A proof is given for the theorem that at least one bound state exists in a one-dimensional attractive potential however weak it may be. The proof is constructive in that it provides a method to explicitly solve the eigenvalue problem for the eigenvalues as well as the eigenfunctions. The method is well suited to precise numerical calculations.

We investigate how weak square principles are denied by Chang’s Conjecture and its generalizations. Among other things we prove that Chang’s Conjecture does not imply the failure of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\omega_1, 2}}$$\end{document}, i.e. Chang’s Conjecture is consistent with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\square_{\omega_1, 2}}$$\end{document}.

Minami–Sakai :883–898, 2016) investigated the cofinal types of the Katětov and the Katětov–Blass orders on the family of all \ ideals. In this paper we discuss these orders on analytic P-ideals and Borel ideals. We prove the following:The family of all analytic P-ideals has the largest element with respect to the Katětov and the Katětov–Blass orders.The family of all Borel ideals is countably upward directed with respect to the Katětov and the Katětov–Blass orders. In the course of the proof of (...) the latter result, we also prove that for any analytic ideal \ there is a Borel ideal \ with \. (shrink)

The essay is a written version of a talk Nakamura Yūjirō gave at the College international de philosophie in Paris in 1983. In the talk Nakamura connects the issue of common sense in his own work to that of place in Nishida Kitarō and the creative imagination in Miki Kiyoshi. He presents this connection between the notions of common sense, imagination, and place as constituting one important thread in contemporary Japanese philosophy. He begins by discussing the significance of (...) place (basho) that is being rediscovered today in response to the shortcomings of the modern Western paradigm, and discusses it in its various senses, such as ontological ground or substratum, the body, symbolic space, and linguistic or discursive topos in ancient rhetoric. He then relates this issue to the philosophy of place Nishida developed in the late 1920s, and after providing an explication of Nishida’s theory, discusses it further in light of some linguistic and psychological theories. Nakamura goes on to discuss his own interest in the notion of common sense traceable to Aristotle and its connection to the rhetorical concept of topos, and Miki’s development of the notion of the imagination in the 1930s in response to Nishida’s theory. And in doing so he ties all three—common sense, place, and imagination—together as suggestive of an alternative to the modern Cartesian standpoint of the rational subject that has constituted the traditional paradigm of the modern West. (shrink)

In this paper we will study a formal system of intuitionistic modal predicate logic. The main result is its semantic completeness theorem with respect to algebraic structures. At the end of the paper we will also present a brief consideration of its syntactic relationships with some similar systems.

We propose an efficient algorithm for deciding the reachability between any nodes on XML data represented by connected directed graphs. We develop a technique to reduce the size of the reference table for the reachability test. Using the small table and the standard range labeling method for rooted ordered trees, we show that our algorithm answers almost queries in a constant time preserving the space efficiency and a reasonable preprocessing time.

The weakly compact reflection principle\\) states that \ is a weakly compact cardinal and every weakly compact subset of \ has a weakly compact proper initial segment. The weakly compact reflection principle at \ implies that \ is an \-weakly compact cardinal. In this article we show that the weakly compact reflection principle does not imply that \ is \\)-weakly compact. Moreover, we show that if the weakly compact reflection principle holds at \ then there is a forcing extension preserving (...) this in which \ is the least \-weakly compact cardinal. Along the way we generalize the well-known result which states that if \ is a regular cardinal then in any forcing extension by \-c.c. forcing the nonstationary ideal equals the ideal generated by the ground model nonstationary ideal; our generalization states that if \ is a weakly compact cardinal then after forcing with a ‘typical’ Easton-support iteration of length \ the weakly compact ideal equals the ideal generated by the ground model weakly compact ideal. (shrink)

We study the relationship between the semistationary reflection principle and stationary reflection principles. We show that for all regular cardinals Λ ≥ ω₂ the semistationary reflection principle in the space [Λ](1) implies that every stationary subset of $E_{\omega}^{\lambda}\coloneq \{\alpha \in \lambda \,|\,{\rm cf}(\alpha)=\omega \}$ reflects. We also show that for all cardinals Λ ≥ ω₃ the semistationary reflection principle in [Λ](1) does not imply the stationary reflection principle in [Λ](1).

This book explores the contributions of East Asian traditions, particularly Buddhism and (Euro)Daoism, to environmental philosophy. It critically examines the conceptions of human responsibility toward nature and across time presented within these traditions as well as in European philosophy. The volume rethinks human relationships to the natural world by focusing on three main themes: Daoist and Eurodaoist perspectives on nature, human responsibility toward nature, and Buddhist perspectives on life and nature. By way of discussing East Asian traditions and European thinkers, (...) this collection reveals that the impact of humanity on the environment is shaped not only by distinctive modes of economic production, but also by cultural beliefs and practices. Representing a unique constellation of environmental and intercultural philosophy, the contributions present systematic approaches to the global need for cultivating environmental responsibility across cultures and generations to address the political, ethical, and aesthetic challenges arising from humanity’s transformative impact on the natural world. (shrink)

The primary objective of this anthology is to make intergenerational justice an issue for intercultural philosophy, and, conversely, to allow the latter to enrich the former. In times of large-scale environmental destabilization, fair- ness between generations is an urgent issue of justice across time, but it is also a global issue of justice across geographical and nation-state borders. This means that the future generations envisioned by the currently living also cross these borders. Thus, different philosophical cultures and traditions of thought (...) should converse to re ect on what is fair to future people. In the remainder of this introduction, we will detail these claims and give an overview of the volume’s chapters. (shrink)

This paper presents a new method that improves robustness of real-coded Genetic Algorithm (GA) for function optimization. It is reported that most of crossover operators for real-coded GA have sampling bias, which prevents to find the optimum when it is near the boundary of search space. They like to search the center of search space much more than the other. Therefore, they will not work on functions that have their optima near the boundary of the search space. Although several methods (...) have been proposed to relax this sampling bias, they could not cancel whole bias. In this paper, we propose a new method, Toroidal Search Space Conversion (TSC), to remove this sampling bias. TSC converts bounded search space into toroidal one without any parameter. Experimental results show that a GA with TSC has higher performance to find the optimum near the boundary of search space and the GA has more robustness concerning the relative position of the optimum. (shrink)

In this paper, we study the relationship among classical logic, intuitionistic logic, and quantum logic . These logics are related in an interesting way and are not far apart from each other, as is widely believed. The results in this paper show how they are related with each other through a dual intuitionistic logic . Our study is completely syntactical.

We give simple proofs of the Singular Cardinal Hypothesis from the Weak Reflection Principle and the Fodor-type Reflection Principle which do not use better scales.