Search results for: mixed integer non-linear program

Authors: Ming-Jong Yao, Chin-Sum Shui, Chih-Han Wang

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This paper is developed based on a real-world decision scenario that an industrial gas company that applies the Vendor Managed Inventory model and supplies liquid oxygen with a self-operated heterogeneous vehicle fleet to hospitals in nearby cities. We name it as a Joint Replenishment and Heterogeneous Vehicle Routing Problem with Cyclical Schedule and formulate it as a non-linear mixed-integer linear programming problem which simultaneously determines the length of the planning cycle (PC), the length of the replenishment cycle and the dates of replenishment for each customer and the vehicle routes of each day within PC, such that the average daily operation cost within PC, including inventory holding cost, setup cost, transportation cost, and overtime labor cost, is minimized. A solution method based on genetic algorithm, embedded with an encoding and decoding mechanism and local search operators, is then proposed, and the hash function is adopted to avoid repetitive fitness evaluation for identical solutions. Numerical experiments demonstrate that the proposed solution method can effectively solve the problem under different lengths of PC and number of customers. The method is also shown to be effective in determining whether the company should expand the storage capacity of a customer whose demand increases. Sensitivity analysis of the vehicle fleet composition shows that deploying a mixed fleet can reduce the daily operating cost.

Keywords: cyclic inventory routing problem, joint replenishment, heterogeneous vehicle, genetic algorithm

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Authors: Tudor Barbu

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We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Hua Cao, Laurent Peyrodie, Olivier Agnani, Cecile Donze

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Multiple sclerosis (MS) is a disease, which affects the central nervous system, and causes balance problem. In clinical, this disorder is usually evaluated using static posturography. Some linear or nonlinear measures, extracted from the posturographic data (i.e. center of pressure, COP) recorded during a balance test, has been used to analyze postural control of MS patients. In this study, the trend (TREND) and the sample entropy (SampEn), two nonlinear parameters were chosen to investigate their relationships with the expanded disability status scale (EDSS) score. Forty volunteers with different EDSS scores participated in our experiments with eyes open (EO) and closed (EC). TREND and two types of SampEn (SampEn1 and SampEn2) were calculated for each combined COP’s position signal. The results have shown that TREND had a weak negative correlation to EDSS while SampEn2 had a strong positive correlation to EDSS. Compared to TREND and SampEn1, SampEn2 showed a better significant correlation to EDSS and an ability to discriminate the MS patients in the EC case. In addition, the outcome of the study suggests that the multi-dimensional nonlinear analysis could provide some information about the impact of disability progression in MS on dynamics of the COP data.

Keywords: balance, multiple sclerosis, nonlinear analysis, postural sway

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Authors: T. Sanches, K. Bousson

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As part of the development of a 4D autopilot system for unmanned aerial vehicles (UAVs), i.e. a time-dependent robust trajectory generation and control algorithm, this work addresses the problem of optimal path control based on the flight sensors data output that may be unreliable due to noise on data acquisition and/or transmission under certain circumstances. Although several filtering methods, such as the Kalman-Bucy filter or the Linear Quadratic Gaussian/Loop Transfer Recover Control (LQG/LTR), are available, the utter complexity of the control system, together with the robustness and reliability required of such a system on a UAV for airworthiness certifiable autonomous flight, required the development of a proper robust filter for a nonlinear system, as a way of further mitigate errors propagation to the control system and improve its ,performance. As such, a nonlinear algorithm based upon the LQG/LTR, is validated through computational simulation testing, is proposed on this paper.

Keywords: autonomous flight, LQG/LTR, nonlinear state estimator, robust flight control

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Authors: M. Altekin, R. F. Yükseler

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Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

Keywords: Bending, Nonlinear, Plate, Point support, Shell.

