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Grey number has been a very important and useful tool to describe the pay-off matrix of game due to the inevitable defect of information and the limited rationality of human. The conception system of Grey Potential Degrees, including Grey Superiority Potential Degree, Grey Inferior Potential Degree and Grey Total Potential Degree of two grey numbers were built up in exiting research. This paper is to further discuss the distribution, the characters and the changing of these Grey Potential Degrees. Distribution of Grey Potential Degree is discussed in the paper and Grey Superiority Degree is divided into three areas, Absolutely Superiority, Relative Superiority and None Superiority. And Grey Inferior Potential Degree is divided into three parts, Absolutely Inferiority, Relative Inferiority and None Inferiority. It is found that any pair of grey numbers could be in some special situation of None Superiority to Each other, None Inferiority to Each other, Unit Superiority Potential. When they are the same grey numbers, all Grey Potential Degrees are in value of zero. Grey Potential Degrees of Grey Numbers could be in mutual influence. They are connected with the length of grey numbers. According to the dimension of position and the dimension of length of grey umbers, the changing and tendency of three kinds of Grey Potential Degrees are stimulated, accounted and figured in paper. The growing tendencies of Grey Potential Degrees are presented when one grey number moves from left side to right side of the other grey number. Closer the lengths of two grey numbers are, nearer the Grey Superiority Potential Degree and Grey Inferior Potential Degree are. [ABSTRACT FROM AUTHOR]

Recent papers at ICTMT conferences have highlighted different aspects of technology in mathematics teaching: computer based learning with computer algebra (1997), on-line assessment (1999), computer assisted assessment for higher level learning (2001) and interactive classrooms (2003). Blended learning and creative assessment have become increasingly important throughout this period. This paper explains how a virtual learning environment (WebCT) has been used to support the blending of established and newly created learning resources for selected university level 1 and 2 mathematics units. It will focus on the role of technology in the development of student assessment: from face-to-face questioning with interactive classrooms (formative) to objective computer marked tests (formative and summative), from computer algebra to learning diaries (formative and summative). The basic components ABC: Assessment - Blending - Creativity are identified as driving the learning of mathematics. [ABSTRACT FROM AUTHOR]

In this paper we present a qualitative analysis based on data collected by means of an eye-tracker tool, concerning the outcome of a mathematical analysis question administered to a group of candidates of university level or higher. One of the research aims is to highlight similarities and differences in the visual observation of the question itself between candidates considered experts and non-experts. This analysis should provide useful information and clues about the way a matheniatical problem is tackled (and the underlying cognitive processes used to tackle it) for eventual research ilse in Mathematics education, also at university level. [ABSTRACT FROM AUTHOR]

The paper presents a model of a redundant robot configuration with a built-in safety. By the method of strong continuous semi-group, the paper analyzes the essential spectrum of the system operator before and after perturbation. The results show that in s special condition, the dynamic solution of the system is exponential stability and tends to the steady solution of the system. [ABSTRACT FROM AUTHOR]

Based on both white response and connotation expression are geometric progression in the most primitive grey differential equation of GM(1,1)x(0)(k)+ax(1)(k) = b, this paper begins with generation of the time response function's grey derivative at discrete points. Through derivative's definition, establishing a new GM(1,1) by optimizing grey derivative and background value. Then, getting the best coefficient c by introducing criterion function and it has proved that the new expression has the whitened exponent law coincident property and the whitened coefficient coincident property in theory. Finally, some examples show the new model has higher prediction precision. [ABSTRACT FROM AUTHOR]

With the further aggravation of international competition, the science & technology development has already become the most important factor that it influences a country's competitiveness. This paper structures the evaluation index system of regional science and technology development. It also utilizes AHP and main component projection to analyze the current science and technology development situations of eight areas in our country and receive the final result. [ABSTRACT FROM AUTHOR]

To solve the difficult problem of quantitative evaluation on fracture union quality, this paper puts forward a new assessment method of grey relational analysis, taking the stress data under ideal union process (Jorgensen curve) as reference data sequence while the stress data on trauma section detected in real time as the comparing data sequence can be obtained from grey relational analysis to reflect the quality of fracture union. The evaluation on healing quality based on grey relational analysis has been done with the measured stress data from femoral fracture of adult live goat The evaluation results show that: the evaluation method based on grey relational analysis proposed in this paper is simple and effective with a reliable assessment result, which can be applied in the assessment on clinical treatment result. [ABSTRACT FROM AUTHOR]

