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Minimal Generating Sets of the Monoid of Partial Order-Preserving Injections
Get PDFMonoids arise in such fields as computer science, physics, and numerous branches of mathematics including abstract algebra, cryptography and operator theory. In this research project we seek to determine minimal generating sets for the monoid of partial order-preserving injections of an n-element set, POI(n). A generating set for a monoid is a collection of elements S such that every element of the monoid can be expressed as a product of elements from S. Generating sets are of fundamental importance across math and science, and mathematicians have great interest in studying generating sets of a variety of algebraic structures. By a minimal generating set, we refer to a generating set for which no proper subset is a generating set. In this paper, we provide necessary and sufficient conditions for a set to be a minimal generating set for POI(n), and we show that there are exactly (n-1)! minimal generating sets for POI(n)
“Am I Doing What I think I’m Doing?”: The Importance of a Theoretical Frame when Integrating Tablets in Teacher Education
Get PDFIn the following self-study, we share our investigation of the shifts in faculty pedagogical beliefs, instructional practices, and curricular decision-making while engaged in a cycle of reflection on tablet-focused teacher education course. We conducted this inquiry into our practice, using Technological Pedagogical Content Knowledge (TPCK) and the Substitution-Augmentation-Modification-Redefinition (SAMR) model as frameworks to examine data from interviews and reflective writing. We conclude the need for the explicit connection of technology professional development, specifically tablet technology, with a meaningful theoretical framework, in order for faculty to engage in effective integration. We also share our model for examining the development of instructor’s thinking about integrating technology, including influences on thinking and classification of instructional decisions into the SAMR taxonomy
COMPARISON AS POETRY: READING EURIPIDES’ BACCHAE AND THE ZHUANGZI
Get PDFThis essay has two major parts. First, a comparison between poetry and comparative work itself. Second, a comparison of the Zhuangzi and Euripides’ Bacchae. Comparison is like a poem in that both are imaginative constructions that rely on the creativity of the comparatist or poet. Comparison and poetry take features of the world and alter them in such a way as to suggest an alternative. The Zhuangzi and the Bacchae, via the theme of forgetting, do the same thing—unsettle our fixed suppositions or knowledge. The argument that a comparative work is like a poem thus relies on the comparison of Zhuangzi and Euripides as an illustration. Both the Zhuangzi and the Bacchae invite a relinquishing of fixed knowledge, and depict a human nature that is tenuous and given to change. This article suggests that a similar experience characterizes the practice of comparison, and that such an experience is something we often see in poetry
“STAND FIXED IN STEADFAST GAZE”: AN EDITORIAL NOTE
Get PDFIn this issue, we hereby present to our readers a group of four essays on literary studies from young scholars. While they are arranged in alphabetical order of the authors’ last names, we would like to offer a brief introduction to them in the chronological order of their topics
WANG GUOWEI, GU HONGMING AND CHINESE PHILOSOPHICAL MODERNITY
Get PDFThis paper aims to explore the issue of modernity in Chinese philosophy in the early 20th century. The case study focuses on modern scholar Wang Guowei 王國維 (1877-1927)’s criticism of his contemporary Gu Hongming辜鴻銘 (1857-1928)’s English translation of the classical Confucian text Zhongyong. I argue that Wang Guowei and Gu Hongming’s case in fact demonstrates two alternative approaches towards philosophical dialogue and cultural exchange. Wang’s approach is a very cultural context-sensitive one: understanding the differences and selecting what is needed for cultural inspiration and reformation—we could call this approach nalaizhuyi拿來主義 (taking-inism)—borrowing without touching the cultural essence. Gu’s approach is more a songchuzhuyi送出主義 (sending-outism). It is a global-local context sensitive one: searching for the local’s path towards the global. Reevaluating Gu’s not very exact cultural translation can provide an opportunity to look