Lightlike surfaces of spacelike curves in de Sitter 3-space

The Lorentzian space form with the positive curvature is called de Sitter space which is an important subject in the theory of relativity. In this paper we consider spacelike curves in de Sitter 3-space. We define the notion of lightlike surfaces of spacelike curves in de Sitter 3-space. We investigate the geometric meanings of the singularities of such surfaces. Work partially supported by Grant-in-Aid for formation of COE. ‘Mathematics of Nonlinear Structure via Singularities’     

Constructing greedy linear extensions by interchanging chains

A natural way to prove that a particular linear extension of an ordered set is ‘optimal’ with respect to the ‘jump number’ is to transform this linear extension ‘canonically’ into one that is ‘optimal’. We treat a ‘greedy chain interchange’ transformation which has applications to ordered sets for which each ‘greedy’ linear extension is ‘optimal’.     

An alternative moving frame for a tubular surface around a spacelike curve with a spacelike normal in Minkowski 3-space

We describe a robust method for constructing a tubular surface surrounding a spacelike curve with a spacelike principal normal in Minkowski 3-Space. Our method is designed to eliminate undesirable twists and wrinkles in the tubular surface’s skin at points where the curve experiences high torsion. In our construction the tubular surface’s twist is bounded by the spacelike curve’s curvature and is independent of the spacelike curve’s torsion.      

Proper,reflecting and absorbing facts of complementary cones

A common approach in studying the linear complementarity problem is via the geometry of the complementary cones. In the case of nondegeneracy, the concept of a ‘proper facet’ and a ‘reflecting facet’ have proven useful. This paper extends these concepts to the degenerate case. Under degeneracy, a facet may turn out to be neither proper nor reflecting, but, a third type which we designate as ‘absorbing’. Previous results in this area can be easily extended using these more general definitions.     

On Estimating a Dynamic Function of a Stochastic System with Averaging

We consider a two-scaled diffusion system, when drift and diffusion parameters of the ‘slow’ component are contaminated by the ‘fast’ unobserved component. The goal is to estimate the dynamic function which is defined by averaging the drift coefficient of the ‘slow’ component w.r.t. the stationary distribution of the ‘fast’ one. We apply a locally linear smoother with a data-driven bandwidth choice. The procedure is fully adaptive and nearly optimal up to a log log factor. This revised version was published online in June 2006 with corrections to the Cover Date.     

Localization in right (*)-serial coalgebras

In this article, we apply the localization techniques to right (*)-serial coalgebras and obtain some interesting results. In particular, we give a characterization of right (*)-serial coalgebras by means of its ‘local structure’, which is the localized right (*)-serial coalgebras, and we get a main result—the periodicity theorem.     

Test of symmetry of a one-dimensional distribution against positive biasedness

Summary Definitions of different strengths are given to the notion of ‘a positively biased random variable’. This notion is related to that of ‘a stochastically larger component of a two-dimensional random vector’, which was introduced previously by the authors. Properties of common rank tests of symmetry about zero against our specification of alternatives are studied in detail. The positive biasedness is extended to ‘positively more biased’. Test of symmetry of a two-dimensional random vector is also referred to.     

Qualia and the Argument from Illusion: A Defence of Figment

This paper resurrects two discredited ideas in the philosophy of mind. The first: the idea that perceptual illusion might have something metaphysically significant to tell us about the nature of phenomenal consciousness. The second: that the colours and other qualities that ‘fill’ our sensory fields are occurrent properties (rather than representations of properties) that are, nevertheless, to be distinguished from the ‘objective’ properties of things in the external world. Theories of consciousness must recognize the existence of what Daniel Dennett mockingly labels ‘figment,’ but this result—though metaphysically and epistemologically significant—is not incompatible with either physicalism or naturalized semantics.

Isotonic tests for spread and tail

Summary One-sample test problem for ‘stochastically more (or less) spread’ is defined and a family of tests with isotonic power is given. The problem is closely related to that for ‘longer (or shorter) tail’ in the reliability theory and the correspondence between them is shown. To characterize the tests three spread preorders inR ⁿ and corre-sponding tail preorders inR ₊ ⁿ are introduced. Functions which are ‘monotone’ in these orders, and subsets which are ‘centrifugal’ or ‘centripetal’ with respect to these orders are studied. These notions generalize the Schur convexity. The Institute of Statistical Mathematics     

Potential,value, and coalition formation

In this paper, a simple probabilistic model of coalition formation provides a unified interpretation for several extensions of the Shapley value. Weighted Shapley values, semivalues, weak (weighted or not) semivalues, and the Shapley value itself appear as variations of this model. Moreover, some notions that have been introduced in the search of alternatives to Shapley’s seminal characterization, as ‘balanced contributions’ and the ‘potential’ are reinterpreted from this point of view. Natural relationships of these conditions with some mentioned families of ‘values’ are shown. These reinterpretations strongly suggest that these conditions are more naturally interpreted in terms of coalition formation than in terms of the classical notion of ‘value.’      