For a graph, its boxicity is the minimum dimension k such that G is representable as the intersection graph of axis-parallel boxes'in the k-dimension space. When the boxes are restricted to be axis-parallel k-dimension cube's, the minimum k required to represent G is called the cubicity of G. In this paper, a special graph called unit-interval graph. IG[X, Y] is given, then 2n such graphs which have the same vertices as V(FQn) are constructed, where FQn is the n-dimension folded hypercube. Thanks to the special structure of IG[X, Y], the result that cubicity(FQn)≤2n is proved. [ABSTRACT FROM AUTHOR]

The aim of the paper is to construct a kind of new strengthening buffer operator that is suitable for non-equigap GM(1, 1) model, and the examples have shown that the new strengthening buffer operator can enhance the forecasting simulation precision of non-equigap GM(1, 1) in shock disturbed system. The strengthening new buffer operator has certain usability and validity. This paper provides methods for solving the contradiction between quantitative forecasting results and qualitative analysis conclusion. [ABSTRACT FROM AUTHOR]

This paper aims to propose ERT (Expected Reaching Time), a new risk adverse evaluation criterion of finite multiplication processes, and to examine its properties in relation to the dominance criterion. The ERT means the expected time that takes for an objective valiable to reach a target value. To deal with the environmental risk involved in the process, the expectation maximizing strategy may be the most well known. However, for many cases the dominance strategy rather than the expectation maximizing strategy is adopted and works very well. In this paper we first prove rigorously that minimization of the ERT is equivalent to the dominance criterion in the infinite period. Then we demonstrate by simulation that the ERT gives almost equal evaluation as the dominance criterion even for the finite multiplications, after showing that it is approximately proportional to the logarithm of the target value. [ABSTRACT FROM AUTHOR]

Chinese environmental and economic factors vary from one region to another, which leads to the result that the operational performance of environmental protection institutional system (EPIS) remains to be improved according to the regional features. This paper analyzes the internal performance structure of Chinese regional EPIS so as to optimize the operation of system. First, the constitution and operational mechanism of Chinese EPIS is investigated with considering the coordination development of each subsystem. Then, A grey TODIM (G-TODIM) method is proposed not only to evaluate the operational performance of Chinese regional EPIS but also to quantify the influence of internal systemic factors on operational performance. The last empirical analysis of 30 Chinese provinces shows that the completeness and operational performance of Chinese EPIS decrease from east to west, showing a significant decrease in regional gradient. The Chinese provinces could be divided into three category of institutional modes according to the contribution rate of each factor to comprehensive performance, and the optimization suggestions of Chinese regional EPIS are proposed correspondingly. [ABSTRACT FROM AUTHOR]

Aiming at the problems existing in previous grey-chaos prediction methods, with phase space reconstruction theory and residual GM(1,1) model, a novel prediction method based on L1 norm of reconstructed phase points is proposed in the paper. For chaotic time series, phase space delay coordinate reconstitution theory is applied to reconstruct phase space firstly, and then residual GM(1,1) model is used to study the change law of phase point LI norm, finally predicted values of time series are obtained with the Li norm inverse solution. To test the prediction method, three criteria of MAPE, MSE and FEM are employed here. And at the end, simulation with measured data from stabilized platform experiment demonstrates that the newly proposed method is effective, and it can overcome the difficulties existing in some previous grey-chaos prediction methods. [ABSTRACT FROM AUTHOR]

This paper presents the existence and uniqueness of the positive solution of the repairable reliability system with early standby activation in Banach space, and presents the optimal control at time T. [ABSTRACT FROM AUTHOR]

This paper examines various cognitive strategies applied while CAS (Computer Algebra System) are used in undergraduate-level engineering mathematics teaching and learning. We posed some questions in relation to such CAS use: What kind of tools can CAS offer to enhance different cognitive strategies of students? How can the use of CAS widen the range of students' cognitive strategies and affect pragmatic, heuristic, and epistemic thinking schemes? How can CAS enhance metacognition and cognitive self- efficacy? How can CAS-enhanced curricula benefit from the examination of various cognitive strategies? How can the examination of CAS-related cognitive strategies assist modularisation of topics and thickening the "knowledge-representation network"? In this paper, we offer some examples to illustrate issues raised by the questions above. [ABSTRACT FROM AUTHOR]

