On the homology of mapping spaces

Following a Bendersky-Gitler idea, we construct an isomorphism between Anderson’s and Arone’s complexes modelling the chain complex of a mapping space. This allows us to apply Shipley’s convergence theorem to Arone’s model. As a corollary, we reduce the problem of homotopy equivalence for certain “toy” spaces to a problem in homological algebra.     

On the Equivalence and Generalized of Weyl Theorem Weyl Theorem

We know that an operator T acting on a Banach space satisfying generalized Weyl＇s theorem also satisfies Weyl＇s theorem. Conversely we show that if all isolated eigenvalues of T are poles of its resolvent and if T satisfies Weyl＇s theorem, then it also satisfies generalized Weyl＇s theorem. We give also a sinlilar result for the equivalence of a-Weyl＇s theorem and generalized a-Weyl＇s theorem. Using these results, we study the case of polaroid operators, and in particular paranormal operators.     

The behaviour of the modified Levene’s test when data are not normally distributed

This is a simulation study that analyzes the robustness properties of tests for equality of variances in terms of both, Type I error rate and power. The well-known Levene’s and Bartlett’s tests, along with different modifications proposed for Levene’s test with and without bootstrapping are examined. Without bootstrapping, some of the modifications may produce better homogeneity tests. Bootstrapping Levene’s test based on the median and this test simultaneously modified by Keyes–Levy’s adjustment and Satterthwaite’s correction are always robust for the significance level under any kind of distribution and combination of sample sizes. None of the tests examined provides protection against extreme values in symmetric distributions.     

Quadratic relations for a q-analogue of multiple zeta values

We obtain a class of quadratic relations for a q-analogue of multiple zeta values (qMZV’s). In the limit q→1, it turns into Kawashima’s relation for multiple zeta values. As a corollary we find that qMZV’s satisfy the linear relation contained in Kawashima’s relation. In the proof we make use of a q-analogue of Newton series and Bradley’s duality formula for finite multiple harmonic q-series.     

A simple proof of some ergodic theorems

Some ideas of T. Kamae’s proof using nonstandard analysis are employed to give a simple proof of Birkhoff’s theorem in a classical setting as well as Kingman’s subadditive ergodic theorem.     

On the applicability of two Newton methods for solving equations in Banach space

In this study we examine the applicability of Newton’s method and the modified Newton’s method for approximating a locally unique solution of a nonlinear equation in a Banach space. We assume that the Newton-Kantorovich hypothesis for Newton’s method is violated, but the corresponding condition for the modified Newton method holds. Under these conditions there is no guarantee that Newton’s method starting from the same initial guess as the modified Newton’s method converges. Hence, it seems that we must always use the modified Newton method under these conditions. However, we provide a numerical example to demonstrate that in practice this may not be a good decision.     

Random trees under CH

We extend Jensen’s Theorem that Souslin’s Hypothesis is consistent with CH, by showing that the statement Souslin’s Hypothesis holds in any forcing extension by a measure algebra is consistent with CH. We also formulate a variation of the principle (*) (see [AT97], [Tod00]) for closed sets of ordinals, and show its consistency relative to the appropriate large cardinal hypothesis. Its consistency with CH would extend Silver’s Theorem that, assuming the existence of an inaccessible cardinal, the failure of Kurepa’s Hypothesis is consistent with CH, by its implication that the statement Kurepa’s Hypothesis fails in any forcing extension by a measure algebra is consistent with CH.     

Relations of core mass-stellar luminosity and core mass-stellar radius for AGB and FGB stars

The relations between core mass and stellar luminosity and radius for AGB and FGB stars are systematically investigated with the latest stellar models. A single unique relation between the core mass and giant’s luminosity is obtained. The core mass-giant’s radius relations are given for both Pop I and Pop II stars. The core mass-giant’s luminosity relation is almost independent of the stellar parameters, such as stellar metallicity, mixing length parameter α, and stellar winds. The core mass-giant’s radius relation is somewhat affected by the parameters. The giant’s radius at anM _c (core mass) for Pop II is smaller than that for Pop I (by a factor of ≈ 1.5). A larger mixing length parameter α also tends to reduce the giant’s radius. Project supported by the Climbing Program of the National Science Foundation of China.     

