Search results for: difference of convex functions.

Authors: Maria Hussin, Malik Zawwar Hussain, Mubashrah Saddiqa

Abstract:

We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach to reproduce a circular arc. The radius error is calculated and found less than the existing techniques.

Keywords: Control points, rational trigonometric Bézier curves, radius error, shape measure, weight functions.

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Authors: C. C. Liang

Abstract:

MSN used to be the most popular application for communicating among social networks, but Facebook chat is now the most popular. Facebook and MSN have similar characteristics, including usefulness, ease-of-use, and a similar function, which is the exchanging of information with friends. Facebook outperforms MSN in both of these areas. However, the adoption of Facebook and abandonment of MSN have occurred for other reasons. Functions can be improved, but users’ willingness to use does not just depend on functionality. Flow status has been established to be crucial to users’ adoption of cyber applications and to affects users’ adoption of software applications. If users experience flow in using software application, they will enjoy using it frequently, and even change their preferred application from an old to this new one. However, no investigation has examined choice behavior related to switching from Facebook to MSN based on a consideration of flow experiences and functions. This investigation discusses the flow experiences and functions of social-networking applications. Flow experience is found to affect perceived ease of use and perceived usefulness; perceived ease of use influences information ex-change with friends, and perceived usefulness; information exchange influences perceived usefulness, but information exchange has no effect on flow experience.

Keywords: Consumer behavior, social media, technology acceptance model.

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Authors: Yaping Ren, Yongkun Li

Abstract:

In this paper, by using the continuation theorem of coincidence degree theory, M-matrix theory and constructing some suitable Lyapunov functions, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of recurrent neural networks with distributed delays and impulses on time scales. Without assuming the boundedness of the activation functions gj, hj , these results are less restrictive than those given in the earlier references.

Keywords: Recurrent neural networks, global exponential stability, periodic solutions, distributed delays, impulses, time scales.

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Authors: Padmanabhan Balasubramanian, Ryuta Arisaka

Abstract:

Factoring Boolean functions is one of the basic operations in algorithmic logic synthesis. A novel algebraic factorization heuristic for single-output combinatorial logic functions is presented in this paper and is developed based on the set theory paradigm. The impact of factoring is analyzed mainly from a low power design perspective for standard cell based digital designs in this paper. The physical implementation of a number of MCNC/IWLS combinational benchmark functions and sub-functions are compared before and after factoring, based on a simple technology mapping procedure utilizing only standard gate primitives (readily available as standard cells in a technology library) and not cells corresponding to optimized complex logic. The power results were obtained at the gate-level by means of an industry-standard power analysis tool from Synopsys, targeting a 130nm (0.13μm) UMC CMOS library, for the typical case. The wire-loads were inserted automatically and the simulations were performed with maximum input activity. The gate-level simulations demonstrate the advantage of the proposed factoring technique in comparison with other existing methods from a low power perspective, for arbitrary examples. Though the benchmarks experimentation reports mixed results, the mean savings in total power and dynamic power for the factored solution over a non-factored solution were 6.11% and 5.85% respectively. In terms of leakage power, the average savings for the factored forms was significant to the tune of 23.48%. The factored solution is expected to better its non-factored counterpart in terms of the power-delay product as it is well-known that factoring, in general, yields a delay-efficient multi-level solution.

Keywords: Factorization, Set theory, Logic function, Standardcell based design, Low power.

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Authors: F. Castillo, J. Arellano, S. Sánchez

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In this paper an alternative analysis in the time domain is described and the results of the interpolation process are presented by means of functions that are based on the rule of conditional mathematical expectation and the covariance function. A comparison between the interpolation error caused by low order filters and the classic sinc(t) truncated function is also presented. When fewer samples are used, low-order filters have less error. If the number of samples increases, the sinc(t) type functions are a better alternative. Generally speaking there is an optimal filter for each input signal which depends on the filter length and covariance function of the signal. A novel scheme of work for adaptive interpolation filters is also presented.

