International Journal of Mathematical Combinatorics, Vol.2

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

On the Basis Number of the Strong Product of Theta Graphs with Cycles

In graph theory, there are many numbers that give rise to a better understanding and interpretation of the geometric properties of a given graph such as the crossing number, the thickness, the genus, the basis number, etc.

Fastest mixing Markov chain on graphs with symmetries

We show how to exploit symmetries of a graph to efficiently compute the fastest mixing Markov chain on the graph (i.e., find the transition probabilities on the edges to minimize the second-largest eigenvalue modulus of the transition probability matrix). Exploiting symmetry can lead to significant reduction in both the number of variables and the size of matrices in the corresponding semidefinite program, thus enable numerical solution of large-scale instances that are otherwise computationally infeasible. We obtain analytic or semi-analytic results for particular classes of graphs, such as edge-transitive and distance-transitive graphs. We describe two general approaches for symmetry exploitation, based on orbit theory and block-diagonalization, respectively. We also establish the connection between these two approaches.Comment: 39 pages, 15 figure

Evangelical Visitor - February 01, 1965 Vol. LXXVIII. No. 3.

Vol. LXXVIII. No. 3

Arkhipov's theorem, graph minors, and linear system nonlocal games

The perfect quantum strategies of a linear system game correspond to certain representations of its solution group. We study the solution groups of graph incidence games, which are linear system games in which the underlying linear system is the incidence system of a (non-properly) two-coloured graph. While it is undecidable to determine whether a general linear system game has a perfect quantum strategy, for graph incidence games this problem is solved by Arkhipov's theorem, which states that the graph incidence game of a connected graph has a perfect quantum strategy if and only if it either has a perfect classical strategy, or the graph is nonplanar. Arkhipov's criterion can be rephrased as a forbidden minor condition on connected two-coloured graphs. We extend Arkhipov's theorem by showing that, for graph incidence games of connected two-coloured graphs, every quotient closed property of the solution group has a forbidden minor characterization. We rederive Arkhipov's theorem from the group theoretic point of view, and then find the forbidden minors for two new properties: finiteness and abelianness. Our methods are entirely combinatorial, and finding the forbidden minors for other quotient closed properties seems to be an interesting combinatorial problem.Comment: Minor updates. Also see video abstract at https://youtu.be/uTudADhT1p

Farmstead Magazine, Fall / Winter 1974 1975

https://digitalmaine.com/farmstead_magazine/1002/thumbnail.jp

Teaching with Passion: A Narrative Inquiry into Elementary Teachers\u27 Identity Development, Personal and Professional Knowledge, and Love of Teaching

This is a study of elementary teachers\u27 identity development, personal and professional knowledge, and love of teaching. The participants of this inquiry are six teachers who teach at Hesse Elementary School in Savannah, Georgia. Diane, Julie, Mary, Susan, Uticia, and Yolanda provide viable insights about their journey as teachers. Their stories offer narrative truisms concerning their identity evolution and the transformation of their professional personality as they live their lives in the classroom. William Ayres\u27 (1989, 2001, 2004, 2004) work on teacher identity and teacher knowledge development provides a framework for this study. Robert Fried\u27s (2001) devotion to passion for teaching also informs this inquiry. Amid the overwhelming obstacles teachers face each day, the nuances of these teachers\u27 experiences of developing passion for teaching or becoming dispassionate about teaching are found in the stories of my teacher participants. From the desire to become teachers at their early ages to the joys and sorrows they have experienced or are experiencing, my participants divulge what it takes to be a teacher today. Sonia Nieto\u27s (2003) lament that, Even under the best of circumstances, teaching is a demanding job, and most teachers do not work under the best of circumstances. The enthusiasm and idealism that bring them to teaching quickly dissipate for many (p. 3), supports the need for more research in the area of teacher burnout and attrition. Found within the lived experiences of Susan, Mary, Uticia, Diane, and Yolanda are antidotes for addressing the demands of teaching. In order to present viable narratives, I utilize Jean Clandinin and Michael Connelly\u27s (2000) narrative inquiry methods to collect the stories of my participants. Participant profiles, autobiographical writings, and reflective journals, are presented in this study. This inquiry also includes interviews, informal conversations and participant observations. Common pedagogical beliefs or disbeliefs are revealed in this study. This study is significant for pre-service and in-service teachers, educators, administrators, and policy makers. For pre-service teachers, this study helps prepare them to develop courage, knowledge, and passion to meet the challenge in the teaching profession. For in-service teachers, the experiences of my teacher participants reveal how passionate veteran teachers go against the grain (Hooks, 1994, p. 203) and fight oppressive mandates with silent opposition. For educators, narrative texts offer additional information about what keeps teachers going (Nieto, 2003). For administrators, my participants\u27 stories provide a much needed megaphone for teachers\u27 voices that are often silenced in fear. These important axioms give administrators guidance for encouraging, supporting, and sometimes defending their teachers. For policy makers, critical nuances concerning teacher identity and professional development reveal what works in my participants\u27 classrooms and provide viable information for curriculum reform. In a time when teacher shortages plague our nations\u27 schools, passionate teachers hold viable information for strengthening teacher commitment to the teaching profession. This narrative inquiry provides keys, often overlooked, for unlocking a treasure chest of encouragement for pre-service and in-service teachers who aspire to make a difference in the world

