Search results for: program dependence graph

Authors: Sh. Javadi, A. Alijani, A.H. Mazinan

Abstract:

This paper reviews the optimization available transmission capability (ATC) of power systems using a device of FACTS named SSSC equipped with energy storage devices. So that, emplacement and improvement of parameters of SSSC will be illustrated. Thus, voltage magnitude constraints of network buses, line transient stability constraints and voltage breakdown constraints are considered. To help the calculations, a comprehensive program in DELPHI is provided, which is able to simulate and trace the parameters of SSSC has been installed on a specific line. Furthermore, the provided program is able to compute ATC, TTC and maximum value of their enhancement after using SSSC.

Keywords: available transmission capability (ATC), total transmission capability (TTC), voltage constraints, stability constraints, FACTS, SSSC.

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Authors: M. Alqhatani, S. Bajwa, S. Setunge

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Metropolitan areas have suffered from traffic problems, which have steadily increased in many monocentric cities. Urban expansion, population growth, and road network development have resulted in a structural shift toward urban sprawl, increasing commuters’ dependence on private modes of transport. This paper aims to model the influence of socioeconomic and land-use factors on mode choice using a multinomial and nested logit model. Land-use patterns—such as residential, commercial, retail, educational and employment related—affect the choice of mode and destination in the short and medium term. Socioeconomic factors—such as age, gender, income, household size, and house type—also affect choice, while residential location is affected in the long term. Riyadh in Saudi Arabia and Melbourne in Australia were chosen as case studies. Riyadh is a car-dependent city with limited public transport, whereas Melbourne has good public transport but an increase in car dependence. Aggregate level land-use data and disaggregate level individual, household, and journey-to-work data are used to determine the effects of land use and socioeconomic factors on mode choice. The model results determined that urban sprawl is the main factor that affects mode choice, income, and house type.

Keywords: Socioeconomic, land use, mode choice, multinomial logit and nested logit.

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Authors: Nutthapat Kaewrattanapat, Wannarat Bunchongkien

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The purposes of this research are to study and develop the algorithm of Thai spoonerism words by semi-automatic computer programs, that is to say, in part of data input, syllables are already separated and in part of spoonerism, the developed algorithm is utilized, which can establish rules and mechanisms in Thai spoonerism words for bi-syllables by utilizing analysis in elements of the syllables, namely cluster consonant, vowel, intonation mark and final consonant. From the study, it is found that bi-syllable Thai spoonerism has 1 case of spoonerism mechanism, namely transposition in value of vowel, intonation mark and consonant of both 2 syllables but keeping consonant value and cluster word (if any). From the study, the rules and mechanisms in Thai spoonerism word were applied to develop as Thai spoonerism word software, utilizing PHP program. the software was brought to conduct a performance test on software execution; it is found that the program performs bi-syllable Thai spoonerism correctly or 99% of all words used in the test and found faults on the program at 1% as the words obtained from spoonerism may not be spelling in conformity with Thai grammar and the answer in Thai spoonerism could be more than 1 answer.

Keywords: Algorithm, Spoonerism, Computational Linguistics.

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Authors: Ali Eryılmaz

Abstract:

Children and adolescents developing in the worlds of today are facing a getting array of new and old challenges. School counselling is improving rapidly in contemporary education systems around the world. It can be said that counselling system in Turkey was newly borning. In this study, “Family of the Blood" activity is improved with respect to compherensive guidance school program. The sample included 22 adolescents who were high school students. The activity was carried out in 4 sessions, each of which lasted 45 minutes. In the first session, students- personal-social needs were determined. In the second session, in order to warm up, the students were asked three questions consisting of the constructional aspect. In the third session, the counselor and the teacher shared the results of students- responses obtained in the previous session. In the fourth session, the tables formed by students were presented in the classroom. In order to evaluate the activity, three questions were asked of the teacher and counselor. According to the results, the lesson aims of curriculum and counselling aims of curriculum were attained. In the light of literature, the results were discussed and some suggestions were made. It is taken into consideration that the activitiy was beneficial in many respects, similar studies should be carried out in the near future.

Keywords: Comprehensive guidance program, education, family

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Authors: Decha Samana, Vites Longani

Abstract:

For positive integer s and t, the Ramsey number R(s, t) is the least positive integer n such that for every graph G of order n, either G contains Ks as a subgraph or G contains Kt as a subgraph. We construct the circulant graphs and use them to obtain lower bounds of some small Ramsey numbers.