A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right answer", typically calculus questions. Here we look at some other cases, notably in linear algebra, where there can be many "right answers", but still there can be answers that are mathematically right but pedagogically wrong. We reformulate the problem in terms of articulating the soughtafter properties, which may include both mathematical equivalence and algebraic form. [ABSTRACT FROM AUTHOR]

To overcome the shortcoming of the algorithm based on the classical grey relational analysis in the transformation of matrix of pixels to sequence, the grey relational analysis is extended in this paper, and a matrix absolute degree of grey incidences is presented. Then a novel algorithm of image edge detection is proposed which is based on matrix absolute degree of grey incidences. In the new algorithm, the characteristics of pixels are analyzed to decide non-edge referential matrix and the matrix to be compared, and the matrix absolute degree of grey incidences is employed to distinguish non-edge pixels and edge pixels. Finally the results of the experiments show that the proposed algorithm can gain more precise edges than some traditional methods, and can also tolerate some noises. Furthermore the quantity of edges ca be controlled by adjusting threshold of degree of grey incidences. So the technique is a new effective adjustable method of edge detection. [ABSTRACT FROM AUTHOR]

The integration of financial services benefits consumers with a "one-stop shopping" convenience. Furthermore, bancassurance has enjoyed considerable success in Europe. Thus the aim of this paper is searching for the preferable bancassurance alliance model to customers. First, we define three criteria and nine sub-criteria for use in evaluating six forms of bancassurance alliance. Next. we establish a framework for the criteria and sub-criteria using a modified Delphi method. As a decision support system, we incorporate the opinions of industry, experts and apply the analytic hierarchy process (AHP) and Grey Relational Analysis (GRA). Based on the evaluations of the expert panel, the financial holding company is customers' preference. [ABSTRACT FROM AUTHOR]

Electrocardiogram (ECG) signal plays an important role to diagnose cardiovascular disease. The related factors of cardiovascular diseases are urged to be studied to improve the health of people in recent society. This paper proposes grey relational analysis (GRA) to evaluate the relation between electrocardiogram variety of rest, listening to lyrical music and rock music. [ABSTRACT FROM AUTHOR]

This paper details the motivation, background, and analysis for studying the effect that an Increasing Achievement on Algebra Assessment (IAAA) workshop for a group of Florida high school teachers had on student performance in statewide testing. The main focus of the workshop was to provide participating teachers with both instruction and activities related to problem-solving techniques using the TI-83 Plus handheld graphing calculator that the teachers could then use in an effort to better prepare their students for state-wide testing. Overall, students (n = 328) who were taught by IAAA-trained teachers between consecutive annual statewide assessments had a greater gain in test scores than students (n = 202) who were taught by non-trained teachers. In particular, the data indicates a significant increase in scores for students taught by IAAA-trained teachers in a general mathematics course, as compared to no significant increase in scores for students taking that same course taught by non-trained teachers. [ABSTRACT FROM AUTHOR]

In view of the surface water that is polluted in the different degrees, it is necessary to carry out periodical monitoring and evaluation, so as to control the water pollution. In this paper, the water environment is considered as a grey system, and the index of the water quality state as a grey class. Considering the indeterminacy of water quality classification boundary, the surface water quality is evaluated with the grey relational analysis (GRA). The calculation results of example show that the evaluation method presented is accurate and reliable. [ABSTRACT FROM AUTHOR]

In this paper, a new generating method of the Generalized Accumulated Generating Operation (GAGO) is proposed based on the traditional AGO. Then the generating space of GAGO is constructed, and the frame of AGO generating space is discussed. These outcomes can widen the application range of AGO and enrich the foundation of grey generating theory. [ABSTRACT FROM AUTHOR]

Based on grey relational theory, a technique to do the interpolation for indexed sequence is proposed in this paper. The simulation results show that the proposed interpolation technique is feasible and effective. [ABSTRACT FROM AUTHOR]

In this paper two new methods for improving the consistency of judgement matrix are presented by two NLP models. Two NLP are worked out by using Accelerating Genetic Algorithm. An example is given and every method is compared respectively. [ABSTRACT FROM AUTHOR]

The aim of the study is to conceptualize the technology-aided mathematical modelling process in the frame of cognitive modelling perspective. The grounded theory approach was adopted in the study. The research was conducted with seven groups consisting o f nineteen prospective mathematics teachers. The data were collected from the video records of the participants 'solutions related to the three mathematical modelling problems, their written solution papers, the GeoGebra solution files and the researchers' observation notes. The technology-aided mathematical modelling process included the eight components, the seven stages and the forty-seven sub stages. The components were complex real world situation, real world problem situation, model of real world problem situation, sub-mathematical models, mathematical model(s), mathematical solution, real world solution, and a brief solution report. Additionally, the seven stages were problem analysis, constructing the systematic structure, mathematization, meta-mathematization, mathematical analysis, interpreting/evaluating, and validating model. It is considered that a comprehensive and different point of view regarding the cognitive activities in the technology-aided mathematical modelling process was introduced. [ABSTRACT FROM AUTHOR]