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Authors: Jungho Moon, Lae-Jeong Park

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This paper introduces a signal monitoring program developed with a view to helping electrical engineering students get familiar with sensors with digital output. Because the output of digital sensors cannot be simply monitored by a measuring instrument such as an oscilloscope, students tend to have a hard time dealing with digital sensors. The monitoring program runs on a PC and communicates with an MCU that reads the output of digital sensors via an asynchronous communication interface. Receiving the sensor data from the MCU, the monitoring program shows time and/or frequency domain plots of the data in real time. In addition, the monitoring program provides a serial terminal that enables the user to exchange text information with the MCU while the received data is plotted. The user can easily observe the output of digital sensors and configure the digital sensors in real time, which helps students who do not have enough experiences with digital sensors. Though the monitoring program was programmed in the Matlab programming language, it runs without the Matlab since it was compiled as a standalone executable.

Keywords: digital sensor, MATLAB, MCU, signal monitoring program

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Authors: Anna K. Wood, Terri Friedline

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In April and May 2020, the private banking industry approved over 1.7 million emergency small business loans, totaling over $650 billion in federal relief funds as part of the Paycheck Protection Program (PPP). Since the program’s rollout, the extensive evidence of discriminatory lending and misuse of funds has been revealed by investigative journalism and academic studies. This study is based on 41 interviews with frontline banking industry professionals conducted during the days and weeks of the PPP rollout, presenting a real-time narrative of the program rollout through the eyes of those in the role of a street-level bureaucrat. We present two themes from this data about the conditions under which these frontline workers experienced the PPP: Exigent Timelines and Defaulting to Existing Workplace Norms and Practices. We analyze these themes using literature on street-level organizations, bureaucratic discretion, and the differences between public and private sector logic. The results of this study present new directions for theorizing sector-level differences in street-level bureaucratic discretion in the context of mixed-sector collaboration on public service delivery, particularly under conditions of crisis and urgency.

Keywords: street level bureaucracy, social policy, bureaucratic discretion, public private partnerships

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Authors: Ellie Abdi, Susana Juniu

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The purpose of this presentation is to describe an interdisciplinary teaching program that integrates physical education concepts using a philosophical approach. The presentation includes a review of: a) the philosophy of American education, b) the philosophy of sports and physical education, c) the interdisciplinary physical education program, d) professional development programs, (e) the Success of this physical education program, f) future of physical education. This unique interdisciplinary program has been implemented in an urban school physical education discipline in East Orange, New Jersey for over 10 years. During the program the students realize that the bodies go through different experiences. The body becomes a place where a child can recognize in an enjoyable way to express and perceive particular feelings or mental states. Children may distinguish themselves to have high abilities in the social or other domains but low abilities in the field of athletics. The goal of this program for the individuals is to discover new skills, develop and demonstrate age appropriate mastery level at different tasks, therefore the program consists of 9 to 12 sports, including many game. Each successful experience increases the awareness ability. Engaging in sports and physical activities are social movements involving groups of children in situations such as teams, friends, and recreational settings, which serve as a primary socializing agent for teaching interpersonal skills. As a result of this presentation the audience will reflect and explore how to structure a physical education program to integrate interdisciplinary subjects with philosophical concepts.

Keywords: interdisciplinary disciplines, philosophical concepts, physical education, interdisciplinary teaching program

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Authors: Sonia Sonia

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This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: Anuar Ishak

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The mixed convection stagnation point flow toward a vertical plate is investigated. The external flow impinges normal to the heated plate and the surface temperature is assumed to vary linearly with the distance from the stagnation point. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the mixed convection parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, mixed convection, stability analysis

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: R. Loukil, M. Chtourou, T. Damak

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In this work, we use the Fault detection and isolation and the Fault tolerant control based on sliding mode observer in order to introduce the well diagnosis of a nonlinear system. The robustness of the proposed observer for the two techniques is tested through a physical example. The results in this paper show the interaction between the Fault tolerant control and the Diagnosis procedure.

