Search results for: Moser’s worm problem

Authors: S. Som-Am, B. Grechuk

Abstract:

Moser’s worm problem is the unsolved problem in geometry which asks for the minimal area of a convex region on the plane which can cover all curves of unit length, assuming that curves may be rotated and translated to fit inside the region. We study a version of this problem asking for a minimal convex cover for closed unit curves. By combining geometric methods with numerical box’s search algorithm, we show that any such cover should have an area at least 0.0975. This improves the best previous lower bound of 0.096694. In fact, we show that the minimal area of convex hull of circle, equilateral triangle, and rectangle of perimeter 1 is between 0.0975 and 0.09763.

Keywords: Moser’s worm problem, closed arcs, convex cover, minimal-area cover

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Authors: A. H. Elkholy, A. H. Falah

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A new approach has been developed to estimate the load share and stress distribution of worm gear sets. The approach is based upon considering the instantaneous tooth meshing stiffness where the worm gear drive was modelled as a series of spur gear slices, and each slice was analyzed separately using the well established formulae of spur gears. By combining the results obtained for all slices, the entire envolute worm gear set loading and stressing was obtained. The geometric modelling method presented, allows tooth elastic deformation and tooth root stresses of worm gear drives under different load conditions to be investigated. On the basis of the method introduced in this study, the instantaneous meshing stiffness and load share were obtained. In comparison with existing methods, this approach has both good analysis accuracy and less computing time.

Keywords: gear, load/stress distribution, worm, wheel, tooth stiffness, contact line

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Authors: Ahmed Elkholy

Abstract:

Most power transmission cases use gearing in general, and worm gearing, in particular for energy utilization. Therefore, designing gears for minimum weight and maximum power transmission is the main target of this study. In this regard, a new approach has been developed to estimate the load share and stress distribution of worm gear sets. The approach is based upon considering the instantaneous tooth meshing stiffness where the worm gear drive was modelled as a series of spur gear slices, and each slice was analyzed separately using a well-established criteria. By combining the results obtained for all slices, the entire worm gear set loading and stressing was determined. The geometric modelling method presented, allows tooth elastic deformation and tooth root stresses of worm gear drives under different load conditions to be investigated. On the basis of the method introduced in this study, the instantaneous meshing stiffness and load share were obtained. In comparison with existing methods, this approach has both good analytical accuracy and less computing time.

Keywords: gear, load/stress distribution, worm, wheel, tooth stiffness, contact line

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Authors: Seyed Hamid Mirmohammad Sadeghi, Raffaella Sesana, Daniela Maffiodo

Abstract:

This study presents a procedure for friction calculation of column electric power steering (C-EPS) system which affects handling and comfort in driving. The friction losses estimation is obtained from experimental tests and mathematical calculation. Parts in C-EPS mainly involved in friction losses are bearings and worm gear. In the theoretical approach, the gear geometry and Hertz law were employed to measure the normal load and the sliding velocity and contact areas from the worm gears driving conditions. The viscous friction generated in the worm gear was obtained with a theoretical approach and the result was applied to model the friction in the steering system. Finally, by viscous friction coefficient and Coulomb friction coefficient, values of friction in worm gear were calculated. According to the Bearing Company and the characteristics of each bearing, the friction torques due to load and due to speed were calculated. A MATLAB Simulink model for calculating the friction in bearings and worm gear in C-EPS were done and the total friction value was estimated.

Keywords: friction, worm gear, column electric power steering system, simulink, bearing, EPS

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Authors: Alyaa Ahmed Farid, Aida Ismail, Ibrahim Rabia, Azza Fahmy, Azza El Amir

Abstract:

This study was designed for assessment of 3 types of Cysteine protease inhibitors (CPIs) fluromethylketone (FMK), vinyl sulfone (VS) and sodium nitro prussid (SNP), to define which of them is the best? The experiments aimed to define the protective power of each inhibitor alone or combined with PZQ for curing S. mansoni infection in mice. In vitro, treated S. mansoni adult worms recorded a mortality rate after 1 hr of exposure to 500 ppm of FMK, VS and SNP as 75, 70 and 60%, while, treated cercaria recorded 75, 60 and 50%, respectively. FMK+PZQ treatment recorded the maximum reduction in worm burden (97.2% at 5 wk PI). VS treatment alone or combined with PZQ increases IgM, total IgG, IgG2 and IgG4 levels. In EM study of worm tegument, while only detachment of spines was observed in PZQ treated group, the completely implanted spines were reported in the degenerated tegument of adult worms in all groups treated with CPIs. Treatment with VS+PZQ increased Igs levels but, its effect was different on worm reduction. So, it is not enough to eliminate the infection and FMK+PZQ considered the antischistosomicidal drug of choice.