Keywords: Interpolation, basis function, over-sampling.

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Authors: Suparat Niwitpong

Abstract:

Motivated by the recent work of Herbert, Hayen, Macaskill and Walter [Interval estimation for the difference of two independent variances. Communications in Statistics, Simulation and Computation, 40: 744-758, 2011.], we investigate, in this paper, new confidence intervals for the difference between two normal population variances based on the generalized confidence interval of Weerahandi [Generalized Confidence Intervals. Journal of the American Statistical Association, 88(423): 899-905, 1993.] and the closed form method of variance estimation of Zou, Huo and Taleban [Simple confidence intervals for lognormal means and their differences with environmental applications. Environmetrics 20: 172-180, 2009]. Monte Carlo simulation results indicate that our proposed confidence intervals give a better coverage probability than that of the existing confidence interval. Also two new confidence intervals perform similarly based on their coverage probabilities and their average length widths.

Keywords: Confidence interval, generalized confidence interval, the closed form method of variance estimation, variance.

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Authors: M. Foroutan, H. Dalayeli, M. Sadeghian

Abstract:

In this paper processes including large deformations of a rubber with hyperelastic material behavior are simulated by the RKPM method. Due to the loss of kronecker delta properties in the mesh less shape functions, the imposition of essential boundary conditions consumes significant CPU time in mesh free computations. In this work transformation method is used for imposition of essential boundary conditions. A RKPM material shape function is used in this analysis. The support of the material shape functions covers the same set of particles during material deformation and hence the transformation matrix is formed only once at the initial stages. A computer program in MATLAB is developed for simulations.

Keywords: RKPM, large deformations, transformation, essentialboundary conditions.

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Authors: Farnaz G. Nezami, Mir B. Aryanezhad, Seyed J. Sadjadi

Abstract:

In this paper a nonlinear model is presented to demonstrate the relation between production and marketing departments. By introducing some functions such as pricing cost and market share loss functions it will be tried to show some aspects of market modelling which has not been regarded before. The proposed model will be a constrained signomial geometric programming model. For model solving, after variables- modifications an iterative technique based on the concept of geometric mean will be introduced to solve the resulting non-standard posynomial model which can be applied to a wide variety of models in non-standard posynomial geometric programming form. At the end a numerical analysis will be presented to accredit the validity of the mentioned model.

Keywords: Geometric programming, marketing, nonlinear optimization, production.

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Authors: F. Ruiz-Fuster

Abstract:

Arnold’s redefinition of human motives can sustain a psychology of education which emphasizes the beauty of knowledge and the exercise of intellectual functions. Thus, education instead of focusing on skills and learning by doing would be centered on ‘the widest reaches of the human spirit’. One way to attain it is by developing children’s inherent interest. Arnold takes into account the fact that the desire to know is the inherent interest which leads students to explore and learn. She also emphasizes the need of exercising human functions as thinking, judging and reasoning. According to Arnold, the influence of psychological theories of motivation in education has derived in considering that all learning and school tasks should derive from children’s needs and impulses. The desire to know and the curiosity have not been considered as basic and active as any instinctive drive or basic need, so there has been an attempt to justify and understand how biological drives guide student’s learning. However, understanding motives and motivation not as a drive, an instinct or an impulse guided by our basic needs, but as a want that leads to action can help to understand, from a psychological perspective, how teachers can motivate students to learn, strengthening their desire and interest to reason and discover the whole new world of knowledge.

Keywords: Academic motivation, interests, desire to know, educational psychology, intellectual functions.

