Search results for: logical framework matrix

Authors: Farshad Badie

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The central focus of this article is on the fact that knowledge is constructed from an interaction between humans’ experiences and over their conceptions of constructed concepts. Logical characterisation of ‘human inductive learning over human’s constructed concepts’ within terminological systems and providing a logical background for theorising over the Human Concept Learning Problem (HCLP) in terminological systems are the main contributions of this research. This research connects with the topics ‘human learning’, ‘epistemology’, ‘cognitive modelling’, ‘knowledge representation’ and ‘ontological reasoning’.

Keywords: human concept learning, concept construction, knowledge construction, terminological systems

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Authors: Alisa Rekunova

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According to the theory of word meaning structure developed by Lev Vygotsky (and later modified by Aaro Toomela), there are several levels of thought: sensory-based concepts, situation concepts, logical concepts, and structural-systemic concepts. There are differences between people who have relatively easy access to logical thought compared to those who mostly tend to think in everyday concepts. Religious beliefs are connected with unprovable concepts (Christian Jesus’s ascension or Pagan energy) that cannot be non-controversially related to scientific concepts. However, many scientists in the research are believers of some kinds. Religious views can be different: there are believers, non-believers (atheists), and undecided (we can call them agnostics). Some of the respondents say that scientific or professional and religious spheres do not overlap. Therefore, we can assume they do not see any conflict. Some of them, on the contrary, hesitate to answer and we can conclude they see the conflicts, but they do not want (or do not believe they are able to) to solve it. Finally, the third category of respondents says that religious beliefs and scientific concepts cannot coexist in the human mind. It can be expected that the third category of respondents should have higher education (or even work in the scientific field) but many scientists in the research answer that religious and scientific spheres do not overlap. Therefore, there are other things besides the level of education that is connected with resolving conflicts.

Keywords: conflicts in thinking, cultural-historical psychology, heterogeneity of thinking, religious thinking

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Authors: Chimezie P. Nnanwa, Thomas C. Urama, Patrick O. Ezepue

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In this paper we use Random Matrix Theory to analyze the eigen-structure of the empirical correlations of 82 stocks which are consistently traded in the Nigerian Stock Exchange (NSE) over a 4-year study period 3 August 2009 to 26 August 2013. We apply the Marchenko-Pastur distribution of eigenvalues of a purely random matrix to investigate the presence of investment-pertinent information contained in the empirical correlation matrix of the selected stocks. We use hypothesised standard normal distribution of eigenvector components from RMT to assess deviations of the empirical eigenvectors to this distribution for different eigenvalues. We also use the Inverse Participation Ratio to measure the deviation of eigenvectors of the empirical correlation matrix from RMT results. These preliminary results on the dynamics of asset price correlations in the NSE are important for improving risk-return trade-offs associated with Markowitz’s portfolio optimization in the stock exchange, which is pursued in future work.

Keywords: correlation matrix, eigenvalue and eigenvector, inverse participation ratio, portfolio optimization, random matrix theory

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Authors: Emine Tuğba Akyüz

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In this study, the analysis of Hadamard matrices, which is a special type of matrix, was made under three headings: norms, singular values, condition number. Six norm types was applied to Hadamard matrices and the relationship between the results and the size of the matrix has been studied. As a result of the investigation when 2-norm was used on the problem Hx =f, the equation ‖x‖_2= ‖f‖_2/√n was shown (H is n-dimensional Hadamard matrix). Related with this, the relationship between the the singular value of H and 2-norm and eigenvalues was shown. Then, the evaluation of condition number for Hx =f was made.

Keywords: condition number, Hadamard matrix, norm, singular value

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Authors: K. Vinutha

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The stress corrosion resistance of ZA-27 / TiO2 metal matrix composites (MMC’s) in high temperature acidic media has been evaluated using an autoclave. The liquid melt metallurgy technique using vortex method was used to fabricate MMC’s. TiO2 particulates of 50-80 µm in size are added to the matrix. ZA-27 containing 2,4,6 weight percentage of TiO2 are prepared. Stress corrosion tests were conducted by weight loss method for different exposure time, normality and temperature of the acidic medium. The corrosion rates of composites were lower to that of matrix ZA-27 alloy under all conditions.