Keywords: fault detection and isolation FDI, fault tolerant control FTC, sliding mode observer, nonlinear system, robustness, stability

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Authors: Sunghyun Kim, Hong-Gun Park

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In the performance-based design (PBD), by using the nonlinear dynamic analysis (NDA), the actual performance of the structure is evaluated. Unlike frame structures, in the wall structures, base shear force which is resulted from the NDA, is greatly amplified than that from the elastic analysis. This shear amplifying effect causes repeated designs which make designer difficult to apply the PBD. Therefore, in this paper, factors which affect shear amplification were studied. For the 20-story wall model, the NDA was performed. From the analysis results, the base shear amplification factor was proposed.

Keywords: performance based design, shear amplification factor, nonlinear dynamic analysis, RC shear wall

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Authors: Ch. Ramreddy, P. Naveen, D. Srinivasacharya

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The objective of the present study is to investigate the effect of nonlinear temperature and concentration on the mixed convective flow of micropolar fluid over an inclined flat plate in a non-Darcy porous medium in the presence of convective boundary condition. In order to analyze all the essential features, the transformed nonlinear conservation equations are worked out numerically by spectral method. By insisting the comparison between vertical, horizontal and inclined plates, the physical quantities of the flow and its characteristics are exhibited graphically and quantitatively with various parameters. An increase in the coupling number and inclination of angle tend to decrease the skin friction, mass transfer rate and the reverse change is there in wall couple stress and heat transfer rate. The nominal effect on the wall couple stress and skin friction is encountered whereas the significant effect on the local heat and mass transfer rates are found for high enough values of Biot number.

Keywords: convective boundary condition, micropolar fluid, non-darcy porous medium, non-linear convection, spectral method

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Authors: Adi Gielgun-Katz, Alina S. Rusu

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In the last two decades, education systems worldwide have integrated new pedagogical methods and strategies in lesson plans, such as innovative technologies, social-emotional learning (SEL), gamification, mixed learning, multiple literacies, and many others. Visual language, such as photographs, is known to transcend cultures and languages, and it is commonly used by youth to express positions and affective states in social networks. Therefore, visual language needs more educational attention as a linguistic and communicative component that can create connectedness among the students and their teachers. Nowadays, when SEL is gaining more and more space and meaning in the area of academic improvement in relation to social well-being, and taking and sharing pictures is part of the everyday life of the majority of people, it becomes natural to add the visual language to SEL approach as a reinforcement strategy for connecting education to the contemporary culture and language of the youth. This article presents a program conducted in a high school class in Israel, which combines the five SEL with photography techniques, i.e., Social-Emotional Learning Visual Empowerments (SELVEs) program (experimental group). Another class of students from the same institution represents the control group, which is participating in the SEL program without the photography component. The SEL component of the programs addresses skills such as: troubleshooting, uncertainty, personal strengths and collaboration, accepting others, control of impulses, communication, self-perception, and conflict resolution. The aim of the study is to examine the effects of programs on the level of the five SEL aspects in the two groups of high school students: Self-Awareness, Social Awareness, Self-Management, Responsible Decision Making, and Relationship Skills. The study presents a quantitative assessment of the SEL programs’ impact on the students. The main hypothesis is that the students’ questionnaires' analysis will reveal a better understanding and improvement of the five aspects of the SEL in the group of students involved in the photography-enhanced SEL program.

Keywords: social-emotional learning, photography, education program, adolescents

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Authors: Toshanlal Meenpal, Ankita Meenpal

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A very important technique in reversible data hiding field is Difference expansion. Secret message as well as the cover image may be completely recovered without any distortion after data extraction process due to reversibility feature. In general, in any difference expansion scheme embedding is performed by integer transform in the difference image acquired by grouping two neighboring pixel values. This paper proposes an improved reversible difference expansion embedding scheme. We mainly consider edge direction for embedding by modifying the difference of two neighboring pixels values. In general, the larger difference tends to bring a degraded stego image quality than the smaller difference. Image quality in the range of 0.5 to 3.7 dB in average is achieved by the proposed scheme, which is shown through the experimental results. However payload wise it achieves almost similar capacity in comparisons with previous method.