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Authors: Salah R. Al Zaidee, Ali S. Mahdi

Abstract:

Except for simple problems of statically determinate structures, optimum design problems in structural engineering have implicit objective functions where structural analysis and design are essential within each searching loop. With these implicit functions, the structural engineer is usually enforced to write his/her own computer code for analysis, design, and searching for optimum design among many feasible candidates and cannot take advantage of available software for structural analysis, design, and searching for the optimum solution. The meta-model is a regression model used to transform an implicit objective function into objective one and leads in turn to decouple the structural analysis and design processes from the optimum searching process. With the meta-model, well-known software for structural analysis and design can be used in sequence with optimum searching software. In this paper, the meta-model has been used to develop an explicit objective function for plane steel frames subjected to dead, live, and seismic forces. Frame topology is assumed as predefined based on architectural and functional requirements. Columns and beams sections and different connections details are the main design variables in this study. Columns and beams are grouped to reduce the number of design variables and to make the problem similar to that adopted in engineering practice. Data for the implicit objective function have been generated based on analysis and assessment for many design proposals with CSI SAP software. These data have been used later in SPSS software to develop a pure quadratic nonlinear regression model for the explicit objective function. Good correlations with a coefficient, R², in the range from 0.88 to 0.99 have been noted between the original implicit functions and the corresponding explicit functions generated with meta-model.

Keywords: Meta-modal, objective function, steel frames, seismic analysis, design.

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Authors: Pavan S., Sridhar G., Sridhar V.

Abstract:

Super resolution is one of the commonly referred inference problems in computer vision. In the case of images, this problem is generally addressed using a graphical model framework wherein each node represents a portion of the image and the edges between the nodes represent the statistical dependencies. However, the large dimensionality of images along with the large number of possible states for a node makes the inference problem computationally intractable. In this paper, we propose a representation wherein each node can be represented as acombination of multiple regression functions. The proposed approach achieves a tradeoff between the computational complexity and inference accuracy by varying the number of regression functions for a node.

Keywords: Belief propagation, Graphical model, Regression, Super resolution.

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Authors: Jeeoot Singh, Sandeep Singh, K. K. Shukla

Abstract:

The governing differential equations of laminated plate utilizing trigonometric shear deformation theory are derived using energy approach. The governing differential equations discretized by different radial basis functions are used to predict the free vibration behavior of symmetric laminated composite plates. Effect of orthotropy and span to thickness ratio on frequency parameter of simply supported laminated plate is presented. Numerical results show the accuracy and good convergence of radial basis functions.

Keywords: Composite plates, Meshfree method, free vibration, Shear deformation, RBFs

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.

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Authors: Ya-Hui Lee, Ching-Yi Lu, Hui-Chuan Wei

Abstract:

The purpose of this research was to explore the relation between proactive coping and well-being of middle-aged adults. We conducted survey research that with t-test, one way ANOVA, Pearson correlation and stepwise multiple regression to analyze. This research drew on a sample of 395 participants from the senior learning centers of Taiwan. The results provided the following findings: 1.The participants from different residence areas associated significant difference with proactive coping, but not with well-being. 2. The participants’ perceived of financial level associated significant difference with both proactive coping and well-being. 3. There was significant difference between participants’ income and well-being. 4. The proactive coping was positively correlated with well-being. 5. From stepwise multiple regression analysis showed that two dimensions of proactive coping had positive predictability. Finally, these results of this study can be provided as references for designing older adult educational programs in Taiwan.

Keywords: Middle-age adults, learners, proactive coping, well-being.

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Authors: AbdulLateef A. Olanrewaju, Arazi Idrus, Mohd F. Khamidi

Abstract:

Maintenance costs incurred on building differs. The difference can be as results of the types, functions, age, building health index, size, form height, location and complexity of the building. These are contributing to the difficulty in maintenance development of deterministic maintenance cost model. This paper is concerns with reporting the preliminary findings on the creation of building maintenance cost distributions for universities in Malaysia. This study is triggered by the need to provide guides on maintenance costs distributions for decision making. For this purpose, a survey questionnaire was conducted to investigate the distribution of maintenance costs in the universities. Altogether, responses were received from twenty universities comprising both private and publicly owned. The research found that engineering services, roofing and finishes were the elements contributing the larger segment of the maintenance costs. Furthermore, the study indicates the significance of maintenance cost distribution as decision making tool towards maintenance management.