Keywords: autoclave, MMC’s, stress corrosion, vortex method

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Authors: Ratchada Sopakayang, Gerhard A. Holzapfel

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In this study, a new constitutive model is developed to describe the hyperelastic behavior of collagenous tissues with a parallel arrangement of collagen fibers such as ligaments and tendons. The model is formulated using a continuum approach incorporating the structural changes of the main tissue components: collagen fibers, proteoglycan-rich matrix and fiber-matrix interaction. The mechanical contribution of the interaction between the fibers and the matrix is simply expressed by a coupling term. The structural change of the collagen fibers is incorporated in the constitutive model to describe the activation of the fibers under tissue straining. Finally, the constitutive model can easily describe the stress-stretch nonlinearity which occurs when a ligament/tendon is axially stretched. This study shows that the interaction between the fibers and the matrix contributes to the mechanical tissue response. Therefore, the model may lead to a better understanding of the physiological mechanisms of ligaments and tendons under axial loading.

Keywords: constitutive model, fiber-matrix, hyperelasticity, interaction, ligament, tendon

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Authors: Naoki Ohshima, Ken Kaminishi

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Four types of dependencies, which are 'Finish-to-start', 'Finish-to-finish', 'Start-to-start' and 'Start-to-finish (S-F)' as logical relationship are modeled based on the definition by 'the predecessor activity is defined as an activity to come before a dependent activity in a schedule' in PMBOK. However, it is found a self-contradiction in the precedence diagram for S-F relationship by PMBOK. In this paper, author would like to validate logical relationship of S-F by Graph Theory and propose a new interpretation of the precedence diagram for S-F relationship.

Keywords: project time management, sequence activity, start-to-finish relationship, precedence diagram, PMBOK

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Authors: Wided Bakari, Patrice Bellot, Omar Trigui, Mahmoud Neji

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This article constitutes an opening to think of the modeling and analysis of Arabic texts in the context of a question-answer system. It is a question of exceeding the traditional approaches focused on morphosyntactic approaches. Furthermore, we present a new approach that analyze a text in order to extract correct answers then transform it to logical predicates. In addition, we would like to represent different levels of information within a text to answer a question and choose an answer among several proposed. To do so, we transform both the question and the text into logical forms. Then, we try to recognize all entailment between them. The results of recognizing the entailment are a set of text sentences that can implicate the user’s question. Our work is now concentrated on an implementation step in order to develop a system of question-answering in Arabic using techniques to recognize textual implications. In this context, the extraction of text features (keywords, named entities, and relationships that link them) is actually considered the first step in our process of text modeling. The second one is the use of techniques of textual implication that relies on the notion of inference and logic representation to extract candidate answers. The last step is the extraction and selection of the desired answer.

Keywords: NLP, Arabic language, question-answering, recognition text entailment, logic forms

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Authors: Elżbieta Cygan-Bączek, Piotr Wyżga, Sławomir Cygan

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In the presented work, the main goal was to investigate the retention properties, defined as the ability of the matrix material to hold diamond particles in relation to metallized (Ti, Si, Cr, Co, Cu, Ni) and non-metallized diamond crystals. For this purpose, diamond-impregnated specimens were tested for wear rate on abrasive sandstone using a test rig specially designed to simulate tool application conditions. The tests that involved 3- and 2-body abrasion ranked the alloys in different orders. The ability of the matrix to retain diamond crystals was determined using the electron microskopy (SEM, TEM). The specimens were also characterized by X-ray diffraction (XRD) and hardness. The conducted research has shown that Si and Ti metallized diamonds, apart from mechanical jamming in the matrix, are also connected in a metallurgical manner, ensuring the improvement of the retention properties of the matrix material.