In the paper, modeling principle for GM (1, 1) has been made a detailed analysis. First, the model error had been given. Second, the mathematics reason that this model is established by cumulative data has been discussed. Finally, an assessment method of suitable scope for the model has been pointed. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the vertex-fault-tolerant cycles embedding on enhanced hypercube,which is an attractive variant of hypercube and is obtained by adding some complementary edges from hypercube. Let Fv be the set of faulty vertices of Qn,k (1 ≤ k ≤ n - 1, n ≥ 3) and 1 ≤ /Fv/ ≤ n - 1, when n and k have the same parity, there exists a fault-free cycle, which is of even length at least 2n - 2ƒv in Qn,k - Fv. When n and k have the different parity, there exists a fault-free cycle, which is of even length at least 2n - 2ƒv in Qn,k - Fv, and simultaneously, there exists a fault-free cycle, which is of odd length at least 2n - 2ƒv + 1 in Qn,k - Fv. [ABSTRACT FROM AUTHOR]

This paper sets out from the definition of risk given. Based on the attribute of the risk indetermination, banding the information entropy and cluster analysis theories, it provides the Cluster Analysis-risk Entropy measurement. It provides an analysis method to judge the risk classification scientifically according to the risk characteristics of different research object under the uncertain condition. [ABSTRACT FROM AUTHOR]

In order to deal with the long series blending mixed with backbone data and non-backbone along with the nucleus less-data, the Blind-head principle (BH principle) and the nucleus less-data model is pioneered in this paper. [ABSTRACT FROM AUTHOR]

The notion and definition of contingency resources are developed in terms of whose characters and the stock dynamic relationship is studied. The parameter packs of this dynamic relationship with some allocating points are deduced in this paper, some theorems on resource allocation points are obtained. [ABSTRACT FROM AUTHOR]

This paper discusses student difficulties in grasping concepts from Linear Algebra - in particular, the connection of eigenvalues and eigenvectors to other important topics in linear algebra. Based on our prior observations from student interviews, we propose technology-enhanced instructional approaches that might positively impact student understanding of concepts within a problem-solving context. We discuss some barriers to student understanding and suggest ways of using geometrical interpretations and visualisations of eigenvectors and eigenvalues to address these barriers. These technological interventions can readily implement this geometric approach, permitting students to easily experiment with a visual interpretation of eigenvectors and eigenvalues. [ABSTRACT FROM AUTHOR]

This paper reports on a design experiment conducted to explore the construction of meanings by 17 year old students, emerging from their interpretations and uses of algebraic like formalism. The students worked collaboratively in groups of two or three, using MoPiX, a constructionist computational environment with which they could create concrete entities in the form of models by using equations and animate them to link the equations' formalism to the produced visual representation. Our aim was to further study the ways in which the use of formalism in constructionist environments can create contexts for the emerging of mathematical meanings. Some illustrative examples of two groups of students' work indicate the potential of the activities and tools for expressing and reflecting on the mathematical nature of the available formalism. We particularly focused on the students' engagement in reification processes, i.e. making sense of structural aspects of equations, involved in conceptualising them as objects that underlie the behaviour of the respective models. [ABSTRACT FROM AUTHOR]

As an enhancement on the hypercube Qn, the augmented cube AQn, proposed by Choudum and Sunitha [Choudum S.A., Sunitha V., Augmented cubes, Networks, 40(2)(2002), 71-84], possesses some properties superior to the hypercube Qn. In this paper, assuming that (u, v) is an arbitrary fault-free d-link in an n-dimensional augmented cubes, 1 ≤ d ≤ n - 1, n ≥ 4. We show that there exists a fault-free Hamiltonian cycle in the augmented cube contained (u, v), even if there are 2n - 3 link faults. [ABSTRACT FROM AUTHOR]

In this paper we study transport processes on infinite networks with dynamic boundary control nodes. These flows can be modeled by operator semigroups on a suitable Banach space. Using functional analytical and graph theoretical methods, we investigate its spectral properties of the system and positivity of the semigroup under appropriate assumptions on the network. [ABSTRACT FROM AUTHOR]