Keywords: Performance matrix, university buildings, costmodel, Malaysia

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Authors: V. Swarnalatha, A. V. Narasimha Rao, P. Pal

Abstract:

The present research reports the investigation of fast etching of silicon for the fabrication of microelectromechanical systems (MEMS) structures using silicon wet bulk micromachining. Low concentration tetramethyl-ammonium hydroxide (TMAH) and hydroxylamine (NH₂OH) are used as main etchant and additive, respectively. The concentration of NH₂OH is varied to optimize the composition to achieve best etching characteristics such as high etch rate, significantly high undercutting at convex corner for the fast release of the microstructures from the substrate, and improved etched surface morphology. These etching characteristics are studied on Si{100} and Si{110} wafers as they are most widely used in the fabrication of MEMS structures as wells diode, transistors and integrated circuits.

Keywords: KOH, MEMS, micromachining, silicon, TMAH, wet anisotropic etching.

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Authors: Abhijit Mitra, C. Ardil

Abstract:

We investigate sonic cues for binaural sound localization within classrooms and present a structural model for the same. Two of the primary cues for localization, interaural time difference (ITD) and interaural level difference (ILD) created between the two ears by sounds from a particular point in space, are used. Although these cues do not lend any information about the elevation of a sound source, the torso, head, and outer ear carry out elevation dependent spectral filtering of sounds before they reach the inner ear. This effect is commonly captured in head related transfer function (HRTF) which aids in resolving the ambiguity from the ITDs and ILDs alone and helps localize sounds in free space. The proposed structural model of HRTF produces well controlled horizontal as well as vertical effects. The implemented HRTF is a signal processing model which tries to mimic the physical effects of the sounds interacting with different parts of the body. The effectiveness of the method is tested by synthesizing spatial audio, in MATLAB, for use in listening tests with human subjects and is found to yield satisfactory results in comparison with existing models.

Keywords: Auditory localization, Binaural sound, Head related impulse response, Head related transfer function, Interaural level difference, Interaural time difference, Localization cues.

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Authors: Jaipong Kasemsuwan

Abstract:

A numerical solution of the initial boundary value problem of the suspended string vibrating equation with the particular nonlinear damping term based on the finite difference scheme is presented in this paper. The investigation of how the second and third power terms of the nonlinear term affect the vibration characteristic. We compare the vibration amplitude as a result of the third power nonlinear damping with the second power obtained from previous report provided that the same initial shape and initial velocities are assumed. The comparison results show that the vibration amplitude is inversely proportional to the coefficient of the damping term for the third power nonlinear damping case, while the vibration amplitude is proportional to the coefficient of the damping term in the second power nonlinear damping case.

Keywords: Finite-difference method, the nonlinear damped equation, the numerical simulation, the suspended string equation

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Authors: Sukrit Shankar, Pardha Saradhi K., Chetana Shanta Patsa, Jaydev Sharma

Abstract:

Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fractional Fourier Transform and show that the eigenvectors of the proposed matrix has a higher degree of correlation with the Hermite Gaussian functions. Also, the proposed matrix is shown to give better Fractional Fourier responses with various transform orders for different signals.

Keywords: Fractional Fourier Transform, Hamiltonian, Eigen Vectors, Discrete Hermite Gaussians.

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Authors: S. Yordchim, G. Anugkakul, T. Gibbs

Abstract:

The English competence of Thai people was examined in the context of knowledge of English in everyday life for Small and Medium Entrepreneurs (SMEs), and also integrated with Second language acquisition (SLA) students’ classroom. Second language acquisition was applied to the results of the questionnaires and interview forms. Levels of the need on English used for SME entrepreneurs in Thailand, satisfaction on joining the street classroom project were shown to be significantly high for some certain language functions and satisfaction. Finding suggests that the language functions on etiquette for professional use is essential and useful because lesson learned can be used in the real situation for their career. Implications for the climate of the street classroom are discussed.