Keywords: praziquantel, fluromethylketone, vinyl sulfone, worm burden, immunoglobulin pattern

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Authors: Surapol Raadnui

Abstract:

This particular work describes an experimental investigation on gear wear in which wear and pitting were intentionally allowed to occur, namely, moisture corrosion pitting, acid-induced corrosion pitting, hard contaminant-related pitting and mechanical induced wear. A back to back spur gear test rig and a grease lubricated worm gear rig were used. The tests samples of wear debris were collected and assessed through the utilization of an optical microscope in order to correlate and compare the debris morphology to pitting and wear degradation of the worn gears. In addition, weight loss from all test gear pairs were assessed with utilization of statistical design of experiment. It can be deduced that wear debris characteristics from both cases exhibited a direct relationship with different pitting and wear modes. Thus, it should be possible to detect and diagnose gear pitting and wear utilization of worn surfaces, generated wear debris and quantitative measurement such as weight loss.

Keywords: predictive maintenance, worm gear, spur gear, wear debris analysis, problem diagnostic

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Authors: Jun-ya Nagase

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There are many pipes such as a water pipe and a gas pipe in a chemical plant and house. It is possible to prevent accidents by these inspections. However, many pipes are very narrow and it is difficult for people to inspect directly. Therefore, development of a robot that can move in narrow pipe is necessary. A wheel movement type robot, a snake-like robot and a multi-leg robot are all described in the relevant literature as pipe inspection robots that are currently studied. Among them, the tracked crawler robot can travel by traversing uneven ground flexibly with a crawler belt attached firmly to the ground surface. Although conventional crawler robots have high efficiency and/or high ground-covering ability, they require a comparatively large space to move. In this study, a cylindrical crawler robot based on worm-rack mechanism, which does not need large space to move and which has high ground-covering ability, is proposed. Experiments have demonstrated smooth operation and a forward movement of the robot by application of voltage to the motor. In addition, performance tests show that it can propel itself in confined spaces. This paper reports the structure, drive mechanism, prototype, and experimental evaluation.

Keywords: tracked-crawler, pipe inspection robot, worm-rack mechanism, amoeba locomotion

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Authors: Barenten Suciu

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In this paper, effectiveness of a machine design process is evaluated on the basis of the specific output calculus. Concretely, a screw-worm gear mechanical transmission is designed by using the classical and the 3D-CAD methods. Strength analysis and drawing of the designed parts is substantially aided by employing the SolidWorks software. Quality of the design process is assessed by manufacturing (printing) the parts, and by computing the efficiency, specific load, as well as the specific output (work) of the mechanical transmission. Influence of the stroke, travelling velocity and load on the mechanical output, is emphasized. Optimal design of the mechanical transmission becomes possible by the appropriate usage of the acquired results.

Keywords: mechanical transmission, design, screw, worm-gear, efficiency, specific output, 3D-printing

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Authors: Getahun Lemma

Abstract:

