Products of modal logics and tensor products of modal algebras

One of natural combinations of Kripke complete modal logics is the product, an operation that has been extensively investigated over the last 15 years. In this paper we consider its analogue for arbitrary modal logics: to this end, we use product-like constructions on general frames and modal algebras. This operation was first introduced by Y. Hasimoto in 2000; however, his paper remained unnoticed until recently. In the present paper we quote some important Hasimoto's results, and reconstruct the product operation in an algebraic setting: the Boolean part of the resulting modal algebra is exactly the tensor product of original algebras (regarded as Boolean rings). Also, we propose a filtration technique for Kripke models based on tensor products and obtain some decidability results.     

TEM study of defects generated in 4H-SiC by microindentations on the prismatic plane

The deformation microstructure of single crystals of 4H-SiC resulting from microindentations on a prismatic surface was investigated by TEM. Indentations were performed at 400 and 675°C, i.e. below the brittle to ductile transition temperature of 4H-SiC (temperature close to 1100°C). TEM analysis reveals dissociated dislocations as well as extended stacking faults in the basal plane. In addition, perfect edge dislocations are observed on prismatic planes. From the observations, it is assumed that perfect dislocations are nucleated in the prismatic plane and cross-slip on the basal one where they dissociate.     

肿瘤干细胞分离方法研究现状

肿瘤干细胞理论能够解释肿瘤的发生、发展和转移等生物学行为,使人们对恶性肿瘤有一个全新的认识,为临床治疗展现全新视角,使肿瘤靶向治疗找到了新靶点,改变目前药物针对全部癌细胞的治疗策略。本文就肿瘤干细胞分离方法做一简要综述。     

Congruences on Dynamic Algebras

The lattice Cong of all dynamic congruences on a given dynamic algebra is presented. Whenever is separable with zero we define dynamic ideal on , given rise to the lattice Ide. The notions of kernel of a dynamic congruence andthe congruence generated by a dynamic ideal are introduced todescribe a Galois connection between Cong and Ide. We study conditions under which a dynamic congruence is determined byits kernel.     

The Expansion and Restructuring of Intellectual Property and Its Implications for the Developing World

In this paper we begin with a reference to the work of Hernando de Soto The Mystery of Capital: Why Capitalism Triumphs in the West and Fails Everywhere Else, and his characterization of the Western institution of formal property . We note the linkages that he sees between the institution and successful capitalist enterprise. Therefore, given the appropriateness of his analysis, it would appear to be worthwhile for developing and less developed countries to adjust their systems of ownership to conform more closely to the Western system of formal property. However, we go on to point out that property relationships within the Western system have become subject to redefinition through the expansion of Intellectual Property (IP) rights in ways that ultimately work to the disadvantage of the developing and less developed countries. We point out that this restructuring has been given global application through the implementation of the TRIPS agreement by the WTO. In the final section of the paper I suggest ways in which IP rights and relevant institutions can be reformed in order to avoid the disadvantages to the developing and less developed countries.

Circle graphs and monadic second-order logic

This article is part of a project consisting in expressing, whenever possible, graph properties and graph transformations in monadic second-order logic or in its extensions using modulo p cardinality set predicates or auxiliary linear orders. A circle graph is the intersection graph of a set of chords of a circle. Such a set is called a chord diagram. It can also be described by a word with two occurrences of each letter, called a double occurrence word. If a circle graph is prime for the split (or join) decomposition defined by Cunnigham, it has a unique representation by a chord diagram, and this diagram can be defined by monadic second-order formulas with the even cardinality set predicate. By using the (canonical) split decomposition of a circle graph, we define in monadic second-order logic with auxiliary linear orders all its chord diagrams. This construction uses the fact that the canonical split decomposition of a graph can be constructed in monadic second-order logic with help of an arbitrary linear order. We prove that the order of first occurrences of the letters in a double occurrence word w that represents a connected circle graph determines this word in a unique way. The word w can be defined by a monadic second-order formula from the word of first occurrences of letters. We also prove that a set of circle graphs has bounded clique-width if and only if all the associated chord diagrams have bounded tree-width.     

Plato the Democrat？ Some Thoughts on the Politics of the Laws

In the Laws （which Plato calls his ＂second-best society＂） Plato asserts that the best attainable form of society will combine the better features of autocracy and democracy. The democracy will be one where aidos （＂respect＂） will be a prominent feature, as will be the rule of laws underpinned by the belief that God, not man, is the measure of all things. Unlike in the Republic, the accumulation of wealth and property will be the right of all citizens, including rulers. But it will operate under strict limits： a maximum of four quanta of property will be allowed by any citizen, while a minimum of one （which will provide a good life though perhaps not a rich one） will be guaranteed. The affinity of such a view with that of John Rawls is striking. The article ends with a brief interview between the reader and Plato, in which some of the above issues are discussed.     

道德的法律强制探析

由于存在着道德仅靠自身力量所无法解决的问题 ,而这些问题因其对社会秩序和社会生活的重要性又必须获得解决 ,使得道德的法律强制成为必要。多元背景下道德共识的存在 ,道德与法律共同的问题域以及现代社会的立法民主化机制 ,为道德的法律强制提供了可能。道德法律强制的合理性 ,只有通过对于应当予以法律强制的道德的性质、可强制的道德的范围以及道德法律强制的立法和司法程序的学理分析 ,方可予以证成。     

Algebraic Aspects of Cut Elimination

We will give here a purely algebraic proof of the cut elimination theorem for various sequent systems. Our basic idea is to introduce mathematical structures, called Gentzen structures, for a given sequent system without cut, and then to show the completeness of the sequent system without cut with respect to the class of algebras for the sequent system with cut, by using the quasi-completion of these Gentzen structures. It is shown that the quasi-completion is a generalization of the MacNeille completion. Moreover, the finite model property is obtained for many cases, by modifying our completeness proof. This is an algebraic presentation of the proof of the finite model property discussed by Lafont [12] and Okada-Terui [17].