Bipolarization of posets and natural interpolation

The Choquet integral w.r.t. a capacity can be seen in the finite case as a parsimonious linear interpolator between vertices of n[0,1]. We take this basic fact as a starting point to define the Choquet integral in a very general way, using the geometric realization of lattices and their natural triangulation, as in the work of Koshevoy.A second aim of the paper is to define a general mechanism for the bipolarization of ordered structures. Bisets (or signed sets), as well as bisubmodular functions, bicapacities, bicooperative games, as well as the Choquet integral defined for them can be seen as particular instances of this scheme.Lastly, an application to multicriteria aggregation with multiple reference levels illustrates all the results presented in the paper.     

Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay

Vibrations of a beam can be described as an Euler-Bernoulli beam,or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.     

Middle-school students’ concept images of geometric translations

This study explored sixth grade students’ concept images of geometric translations and the possible sources of their conceptions in a non-technological environment. The data were gathered through a written instrument, student and teacher interviews and document analyses. Analyses of student responses revealed two major concept images of geometric translations: (a) translation as translational motion, and (b) translation as both translational and rotational motion. Students who held these conceptions showed various levels of understanding, such as conceiving translations as undefined motion, partially-defined motion, and defined-motion of a single geometric figure on the plane. The findings of the study suggested, in general, consistencies between students’ concept images and their concept definitions. However, most of the students’ concept definitions were inconsistent with the formal concept definition of geometric translations.Data analyses also revealed five interpretations of a translation vector: (a) vector as a reference line, (b) vector as a symmetry line, (c) vector as a direction indicator, (d) vector as a parameter, and (e) vector as an abstract tool. Furthermore, classroom instruction, mathematics and science textbooks, real-life examples and everyday language were the major sources of students’ concept images of geometric translations.     

Optimal payout policy in presence of downside risk

We analyze the determination of a value maximizing dividend payout policy for a broad class of cash reserve processes modeled as spectrally negative jump diffusions. We extend previous results based on continuous diffusion models and characterize the value of the optimal dividend distribution strategy explicitly. We also characterize explicitly the values as well as the optimal dividend thresholds for a class of associated optimal liquidation and sequential lump sum dividend control problems. Our results indicate that both the value as well as the marginal value of the optimal policies are increasing functions of policy flexibility in the discontinuous setting as well.      

Sequential entry and exit decisions with an ergodic performance criterion

We consider a variant of an optimisation problem involving sequential entry and exit decisions that has emerged in the economics literature as a real option model. The problem that we solve aims at maximising an ergodic, or long-term average, performance criterion in a pathwise as well as in an expected sense. Such a performance index is probably better suited to decision making within a sustainable economic environment. Our results include a complete characterisation of the optimal strategy, which can take qualitatively different forms depending on the problem's data, as well as explicit expressions for the maximal value of the associated performance index.     

Nash equilibrium in a pay-as-bid electricity market: Part 1 – existence and characterization

We consider a model of a pay-as-bid electricity market based on a multi-leader-common-follower approach where the producers as leaders are at the upper level and the regulator as a common follower is at the lower level. We fully characterize Nash equilibria for this model by describing necessary and sufficient conditions for their existence as well as providing explicit formulas of such equilibria in the market.     

Simulation methodology — An introduction for queueing theorists

Simulation is a widely used methodology for queueing systems. Its superficial simplicity hides a number of pitfalls which are not all as well known as they should be. In particular simulation experiments need careful design and analysis as well as good presentations of the results. Even the elements of simulation such as the generation of arrival and service times have a chequered history with major problems lying undiscovered for 20 years. On the other hand, good simulation practice can offer much more than is commonly realized.     

关于Sigma-Pi神经网络中的逼近问题

研究Ｒ上不连续函数可作为Ｓｉｇｍａ－Ｐｉ神经网络激励函数的条件,给出了Ｒ一局部黎曼可积函数可作为Ｓｉｇｍａ－Ｐｉ神经网络激励函数的特征条件,本文的结果表明：局部黎曼可积函数作为Ｓｉｇｍａ－Ｐｉ神经网络激励函数的特征条件与连续函数时的情形是一致的。     

The prediction of sequences

The problem of predicting the short-term future behavior of a sequence, after observing it as long as we please, so as to achieve a specified reliability against all possible sequences is considered. For a particular problem, namely, predicting when in a sequence of 0's and 1's the pair (1, 0) in that order is not coming next, a reliability of 3/4 can be approximated as closely as we please, but not achieved. This article appeared as a Research Memorandum of the Rand Corporation, RM-1570, 12 October 1955.     