Introduction Guinea Worm Disease (GWD), also known as dracunculiasisis, is one of the oldest diseases in the history of mankind. Dracunculiasis is caused by a parasitic nematode, Dracunculus medinensis. Infection is acquired by drinking contaminated water with copepods containing infective Guinea Worm (GW) larvae). Almost one year after the infection, the worm usually emerges out through the skin on a lower, causing severe pain and disabilities. Although there is no effective drug or vaccine against the disease, the chain of transmission can be effectively prevented with simple and cost effective public health measures. Death due to dracunculiasis is very rare. However, it results in a wide range of physical, social and economic sequels. The disease is usually common in the rural, remote places of Sub-Saharan African countries among the marginalized societies. Currently, GWD is one of the neglected tropical diseases, which is on the verge of eradication. The global Guinea Worm Eradication Program (GWEP) was started in 1980. Since then, the program has achieved a tremendous success in reducing the global burden and number of GW case from 3.5 million to only 28 human cases at the end of 2018. However, it has recently been shown that not only humans can become infected, with a total of 1,105 animal infections have been reported at the end of 2018. Therefore, the objective of this study was to identify the existing challenges in the last mile of the GWEP in order To inform Policy makers and stakeholders on potential measures to finally achieve eradication. Method Systematic literature review on articles published from January 1, 2000 until May 30, 2019. Papers listed in Cochrane Library, Google Scholar, ProQuest PubMed and Web of Science databases were searched and reviewed. Results Twenty-five articles met inclusion criteria of the study and were selected for analysis. Hence, relevant data were extracted, grouped and descriptively analyzed. Results showed the main challenges complicating the last mile of global GWEP: 1. Unusual mode of transmission; 2. Rising animal Guinea Worm infection; 3. Suboptimal surveillance; 4. Insecurity; 5. Inaccessibility; 6. Inadequate safe water points; 7. Migration; 8. Poor case containment measures, 9. Ecological changes; and 10. New geographic foci of the disease. Conclusion This systematic review identified that most of the current challenges in the GWEP have been present since the start of the campaign. However, the recent change in epidemiological patterns and nature of GWD in the last remaining endemic countries illustrates a new twist in the global GWEP. Considering the complex nature of the current challenges, there seems to be a need for a more coordinated and multidisciplinary approach of GWD prevention and control measures in the last mile of the campaign. These new strategies would help to make history by eradicating dracunculiasis as the first ever parasitic disease.

Keywords: dracunculiasis, eradication program, guinea worm, last mile

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Authors: Yafri Hazbi, Zaenal Bachruddin, Nafiatul Umami, Lies Mira Yusiati

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The objective of this study was to identify the benefits of total mixture concentrate based on tofu waste silage (TMC-TWS) as ration containing lactic acid bacteria on performance of lambs. Fifteen weaning lambs (2-3 months old) were randomly divided into two treatment groups, treatment group I (TI) was fed with TMC-TWS as ration and treatment group II (TII) was fed with TMC-TWS fresh (without silage fermentation). The performance of lambs was evaluated on day 0, 15, and 30 to have data of body weight per day. Meanwhile, blood sampling and feces were made on the 30th day to get an analysis on the blood profile (erythrocytes (mill/ml), hemoglobin (g/dL), packed cell volume (%), and leukocytes (mill/ml)) and the number of worm eggs in feces. The results of this study showed no significant difference between the effect of different feed on the blood profile (erythrocytes (mill/ml), hemoglobin (g/dL), packed cell volume (%), as well as the number of worm eggs in the feces. However the results showed significant differences if it is low (P<0.05) due to the treatment group based on sex on body weight gain per day, feed conversion rate and the number of erythrocytes.

Keywords: lambs, total mixture concentrate, silage, acid lactid bacteria, blood profile, eggs worm in feces

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Authors: Carlos Tadeu Santana Tatum, Suzana Leitão Russo

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This paper aims to show comparative studies of different types of innovation applied to lighting, along with a theoretical review by means of a bibliographic method. We demonstrate that it is possible to understand the impacts of industries with a conventional innovation that uses natural resources to manufacture lights, and the opposite, when a frugal innovation solves the problems of a society at the bottom of the pyramid, helping people without access to electricity to get home lighting. The frugal innovation is simply the use of recycled PET bottles. We achieved the objective of our study by gathering data from environment, electrical engineering, international rules, and innovation, which gave us the best results. With all these variables, we can characterize this work as an interdisciplinary study.

Keywords: frugal, innovation, PET bottle, light

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Authors: S. Aditya, K. T. Nideesh, N. Guruprasad

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Being a subclass of linear programing problem, the Transportation Problem is a classic Operations Research problem where the objective is to determine the schedule for transporting goods from source to destination in a way that minimizes the shipping cost while satisfying supply and demand constraints. In this paper, we are representing the transportation problem for various warehouses along with various dealers situated in Bangalore city to reduce the transportation cost incurred by them as of now. The problem is solved by obtaining the Initial Basic feasible Solution through various methods and further proceeding to obtain optimal cost.