Cultural performance of roadside shrines: a poststructural postmodern ethnography

Marking the site of death on the road with a shrine, an increasingly popular cultural practice in the United States, is a deeply personal, private affair, however, because shrines are placed in the public right-of-way, they attract attention and invite participation, comment, and criticism. These sites, the materials that mark them, how people come to build them, the messages that those who build them hope to convey, and the accumulative force these sites bring to bear in various contexts offer unique insights into our complex, fragmented, and often confounding relationships with death, living memory, and selective forgetting. This project takes roadside shrines, material cultural artifacts, as points of departure for a multi-track journey. This journey locates shrines on the road and in cultural imagination, in historical records and cultural mythology, and in the researcher’s personal archive. The construction of the text makes apparent the researcher’s cultural poesis and invites readers to participate in like manner. Chapter One situates roadside shrines within academic discourse, explains the construction of the written text, provides a brief review of literature pertinent to the study of roadside shrines, and describes the scale, scope and methods employed during the research process. Chapter Two describes roadside shrines from the perspective of the passer-by along two local routes and two cross-country road trips. Chapter Three examines the popularity of shrine-building in the vernacular and academic press, historicizes the practice of shrine-building, explores recent institutional attempts to regulate roadside shrines, and offers a provisional interpretation of shrine-building as resistant performances of protest and warning. Chapter Four explores roadside shrines from the perspective of the participant-observer engaged in various rituals while visiting specific roadside shrines and during additional cross-country road trips. Chapter Five examines shrine-building as social ritual in the popular and academic arts, historicizes shrine-building as a mourning ritual, offers a provisional interpretation of shrine-building as performances that resist normative constraints of “healthy” mourning while simultaneously re-inscribing a dominant formal aesthetic. Chapter Six restlessly concludes as the researcher returns to the field

Feynman Categories

In this paper we give a new foundational, categorical formulation for operations and relations and objects parameterizing them. This generalizes and unifies the theory of operads and all their cousins including but not limited to PROPs, modular operads, twisted (modular) operads, properads, hyperoperads, their colored versions, as well as algebras over operads and an abundance of other related structures, such as crossed simplicial groups, the augmented simplicial category or FI--modules. The usefulness of this approach is that it allows us to handle all the classical as well as more esoteric structures under a common framework and we can treat all the situations simultaneously. Many of the known constructions simply become Kan extensions. In this common framework, we also derive universal operations, such as those underlying Deligne's conjecture, construct Hopf algebras as well as perform resolutions, (co)bar transforms and Feynman transforms which are related to master equations. For these applications, we construct the relevant model category structures. This produces many new examples.Comment: Expanded version. New introduction, new arrangement of text, more details on several constructions. New figure