Engineering design and the development of knowledge for teaching among preservice science teachers

The goal of this article is to inform professional understanding regarding preservice science teachers’ knowledge of engineering and the engineering design process. Originating as a conceptual study of the appropriateness of “knowledge as design” as a framework for conducting science teacher education to support learning related to engineering design, the findings are informed by an ongoing research project. Perkins’s theory encapsulates knowledge as design within four complementary components of the nature of design. When using the structure of Perkins’s theory as a framework for analysis of data gathered from preservice teachers conducting engineering activities within an instructional methods course for secondary science, a concurrence between teacher knowledge development and the theory emerged. Initially, the individuals, who were participants in the research, were unfamiliar with engineering as a component of science teaching and expressed a lack of knowledge of engineering. The emergence of connections between Perkins’s theory of knowledge as design and knowledge development for teaching were found when examining preservice teachers’ development of creative and systematic thinking skills within the context of engineering design activities as well as examination of their knowledge of the application of science to problem‐solving situations.     

An evolving framework for describing student engagement in classroom activities

Student engagement in classroom activities is usually described as a function of factors such as human needs, affect, intention, motivation, interests, identity, and others. We take a different approach and develop a framework that models classroom engagement as a function of students’ conceptual competence in the specific content (e.g., the mathematics of motion) of an activity. The framework uses a spatial metaphor—i.e., the classroom activity as a territory through which students move—as a way to both capture common engagement-related dynamics and as a communicative device. In this formulation, then, students’ engaged participation can be understood in terms of the nature of the “regions” and overall “topography” of the activity territory, and how much student movement such a territory affords. We offer the framework not in competition with other instructional design approaches, but rather as an additional tool to aid in the analysis and conduct of engaging classroom activities.     

Knowledge trees in complex knowledge bases

We extend the use of knowledge trees as a means for questioning knowledge bases with linguistic information. Using Zadeh's theory of approximate reasoning as a tool we provide means for questioning large knowledge bases which have relational, implicational and data type information. We provide a means for answering questions of truth as well as questions of value.     

社会网络分析方法在管理民间信仰活动的应用研究

民间信仰活动是一种复杂的社会现象,其信众群体是一个独特的社会关系网络。本文在国内首次运用社会网络分析的思维和方法,在对冀南地区民间信仰抽样调查的基础上,建立网络模型,通过对民间信仰主体和客体各结点的中心性、凝聚性等进行量化分析,进而探究民间信仰网络的社会结构及其属性,得出信众群体特征、信仰动因、活动特点、社会心态等有益结论,为民间信仰活动的社会治理和政府管理提供科学依据.     

Explicitly given pairs of dual frames with compactly supported generators and applications to irregular B-splines

We consider systems of functions appearing by letting a class of modulations act on a countable collection of functions. These systems correspond to shift-invariant systems, considered on the Fourier side. We provide sufficient conditions for the system to be a frame, as well as an explicit construction of a class of frames and associated duals. We use the result to construct frames based on B-splines with knot sequences satisfying a natural condition, as well as explicitly given duals.     

Optimal design of multi-purpose beam-columns

The paper deals with the optimal design of an elastic pinended member of given volume that is to serve as a beam for a part of its design life and as a column for the rest. The optimal design can be interpreted in two ways. Firstly, it is the design that has the maximum Euler buckling load in column action, subject to a prescribed maximum deflection as a beam. Secondly, it is the design that has the least deflection as a beam under a midspan concentrated load, subject to a minimum permissible Euler buckling load in column action. The effectiveness of the optimal design is judged by comparing it with a prismatic bar of the same volume.     

Arc-Length Method for Frictional Contact Problems Using Mathematical Programming with Complementarity Constraints

A new formulation as well as a new solution technique is proposed for an equilibrium path-following method in two-dimensional quasistatic frictional contact problems. We consider the Coulomb friction law as well as a geometrical nonlinearity explicitly. Based on a criterion of maximum dissipation of energy, we propose a formulation as a mathematical program with complementarity constraints (MPEC) in order to avoid unloading solutions in which most contact candidate nodes become stuck. A regularization scheme for the MPEC is proposed, which can be solved by using a conventional nonlinear programming approach. The equilibrium paths of various structures are computed in cases such that there exist some limit points and/or infinite number of successive bifurcation points.     

Shape identification of anisotropic diffraction gratings for TM-polarized electromagnetic waves

This paper concerns the shape identification problem of anisotropic periodic structures which are known as diffraction gratings. We study the so-called Factorization method as a tool for reconstructing the anisotropic periodic media from measured spectral data involving scattered electromagnetic waves in TM modes. This sampling method provides a simple criterion to compute a picture of shape of diffraction gratings in a rapid way. We propose a rigorous analysis for the method as well as numerical experiments to examine its performance.     

Hereditary crossed products

We characterize when a crossed product order over a maximal order in a central simple algebra by a finite group is hereditary. We need only concentrate on the cases when the group acts as inner automorphisms and when the group acts as outer automorphisms. When the group acts as inner automorphisms, the classical group algebra result holds for crossed products as well; that is, the crossed product is hereditary if and only if the order of the group is a unit in the ring. When the group is acting as outer automorphisms, every crossed product order is hereditary, regardless of whether the order of the group is a unit in the ring.