Keywords: information hiding, wedge direction, difference expansion, integer transform

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Authors: Bernadette F. De La Cruz, Susan Marie R. Dela Cruz, Georgia D. Demavibas

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Pantawid Pamilyang Pilipino Program (4P) is a conditional cash transfer program in the Philippines pay extremely poor household-beneficiaries in order to fulfill the country’s commitment to the number one of the Millennium Development Goals (MDG). 4P's send 10,235,256 school children aged 6-18 from a total of 4,353,597 registered households with an average of two to three children. We analyze this program in Iloilo, Philippines. We show that this program can be made efficient by selecting beneficiaries and calibrating transfer for a maximum breaking of intergenerational poverty cycle of hunger, health and achieve higher education.

Keywords: ESGP-PA, millennium development goals, house hold beneficiaries, cash transfer

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Authors: Pamela K. Coke, Heidi Frederiksen, Ann Sebald

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Over the past three years, the researchers have been tracking a rise in the number of teacher education candidates leaving the field before completing their university’s educator preparation program. At their institution, this rise is most pronounced in English Education. The purpose of this qualitative research study is to understand English Education teacher candidates' expectations in becoming prepared educators at each phase of their four phase teacher education program at one institution of higher education in the United States. Research questions include: To what extent do we find differences in teacher candidates' expectations of their teacher training program and student teaching experiences based upon undergraduate and graduate programs? Why do (or do not) teacher candidates persist in their teacher training program and student teaching experiences? How do dispositions develop through the course of the teacher training program? What supports do teacher candidates self-identify as needing at each phase of the teacher training program? Based upon participant interviews at each phase of the teacher education program, the researchers, all teacher educators, examine the extent to which English Education students feel prepared to student teach, focusing on preparation, persistence, and dispositions. The Colorado State University Center for Educator Preparation (CEP) provides students with information about teaching dispositions, or desired professional behaviors, throughout their education program. CEP focuses these dispositions around nine categories: Professional Behaviors, Initiative and Dependability, Tact and Judgment, Ethical Behavior and Integrity, Collegiality and Responsiveness, Effective Communicator, Desire to Improve Own Performance, Culturally Responsive, and Commitment to the Profession. Currently, in the first phase of a four phase study, initial results indicate participants expect their greatest joys will be working with and learning from students. They anticipate their greatest challenges will involve discipline and confidence. They predict they will persist in their program because they believe the country needs well-prepared teachers and they have a commitment to their professional growth. None of the participants thus far could imagine why they would leave the program. With regard to strongest and weakest dispositions, results are mixed. Some participants see Tact and Judgment as their strongest disposition; others see it as their weakest. All participants stated mentoring is a necessary support at every phase of the teacher preparation process. This study informs the way teacher educators train and evaluate teacher candidates, and has implications for the frequency and types of feedback students receive from mentors and supervisors. This research contributes to existing work on teacher retention, candidate persistence, and dispositional development.

Keywords: English education, dispositions, persistence, teacher preparation

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Authors: Shuko Takeshita

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This study investigates the identity formation of mixed-race children in Japan. From the latter half of the 1980s to the mid-2000s, Japan experienced an 'intermarriage boom,' which was soon followed by a fairly significant number of children born to these unions. These children are now coming of age. Among mixed-race children, some embraced both cultural traditions, while others chose a monocultural path despite exposure to two cultural traditions as they grew up. What factors are involved in shaping the identity of mixed-race children? How does identity formation actually occur in these children? This study addresses these questions through an interview survey of 139 cross-cultural families since 1999, including 23 Pakistani-Japanese families, 20 Turkish-Japanese families, 26 families comprising other international Muslim husbands and Japanese wives, 33 Filipino-Japanese families, and 37 Brazilian-Japanese families. The results of this two-decade-long study reveal that in cases where one cannot tell at first glance that children are mixed race, there is a tendency for them to hide their mixed background due to fear of bullying at school, as well as for their parents to encourage them to do this. To pass as a Japanese is one strategy for avoiding discrimination and prejudice, and it can provide a measure of ethnic security or a way of coping with social intolerance. Certainly, among my informants, there are some children who were bullied or teased at school, and as a result, they stopped attending or transferred to other schools. But the mixed-race experience is not always a negative thing in Japan. There is clearly a double standard involved in that mixed-race children of a Caucasian parent are more readily accepted by society than those of a non-Caucasian parent. The perceived social status of mixed-race individuals is usually understood in relation to the hierarchical positionings of monoracial groups. Mixed-race children could be guaranteed the right to enjoy the benefit of maintaining and developing an identity as a Japanese, in addition to one more identity. We need to encourage a new awareness of the children as agents for a transition from a monocultural system to a multicultural system in Japanese society.