Keywords: NW method, optimum utilization, transportation problem, Vogel’s approximation method

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Authors: Song Ni, Junxiang Xu

Abstract:

This paper concerns quasi-periodic perturbations with parameters of 2-dimensional degenerate systems. If the equilibrium point of the unperturbed system is elliptic-type degenerate. Assume that the perturbation is real analytic quasi-periodic with diophantine frequency. Without imposing any assumption on the perturbation, we can use a path of equilibrium points to tackle with the Melnikov non-resonance condition, then by the Leray-Schauder Continuation Theorem and the Kolmogorov-Arnold-Moser technique, it is proved that the equation has a small response solution for many sufficiently small parameters.

Keywords: quasi-periodic systems, KAM-iteration, degenerate equilibrium point, response solution

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Authors: C. U. Om Kumar, S. Kishore, A. Geetha

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An Operating system (OS) is software that manages computer hardware and software resources by providing services to computer programs. One of the important user expectations of the operating system is to provide the practice of defending information from unauthorized access, disclosure, modification, inspection, recording or destruction. Operating system is always vulnerable to the attacks of malwares such as computer virus, worm, Trojan horse, backdoors, ransomware, spyware, adware, scareware and more. And so the anti-virus software were created for ensuring security against the prominent computer viruses by applying a dictionary based approach. The anti-virus programs are not always guaranteed to provide security against the new viruses proliferating every day. To clarify this issue and to secure the computer system, our proposed expert system concentrates on authorizing the processes as wanted and unwanted by the administrator for execution. The Expert system maintains a database which consists of hash code of the processes which are to be allowed. These hash codes are generated using MD5 message-digest algorithm which is a widely used cryptographic hash function. The administrator approves the wanted processes that are to be executed in the client in a Local Area Network by implementing Client-Server architecture and only the processes that match with the processes in the database table will be executed by which many malicious processes are restricted from infecting the operating system. The add-on advantage of this proposed Expert system is that it limits CPU usage and minimizes resource utilization. Thus data and information security is ensured by our system along with increased performance of the operating system.

Keywords: virus, worm, Trojan horse, back doors, Ransomware, Spyware, Adware, Scareware, sticky software, process table, MD5, CPU usage and resource utilization

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Authors: Keng Keh Lim, Zaleha Ismail, Yudariah Mohammad Yusof

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This paper aims to find out how students using convergent and divergent thinking in creative problem solving to solve mathematical problems creatively. Eight engineering undergraduates in a local university took part in this study. They were divided into two groups. They solved the mathematical problems with the use of creative problem solving skills. Their solutions were collected and analyzed to reveal all the processes of problem solving, namely: problem definition, ideas generation, ideas evaluation, ideas judgment, and solution implementation. The result showed that the students were able to solve the mathematical problem with the use of creative problem solving skills.

Keywords: convergent thinking, divergent thinking, creative problem solving, creativity

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Authors: G. Sirbiladze, B. Ghvaberidze, B. Matsaberidze

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A fuzzy vehicle routing problem is considered in the possibilistic environment. A new criterion, maximization of expectation of reliability for movement on closed routes is constructed. The objective of the research is to implement a two-stage scheme for solution of this problem. Based on the algorithm of preferences on the first stage, the sample of so-called “promising” routes will be selected. On the second stage, for the selected promising routes new bi-criteria problem will be solved - minimization of total traveled distance and maximization of reliability of routes. The problem will be stated as a fuzzy-partitioning problem. Two possible solutions of this scheme are considered.

Keywords: vehicle routing problem, fuzzy partitioning problem, multiple-criteria optimization, possibility theory

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Authors: Terence Soule, Tami Al Ghamdi

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To study how the partial knowledge transfer may affect the Genetic Algorithm (GA) performance, we model the Transfer Learning (TL) process using GA as the model solver. The objective of the TL is to transfer the knowledge from one problem to another related problem. This process imitates how humans think in their daily life. In this paper, we proposed to study a case where the knowledge transferred from the S problem has less information than what the T problem needs. We sampled the transferred population using different strategies of TL. The results showed transfer part of the knowledge is helpful and speeds the GA process of finding a solution to the problem.