beyond the “modernization complex,” deconstruct westernization “spell,” and build a new internationalism. I further argue that Gu’s case represents a kind of risky songchuzhuyi and a false internationalism which makes the native culture speak in the other’s terms while Wang’s cultural stand and his “journey” back to his own cultural sensibility sticks to its own terms and discovers the value of the culture. I then further look at Wang Guowei’s ideal of shenshengzhuyi生生主義 (live-life-ism) which was originally expressed in his Hongloumeng Pinglun 《红楼梦评论》(Critique of A Dream of Red Mansions, 1904) and claim that not only can the ideal of shengshengzhuyi explain the underlying reason for an essential turn in Wang’s academic interests from Western philosophy to Chinese history and archaeology, but it can also be applied positively to the contemporary world
SELF PLANTING OF SPIRITUAL ROOTS: CHINESE PHILOSOPHY AND CHINESE IN THE WORLD (BOOK REVIEW)
No full textSelf planting of Spiritual Roots: Chinese Philosophy and Chinese in the World 灵根自植 中国哲学与世界华人 ). Edited by Chenyang Li and Hong Xiao. Singapore: Confucius Institute, Nanyang Technological University, 2019. 430 Pp
On Numerical Semigroups with Almost-Maximal Genus
Get PDFA numerical semigroup is a cofinite subset of N0, containing 0, that is closed under addition. Its genus is the number of nonnegative integers that are missing. A numerical set is a similar object, not necessarily closed under addition. If T is a numerical set, then A(T)={n in N0 : n+T is a subset of T} is a numerical semigroup. Recently a paper appeared counting the number of numerical sets T where A(T) is a numerical semigroup of maximal genus. We count the number of numerical sets T where A(T) is a numerical semigroup of almost-maximal genus, i.e. genus one smaller than maximal
The conquest of Guatemala: a Nahua and Kaqchikel conquest
No full text Traditionally history has been narrated through a Eurocentric lens and has omitted indigenous perspectives about the Mexican conquests. When learning about the conquest, Iberians have been the main focus of the discussion. However, recent scholars have refocused their attention on indigenous sources that profoundly reshape the historical narrative. As Guatemalan myself, it was not until reading the book Seven Myths of the Spanish Conquests by Matthew Restall that I learned the contributions of indigenous people not only in the conquest of the Mexica Empire but also in the conquest of Guatemala. Acknowledges the contributions of indigenous groups in the conquest of Guatemala, a new approach started by anthropologist Florine G.L. Asselbergs in her book Conquered Conquistadors. This paper seeks to emphasize the agency of indigenous groups in the conquests of Mexico and Guatemala, as the story of their alliance is often ignored and their accomplishments forgotten, as the Iberians’ self-proclaimed superiority has marginalized native contributions.
 
Geometry of a Family of Complex Polynomials
No full textLet Pa be the family of complex-valued polynomials of the form p(z)=(z-a)(z-r)(z-s) with a in [0,1] and r and s on the unit circle. The Gauss-Lucas Theorem implies that the critical points of a polynomial in Pa lie in the unit disk. This paper characterizes the location and structure of these critical points. We show that the unit disk contains an open circular disk in which critical points of polynomials in Pa do not occur. Furthermore, almost every c inside the unit disk and outside of the desert region is the critical point of a unique polynomial in Pa
The Mexican Revolution: American Influence and Working Class Ideologies
No full textThis paper will look at the Mexican Revolution and analyze the relationship between the working class and the Revolutionary leaders in the Northern states. Generally, the working class resided in the northern states of Mexico due to the massive industrialization in those areas by the United States and other foreign entities. Emphasizing the importance of the working class and its relationship with the United States investors and Mexican Revolutionaries I argue that because of massive American influence in the Northern States the working class supported policies that benefited them such as labor reform, opposing any U.S. Involvement, and having quality accessible education. Thereby, motivating Revolutionary leaders to align their political views with those of the working class to build alliances and consolidate power