Tensorial properties of multiple view constraints

We define and derive some properties of the different multiple view tensors. The multiple view geometry is described using a four‐dimensional linear manifold in ℝ^3m, where m denotes the number of images. The Grassman co‐ordinates of this manifold build up the components of the different multiple view tensors. All relations between these Grassman co‐ordinates can be expressed using the quadratic p‐relations. From this formalism it is evident that the multiple view geometry is described by four different kinds of projective invariants; the epipoles, the fundamental matrices, the trifocal tensors and the quadrifocal tensors. We derive all constraint equations on these tensors that can be used to estimate them from corresponding points and/or lines in the images as well as all transfer equations that can be used to transfer features seen in some images to another image. As an application of this formalism we show how a representation of the multiple view geometry can be calculated from different combinations of multiple view tensors and how some tensors can be extracted from others. We also give necessary and sufficient conditions for the tensor components, i.e. the constraints they have to obey in order to build up a correct tensor, as well as for arbitrary combinations of tensors. Finally, the tensorial rank of the different multiple view tensors are considered and calculated. Copyright © 2000 John Wiley & Sons, Ltd.     

论大学数学的教育思想

提出了大学数学教育既要注重知识传播 ,更要注重教会学生用数学的方式思维的观点 .围绕这一观点 ,对数学素养的内涵、教学内容的取舍 ,教学和考试的关系等作了较为详细的论述     

中国股票市场的收益-风险关系和惯性分析

本文采用非对称 EGARCH-M模型刻画了中国股票市场的个股风险 ,并对全市场的收益 -风险特征进行了横向分析 ,结果表明 ,从长期的角度来讲 ,在正常的市场条件下 ,中国股票市场存在着一定的高风险 -高收益、低风险 -低收益的关系 ,但从短期来看 ,由于不确定性因素较多 ,这种风险收益关系并不显著 .其次 ,本文分别采用每只股票历史 3个月的累积收益率、6个月的累积收益率以及 1 2个月的累积收益率分析了中国股票市场的惯性 ,我们发现 ,无论是从短期还是从比较长的时间来看 ,中国股票市场都不存在市场惯性 ,而表现出一定的反转现象 ,但反转现象会随着时间的推移逐渐减弱     

Justification,Justifying, and Leite’s Localism

In a series of papers, Adam Leite has developed a novel view of justification tied to being able to responsibly justify a belief. Leite touts his view as (i) faithful to our ordinary practice of justifying beliefs, (ii) providing a novel response to an epistemological problem of the infinite regress, and (iii) resolving the “persistent interlocutor” problem. Though I find elements of Leite’s view of being able to justify a belief promising, I hold that there are several problems afflicting the overall picture of justification. In this paper, I argue that despite its ambitions, Leite’s view fails to solve the persistent interlocutor problem and does not avoid a vicious regress.     

An Exponential Growth Learning Trajectory: Students’ Emerging Understanding of Exponential Growth Through Covariation

This article presents an Exponential Growth Learning Trajectory (EGLT), a trajectory identifying and characterizing middle grade students’ initial and developing understanding of exponential growth as a result of an instructional emphasis on covariation. The EGLT explicates students’ thinking and learning over time in relation to a set of tasks and activities developed to engender a view of exponential growth as a relation between two continuously covarying quantities. Developed out of two teaching experiments with early adolescents, the EGLT identifies three major stages of students’ conceptual development: prefunctional reasoning, the covariation view, and the correspondence view. The learning trajectory is presented along with three individual students’ progressions through the trajectory as a way to illustrate the variation present in how the participants made sense of ideas about exponential growth.     

In Defence of Powerful Qualities

The ontology of ‘powerful qualities’ is gaining an increasing amount of attention in the literature on properties. This is the view that the so-called categorical or qualitative properties are identical with ‘dispositional’ properties. The position is associated with C.B. Martin, John Heil, Galen Strawson and Jonathan Jacobs. Robert Schroer (2012) has recently mounted a number of criticisms against the powerful qualities view as conceived by these main adherents, and has also advanced his own (radically different) version of the view. In this paper I have three main aims: firstly, I shall defend the ontology from his critique, arguing that his criticisms do not damage the position. Secondly, I shall argue that Schroer’s own version of the view is untenable. Thirdly, the paper shall serve to clear up some conceptual confusions that often bedevil the powerful qualities view.     

Freedom and trying: Understanding agent-causal exertions

In this paper, I argue that trying is the locus of freedom and moral responsibility. Thus, any plausible view of free and responsible action must accommodate and account for free tryings. I then consider a version of agent causation whereby the agent directly causes her tryings. On this view, the agent is afforded direct control over her efforts and there is no need to posit—as other agent-causal theorists do—an uncaused event. I discuss the potential advantages of this sort of view, and its challenges.     

An approach to quasi-Hopf algebras via Frobenius coordinates

We study quasi-Hopf algebras and their subobjects over certain commutative rings from the point of view of Frobenius algebras. We introduce a type of Radford formula involving an anti-automorphism and the Nakayama automorphism of a Frobenius algebra, then view several results in quantum algebras from this vantage-point. In addition, separability and strong separability of quasi-Hopf algebras are studied as Frobenius algebras.     