Keywords: identity formation, intermarriage, mixed race, multicultural children

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Authors: Lisa Gray, Henry Kronner, Tameca Harris-Jackson, Mimi Sodhi, Ruth Gerritsen-McKane, Donette Considine

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The MSW Peer Mentorship Program (PMP) was developed as one of several approaches to foster student success. The key purposes of the PMP are to help new graduate students transition to a graduate program, facilitate relationship building between students, grow and sustain student satisfaction, and build a strong connection to the MSW program. This pilot program also serves as an additional source of support for students during the era of the Covid-19 pandemic. Further, the long-term goals of the program are to assist in student retention. Preliminary findings suggest that both mentors and mentees enrolled in PMP find the peer mentoring relationship to have a positive impact on their graduate learning experience.

Keywords: covid-19, mentorship, peer support, student success

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Authors: Jayson Vicente

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The young men and women of Philippine Military Academy Cadet Corps Armed Forces of the Philippines (PMA CCAFP) are bred to be front liners and last line of defense during war and times of peace; as such, they must be equipped with the most practical and most effective combat-ready Martial Arts and Combative skills to effectively fulfill their duty, as well as to protect and safeguard themselves to continue serving the people and their country. This study shall assess the current Martial Arts and Combative Program of the PMA CCAFP using descriptive methodology by interviews and floating questionnaires. The current Martial Arts and Combative Program of the PMA CCAFP with all of the subjects involved are more sports inclined rather than combat-equipped. Picking the best from each subject used in the program, this study seeks to recommend improvements or create a better Martial Arts and Combative Program that will satisfy the objective of producing Martial Arts combatant graduates. A good Martial Arts and Combative Program for PMA is essential to prepare them for what lies ahead, which is unforgiving and no rules to pacify threat.

Keywords: combative, martial arts, military, program

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Authors: Maria Da Glória Diniz De Almeida, Andreia M. P. Salgado

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This paper aims to present the creation of a mentoring program to be applied in developing future junior industrial engineers acting professionally. Its objective is to contribute to a better professional performance as engineers. It is a case-study for the RIP region (including the cities of Resende, Itatiaia and Porto Real), which is located in an industrial area in Rio de Janeiro State, in Brazil. As a result, 87% of mentors and mentees approved the program as efficient, based on the initial targets.

Keywords: mentoring program, mentors and mentees, student professional development, young engineers education

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Authors: Mohsen Ziaee

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Almost all existing researches on the flowshop scheduling problems focus on the permutation schedules and there is insufficient study dedicated to the general flowshop scheduling problems in the literature, since the modeling and solving of the general flowshop scheduling problems are more difficult than the permutation ones, especially for the large-size problem instances. This paper considers the general flowshop scheduling problem with the objective function of the makespan (F//Cmax). We first find the optimal solution of the problem by solving a mixed integer linear programming model. An efficient heuristic method is then presented to solve the problem. An ant colony optimization algorithm is also proposed for the problem. In order to evaluate the performance of the methods, computational experiments are designed and performed. Numerical results show that the heuristic algorithm can result in reasonable solutions with low computational effort and even achieve optimal solutions in some cases.