Keywords: diamond, metallic-diamond segments, retention, abrasive wear resistance

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Authors: M. E. Turan, H. Zengin, E. Cevik, Y. Sun, Y. Turen, H. Ahlatci

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In this study, the effects of B₄C and SiC particle reinforcements on wear properties of magnesium matrix metal composites produced by pressure infiltration method were investigated. AZ91 (9%Al-1%Zn) magnesium alloy was used as a matrix. AZ91 magnesium alloy was melted under an argon atmosphere. The melt was infiltrated to the particles with an appropriate pressure. Wear tests, hardness tests were performed respectively. Microstructure characterizations were examined by light optical (LOM) and scanning electron microscope (SEM). The results showed that uniform particle distributions were achieved in both B₄C and SiC reinforced composites. Wear behaviors of magnesium matrix metal composites changed as a function of type of particles. SiC reinforced composite has better wear performance and higher hardness than B₄C reinforced composite.

Keywords: magnesium matrix composite, pressure infiltration, SEM, wear

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Authors: Sofiane Bououden, Ilyes Boulkaibet

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In this paper, a robust model predictive controller (RMPC) for uncertain nonlinear system under actuator saturation is designed to control a DC-DC buck converter in PV pumping application, where this system is subject to actuator saturation and parameter uncertainties. The considered nonlinear system contains a linear constant part perturbed by an additive state-dependent nonlinear term. Based on the saturating actuator property, an appropriate linear feedback control law is constructed and used to minimize an infinite horizon cost function within the framework of linear matrix inequalities. The proposed approach has successfully provided a solution to the optimization problem that can stabilize the nonlinear plants. Furthermore, sufficient conditions for the existence of the proposed controller guarantee the robust stability of the system in the presence of polytypic uncertainties. In addition, the simulation results have demonstrated the efficiency of the proposed control scheme.

Keywords: PV pumping system, DC-DC buck converter, robust model predictive controller, nonlinear system, actuator saturation, linear matrix inequality

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Authors: Tobias Strübing, Fatemeh Ziaeetabar

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Humans usually manipulate objects with their hands. To represent these actions in a simple and understandable way, we need to use a semantic framework. For this purpose, the Semantic Event Chain (SEC) method has already been presented which is done by consideration of touching and non-touching relations between manipulated objects in a scene. This method was improved by a computational model, the so-called enriched Semantic Event Chain (eSEC), which incorporates the information of static (e.g. top, bottom) and dynamic spatial relations (e.g. moving apart, getting closer) between objects in an action scene. This leads to a better action prediction as well as the ability to distinguish between more actions. Each eSEC manipulation descriptor is a huge matrix with thirty rows and a massive set of the spatial relations between each pair of manipulated objects. The current eSEC framework has so far only been used in the category of manipulation actions, which eventually involve two hands. Here, we would like to extend this approach to a whole body action descriptor and make a conjoint activity representation structure. For this purpose, we need to do a statistical analysis to modify the current eSEC by summarizing while preserving its features, and introduce a new version called Enhanced eSEC or (e2SEC). This summarization can be done from two points of the view: 1) reducing the number of rows in an eSEC matrix, 2) shrinking the set of possible semantic spatial relations. To achieve these, we computed the importance of each matrix row in an statistical way, to see if it is possible to remove a particular one while all manipulations are still distinguishable from each other. On the other hand, we examined which semantic spatial relations can be merged without compromising the unity of the predefined manipulation actions. Therefore by performing the above analyses, we made the new e2SEC framework which has 20% fewer rows, 16.7% less static spatial and 11.1% less dynamic spatial relations. This simplification, while preserving the salient features of a semantic structure in representing actions, has a tremendous impact on the recognition and prediction of complex actions, as well as the interactions between humans and robots. It also creates a comprehensive platform to integrate with the body limbs descriptors and dramatically increases system performance, especially in complex real time applications such as human-robot interaction prediction.