In this paper, we give a solving approach based on a logarithmic-exponential multiplier penalty function for the constrained minimization problem. It is proved exact in the sense that the global optimizers of a nonlinear problem are precisely the global optimizers of the logarithmic-exponential multiplier penalty problem. [ABSTRACT FROM AUTHOR]

A digraph D(V, E) is said to be graceful if there exists an injection f V(G) → {0, 1,⋯∣E∣} such that the induced function f′ : E(G) → {1, 2, ⋯ ∣E∣} which is defined by f′ (u,v) = (1(v) - f(u)] (mod ∣E∣ + 1) for every directed edge (u,v) is a bijection. Here, I is called a graceful labeling (graceful numbering) of D(V, E), while f′ is called the induced edge's graceful labeling of D. In this paper we discuss the gracefulness of the digraph n· ∣Cm and prove that n · ∣Cm is a graceful digraph for m = 15, 17 and even n. [ABSTRACT FROM AUTHOR]

A tourism country's competitiveness is important especially when countries strive for bigger market shares. Asian countries need to examine competitiveness in tourism especially on essential capability for enhancing nation tourism competitiveness. The aim of this paper is to apply the grey relational analysis (GRA) and sensitivity analysis in order to be able to evaluate the tourism competitive potential and to identify and analyse the essential criteria of tourism competitiveness in Asian countries. The result shows that GRA can effectively perform the evaluation of tourism competitiveness of Asian countries and sensitivity analysis express that any change in the base quantifier might have structural effect on the results. [ABSTRACT FROM AUTHOR]

A novel notion of binary incidence is pioneered in this paper. Predicated on these, a novel GRA: BGRA is pioneered, which challenges classical GRA (CGRA) with less series. The latter is characterized by numerous compared series (more than 3), and it is preferable to express the impelling synchronism among series. [ABSTRACT FROM AUTHOR]

This paper shows the basic concept of Functional Modelling in mathematics education which has become more and more important in recent years. Hence it is necessary to think about suitable graphical methods to explain the fundamental idea of a function and its influence on values and other functions. PROGRAPH diagrams are a potentially good way to explain these combinations effectively. The basic idea of a function, composition of functions or returning values of a function can be shown impressively. It is also possible to find easily nested diagrams for recursive functions. So the mathematical insights into topics which can be handled through functions gets opened up and the possibilities for working with functions increase. With the help of a selection of examples the idea of this type of diagram becomes clearer and through its implementation with CAS the effective use of functions is demonstrated. Hence the combination of PROGRAPH diagrams and CAS allows an understanding of and insight into functions so that the Black-Box-Principle is eliminated. For modern and effective education Functional Modelling is absolutely necessary. With the combination of graphical representation and CAS, learners are able to see and learn the common foundation of mathematical ideas and applications. [ABSTRACT FROM AUTHOR]

The aim of this paper is to direct the attention of the international mathematics education community to the emergence of a growing network of teachers, researchers, and developers who are using and discussing an open-source software package entitled GeoGebra. Created by Markus Hohenwarter in 2001, GeoGebra represents a digital learning environment that was designed to combine geometry, algebra, and calculus in a single, dynamic user interface. The emergence of GeoGebra as an increasingly popular mathematics education resource is likely due to a number of key characteristics: open-source status, multiple language translations, versatility (i.e., algebraic and geometric representations), and an on-line wiki and user forum. The authors provide a brief history and description of the GeoGebra software, and also discuss the nascent International GeoGebra Institute (IGI) in terms of its vision and related international developments. [ABSTRACT FROM AUTHOR]

This work recommends and analyzes the most appropriate curricula for students in departments of risk management and insurance from the perspective of life insurance companies in Taiwan. The paper proposes a curriculum performance evaluation method combining the Analytical Network Process (ANP) and the Grey Relational Analysis (GRA). The results suggest that Tamkang University (TKU) provides the most appropriate curriculum and its students are the most employable graduates by life insurance companies in Taiwan. The proposed ANP and GRA-based algorithm, which is objective and systematic in selection procedures, can significantly help faculty in departments of risk management and insurance to improve their curriculum design and human resources managers recruit highly qualified graduates for their companies. [ABSTRACT FROM AUTHOR]