A theorem of the maximin and applications to Bayesian zero-sum games

Consider a family of zero-sum games indexed by a parameter that determines each player’s payoff function and feasible strategies. Our first main result characterizes continuity assumptions on the payoffs and the constraint correspondence such that the equilibrium value and strategies depend continuously and upper hemicontinuously (respectively) on the parameter. This characterization uses two topologies in order to overcome a topological tension that arises when players’ strategy sets are infinite-dimensional. Our second main result is an application to Bayesian zero-sum games in which each player’s information is viewed as a parameter. We model each player’s information as a sub-σ-field, so that it determines her feasible strategies: those that are measurable with respect to the player’s information. We thereby characterize conditions under which the equilibrium value and strategies depend continuously and upper hemicontinuously (respectively) on each player’s information.     

Arithmetic height functions over finitely generated fields

In this paper, we propose a new height function for a variety defined over a finitely generated field over ℚ. For this height function, we prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (Manin-Mumford’s conjecture). Oblatum 7-VI-1999 & 21-IX-1999 / Published online: 24 January 2000     

Moral coherence,moral worth and explanations of moral motivation

Moral internalism and moral externalism compete over the best explanation of the link between judgment and relevant motivation but, it is argued, they differ at best only verbally. The internalist rational-conceptual nature of the link’ as accounted by M. Smith in The Moral Problem is contrasted to the externalist, also rational, link that requires in addition support from the agent’s psychological-dispositional profile; the internalist link, however, is found to depend crucially on a, similarly to the externalist, psychologically ‘loaded’ profile. It is also argued that the differentiation of the two competing explanations is insufficient partly because they both fail to consider crucial quantitative parameters of the judgment-motivation link. Such parameters become very important particularly in the light of Smith’s claim that this link is grounded on the observable “striking fact” where changes in the set of one’s moral beliefs systematically bring about changes in one’s moral behavior. Examples of algorithms measuring moral coherence and moral worth are provided to serve as evidence for what it comes down to, vis-à-vis the alleged fact, only a verbal dispute between the two camps. Finally, the ‘misfiring’ of these explanations is understood in connection to the irreducibility of concepts such as ‘moral worth’, and/or, ‘moral sensitivity’.     

Artistic Expression Goes Green

The paper is a critical discussion of the rich and insightful final chapter of Mitchell Green’s Self-Expression. There, Green seeks to elucidate the compelling, but inchoate intuition that when we’re fully and most expertly expressing ourselves, we can ‘push out’ from within not just our inner representations, but also the ways that we feel. I question, first, whether this type of ‘qualitative expression’ is really distinct from the other expressive forms that Green explores, and also whether it’s genuinely ‘expressive’. I then scrutinize the nature of the ‘qualitative congruences’ that lie at the heart of Green’s theory; and I wonder whether they can play the role Green claims they can in providing a novel account of artistic expression.     

P-distances, q-distances and a generalized Ekeland’s variational principle in uniform spaces

In this paper, we attempt to give a unified approach to the existing several versions of Ekeland’s variational principle. In the framework of uniform spaces, we introduce p-distances and more generally, q-distances. Then we introduce a new type of completeness for uniform spaces, i.e., sequential completeness with respect to a q-distance (particularly, a p-distance), which is a very extensive concept of completeness. By using q-distances and the new type of completeness, we prove a generalized Takahashi’s nonconvex minimization theorem, a generalized Ekeland’s variational principle and a generalized Caristi’s fixed point theorem. Moreover, we show that the above three theorems are equivalent to each other. From the generalized Ekeland’s variational principle, we deduce a number of particular versions of Ekeland’s principle, which include many known versions of the principle and their improvements.     