Keywords: English classroom, second language acquisition, Small and Medium Entrepreneurs, Thai students.

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Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the automatic choosing functions of gradient optimization type for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by minimizing the Hamiltonian with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Hiroki Shinkawa, Tadaaki Tomiie

Abstract:

Many interventions for social skills acquisition aim to decrease the gap between social skills deficits in the individual and normative social skills; nevertheless little is known of typical social skills according to age difference in students. In this study, we developed new quintet of Hokkaido Social Skills Inventory (HSSI) to identify age-appropriate social skills for school adaptation. First, we selected 13 categories of social skills for school adaptation from previous studies, and created questionnaire items through discussion by 25 teachers in all three levels from elementary schools to senior high schools. Second, the factor structures of five versions of the social skills scale were investigated on 2nd grade (n = 1,864), 4th grade (n = 1,936), 6th grade (n = 2,085), 7th grade (n = 2,007), and 10th grade (n = 912) students, respectively. The exploratory factor analysis showed that a number of constructing factors of social skills increased as one’s grade in school advanced. The results in the present study can be useful to characterize the age-appropriate social skills for school adaptation. 

Keywords: Social skills, age difference, children, adolescents.

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Authors: E. Aruchunan, J. Sulaiman

Abstract:

The objective of this paper is to analyse the application of the Half-Sweep Gauss-Seidel (HSGS) method by using the Half-sweep approximation equation based on central difference (CD) and repeated trapezoidal (RT) formulas to solve linear fredholm integro-differential equations of first order. The formulation and implementation of the Full-Sweep Gauss-Seidel (FSGS) and Half- Sweep Gauss-Seidel (HSGS) methods are also presented. The HSGS method has been shown to rapid compared to the FSGS methods. Some numerical tests were illustrated to show that the HSGS method is superior to the FSGS method.

Keywords: Integro-differential equations, Linear fredholm equations, Finite difference, Quadrature formulas, Half-Sweep iteration.

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Authors: Miaomiao Yang, Shouming Zhong

Abstract:

This paper studies the problem of exponential stability analysis for uncertain neural networks with discrete and distributed time-varying delays. Together with a suitable augmented Lyapunov Krasovskii function, zero equalities, reciprocally convex approach and a novel sufficient condition to guarantee the exponential stability of the considered system. The several exponential stability criterion proposed in this paper is simpler and effective. Finally,numerical examples are provided to demonstrate the feasibility and effectiveness of our results.

Keywords: Exponential stability, Uncertain Neural networks, LMI approach, Lyapunov-Krasovskii function, Time-varying.

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Authors: Saghir Ahmad, Abid Hussain Ch., Atif Khalil, Misbah Malik

Abstract:

The major purpose of the study was to identify the institutional environments’ strengths, weaknesses, opportunities and threats of University of the Punjab, Lahore. The target population of the study was teachers of University of the Punjab Lahore. The sample of 235 teachers (155 males, 80 females) were selected through multistage stratified sampling technique. A questionnaire regarding the institutional environments of University SWOT Analysis “Strengths, Weaknesses, Opportunities, and Threats” was used to collect the required data for this study. The questionnaire consisted of two parts. The first part comprised of the demographic information (faculty, department, gender, teacher rank), while the second part included the statements regarding SWOT analysis (strengths, weaknesses, opportunities and threats). Reliability index (Cronbach’s Alpha) of the questionnaire was 0.87, which is statistically acceptable. Analysis of the data indicated that there was significant difference in the opinion of respondents. Teachers of Islamic studies and Laws had difference in their opinions regarding the institutional environment strengths, and opportunities and it was supported by the findings of the study. There was significant difference in opinions of male and female teachers regarding strengths and opportunities of university. And there was no significant difference in opinions of male and female teachers regarding weaknesses and threats of university.

Keywords: Institutional environments, SWOT analysis, teachers, University of the Punjab.