Keywords: Lower bound, Ramsey numbers, Graphs, Distance line.

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Authors: Hyeon Seok Kim, Inhoi Lee, Seong Baeg Kim, Kyunghee Ko, Kyung Eon Lee, Dong Sik Kang

Abstract:

In the age of globalization, higher education  institutions attempt to equip students with global competence. In  response, most universities have been developing and running various  international programs. However, teacher education has been a  neglected area in this trend. Therefore, in this study, we suggest a  program that offers a dual bachelor’s degree from both universities  located on different countries, focusing on teacher education  institutions with different policies and regulations of teacher education  programs that may become obstacles to designing a dual degree  program. We discuss a possible way to get a dual degree including a  teaching certificate at a specialized college, college of secondary  education. To be specific, this research presents a way to attain two  diplomas from Jeju National University (JNU) in Korea and Boise  State University (BSU) in the U.S. It attempts to build an effective  plan for students to declare simultaneous degrees at both universities.  From the study, we find that it takes about 5 years to fulfill  requirements for the dual degree at the undergraduate level.

 

Keywords: Dual degree, curriculum, teaching certificate, college of secondary education, international program.

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Authors: Asmaa M. El-Bandrawy, Afaf M. Botla, Ghada E. El-Refaye, Hassan O. Ghareeb

Abstract:

Background: Urinary incontinence is a common problem among adults. Its incidence increases with age and it is more frequent in women. Pelvic floor muscle training (PFMT) is the first-line therapy in the treatment of pelvic floor dysfunction (PFD) either alone or combined with biofeedback-assisted PFMT. The aim of the work: The purpose of this study is to evaluate the efficacy of biofeedback-assisted PFMT in postoperative stress urinary incontinence. Settings and Design: A single blind controlled trial design was. Methods and Material: This study was carried out in 30 volunteer patients diagnosed as severe degree of stress urinary incontinence and they were admitted to surgical treatment. They were divided randomly into two equal groups: (Group A) consisted of 15 patients who had been treated with post-operative biofeedback-assisted PFMT and home exercise program (Group B) consisted of 15 patients who had been treated with home exercise program only. Assessment of all patients in both groups (A) and (B) was carried out before and after the treatment program by measuring intra-vaginal pressure in addition to the visual analog scale. Results: At the end of the treatment program, there was a highly statistically significant difference between group (A) and group (B) in the intra-vaginal pressure and the visual analog scale favoring the group (A). Conclusion: biofeedback-assisted PFMT is an effective method for the symptomatic relief of post-operative female stress urinary incontinence.

Keywords: Stress urinary incontinence, pelvic floor muscles, pelvic floor exercises, biofeedback.

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Authors: D. Allison, A. Didenko, G. Miller

Abstract:

The link between coordinate transformations in the plane and their effects on the graph of a function can be difficult for students studying college level mathematics to comprehend. To solidify this conceptual link in the mind of a student Microsoft Excel can serve as a convenient graphing tool and pedagogical aid. The authors of this paper describe how various transformations and their related functional symmetry properties can be graphically displayed with an Excel spreadsheet.

Keywords: Mathematics education, Microsoft Excel spreadsheet, technology.

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Authors: Ali M. Alakeel

Abstract:

Assertion-Based software testing has been shown to be a promising tool for generating test cases that reveal program faults. Because the number of assertions may be very large for industry-size programs, one of the main concerns to the applicability of assertion-based testing is the amount of search time required to explore a large number of assertions. This paper presents a new approach for assertions exploration during the process of Assertion- Based software testing. Our initial exterminations with the proposed approach show that the performance of Assertion-Based testing may be improved, therefore, making this approach more efficient when applied on programs with large number of assertions.

Keywords: Software testing, assertion-based testing, program assertions.

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Authors: M. A. Foda, K. A. Alsaif, M. M. ElMadany, A.S. Aguib

Abstract:

In this paper, the noise maps for the area encircled by the Second Ring Road in Riyadh city are developed based on real measured data. Sound level meters, GPS receivers to determine measurement position, a database program to manage the measured data, and a program to develop the maps are used. A baseline noise level has been established at each short-term site so subsequent monitoring may be conducted to describe changes in Riyadh-s noise environment. Short-term sites are used to show typical daytime and nighttime noise levels at specific locations by short duration grab sampling.