The selectope for cooperative games

The selectope of a cooperative transferable utility game is the convex hull of the payoff vectors obtained by assigning the Harsanyi dividends of the coalitions to members determined by so-called selectors. The selectope is studied from a set-theoretic point of view, as superset of the core and of the Weber set; and from a value-theoretic point of view, as containing weighted Shapley values, random order values, and sharing values. Received May 1997/Revised version September 1999     

Vagueness as Semantic Indecision: Metaphysical Vagueness vs Indeterminate Reference

After presenting a negative characterization of metaphysical vagueness and the main tenets of the view of vagueness as semantic indecision, the paper critically discusses the objection that such a view requires that at least some vagueness not be just constituted by semantic indecision—but rather by the metaphysical vagueness of some semantic relations themselves submitted by Trenton Merricks and, more recently, Nathan Salmon.     

Regular polyhedra—old and new

Although it is customary to define polygons as certain families of edges, when considering polyhedra it is usual to view polygons as 2-dimensional pieces of the plane. If this rather illogical point of view is replaced by consistently understanding polygons as 1-dimensional complexes, the theory of polyhedra becomes richer and more satisfactory. Even with the strictest definition of regularity this approach leads to 17 individual regular polyhedra in the Euclidean 3-space and 12 infinite families of such polyhedra, besides the traditional ones (which consist of 5 Platonic polyhedra, 4 Kepler—Poinsot polyhedra, 3 planar tessellations and 3 Petrie—Coxeter polyhedra). Among the many still open problems that naturally arise from the new point of view, the most obvious one is the question whether the regular polyhedra found in the paper are the only ones possible in the Euclidean 3-space.This work was supported in part by National Science Foundation Grant MPS74-07547 A01.     

Black-Litterman投资组合模型的进一步推导分析

在理论上通过推导首次得出了Black-Litterman模型(B-L模型)最优权重与信心水平的公式.在各资产收益不相关及单一绝对观点的假设下,得出各资产的B-L模型最优权重与信心水平的简化表达式.借助于此,还对信心水平与最优权重公式的进一步理论分析,并以光大证券的"乌龙指"做实证,详细分析投资者在没有市场观点、拥有内幕信息、以及信心水平在某范围变化时,其所持各投资品权重的特点.     

Particularist semantic normativity

We sketch the view we call contextual semantics. It asserts that truth is semantically correct affirmability under contextually variable semantic standards, that truth is frequently an indirect form of correspondence between thought/language and the world, and that many Quinean commitments are not genuine ontological commitments. We argue that contextualist semantics fits very naturally with the view that the pertinent semantic standards are particularist rather than being systematizable as exceptionless general principles.     

碳排放问题面板数据曲线的棱镜模型聚类分析

采用类比方法构建出一种面板数据曲线的棱镜模型,把时间横坐标与经济问题纵坐标加以角度化变换,选取恰当的经济变量作为棱镜的折射率和顶角,可将面板数据曲线用棱镜曲线进行再描绘.在碳排放问题上,列举大量的面板数据曲线作为具有棱镜曲线形状的证据,并给出聚类分析,解决了棱镜模型的应用问题,得出了存在经济折射定律的观点结论,从而为应用经济学研究提供一种全新视角的分析工具.     

Functionalism about Truth and the Metaphysics of Reduction

Functionalism about truth is the view that truth is an explanatorily significant but multiply-realizable property. According to this view the properties that realize truth vary from domain to domain, but the property of truth is a single, higher-order, domain insensitive property. We argue that this view faces a challenge similar to the one that Jaegwon Kim laid out for the multiple realization thesis. The challenge is that the higher-order property of truth is equivalent to an explanatorily idle disjunction of its realization bases. This consequence undermines the alethic functionalists’ non-deflationary ambitions. A plausible response to Kim’s argument fails to carry over to alethic functionalism on account of significant differences between alethic functionalism and psychological functionalism. Lynch’s revised view in his book Truth as One and Many (2009) fails to answer our challenge. The upshot is that, while mental functionalism may survive Kim’s argument, it mortally wounds functionalism about truth.     

对冯·诺意曼“量子概率论”的两点质疑

本文对于公认的量子力学数学基础—冯·诺意曼概率论提出了两点质疑。从物理上讲,它将导致“粒子的势能以一定的概率超过总能量”这种违背能量守恒原理的结论。从数学上讲,它在某些方面还不如玻恩的概率解释(即常被物理学家称为“经典概率论”的数学意义的概率论)。因此,量子力学的数学基础似乎需要进一步发展和完善。     

OR as Technology: Some Issues and Implications

There has been a growing acceptance of the view that OR can be more appropriately understood as a technology rather than as a science. This view has, however, not been fully developed. This paper seeks to extend this area of investigation by addressing three issues: first, to consider why it is inappropriate to see OR as a science; second, if OR is to be seen as a technology, to ask what model of a technology, the classical or the modern, should be adopted; finally, to explore what implications for understanding OR are held by the most appropriate model of OR as technology. This paper shows that valuable insights might be gained for understanding and guiding the development of OR by seeing it as a technology.     

Ferrers digraphs and threshold graphs

We deduce a set of known characterizations of threshold graphs (Theorem 3) from a set of characterizations of Ferrers digraphs (Theorem 1) by investigating the connection between symmetric Ferrers digraphs and threshold graphs. A direct proof of Theorem 3 is easier than the one provided in here, but the purpose of this paper is to view Theorem 1 as an extension of Theorem 3 to the directed case (this extension point of view still holds on an algorithmic ground).