Roof duality,complementation and persistency in quadratic 0–1 optimization

The paper is concerned with the ‘primal’ problem of maximizing a given quadratic pseudo-boolean function. Four equivalent problems are discussed—the primal, the ‘complementation’, the ‘discrete Rhys LP’ and the ‘weighted stability problem of a SAM graph’. Each of them has a relaxation—the ‘roof dual’, the ‘quadratic complementation,’ the ‘continuous Rhys LP’ and the ‘fractional weighted stability problem of a SAM graph’. The main result is that the four gaps associated with the four relaxations are equal. Furthermore, a solution to any of these problems leads at once to solutions of the other three equivalent ones. The four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem. The optimal solutions of the ‘roof-dual’ define ‘best’ linear majorantsp(x) off, having the following persistency property: if theith coefficient inp is positive (negative) thenx _i=1 (0) in every optimum of the primal problem. Several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal. On the other hand, a class of gap-free functions (properly including the supermodular ones) is exhibited.     

Extending the Ehresmann-Schein-Nambooripad Theorem

We extend the ‘∨-premorphisms’ part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive categories, following on from a result of Lawson (J. Algebra 141:422–462, 1991) for the ‘morphisms’ part. However, it is so-called ‘∧-premorphisms’ which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type theorem for (ordered) ∧-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem in the inverse case.     

A changing trajectory of proof learning in the geometry inquiry classroom

The purpose of this study is to explore how students changes through learning to construct mathematical proofs in an inquiry-based middle school geometry class in Korea. Although proof has long been considered as one of the most important aspects of mathematics education, it is well-known that it is one of the most difficult areas of school mathematics for students. The geometry inquiry classroom (GIC) is an experimental class designed to teach geometry, especially focusing on teaching proof, based on students’ own inquiry. Based on a 2-year participant observation in the GIC, this study was conducted to address the following research question: how has students’ practice of mathematical proof been changed through their participation in the GIC? The in-depth analysis of the classroom discourse identified three stages through which the students’ practice of mathematical proof was transformed in the GIC: ‘emergent understanding of proof’, ‘proof learning as a goal-oriented activity’, ‘experiencing proof as the practice of mathematics’. The study found that as learning evolved through these stages, so the mathematics teacher’s role shifted from being an instructor to a mediator of communication. Most importantly, this research showed that the GIC has created a learning environment where students develop their competence in constructing meaningful mathematical proof and grow to be ‘a human who proves’, ultimately ‘a person who playfully engages with mathematics’.     

Program explanations and causal relevance

Frank Jackson and Philip Pettit have defended a non-reductive account of causal relevance known as the ‘program explanation account’. Allegedly, irreducible mental properties can be causally relevant in virtue of figuring in non-redundant program explanations which convey information not conveyed by explanations in terms of the physical properties that actually do the ‘causal work’. I argue that none of the possible ways to spell out the intuitively plausible idea of a program explanation serves its purpose, viz., defends non-reductive physicalism against Jaegwon Kim’s Causal Exclusion Argument according to which non-reductive physicalism is committed to epiphenomenalism because irreducible mental properties are ‘screened off’ from causal relevance by their physical realizers. Jackson and Pettit’s most promising explication of a program explanation appeals to the idea of invariance of effect under variation of realization, but I show that invariance of effect under variation of realization is neither necessary nor sufficient for causal relevance.     