Keywords: Noise mapping, Noise measurements, GPS, noise level.

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Authors: S. Babitha, J. Baskar Babujee

Abstract:

A prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, ..., |V |} such that each edge uv is assigned the label 1 if gcd(f(u), f(v)) = 1 and 0 if gcd(f(u), f(v)) > 1, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In this paper we exhibit some characterization results and new constructions on prime cordial graphs.

Keywords: Prime cordial, tree, Euler, bijective, function.

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Authors: N. Shen, Z. X. Chen, K.D. Buddharaju, H. M. Chua, X. Li, N. Singh, G.Q Lo, D.-L. Kwong

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In this paper, we present a vertical wire NMOS device fabricated using CMOS compatible processes. The impact of temperature on various device parameters is investigated in view of usual increase in surrounding temperature with device density.

Keywords: Gate-all-around, temperature dependence, silicon nanowire

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Authors: Kanate Pantusavase, Jaramporn Hassamontr

Abstract:

This research aims to develop an algorithm to generate a schedule of multiple cranes that will maximize load throughputs in anodizing operation. The algorithm proposed utilizes an enumerative strategy to search for constant time between successive loads and crane covering range over baths. The computer program developed is able to generate a near-optimal crane schedule within reasonable times, i.e. within 10 minutes. Its results are compared with existing solutions from an aluminum extrusion industry. The program can be used to generate crane schedules for mixed products, thus allowing mixed-model line balancing to improve overall cycle times.

Keywords: Crane scheduling, anodizing operations, cycle time minimization.

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Authors: Seongmin Yim

Abstract:

The Korean government has applied preliminary feasibility study for new and huge R&D programs since 2008.The study is carried out from the viewpoints of technology, policy, and Economics. Then integrate the separate analysis and finally arrive at a definite result; whether a program is feasible or unfeasible, This paper describes the concept and method of the feasibility analysis focused on technological viability assessment for technical analysis. It consists of technology trend assessment and technology level assessment. Through the analysis, we can determine the chance of schedule delay or cost overrun occurring in the proposed plan.

Keywords: Preliminary Feasibility Study, Technological viability, Technology Trend Assessment, Technology Level Assessment

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Authors: Hans H. Diel

Abstract:

A computer model of Quantum Theory (QT) has been developed by the author. Major goal of the computer model was support and demonstration of an as large as possible scope of QT. This includes simulations for the major QT (Gedanken-) experiments such as, for example, the famous double-slit experiment. Besides the anticipated difficulties with (1) transforming exacting mathematics into a computer program, two further types of problems showed up, namely (2) areas where QT provides a complete mathematical formalism, but when it comes to concrete applications the equations are not solvable at all, or only with extremely high effort; (3) QT rules which are formulated in natural language and which do not seem to be translatable to precise mathematical expressions, nor to a computer program. The paper lists problems in all three categories and describes also the possible solutions or circumventions developed for the computer model.

Keywords: Computability, Foundation of Quantum Mechanics, Measurement Process, Modeling.

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Authors: Kang-Le Guan, Seung-Jae Lee, Myeon-Song Choi

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The protection issues in distribution systems with open and closed-loop are studied, and a generalized protection setting scheme based on the traditional over current protection theories is proposed to meet the new requirements. The setting method is expected to be easier realized using computer program, so that the on-line adaptive setting for coordination in distribution system can be implemented. An automatic setting program is created and several cases are taken into practice. The setting results are verified by the coordination curves of the protective devices which are plotted using MATLAB.

Keywords: protection setting, on-line system analysis, over current protection, closed-loop distribution system

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Authors: Tien-Tung Chung, Chin-Te Lin, Chung-Yun Lee, Kuang-Chao Fan, Shou-Heng Chen

Abstract:

This paper studies the optimum design for reducing optical loss of an 8x8 mechanical type optical switch due to the temperature change. The 8x8 optical switch is composed of a base, 8 input fibers, 8 output fibers, 3 fixed mirrors and 17 movable mirrors. First, an innovative switch configuration is proposed with thermal-compensated design. Most mechanical type optical switches have a disadvantage that their precision and accuracy are influenced by the ambient temperature. Therefore, the thermal-compensated design is to deal with this situation by using materials with different thermal expansion coefficients (α). Second, a parametric modeling program is developed to generate solid models for finite element analysis, and the thermal and structural behaviors of the switch are analyzed. Finally, an integrated optimum design program, combining Autodesk Inventor Professional software, finite element analysis software, and genetic algorithms, is developed for improving the thermal behaviors that the optical loss of the switch is reduced. By changing design parameters of the switch in the integrated design program, the final optimum design that satisfies the design constraints and specifications can be found.

