• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.561-570
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• 2005

Weak Crossed Product Algebras correspond to certain graphs called lower subtractive graphs. The properties of such algebras can be obtained by studying this kind of graphs ([4], [5]). In [1], the author showed that a weak crossed product is Frobenius and its restricted subalgebra is symmetric if and only if its associated graph has a unique maximal vertex. A special construction of these graphs came naturally and was known as standard lower subtractive graph. It was a deep question that when such a special graph possesses unique maximal vertex? This work is to answer the question partially and to give a particular characterization for such graphs at which the corresponding algebras are isomorphic. A graph that follows the mentioned characterization is called flexible. Flexibility is to some extend a generalization of the so-called Coxeter groups and its weak Bruhat ordering.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.95-111
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• 2017

Recently, interval-valued fuzzy graph is a growing research topic as it is the generalization of fuzzy graphs. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that they allowed the degree of membership of a vertex to an edge to be represented by interval values in [0.1] rather than the crisp values between 0 and 1. In this paper, we introduce the concepts of regular and totally regular interval-valued fuzzy graphs and discusses some properties of the ${\mu}$-complement of interval-valued fuzzy graph. Self ${\mu}$-complementary interval-valued fuzzy graphs and self-weak ${\mu}$-complementary interval-valued fuzzy graphs are defined and a necessary condition for an interval valued fuzzy graph to be self ${\mu}$-complementary is discussed. We define busy vertices and free vertices in interval valued fuzzy graph and study their image under an isomorphism.

• Communications of Mathematical Education
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• v.26 no.2
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• pp.177-203
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• 2012

The purpose of this research was to look at whether small group drawing activities can be applied to learning content that combine mathematics and art, by analyzing the changes in $10^{th}$ grade students' interests in mathematics and particular features of their strategic thinking that were reflected in small group drawing activities using graphs and inequations. The results of the study are as follows: 1. The small group drawing activity using graphs and inequations demonstrated that students interests in mathematics could experience positive changes. 2. The small group drawing activity using graphs and inequations was effective in stimulating the students' strategic thinking skills, which are higher level thinking activities necessary for creating problem solving. As the students went through the whole process of accomplishing a complete goal, the students engaged in integrated thinking activities that brought understandings of basic graphs and inequations together, and were also found to use such higher level thinking functions needed in achieving creative problem solving such as critical thinking, flexible thinking, development-oriented thinking, and inferential thinking. 3. The small group drawing activity using graphs and in equations could be expected to constitute learning content that integrate mathematics and art, and is an effective solution in boosting students' strengths in mathematics by way of activities that consider students' unique cognitive and qualitative peculiarities and through integration with art.

• Journal of Internet Computing and Services
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• v.18 no.4
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• pp.79-87
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• 2017

Company A, an embedded system manufacturer, provides its products to Company P which is the parent company of Company A. Both companies learned that they needed to find over 4,000 bugs before market release in order to meet the acceptable quality level. Traditionally, they had utilized time-series line graphs as their common performance measurement tool. These graphs compared accumulated numbers of bugs fixed with accumulated numbers of bugs found. Engineers in Company A had been under pressure to improve the process capacity because the line for bugs fixed was always below than the line for bugs found. By using a newly designed Bipolar diagram, engineers in Company A analyzed the process performance. And they were in a position to be more flexible for internal or inter-companies meeting. Authors explain an empirical study of a graphical and practical performance measurement tools relating to mainly the Bipolar diagram. As a result, the Bipolar diagram provides workload monitoring and performance measurement functions in a given timeframe by using the concepts of Optimum Process Line (or band) and Fair Process Capacity Zone.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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• pp.330-335
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• 1993

This paper presents an efficient solution for a class of forbidden state problems by introducing a cyclic timed controlled marked graphs (TCMG's), a special class of timed controlled Petri nets (TCPN's) as a model of a class of discrete event systems (DES's). The state feedback control is synthesized, which is maximally permissive while guaranteeing the forbidden states will be avoided. The practical applications or tire theoretical results for an automated guided vehicle (ACV) coordination problem in a flexible manufacturing facility is illustrated.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1724-1727
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• 2002