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Authors: Hussein Alahmer, Amr Ahmed

Abstract:

Liver cancer is one of the common diseases that cause the death. Early detection is important to diagnose and reduce the incidence of death. Improvements in medical imaging and image processing techniques have significantly enhanced interpretation of medical images. Computer-Aided Diagnosis (CAD) systems based on these techniques play a vital role in the early detection of liver disease and hence reduce liver cancer death rate.  This paper presents an automated CAD system consists of three stages; firstly, automatic liver segmentation and lesion’s detection. Secondly, extracting features. Finally, classifying liver lesions into benign and malignant by using the novel contrasting feature-difference approach. Several types of intensity, texture features are extracted from both; the lesion area and its surrounding normal liver tissue. The difference between the features of both areas is then used as the new lesion descriptors. Machine learning classifiers are then trained on the new descriptors to automatically classify liver lesions into benign or malignant. The experimental results show promising improvements. Moreover, the proposed approach can overcome the problems of varying ranges of intensity and textures between patients, demographics, and imaging devices and settings.

Keywords: CAD system, difference of feature, Fuzzy c means, Liver segmentation.

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Authors: Sofia Douklia

Abstract:

The present context paper aims to present the important role of ‘student voice’ and the music teacher in the classroom, which contributes to more student-centered music education. The aim is to focus on the functions of the student voice through the music spectrum, which has been born in the music classroom, and the teacher’s methodologies and techniques used in the music classroom. The music curriculum, the principles of student-centered music education, and the role of students and teachers as music ambassadors have been considered the major music parameters of student voice. The student- voice is a worth-mentioning aspect of a student-centered education, and all teachers should consider and promote its existence in their classroom.

Keywords: Student’s voice, student-centered education, music ambassadors, music teachers.

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Authors: Sook-Yeon Shim, Hwan-Su Seo, Tae-Hyun Kim, Hongkyu Kim

Abstract:

The purpose of this study is to identify ideal urban design elements of waterfronts and to analyze the differences in users- cognition among these elements. This study follows three steps as following: first is identifying the urban design elements of waterfronts from literature review and second is evaluating intended users- cognition of urban design elements in urban waterfronts. Lastly, third is analyzing the users- cognition differences. As the result, evaluations of waterfront areas by users show similar features that non-waterfront urban design elements contain the highest degree of importance. This indicates the difference of users- cognition has dimensions of frequency and distance, and demonstrates differences in the aspect of importance than of satisfaction. Multi-Dimensional Scaling Method verifies differences among their cognition. This study provides elements to increase satisfaction of users from differences of their cognition on design elements for waterfronts. It also suggests implications on elements when waterfronts are built.

Keywords: Cognition Difference, , Multi-Dimensional Scaling , Urban Design Elements , Waterfront

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Authors: M. A. Beisenbi, N. M. Kissikova, S. E. Beisembina, S. T. Suleimenova, S. A. Kaliyeva

Abstract:

The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector-functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: Gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability.

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Authors: U. Prasopchingchana

Abstract:

The temperature distribution and the heat transfer rates through a multi-layer door of a furnace were investigated. The inside of the door was in contact with hot air and the other side of the door was in contact with room air. Radiation heat transfer from the walls of the furnace to the door and the door to the surrounding area was included in the problem. This work is a two dimensional steady state problem. The Churchill and Chu correlation was used to find local convection heat transfer coefficients at the surfaces of the furnace door. The thermophysical properties of air were the functions of the temperatures. Polynomial curve fitting for the fluid properties were carried out. Finite difference method was used to discretize for conduction heat transfer within the furnace door. The Gauss-Seidel Iteration was employed to compute the temperature distribution in the door. The temperature distribution in the horizontal mid plane of the furnace door in a two dimensional problem agrees with the one dimensional problem. The local convection heat transfer coefficients at the inside and outside surfaces of the furnace door are exhibited.

Keywords: Conduction, heat transfer, multi-layer door, natural convection

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