Keywords: Optical switch, finite element analysis, thermal-compensated design, optimum design.

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Authors: M. Nekri, A. Khelladi

Abstract:

The world wide web network is a network with a complex topology, the main properties of which are the distribution of degrees in power law, A low clustering coefficient and a weak average distance. Modeling the web as a graph allows locating the information in little time and consequently offering a help in the construction of the research engine. Here, we present a model based on the already existing probabilistic graphs with all the aforesaid characteristics. This work will consist in studying the web in order to know its structuring thus it will enable us to modelize it more easily and propose a possible algorithm for its exploration.

Keywords: Clustering coefficient, preferential attachment, small world, Web community.

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Authors: Yanshuang Zhang, Byungho Jeong

Abstract:

Data Envelopment Analysis (DEA) is a methodology that computes efficiency values for decision making units (DMU) in a given period by comparing the outputs with the inputs. In many cases, there are some time lag between the consumption of inputs and the production of outputs. For a long-term research project, it is hard to avoid the production lead time phenomenon. This time lag effect should be considered in evaluating the performance of organizations. This paper suggests a model to calculate efficiency values for the performance evaluation problem with time lag. In the experimental part, the proposed methods are compared with the CCR and an existing time lag model using the data set of the 21st century frontier R&D program which is a long-term national R&D program of Korea.

Keywords: DEA, Efficiency, Time Lag

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Authors: Chechen Liao, Chin Yi Yang

Abstract:

Although several factors that affect learning to program have been identified over the years, there continues to be no indication of any consensus in understanding why some students learn to program easily and quickly while others have difficulty. Seldom have researchers considered the problem of how to help the students enhance the programming learning outcome. The research had been conducted at a high school in Taiwan. Students participating in the study consist of 330 tenth grade students enrolled in the Basic Computer Concepts course with the same instructor. Two types of training methods-instruction-oriented and exploration-oriented were conducted. The result of this research shows that the instruction-oriented training method has better learning performance than exploration-oriented training method.

Keywords: Learning performance, programming learning, TDD, training method.

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Authors: Ladda Leungratanamart, Seree Chadcham

Abstract:

Fluid intelligence declines along with age, but it can be developed. For this reason, increasing fluid intelligence in young adults can be possible. This study examined the effects of a two-month treadmill exercise program on fluid intelligence. The researcher designed a treadmill exercise program to promote cardiorespiratory fitness. Thirty-eight healthy voluntary students from the Boromarajonani College of Nursing, Chon Buri were assigned randomly to an exercise group (n=18) and a control group (n=20). The experiment consisted of three sessions: The baseline session consisted of measuring the VO₂max, electroencephalogram and behavioral response during performed the Raven Progressive Matrices (RPM) test, a measure of fluid intelligence. For the exercise session, an experimental group exercises using treadmill training at 60 % to 80 % maximum heart rate for 30 mins, three times per week, whereas the control group did not exercise. For the following two sessions, each participant was measured the same as baseline testing. The data were analyzed using the t-test to examine whether there is significant difference between the means of the two groups. The results showed that the mean VO₂ max in the experimental group were significantly more than the control group (p<.05), suggesting a two-month treadmill exercise program can improve fluid intelligence. When comparing the behavioral data, it was found that experimental group performed RPM test more accurately and faster than the control group. Neuroelectric data indicated a significant increase in percentages of alpha band ERD (%ERD) at P3 and Pz compared to the pre-exercise condition and the control group. These data suggest that a two-month treadmill exercise program can contribute to the development of cardiorespiratory fitness which influences an increase fluid intelligence. Exercise involved in cortical activation in difference brain areas.

Keywords: Treadmill exercise, fluid intelligence, raven progressive matrices test, %ERD of upper Alpha band.