Keywords: transfer learning, partial transfer, evolutionary computation, genetic algorithm

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Authors: Huseyin A. Yavasoglu, Yusuf Ziya Tengiz, Ali Göksenli

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In this study, an automatic feeding machine for different type and class of bovine animals is designed. Daily nutrition of a bovine consists of grass, corn, straw, silage, oat, wheat and different vitamins and minerals. The amount and mixture amount of each of the nutrition depends on different parameters of the bovine. These parameters are; age, sex, weight and maternity of the bovine, also outside temperature. The problem in a farm is to constitute the correct mixture and amount of nutrition for each animal. Faulty nutrition will cause an insufficient feeding of the animal concluding in an unhealthy bovine. To solve this problem, a new automatic feeding machine is designed. Travelling of the machine is performed by four tires, which is pulled by a tractor. The carrier consists of eight bins, which each of them carries a nutrition type. Capacity of each unit is 250 kg. At the bottom of each chamber is a sensor measuring the weight of the food inside. A funnel is at the bottom of each chamber by which open/close function is controlled by a valve. Each animal will carry a RFID tag including ID on its ear. A receiver on the feeding machine will read this ID and by given previous information by the operator (veterinarian), the system will detect the amount of each nutrition unit which will be given to the selected animal for feeding. In the system, each bin will open its exit gate by the help of the valve under the control of PLC (Programmable Logic Controller). The amount of each nutrition type will be controlled by measuring the open/close time. The exit canals of the bins are collected in a reservoir. To achieve a homogenous nitration, the collected feed will be mixed by a worm gear. Further the mixture will be transported by a help of a funnel to the feeding unit of the animal. The feeding process can be performed in 100 seconds. After feeding of the animal, the tractor pulls the travelling machine to the next animal. By the help of this system animals can be feeded by right amount and mixture of nutrition

Keywords: bovine, feeding, nutrition, transportation, automatic

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Authors: Kenza Aida Amara, Bachir Djebbar

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We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.

Keywords: bee colony optimization, bin packing, heuristic algorithm, pretreatment

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Authors: Sukhveer Singh, Sandeep Singh

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A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: uncertain transportation problem, efficient solution, ranking function, fuzzy transportation problem

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Authors: Ravneil Nand

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Cooperative coevolution uses problem decomposition methods to solve a larger problem. The problem decomposition deals with breaking down the larger problem into a number of smaller sub-problems depending on their method. Different problem decomposition methods have their own strengths and limitations depending on the neural network used and application problem. In this paper we are introducing a new problem decomposition method known as Hidden-Neuron Level Decomposition (HNL). The HNL method is competing with established problem decomposition method in time series prediction. The results show that the proposed approach has improved the results in some benchmark data sets when compared to the standalone method and has competitive results when compared to methods from literature.

Keywords: cooperative coevaluation, feed forward network, problem decomposition, neuron, synapse

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Authors: Mrinal Jana, Geetanjali Panda

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In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example.

Keywords: fractional programming, interval valued function, interval inequalities, partial order relation

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Authors: Md. Ahsan Ayub, Kazi A. Kalpoma, Humaira Tasnim Proma, Syed Mehrab Kabir, Rakib Ibna Hamid Chowdhury

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Constraint Satisfaction Problem (CSP) is observed in various applications, i.e., scheduling problems, timetabling problems, assignment problems, etc. Researchers adopt a CSP technique to tackle a certain problem; however, each technique follows different approaches and ways to solve a problem network. In our exhaustive study, it has been possible to visualize the processes of essential CSP algorithms from a very concrete constraint satisfaction example, NQueens Problem, in order to possess a deep understanding about how a particular constraint satisfaction problem will be dealt with by our studied and implemented techniques. Besides, benchmark results - time vs. value of N in N-Queens - have been generated from our implemented approaches, which help understand at what factor each algorithm produces solutions; especially, in N-Queens puzzle. Thus, extended decisions can be made to instantiate a real life problem within CSP’s framework.

Keywords: arc consistency (AC), backjumping algorithm (BJ), backtracking algorithm (BT), constraint satisfaction problem (CSP), forward checking (FC), least constrained values (LCV), maintaining arc consistency (MAC), minimum remaining values (MRV), N-Queens problem

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Authors: Kwok W. Mui, Ling T. Wong, Nai K. K. Fong

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Chronic obstructive pulmonary disease (COPD) is the fifth leading cause of death in Hong Kong. Investigators are eager to explore the environmental risk factors for COPD such as air pollution and occupational exposure. Through a cross-sectional survey, this study investigates the impact of air quality to the quality of life of patients with the COPD in terms of the scores of the (Chinese) chronic respiratory questionnaire (CCRQ) and the measurements of indoor air quality (IAQ) and Moser’s activities of daily living (ADL). Strong relationships between a number of indoor/outdoor environmental parameters were found and CRQ sub-scores for patients of COPD and thus indoor air pollutants must be monitored for future studies related to QOL for patients with COPD.