This paper studies the problems of multi-attribute group decision making in which the attribute values are given in the form of linguistic variables. First of all, the grey interval numbers and a set of linguistic evaluation scales are defined. Then, a grey weighted average (GWA) operator is proposed to aggregate the grey interval numbers. Furthermore, a new model is established for the problems of multi-attribute group decision making via the GWA operator and grey relational grade. Finally, a decision making example is given to illustrate the practicality and effectiveness of this new model. [ABSTRACT FROM AUTHOR]

Computer algebra systems (CASs) have been used by thousands of teachers and students for teaching and learning algebra. They have the ability to perform efficiently almost all of the algebraic expansions and simplifications. Nevertheless, the traditional approach of using paper and pencil in acquiring procedural knowledge is still widely practised. It was hypothesised that developing symbolic manipulation through procedural knowledge is not always favoured by students. This paper investigates this hypothesis and gives a rating of several drawbacks of procedural knowledge using the fuzzy set theory decision making processes. The study involved a survey which consists of four factors for the purpose of giving a rating. A multi-factorial fuzzy evaluation approach was used to analyse the data collected from one hundred and sixty four students sampled from a secondary school in Terengganu, Malaysia. The students were taught the technique of the completing the square method for quadratic functions using both a CAS and a traditional procedural approach. The evaluation indicated that students felt that there were disadvantages with the procedural approach in the presence of a CAS. This rating gives rise to concerns about the relevance of procedural knowledge in the age of computerised mathematics technology. [ABSTRACT FROM AUTHOR]

The criterion for compare the function transformations to raise the smooth degree of grey modeling data is presented in this paper, and some function transformations are compared by using this criterion. [ABSTRACT FROM AUTHOR]

Toward the problem of judgement of enterprise crisis degree, the paper adopts fuzzy classification and fuzzy recognition method, forms enterprise character objective function in fuzzy condition, and brings forward to solve approach of optimal fuzzy classification center matrix, optimal fuzzy recognition matrix and optimal index weight under different crisis degree. By using the method in enterprise crisis early-warning example, it can distinguish enterprise crisis degree effectively. [ABSTRACT FROM AUTHOR]

The subject of q-calculus is a rich source of learning activities that address concept formation, exploration, variation, rich training and proof. This paper is a survey of the subject that shows how high school students using a computer algebra system can explore the field and prove some results. [ABSTRACT FROM AUTHOR]

The paper's aim is to note a remarkable (and apparently unknown) relation for right triangles, its generalisation to arbitrary triangles and the possibility to derive these and some related relations by elimination using Groebner basis computations with a modern computer algebra system. [ABSTRACT FROM AUTHOR]

This paper presents a grey particle swarm optimization learning algorithms to self classify different input patterns as correct subgroups. In our learning stratagem, a grey relational analysis (GRA) is combined with Particle swarm optimization (PSO) to develop a classification system. In our research, the GRA is more effective and accurate than the common-used Euclidean norm measure. The evolutional PSO is a very powerful learning algorithm to optimize the classifying task for complex, irregular and high dimensional input patterns. Several artificial data clustering examples compared with k-means method is presented to demonstrate the robustness of the proposed grey particle swarm optimization clustering algorithm. A real image classifying problem is also provided with the grey particle swarm optimization clustering algorithm. [ABSTRACT FROM AUTHOR]

In a system, Every component has its unique position within system and its unique failure characteristics. When a component's reliability is changed, its effect on system reliability is not equal. Component reliability sensitivity is a measure of effect on system reliability while a component's reliability is changed. In this paper, the definition and relative matrix of component reliability sensitivity is proposed, and some of their characteristics are analyzed. All these will help us to analyse or improve the system reliability. [ABSTRACT FROM AUTHOR]

Traditional, skills-based college algebra has been taught at Francis Marion University since before the school's establishment as a four-year institution in 1970. The majority of students performed poorly in these skills-based courses. To our more senior faculty in the department and in the university, high failure rates are alarming. Through an analysis of data, we attempt to shed light on the fact that these high failure rates make these entry-level courses unsuccessful. To lessen the impact on our student retention, we established a two-course alternative sequence that uses applications and projects to motivate the college algebra. We integrated real-world problems in the form of projects, applications, and activities to motivate students to better understand the basic principles of algebra. Student performance improved, and feedback from most of the students was positive. Based on the overall positive experience, these two new freshman algebra courses have become prerequisites for other mathematics courses instead of just terminal courses. In this paper, we discuss these courses, our "salesmanship", the interdisciplinary projects we used, and how we integrate technology. [ABSTRACT FROM AUTHOR]