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Authors: David Julian Bernal Melgarejo

Abstract:

Inland Waterway Transportation (IWT) is playing an important role in national transport systems, water transportation is considered to be safe, energy efficient and environmentally friendly mode of transport, all benefits of IWT cause national awareness increase, for instance the Colombian government is planning to restore the navigability of the most important river of the country, the Magdalena’s River navigability, embrace waterway transportation in Colombia could strength competitiveness while reduce most of the transport externalities. However, the current situation of the Magdalena is deplorable, the most important river of Colombia has been abandoned for decades and the solution is beyond of a single administrative entity. This paper analyzes the outcomes of the Navigation And Inland Waterway Action and Development in Europe program (NAIADES) as a prospective to develop a similar program in Colombia with similar objectives and guidelines, considering sustainability, guarantying the long-term future results and adaptability of the program. Identifying stakeholders and policy experts, a set of individual interviews were carried out; findings support the idea of lack of integration within governmental institutions and lack of importance in marketing promotion as possible drawbacks on the implementation of IWT projects.

Keywords: Inland waterway transportation, Logistics, Sustainability, Multimodal transport systems, Water transportation.

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Authors: Mary L. G. S. Senna, Afonso R. Aquino, Veruska C. Dutra, Carlos H. C. Tolentino

Abstract:

The quality of life index, despite elucidating many discussions, the conceptual subjectivity of the term does not show precision, and consequently, many researchers seek to develop methods aiming to measure this concept, bringing it to a more concrete approach. In this study, the quality of life index method was used to analyze the population of Mateiros, Tocantins, Brazil for quality of life. After data collection, it was compared the quality of life index between the population and the group of beneficiaries of the Brazilian government assistance program Bolsa Família (Family Allowance). Some of the people interviewed receive financial aid from the federal government program Bolsa Família (22%). Comparisons were made among the final score of the quality of life index of the Mateiros population and the following factors: Gender, age, education, those working or not with tourism and those who receive or do not receive the Bolsa Família. It was observed that only the factor, Bolsa Família (p-score 0.0138), shows an association with quality of life improvement, noticing that those who have financial aid had a higher quality of life improvement than the rest of the population. It was concluded that, government assistance has shown a decisive element on the enhancement of Mateiros population quality of life, indicating that similar actions should be maintained.

Keywords: Quality of life index, government aid to families, sustainable tourism, Bolsa Familia.

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Authors: Gu-Fang Mou, Ting-Zhu Huang

Abstract:

An n×n matrix is called an N1 0 -matrix if all principal minors are non-positive and each entry is non-positive. In this paper, we study the partial non-combinatorially symmetric N1 0 -matrix completion problems if the graph of its specified entries is a transitive tournament or a double cycle. In general, these digraphs do not have N1 0 -completion. Therefore, we have given sufficient conditions that guarantee the existence of the N1 0 -completion for these digraphs.

Keywords: Matrix completion, matrix completion, N10 -matrix, non-combinatorially symmetric, cycle, digraph.

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Authors: M. Kargar, F. Gharbalchi

Abstract:

In this paper a new method is suggested for distributed data-mining by the probability patterns. These patterns use decision trees and decision graphs. The patterns are cared to be valid, novel, useful, and understandable. Considering a set of functions, the system reaches to a good pattern or better objectives. By using the suggested method we will be able to extract the useful information from massive and multi-relational data bases.

Keywords: Data-mining, Decision tree, Decision graph, Pattern, Relationship.

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Authors: Doaa M. Atia, Faten H. Fahmy, Ninet M. Ahmed, Hassen T. Dorrah

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In this paper, the optimum design for renewable energy system powered an aquaculture pond was determined. Hybrid Optimization Model for Electric Renewable (HOMER) software program, which is developed by U.S National Renewable Energy Laboratory (NREL), is used for analyzing the feasibility of the stand alone and hybrid system in this study. HOMER program determines whether renewable energy resources satisfy hourly electric demand or not. The program calculates energy balance for every 8760 hours in a year to simulate operation of the system. This optimization compares the demand for the electrical energy for each hour of the year with the energy supplied by the system for that hour and calculates the relevant energy flow for each component in the model. The essential principle is to minimize the total system cost while HOMER ensures control of the system. Moreover the feasibility analysis of the energy system is also studied. Wind speed, solar irradiance, interest rate and capacity shortage are the parameters which are taken into consideration. The simulation results indicate that the hybrid system is the best choice in this study, yielding lower net present cost. Thus, it provides higher system performance than PV or wind stand alone systems.