Keywords: enriched semantic event chain, semantic action representation, spatial relations, statistical analysis

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Authors: Shabnam Dadparvar, Laijin Shen, Farzad Ravanbod

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Nowadays, the political phenomenon of terrorism is considered as an effective factor on political, social, and economic changes. It has replaced the recognized political phenomena such as revolutions, wars (total war among two or more political units with distinct identities in the form of national states), coups d’état, insurgencies and etc. and has challenged political life in all its levels (sub national, national, and international political groups). In this paper by using descriptive-analytical method, the authors try to explain the spread of this political phenomenon across the world, its definition and types, also analyze different approaches to understand it. The authors believe that the Logical-Rational approach is the best way to explain and understand this phenomenon.

Keywords: logical approach, psychological- social approach, religious approach, terrorism

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Authors: M. Khajezadeh, M. Saied Fallah Niasar, S. Ali Asli, D. Davani Davari, M. Godarzi, Y. Asgari

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This study aims to explore the joint application of both Boston and Ansoff matrices in the operational development of the product. We conduct deep analysis, by utilizing the Artificial Neural Network, to predict the position of the product in the market while the company is interested in increasing its share. The data are gathered from two industries, called hygiene and detergent. In doing so, the effort is being made by investigating the behavior of top player companies and, recommend strategic orientations. In conclusion, this combination analysis is appropriate for operational development; as well, it plays an important role in providing the position of the product in the market for both hygiene and detergent industries. More importantly, it will elaborate on the company’s strategies to increase its market share related to a combination of the Boston Consulting Group (BCG) Matrix and Ansoff Matrix.

Keywords: artificial neural network, portfolio analysis, BCG matrix, Ansoff matrix

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Authors: Nick Farid, Roghoyeh Salmeh

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The planning and operation of the power grid is becoming much more complex because of the introduction of renewable energy resources, the digitalization of the electricity industry, as well as the coupling of efficiency and greener energy trends. These changes, along with new trends, make interactions between grid users and the other stakeholders more complex. This paper focuses on the main “physical” and “logical” interactions between grid users and the grid stakeholders, both from power system equipment and information management standpoints, and proposes a new interoperability model for Smart Grids.

Keywords: user interface, interoperability layers, grid architecture framework, smart grid

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Authors: Xiaoqian Cheng, Jon Kleppe, Ole Torsæter

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The properties of rocks have effects on efficiency of surfactant. One objective of this study is to analyze the effects of rock properties (permeability, porosity, initial water saturation) on surfactant spontaneous imbibition at laboratory scale. The other objective is to evaluate existing upscaling methods and establish a modified upscaling method. A core is put in a container that is full of surfactant solution. Assume there is no space between the bottom of the core and the container. The core is modelled as a cuboid matrix with a length of 3.5 cm, a width of 3.5 cm, and a height of 5 cm. The initial matrix, brine and oil properties are set as the properties of Ekofisk Field. The simulation results of matrix permeability show that the oil recovery rate has a strong positive linear relationship with matrix permeability. Higher oil recovery is obtained from the matrix with higher permeability. One existing upscaling method is verified by this model. The study on matrix porosity shows that the relationship between oil recovery rate and matrix porosity is a negative power function. However, the relationship between ultimate oil recovery and matrix porosity is a positive power function. The initial water saturation of matrix has negative linear relationships with ultimate oil recovery and enhanced oil recovery. However, the relationship between oil recovery and initial water saturation is more complicated with the imbibition time because of the transition of dominating force from capillary force to gravity force. Modified upscaling methods are established. The work here could be used as a reference for the surfactant application in fractured reservoirs. And the description of the relationships between properties of matrix and the oil recovery rate and ultimate oil recovery helps to improve upscaling methods.