Keywords: scheduling, general flow shop scheduling problem, makespan, heuristic

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Authors: Dale Daniel G. Bodo

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This study investigated the status of the Laboratory Tools and Equipment of the BSHRT Program of Eastern Visayas State University, Tacloban City Campus. Descriptive-correlation method was used which Variables include profile age, gender, acquired NC II, competencies in HRT and the status of the laboratory facilities, tools, and equipment of the BSHRT program. The study also identified significant correlation between the profile of the respondents and the implementation of the BSHRT Program in terms of laboratory tools and equipment. A self-structured survey questionnaire was used to gather relevant data among eighty-seven (87) BSHRT-OJT students. To test the correlations of variables, Pearson Product Moment Coefficient Correlation or Pearson r was used. As a result, the study revealed very interesting results and various significant correlations among the paired variables and as to the implementation of the BSHRT Program. Hence, this study was done to update the status of laboratory tools and equipment of the program.

Keywords: status, BSHRT Program, laboratory tools and equipment, descriptive-correlation

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Authors: Edamana Vasudevan Krishnan

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This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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Authors: Felix Jr. Garde, Eric Augustus Tingatinga

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Most analysis procedures of reinforced concrete (RC) slabs are based on elastic theory. When subjected to large forces, however, slabs deform beyond elastic range and the study of their behavior and performance require nonlinear analysis. This paper presents a numerical model to simulate nonlinear behavior of RC slabs using rigid body-spring discrete element method. The proposed slab model composed of rigid plate elements and nonlinear springs is based on the yield line theory which assumes that the nonlinear behavior of the RC slab subjected to transverse loads is contained in plastic or yield-lines. In this model, the displacement of the slab is completely described by the rigid elements and the deformation energy is concentrated in the flexural springs uniformly distributed at the potential yield lines. The spring parameters are determined from comparison of transverse displacements and stresses developed in the slab obtained using FEM and the proposed model with assumed homogeneous material. Numerical models of typical RC slabs with varying geometry, reinforcement, support conditions, and loading conditions, show reasonable agreement with available experimental data. The model was also shown to be useful in investigating dynamic behavior of slabs.

Keywords: RC slab, nonlinear behavior, yield line theory, rigid body-spring discrete element method

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Authors: Janpen Srijan, Nahathai Tanmang, Thanit Purathanang, Anun Dowchern, Saksit Summart, Seangduan Kampimpa

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This paper presents the resistance reader program based on image processing by using MATLAB. The proposed program is divided into six parts; the first part is the web camera; the second part is a watt selection before shooting the resistor; the third part is a part of finding the position of the color on the mid-point of resistor; the fourth part is a part of identifying color code of the resistor; the fifth part is a part of taking the number of values for each color for resistance calculation and the last part is a part of displaying result of resistance value. The experimental result of the resistance reader program based on image processing was able to display the resistance value of resistor. The accuracy of proposed program is 85 percent for 1 watt resistor. It has 15 percent of reading error because a problem with the color code of some resistor was too bright.

Keywords: resistance reader program, image processing, resistor, MATLAB

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Danielle Klassen, Reiko Yeap, Margo Schmitt-Boshnick, Scott Oddie

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The development of the 7-week Alberta Happiness Basics program was initiated in 2010 in response to the need for community mental health programming. This provincial wide program aims to increase overall happiness and reduce negative thoughts and feelings through a positive psychology intervention. While the 7-week program has proven effective, a shortened 4-week program has additionally been developed to address client needs. In this study, participants were interviewed to determine if the 4- and 7-week programs had similar success of producing lasting behavior change at 3, 6, and 9 months post-program. A health quality of life (HQOL) measure was also used to compare the two programs and examine patient outcomes. Quantitative and qualitative analysis showed significant improvements in HQOL and sustainable behavior change for both programs. Findings indicate that the shorter, patient-centered program was effective in increasing happiness and reducing negative thoughts and feelings.

Keywords: primary care, mental health, depression, short duration

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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