Keywords: Wind stand-alone system, Photovoltaic stand-alone system, Hybrid system, Optimum system sizing, feasibility, Cost analysis.

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Authors: Asha Hasnimy Mohd Hashim, Lee Ai Choo

Abstract:

We investigated the effects of modified preprogrammed training mode Chase Trainer from Balance Trainer (BT3, HurLab, Tampere, Finland) on athlete who experienced unilateral Patellofemoral Pain Syndrome (PFPS). Twenty-seven athletes with mean age= 14.23 ±1.31 years, height = 164.89 ± 7.85 cm, weight = 56.94 ± 9.28 kg were randomly assigned to two groups: experiment (EG; n = 14) and injured (IG; n = 13). EG performed a series of Chase Trainer program which required them to shift their body weight at different directions, speeds and angle of leaning twice a week for duration of 8 weeks. The static postural control and perceived pain level measures were taken at baseline, after 6 weeks and 8 weeks of training. There was no significant difference in any of tested variables between EG and IG before and after 6-week the intervention period. However, after 8-week of training, the postural control (eyes open) and perceived pain level of EG improved compared to IG (p<0.05). The postural control with eyes closed of EG improved (p<0.05) but the values were not significantly different compared to IG after training. The results suggest that using Chase Trainer exercise program it is possible to improve individual postural control and decreased perceived pain level in athlete with unilateral Patellofemoral Pain Syndrome (PFPS).

Keywords: Patellofemoral Pain Syndrome, perceived pain level, postural control.

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Authors: Noura Boudiaf, Allaoua Chaoui

Abstract:

One major difficulty that faces developers of concurrent and distributed software is analysis for concurrency based faults like deadlocks. Petri nets are used extensively in the verification of correctness of concurrent programs. ECATNets [2] are a category of algebraic Petri nets based on a sound combination of algebraic abstract types and high-level Petri nets. ECATNets have 'sound' and 'complete' semantics because of their integration in rewriting logic [12] and its programming language Maude [13]. Rewriting logic is considered as one of very powerful logics in terms of description, verification and programming of concurrent systems. We proposed in [4] a method for translating Ada-95 tasking programs to ECATNets formalism (Ada-ECATNet). In this paper, we show that ECATNets formalism provides a more compact translation for Ada programs compared to the other approaches based on simple Petri nets or Colored Petri nets (CPNs). Such translation doesn-t reduce only the size of program, but reduces also the number of program states. We show also, how this compact Ada-ECATNet may be reduced again by applying reduction rules on it. This double reduction of Ada-ECATNet permits a considerable minimization of the memory space and run time of corresponding Maude program.

Keywords: Ada tasking, ECATNets, Algebraic Petri Nets, Compact Representation, Analysis, Rewriting Logic, Maude.

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Authors: Nikolina Ribarić

Abstract:

E-learning is most commonly defined as a set of applications and processes, such as Web-based learning, computer-based learning, virtual classrooms and digital collaboration, that enable access to instructional content through a variety of electronic media. The main goal of an e-learning system is learning, and the way to evaluate the impact of an e-learning system is by examining whether students learn effectively with the help of that system. Testmoz is a program for online preparation of knowledge evaluation assignments. The program provides teachers with computer support during the design of assignments and evaluating them. Students can review and solve assignments and also check the correctness of their solutions. Research into the increase of motivation by the practice of providing teaching content by applying online tests prepared in the Testmoz program, was carried out with students of the 8th grade of Ljubo Babić Primary School in Jastrebarsko. The students took the tests in their free time, from home, for an unlimited number of times. SPSS was used to process the data obtained by the research instruments. The results of the research showed that students preferred to practice teaching content, and achieved better educational results in chemistry, when they had access to online tests for repetition and practicing in relation to subject content which was checked after repetition and practicing in "the classical way" – i.e., solving assignments in a workbook or writing assignments in worksheets.

Keywords: Chemistry class, e-learning, online test, Testmoz.

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Authors: Kejun Zhuang, Zhaohui Wen

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The main purpose of this paper is to investigate a discrete time three–species food chain system with ratio dependence. By employing coincidence degree theory and analysis techniques, sufficient conditions for existence of periodic solutions are established.

Keywords: Food chain, ratio–dependent, coincidence degree, periodic solutions.

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