Keywords: initial water saturation, permeability, porosity, surfactant EOR

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Authors: Temesgen Takele Kasa

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The main aim of this paper is to suggest one active slip based continuum dislocation approach to matrix dominated MMC plasticity analysis. The approach centered the free energy principles through the continuum behavior of dislocations combined with small strain continuum kinematics. The analytical derivation of this method includes the formulation of one active slip system, the thermodynamic approach of dislocations, determination of free energy, and evolution of dislocations. In addition zero and non-zero energy dissipation analysis of dislocation evolution is also formulated by using varational energy minimization method. In general, this work shows its capability to analyze the plasticity of matrix dominated MMC with inclusions. The proposed method is also found to be capable of handling plasticity of MMC.

Keywords: active slip, continuum dislocation, distortion, dominated, energy dissipation, matrix dominated, plasticity

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Authors: Elham Allahmoradi, Bahman Allahmoradi, Ali Bonyadi Naeini

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Complex systems have many aspects. A variety of methods have been developed to analyze these systems. The most efficient of these methods should not only be simple, but also provide useful and comprehensive information about many aspects of the system. Matrix methods are considered the most commonly methods used to analyze and design systems. Each matrix method can examine a particular aspect of the system. If these methods are combined, managers can access to more comprehensive and broader information about the system. This study was conducted in four steps. In the first step, a process model of a real project has been extracted through IDEF3. In the second step, activity levels have been attained by writing a process model in the form of a design structure matrix (DSM) and sorting it through triangulation algorithm (TA). In the third step, sub-processes have been obtained by writing the process model in the form of an interface structure matrix (ISM) and clustering it through cluster identification algorithm (CIA). In the fourth step, a mixed model has been developed to provide a unified picture of the project structure through the simultaneous presentation of activities and sub-processes. Finally, the paper is completed with a conclusion.

Keywords: integrated definition for process description capture (IDEF3) method, design structure matrix (DSM), interface structure matrix (ism), mixed matrix model, activity level, sub-process

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Authors: Bharath R., Tharun Sai N., Bhuvan G.

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This project focuses on developing a Parallel Computing method aimed at optimizing matrix multiplication through GPU acceleration. Addressing algorithmic challenges, GPU programming intricacies, and integration issues, the project aims to enhance efficiency and scalability. The methodology involves algorithm design, GPU programming, and optimization techniques. Future plans include advanced optimizations, extended functionality, and integration with high-level frameworks. User engagement is emphasized through user-friendly interfaces, open- source collaboration, and continuous refinement based on feedback. The project's impact extends to significantly improving matrix multiplication performance in scientific computing and machine learning applications.

Keywords: matrix multiplication, parallel processing, cuda, performance boost, neural networks