Ploucquet’s “Refutation” of the Traditional Square of Opposition

In the 18th century, Gottfried Ploucquet developed a new syllogistic logic where the categorical forms are interpreted as set-theoretical identities, or diversities, between the full extension, or a non-empty part of the extension, of the subject and the predicate. With the help of two operators ‘O’ (for “Omne”) and ‘Q’ (for “Quoddam”), the UA and PA are represented as ‘O(S) – Q(P)’ and ‘Q(S) – Q(P)’, respectively, while UN and PN take the form ‘O(S) > O(P)’ and ‘Q(S) > O(P)’, where ‘>’ denotes set-theoretical disjointness. The use of the symmetric operators ‘–’ and ‘>’ gave rise to a new conception of conversion which in turn lead Ploucquet to consider also the unorthodox propositions O(S) – O(P), Q(S) – O(P), O(S) > Q(P), and Q(S) > Q(P). Although Ploucquet’s critique of the traditional theory of opposition turns out to be mistaken, his theory of the “Quantification of the Predicate” is basically sound and involves an interesting “Double Square of Opposition”. My thanks are due to Hanno von Wulfen for helpful discussions and for transforming the word-document into a Latex-file.     

Experiments with an interactive paired comparison simplex method for molp problems

In this paper, an interactive paired comparison simplex based method formultiple objective linear programming (MOLP) problems is developed and compared to other interactive MOLP methods. The decision maker (DM)’s utility function is assumed to be unknown, but is an additive function of his known linearized objective functions. A test for ‘utility efficiency’ for MOLP problems is developed to reduce the number of efficient extreme points generated and the number of questions posed to the DM. The notion of ‘strength of preference ’ is developed for the assessment of the DM’s unknown utility function where he can express his preference for a pair of extreme points as ‘strong ’, ‘weak ’, or ‘almost indifferent ’. The problem of ‘inconsistency of the DM’ is formalized and its resolution is discussed. An example of the method and detailed computational results comparing it with other interactive MOLP methods are presented. Several performance measures for comparative evaluations of interactive multiple objective programming methods are also discussed. All rights reserved. This study, or parts thereof, may not be reproduced in any form without written permission of the authors.     

Le flux d'énergie en mécanique: Application aux turbo-machines

Summary The concept of flux of energy, first introduced in electrodynamics byJ. H. Poynting, can be extended to the domain of fluid-mechanics. It conduces to recognize in the flux of energy for a continuous portion of matter two parts: the first one, which can be called ‘transported’, corresponds to the energy localized in the matter and carried with it as a consequence of its displacement; the other results from the work developed by the stresses and can be called ‘transmitted’. The expression of this flux of energy in the general case of variable motion of a compressible fluid introduces the concept of enthalpy. Its application to an extension ofHelmholtz's theorem on the conservation of vorticity in a perfect fluid, according which bound vortexes have a definite relative motion across the fluid, contributes to explain the mechanism by which, even in the case of grids with a large pitch: chord ratio (Kaplan turbines, screw propellers), the energy of all parts of fluid is finally transmitted to the moving blades.      

Cohomological stratification of diagram algebras

The class of cellularly stratified algebras is defined and shown to include large classes of diagram algebras. While the definition is in combinatorial terms, by adding extra structure to Graham and Lehrer’s definition of cellular algebras, various structural properties are established in terms of exact functors and stratifications of derived categories. The stratifications relate ‘large’ algebras such as Brauer algebras to ‘smaller’ ones such as group algebras of symmetric groups. Among the applications are relative equivalences of categories extending those found by Hemmer and Nakano and by Hartmann and Paget, as well as identities between decomposition numbers and cohomology groups of ‘large’ and ‘small’ algebras.     

Analysis and design of selection committees: a game theoretic secretary problem

Firms often delegate important decisions to committees which are set up specifically for that purpose; for example selection committees. We analyze the equilibrium behavior of a game in which committee members (the players) interview candidates sequentially, either hiring or going on to the next one. The players have differing evaluations of candidates (e.g. one cares about typing skills; the other about IT skills), which become their utilities if the candidate is hired. We then consider the optimal design (rules of the game) of such a committee, from the point of view of the firm. That is, which rules hire candidates which maximize the firm’s utility. Our committee game has a first round in which the members sequentially, by order of player number, say ‘yea’ or ‘nea’ to the candidate. If there are sufficient ‘yeas’ then she is tentatively hired; otherwise she is rejected. In the former case, members who said nea can veto the candidate in the second round. Thus the candidate is either hired, rejected, or vetoed. In the last case, the member casting a veto has one less to use on later candidates. We analyze equilibria where a player may say ‘yea’ to a candidate he would prefer not to hire, in order to force the other player to use up a valuable veto. We show that for the uniform candidate distribution there is a unique equilibrium and better candidates for the firm are hired when there are more vetoes. However we exhibit a candidate distribution where increasing the numbers of vetoes results in hiring worse candidates.