Asynchronous circuits have the potential to solve the problems related to parameter variations such as gate delays in deep sub-micron technologies. However, current CAD tools for large-scale asyn-chronous circuits partition specification irrelevantly, because these tools cannot control the granularity of circuit decomposition. In this paper we propose a hierarchical Control/Data Flow Graph (CDFG) containing nodes that are flexibly partitioned or merged into other nodes. We show a partitioning algorithm for such CDFGs to generate handleable Signal Transition Graphs (STGs) for asynchronous synthesis tools. The algorithm a1lows designers to assign the maximum number of signals of partitioned nodes considering of timality. From an experiment, this algorithm can flexibly partition and result in more compact asynchronous controllers.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.137-162
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• 2012

Learning graphical representations for statistical data requires understanding of the context related to measurement in statistical investigation since the choice of representation and the features of the selected graph to represent the data are determined by the purpose and context of data collection and the types of the data collected. This study investigated whether middle school students can think critically about measurement and scales integrating contextual knowledge and statistical knowledge. According to our results, the students lacked critical thinking related to measurement process of data and scales of graphical representations. In particular, the students had a tendency not to question upon information provided from data and graphs. They also lacked competence to critique data and graphs and to make a flexible judgement in light of context including statistical purpose.

• Earthquakes and Structures
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• v.13 no.2
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• pp.103-118
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• 2017

In vertical seismic isolation (VSI), a building is partitioned intentionally by vertical layers into two dynamically different substructures for seismic response reduction. Initially, a 1-story frame was partitioned into two substructures, interconnected by viscous and visco-elastic links, and seismic responses of the original and the vertically isolated structures (VIS) were obtained, considering a large number of stiffness and mass ratios of substructures with respect to the original structure. Color contour graphs were defined for presentation and investigation of large amounts of output results. Dynamic characteristics of the isolated structures were studied by considering the non-classical damping of the system, and then the effects of viscous and visco-elastic link parameters on the modal damping ratios were discussed. On this basis, three states of mass isolation, interactional state, and control mass were differentiated. Response history analyses were performed by Runge-Kutta numerical method. In these analyses, interaction of isolation ratios and link parameters, on response control of VIS was studied and the appropriate ranges for link parameters as well as the optimal ranges for isolation ratios were suggested. Results show that by using the VSI technique, seismic response reduction up to 50% in flexible substructure and even more in stiff substructure is achievable.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.3 no.1
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• pp.5-25
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• 2009

In recent years the popularity of multi-hop wireless networks has been growing. Its flexible topology and abundant routing path enables many types of applications. However, the lack of a centralized controller often makes it difficult to design a reliable service in multi-hop wireless networks. While packet routing has been the center of attention for decades, recent research focuses on data discovery such as file sharing in multi-hop wireless networks. Although there are many peer-to-peer lookup (P2P-lookup) schemes for wired networks, they have inherent limitations for multi-hop wireless networks. First, a wired P2P-lookup builds a search structure on the overlay network and disregards the underlying topology. Second, the performance guarantee often relies on specific topology models such as random graphs, which do not apply to multi-hop wireless networks. Past studies on wireless P2P-lookup either combined existing solutions with known routing algorithms or proposed tree-based routing, which is prone to traffic congestion. In this paper, we present two wireless P2P-lookup schemes that strictly build a topology-dependent structure. We first propose the Ring Interval Graph Search (RIGS) that constructs a DHT only through direct connections between the nodes. We then propose the ValleyWalk, a loosely-structured scheme that requires simple local hints for query routing. Packet-level simulations showed that RIGS can find the target with near-shortest search length and ValleyWalk can find the target with near-shortest search length when there is at least 5% object replication. We also provide an analytic bound on the search length of ValleyWalk.

• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.539-560
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• 2013

The purpose of this study was to investigate characteristics of mathematically gifted high school students' thinking in design activities using GrafEq. Eight mathematically gifted high school students, who already learned graphs of functions and inequalities necessary for design activities, were selected to work in pairs in our experiment. Results indicate that logical thinking and mathematical abstraction, intuitive and structural insights, flexible thinking, divergent thinking and originality, generalization and inductive reasoning emerged in the design activities. Nonetheless, fine-grained analysis of their mathematical activities also implies that teachers for gifted students need to emphasize both geometric and algebraic aspects of mathematical subjects, especially, algebraic expressions, and the tasks for the students are to be rich enough to provide a variety of ways to simplify the expressions.