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Authors: Nathan Garcia

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The polarizing dialogue of contemporary political America results from core philosophical differences. But these differences are beyond ideological and reach metaphysical distinction. Good intellectual historians have theorized that fundamental concepts such as freedom, God, and nature have been sterilized of their intellectual vigor. They are partially correct. 19th-century pragmatist Charles Sanders Peirce offers a penetrating philosophy which can yield greater insight into the contemporary political divide. Peirce argues that metaphysical and ethical issues are derivative of operational logic. His triadic logical structure and ensuing metaphysical principles constructed therefrom is contemporaneously applicable for three reasons. First, Peirce’s logic aptly scrutinizes the logical processes of liberal and conservative mindsets. Each group arrives at a cosmological root metaphor (abduction), resulting in a contemporary assessment (deduction), ultimately prompting attempts to verify the original abduction (induction). Peirce’s system demonstrates that liberal citizens develop a cosmological root metaphor in the concept of fairness (abduction), resulting in a contemporary assessment of, for example, underrepresented communities being unfairly preyed upon (deduction), thereby inciting anger toward traditional socio-political structures suspected of purposefully destabilizing minority communities (induction). Similarly, conservative citizens develop a cosmological root metaphor in the concept of freedom (abduction), resulting in a contemporary assessment of, for example, liberal citizens advocating an expansion of governmental powers (deduction), thereby inciting anger towards liberal communities suspected of attacking freedoms of ordinary Americans in a bid to empower their interests through the government (induction). The value of this triadic assessment is the categorization of distinct types of inferential logic by their purpose and boundaries. Only deductive claims can be concretely proven, while abductive claims are merely preliminary hypotheses, and inductive claims are accountable to interdisciplinary oversight. Liberals and conservative logical processes preclude constructive dialogue because of (a) an unshared abductive framework, and (b) misunderstanding the rules and responsibilities of their types of claims. Second, Peircean metaphysical principles offer a greater summary of the contemporaneously divisive political climate. His insights can weed through the partisan theorizing to unravel the underlying philosophical problems. Corrosive nominalistic and essentialistic presuppositions weaken the ability to share experiences and communicate effectively, both requisite for any promising constructive dialogue. Peirce’s pragmatist system can expose and evade fallacious thinking in pursuit of a refreshing alternative framework. Finally, Peirce’s metaphysical foundation enables a logically coherent, scientifically informed orthopraxis well-suited for American dialogue. His logical structure necessitates radically different anthropology conducive to shared experiences and dialogue within a dynamic, cultural continuum. Pierce’s fallibilism and sensitivity to religious sentiment successfully navigate between liberal and conservative values. In sum, he provides a normative paradigm for intranational dialogue that privileges individual experience and values morally defensible notions of freedom, God, and nature. Utilizing Peirce’s thought will yield fruitful analysis and offers a promising philosophical alternative for framing and engaging in contemporary American political discourse.

Keywords: Charles s. Peirce, american politics, logic, pragmatism

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Authors: Purnomo Yustianto, Robin Doss

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As a process of developing a service system, the term ‘service engineering’ evolves in scope and definition. To achieve an integrated understanding of the process, a general framework and an ontology are required. This paper extends a previously built service engineering framework by exploring metamodels for the framework artefacts based on a foundational ontology and a metamodel landscape. The first part of this paper presents a correlation map between the proposed framework with the ontology as a form of evaluation for the conceptual coverage of the framework. The mapping also serves to characterize the artefacts to be produced for each activity in the framework. The second part describes potential metamodels to be used, from the metamodel landscape, as alternative formats of the framework artefacts. The results suggest that the framework sufficiently covers the ontological concepts, both from general service context and software service context. The metamodel exploration enriches the suggested artefact format from the original eighteen formats to thirty metamodel alternatives.

Keywords: artefact, framework, service, metamodel

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Authors: Phuoc Si Nguyen

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Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: frequency transformation, bilinear z-transformation, pre-warping frequency, digital filters, analog filters, pascal’s triangle

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Authors: Jing Wu, Wei Lv, Yibing Li, Yuanfan You

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The separation of speech signals has become a research hotspot in the field of signal processing in recent years. It has many applications and influences in teleconferencing, hearing aids, speech recognition of machines and so on. The sounds received are usually noisy. The issue of identifying the sounds of interest and obtaining clear sounds in such an environment becomes a problem worth exploring, that is, the problem of blind source separation. This paper focuses on the under-determined blind source separation (UBSS). Sparse component analysis is generally used for the problem of under-determined blind source separation. The method is mainly divided into two parts. Firstly, the clustering algorithm is used to estimate the mixing matrix according to the observed signals. Then the signal is separated based on the known mixing matrix. In this paper, the problem of mixing matrix estimation is studied. This paper proposes an improved algorithm to estimate the mixing matrix for speech signals in the UBSS model. The traditional potential algorithm is not accurate for the mixing matrix estimation, especially for low signal-to noise ratio (SNR).In response to this problem, this paper considers the idea of an improved potential function method to estimate the mixing matrix. The algorithm not only avoids the inuence of insufficient prior information in traditional clustering algorithm, but also improves the estimation accuracy of mixing matrix. This paper takes the mixing of four speech signals into two channels as an example. The results of simulations show that the approach in this paper not only improves the accuracy of estimation, but also applies to any mixing matrix.