On the proof of the reciprocity law for arithmetic Siegel modular functions

Earlier we obtained a new proof of Shimura’s reciprocity law for the special values of arithmetic Hilbert modular functions. In this note we show how from this result one may derive Shimura’s reciprocity law for special values of arithmetic Siegel modular functions. To achieve this we use Shimura’s classification of the special points of the Siegel space, Satake’s classification of the equivariant holomorphic imbeddings of Hilbert-Siegel modular spaces into a larger Siegel space, and, finally, a corrected version of some of Karel’s results giving an action of the Galois group Gal(Q_ab/Q) on arithmetic Siegel modular forms. Research supported in part by the NSF Grant No. DMS-8601130.     

Study on the model of an insurer’s solvency ratio in Markov-modulated Brownian markets

In this paper the insurer’s solvency ratio model with or without jump diffusion process in the presence of financial distress cost is constructed, where an insurer’s solvency ratio is characterized by a Markov-modulated dynamics. By Girsanov’s theorem and the option pricing formula, the expected present value of shareholders’ terminal payoff is provided.     

On Ha＇s Version of Set-valued Ekeland＇s Variational Principle

By using the concept of cone extensions and Dancs-Hegedus-Medvegyev theorem, Ha [Some variants of the Ekeland variational principle for a set-valued map. J. Optim. Theory Appl., 124, 187–206 (2005)] established a new version of Ekeland’s variational principle for set-valued maps, which is expressed by the existence of strict approximate minimizer for a set-valued optimization problem. In this paper, we give an improvement of Ha’s version of set-valued Ekeland’s variational principle. Our proof is direct and it need not use Dancs-Hegedus-Medvegyev theorem. From the improved Ha’s version, we deduce a Caristi-Kirk’s fixed point theorem and a Takahashi’s nonconvex minimization theorem for set-valued maps. Moreover, we prove that the above three theorems are equivalent to each other.     

Algebraic properties of Hamel functions

We say that f: ℝ → ℝ is LIF if it is linearly independent over ℚ as a subset of ℝ² and that it is a Hamel function (HF) if it is a Hamel basis of ℝ². We construct an example of HF bijection and use a similar method to prove that any function can be represented as the composition of three HF’s as well as the limit of uniformly convergent sequence of HF’s. Finally we consider products of HF’s, maximal invariant classes (with respect to several algebraic operations) and pose some open problems concerning sets of continuity points of HF’s.     

Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment

The aim of this article is further extending the linear programming techniques for multidimensional analysis of preference (LINMAP) to develop a new methodology for solving multiattribute decision making (MADM) problems under Atanassov’s intuitionistic fuzzy (IF) environments. The LINMAP only can deal with MADM problems in crisp environments. However, fuzziness is inherent in decision data and decision making processes. In this methodology, Atanassov’s IF sets are used to describe fuzziness in decision information and decision making processes by means of an Atanassov’s IF decision matrix. A Euclidean distance is proposed to measure the difference between Atanassov’s IF sets. Consistency and inconsistency indices are defined on the basis of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance to an Atanassov’s IF positive ideal solution (IFPIS) which is unknown a prior. The Atanassov’s IFPIS and the weights of attributes are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally, the distance of each alternative to the Atanassov’s IFPIS can be calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that the methodology proposed in this article can deal with MADM problems under not only Atanassov’s IF environments but also both fuzzy and crisp environments.     

Dancy Cartwright: Particularism in the philosophy of science

This paper aims to explore the space of possible particularistic approaches to Philosophy of Science by examining the differences and similarities between Jonathan Dancy’s moral particularism—as expressed in both his earlier writings (e.g., Moral Reasons, 1993), and, more explicitly defended in his book Ethics without Principles (2004)—and Nancy Cartwright’s particularism in the philosophy of science, as defended in her early collection of essays, How the Laws of Physics Lie (1983), and her later book, The Dappled World: A Study of the Boundaries of Science (1999). I shall argue that Dancy’s particularism is more radical, but also more plausible, than Cartwright’s, concluding that we have good reason to embrace a scientific particularism that is far closer to Dancy’s ethical particularism than any view defended by Nancy Cartwright, or any other philosopher from the ‘Stanford school’ of scientific theory.     

On the algebraic integrals of the dynamical equations

We bring to the reader’s attention a translation of Levi-Civita’s work “Sugli integrali algebrici delle equazioni dinamiche” (1896).