semilinear heat equation u_t = Δu - u^{-q} in Ω × (0, T) under the nonlinear boundary condition \frac{∂u}{∂v} = u^p on ∂Ω × (0, T). Criteria for finite time quenching and blow-up are established, quenching and blow-up sets are discussed, and the rates of quenching and blow-up are obtained.     

Small quasimultiple affine and projective planes: Some improved bounds

We improve the known bounds on r(n): = min {λ| an (n², n, λ)-RBIBD exists} in the case where n + 1 is a prime power. In such a case r(n) is proved to be at most n + 1. If, in addition, n − 1 is the product of twin prime powers, then r(n) ${\ \le \ }{n \over 2}$. We also improve the known bounds on p(n): = min{λ| an (n² + n + 1, n + 1, λ)-BIBD exists} in the case where n² + n + 1 is a prime power. In such a case p(n) is bounded at worst by but better bounds could be obtained exploiting the multiplicative structure of GF(n² + n + 1). Finally, we present an unpublished construction by M. Greig giving a quasidouble affine plane of order n for every positive integer n such that n − 1 and n + 1 are prime powers. © 1998 John Wiley & Sons, Inc. J Combin Designs 6: 337–345, 1998     

On a decomposition for infinite transition matrices

Heyman gives an interesting factorization of I-P, where P is the transition probability matrix for an ergodic Markov chain. We show that this factorization is valid if and only if the Markov chain is recurrent. Moreover, we provide a decomposition result which includes all ergodic, null recurrent as well as the transient Markov chains as special cases. Such a decomposition has been shown to be useful in the analysis of queues. This revised version was published online in June 2006 with corrections to the Cover Date.     

了解积分——分割的艺术

求一个函数的黎曼积分,实际上就是一个分割、近似代替、求和、取极限的过程．分割是整个过程的初始点．本文以黎曼积分中的分割问题做背景知识,用通俗的语言,而不是严格的数学语言,介绍了分割的过程是如何实现的,应该注意哪些基本问题,整体与局部的联系,如何保证分割是我们期望的、有效的、均匀分割,以及对一个空间的或者集合的分割如何实现等,做了些许描述．为初学者在学习中并应用这样的方法时,应该如何思考问题,如何动手解决问题,进而如何创造新的知识,提供一个可以借鉴的途径．     

t-Extending Modules and t-Baer Modules

We introduce the notions of “t-extending modules,” and “t-Baer modules,” which are generalizations of extending modules. The second notion is also a generalization of nonsingular Baer modules. We show that a homomorphic image (hence a direct summand) of a t-extending module and a direct summand of a t-Baer module inherits the property. It is shown that a module M is t-extending if and only if M is t-Baer and t-cononsingular. The rings for which every free right module is t-extending are called right Σ-t-extending. The class of right Σ-t-extending rings properly contains the class of right Σ-extending rings. Among other equivalent conditions for such rings, it is shown that a ring R is right Σ-t-extending, if and only if, every right R-module is t-extending, if and only if, every right R-module is t-Baer, if and only if, every nonsingular right R-module is projective. Moreover, it is proved that for a ring R, every free right R-module is t-Baer if and only if Z ₂(R _R ) is a direct summand of R and every submodule of a direct product of nonsingular projective R-modules is projective.     

Cauchy's Problem for Degenerate Quasilinear Hyperbolic Equations with Measures as Initial Values

The aim of this paper is to discuss the Cauchy problem for degenerate quasilinear hyperbolic equations of the form \frac{∂u}{∂t} + \frac{∂u^m}{∂x} = -u^p, m > 1, p > 0 with measures as initial conditions. The existence and uniqueness of solutions are obtained. In particular, we prove the following results: (1) 0 < p < 1 is a necessary and sufficient condition for the above equations to have extinction property; (2) 0 < p < m is a necessary and sufficient condition for the above equations to have localization property of the propagation of perturbations.     

ParadisEO: A Framework for the Reusable Design of Parallel and Distributed Metaheuristics

In this paper, we present the ParadisEO white-box object-oriented framework dedicated to the reusable design of parallel and distributed metaheuristics (PDM). ParadisEO provides a broad range of features including evolutionary algorithms (EA), local searches (LS), the most common parallel and distributed models and hybridization mechanisms, etc. This high content and utility encourages its use at European level. ParadisEO is based on a clear conceptual separation of the solution methods from the problems they are intended to solve. This separation confers to the user a maximum code and design reuse. Furthermore, the fine-grained nature of the classes provided by the framework allow a higher flexibility compared to other frameworks. ParadisEO is of the rare frameworks that provide the most common parallel and distributed models. Their implementation is portable on distributed-memory machines as well as on shared-memory multiprocessors, as it uses standard libraries such as MPI, PVM and PThreads. The models can be exploited in a transparent way, one has just to instantiate their associated provided classes. Their experimentation on the radio network design real-world application demonstrate their efficiency.     

ETA INVARIANTS, DIFFERENTIAL CHARACTERS AND FLAT VECTOR BUNDLES

The purpose of this paper is to give a refinement of the Atiyah-Singer families index theorem at the level of differential characters. Also a Riemann-Roch-Grothendieck theorem for the direct image of flat vector bundles by proper submersions is proved, with Chern classes with coefficients in C/Q. These results are much related to prior work of Gillet-Soule, Bismut-Lott and Lott.     

The dial-a-ride problem: models and algorithms

The Dial-a-Ride Problem (DARP) consists of designing vehicle routes and schedules for n users who specify pickup and delivery requests between origins and destinations. The aim is to plan a set of m minimum cost vehicle routes capable of accommodating as many users as possible, under a set of constraints. The most common example arises in door-to-door transportation for elderly or disabled people. The purpose of this article is to review the scientific literature on the DARP. The main features of the problem are described and a summary of the most important models and algorithms is provided. This is an updated version of a paper that appeared in 4OR 1:89–101, 2003.