Keywords: DBSCAN, potential function, speech signal, the UBSS model

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Authors: Anand Ankush, Wani Mohammed Farooq

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A procedure based on digraph and matrix method is developed for modelling and evaluation of sustainability of Mechanical System in a concurrent engineering environment.The sustainability parameters of a Mechanical System are identified and are called sustainability attributes. Consideration of attributes and their interrelations is rudiment in modeling and evaluation of sustainability index. Sustainability attributes of a Mechanical System are modelled in termsof sustainability digraph. The graph is represented by a one-to-one matrix for sustainability expression which is based on sustainability attributes. A variable sustainability relationship permanent matrix is defined to develop sustainability expression(VPF-t) which is also useful in comparing two systems in a concurrent environment. The sustainability index of Mechanical System is obtained from permanent of matrix by substituting the numerical values of attributes and their interrelations. A higher value of index implies better sustainability of system.The ideal value of index is obtained from matrix expression which is useful in assessing relative sustainability of a Mechanical System in a concurrent engineering environment. The procedure is not only useful for evaluation of sustainability of a Mechanical System at conceptual design stage but can also be used for design and development of systems at system design stage. A step-by-step procedure for evaluation of sustainability index is also suggested and is illustrated by means of an example.

Keywords: digraph, matrix method, mechanical system, sustainability

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Authors: Ezgi Kaya, A. Dilek Maden

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A topological index is a number related to graph which is invariant under graph isomorphism. In theoretical chemistry, molecular structure descriptors (also called topological indices) are used for modeling physicochemical, pharmacologic, toxicologic, biological and other properties of chemical compounds. Let G be a graph with n vertices and m edges. For a given edge uv, the quantity nu(e) denotes the number of vertices closer to u than v, the quantity nv(e) is defined analogously. The vertex PI index defined as the sum of the nu(e) and nv(e). Here the sum is taken over all edges of G. The energy of a graph is defined as the sum of the eigenvalues of adjacency matrix of G and the Laplacian energy of a graph is defined as the sum of the absolute value of difference of laplacian eigenvalues and average degree of G. In theoretical chemistry, the π-electron energy of a conjugated carbon molecule, computed using the Hückel theory, coincides with the energy. Hence results on graph energy assume special significance. The Laplacian matrix of a graph G weighted by the vertex PI weighting is the Laplacian vertex PI matrix and the Laplacian vertex PI eigenvalues of a connected graph G are the eigenvalues of its Laplacian vertex PI matrix. In this study, Laplacian vertex PI energy of a graph is defined of G. We also give some bounds for the Laplacian vertex PI energy of graphs in terms of vertex PI index, the sum of the squares of entries in the Laplacian vertex PI matrix and the absolute value of the determinant of the Laplacian vertex PI matrix.

Keywords: energy, Laplacian energy, laplacian vertex PI eigenvalues, Laplacian vertex PI energy, vertex PI index

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Authors: Aiman Elragig, Hanan Dreiwi, Dung Ly, Idriss Elmabrook

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This paper highlights a new approach to look at online principle components analysis (OPCA). Given a data matrix X ∈ R,^m x n we characterise the online updates of its covariance as a matrix perturbation problem. Up to the principle components, it turns out that online updates of the batch PCA can be captured by symmetric matrix perturbation of the batch covariance matrix. We have shown that as n→ n0 >> 1, the batch covariance and its update become almost similar. Finally, utilize our new setup of online updates to find a bound on the angle distance of the principle components of X and its update.

Keywords: online data updates, covariance matrix, online principle component analysis, matrix perturbation

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Authors: Khondaker Sakil Ahmed, Ang Kok Keng, Shah Md Muniruzzaman

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Spherical and Berkovich indentation tests are carried out numerically using finite element method for uniformly dispersed Carbon Nanotube (CNT) in the polymer matrix in which perfectly bonded CNT/matrix interface is considered. The Large strain elasto-plastic analysis is performed to investigate the actual scenario of nanoindentation test. This study investigates how the addition of CNT in polymer matrix influences the mechanical properties like hardness, elastic modulus of the nanocomposite. Since the wall thickness to radius ratio (t/r) is significantly small for SWCNT there is a huge possibility of lateral buckling which is a function of the location of indentation tip as well as the mechanical properties of matrix. Separate finite element models are constructed to compare the result with Berkovich indentation. This study also investigates the buckling behavior of different nanotube in a different polymer matrix.

Keywords: carbon nanotube, elasto-plastic, finite element model, nano-indentation

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Authors: Igor Kontorovich, Rina Zazkis

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We present a framework of researcher knowledge ‎development in conducting a study in mathematics education. The key ‎components of the framework are: knowledge germane to conducting a ‎particular study, processes of knowledge accumulation, and catalyzing ‎filters that influence a researcher decision making. The components of ‎the framework originated from a confluence between constructs and ‎theories in Mathematics Education, Higher Education and Sociology. ‎Drawing on a self-reflective interview with a leading researcher in ‎mathematics education, professor Michèle Artigue, we illustrate how ‎the framework can be utilized in data analysis. Criteria for framework ‎evaluation are discussed. ‎

Keywords: community of practice, knowledge development, mathematics education research, researcher knowledge

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Authors: Kerim Emre Öksüz, Mehmet Çevik, A. Enbiya Bozdağ, Ali Özer, Mehmet Şimşir

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Metal matrix composites (MMCs) have gained a considerable interest in the last three decades. Conventional powder metallurgy production route often involves the addition of reinforcing phases into the metal matrix directly, which leads to poor wetting behavior between ceramic phase and metal matrix and the segregation of reinforcements. The commonly used elements for ceramic phase formation in iron based MMCs are Ti, Nb, Mo, W, V and C, B. The aim of the present paper is to investigate the effect of sintering temperature and V-B addition on densification, phase development, microstructure, and hardness of Fe–V-B composites (Fe-(5-10) wt. %B – 25 wt. %V alloys) prepared by powder metallurgy process. Metal powder mixes were pressed uniaxial and sintered at different temperatures (ranging from 1300 to 1400ºC) for 1h. The microstructure of the (V, B) Fe composites was studied with the help of high magnification optical microscope and XRD. Experimental results show that (V, B) Fe composites can be produced by conventional powder metallurgy route.

Keywords: hardness, metal matrix composite (MMC), microstructure, powder metallurgy

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Authors: Ruitao Li, Zhili Dong, Nay Win Khun, Khiam Aik Khor

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In this study, microstructure and sintering mechanism as well as wear resistance properties of Ti/Al-Cr-Fe metal matrix composites (MMCs) fabricated by spark plasma sintering (SPS) with Ti as matrix and Al-Cr-Fe as reinforcement were investigated. Phases and microstructure of the sintered samples were analyzed using X-ray diffractometry (XRD), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS) and transmission electron microscopy (TEM). Wear resistance properties were tested by ball-on-disk method. An Al3Ti ring forms around each Al-Cr-Fe particle as the bonding layer between Ti and Al-Cr-Fe particles. The Al content in Al-Cr-Fe particles experiences a decrease from 70 at.% to 60 at.% in the sintering process. And these particles consist of quasicrystalline icosahedral AlCrFe and quasicrystal approximants γ-brass Al8(Cr,Fe)5 and Al9(Cr,Fe)4 in the sintered compact. The addition of Al-Cr-Fe particles into the Ti matrix can improve the microhardness by about 40% and the wear resistance is improved by more than 50% due to the increase in the microhardness and the change of wear mechanism.

Keywords: metal matrix composites, spark plasma sintering, phase transformation, wear

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