Keywords: chronic obstructive pulmonary disease (COPD), indoor air pollutants, quality of life, chronic respiratory questionnaire (CRQ)

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Authors: Mohammad Farid

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In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

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Authors: Deyadeen Ali Alshibani

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In the literature, the multi-armed bandit problem as a statistical decision model of an agent trying to optimize his decisions while improving his information at the same time. There are several different algorithms models and their applications on this problem. In this paper, we evaluate the Regret-regression through comparing with Q-learning method. A simulation on determination of optimal treatment regime is presented in detail.

Keywords: optimal, bandit problem, optimization, dynamic programming

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Authors: Sujeet Kumar Singh, Shiv Prasad Yadav

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This paper develops an approach for solving intuitionistic fuzzy linear fractional programming (IFLFP) problem where the cost of the objective function, the resources, and the technological coefficients are triangular intuitionistic fuzzy numbers. Here, the IFLFP problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using fuzzy mathematical programming approach the transformed MOLFP problem is reduced into a single objective linear programming (LP) problem. The proposed procedure is illustrated through a numerical example.

Keywords: triangular intuitionistic fuzzy number, linear programming problem, multi objective linear programming problem, fuzzy mathematical programming, membership function

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem solves the problem of fitting 3 circles into a right triangle such that these 3 circles are tangent to each other, and each circle is also tangent to a pair of the triangle’s sides. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles inside the triangle with special tangency properties among circles and triangle sides; we call it extended general Malfatti’s problem. In the extended general Malfatti’s problem, call it Tri(Tn), where Tn is the triangle number, there are closed-form solutions for Tri(T₁) (inscribed circle) problem and Tri(T₂) (3 Malfatti’s circles) problem. These problems become more complex when n is greater than 2. In solving Tri(Tn) problem, n>2, algorithms have been proposed to solve these problems numerically. With a similar idea, this paper proposed an algorithm to find the radii of circles with the same tangency properties. Instead of the boundary of the triangle being a straight line, we use a convex circular arc as the boundary and try to find Tn circles inside this convex circular triangle with the same tangency properties among circles and boundary Carc. We call these problems the Carc(Tn) problems. The CPU time it takes for Carc(T16) problem, which finds 136 circles inside a convex circular triangle with specified tangency properties, is less than one second.

Keywords: circle packing, computer-aided geometric design, geometric constraint solver, Malfatti’s problem

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Authors: Noppadon Phumeechanya, Panita Wannapiroon

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The purpose of this research is to design the ubiquitous scaffold learning environment using problem-based learning activities that enhance problem-solving skills and context awareness, and to evaluate the suitability of the ubiquitous scaffold learning environment using problem-based learning activities. We divide the research procedures into two phases. The first phase is to design the ubiquitous scaffold learning environment using problem-based learning activities, and the second is to evaluate the ubiquitous scaffold learning environment using problem-based learning activities. The sample group in this study consists of five experts selected using the purposive sampling method. We analyse data by arithmetic mean and standard deviation. The research findings are as follows; the ubiquitous scaffold learning environment using problem-based learning activities consists of three major steps, the first is preparation before learning. This prepares learners to acknowledge details and learn through u-LMS. The second is the learning process, where learning activities happen in the ubiquitous learning environment and learners learn online with scaffold systems for each step of problem solving. The third step is measurement and evaluation. The experts agree that the ubiquitous scaffold learning environment using problem-based learning activities is highly appropriate.

Keywords: ubiquitous learning environment scaffolding, learning activities, problem-based learning, problem-solving skills, context awareness

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Authors: Kamariah Abu Bakar, Jennifer Way

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This study investigated how young children (six years old) constructed and used representations in mathematics classroom; particularly in problem solving. The purpose of this study is to explore the ways children used representations in solving addition problems and to determine whether their representations can play a supportive role in understanding the problem situation and solving them correctly. Data collection includes observations, children’s artifact, photographs and conversation with children during task completion. The results revealed that children were able to construct and use various representations in solving problems. However, they have certain preferences in generating representations to support their problem solving.

Keywords: young children, representations, addition, problem solving

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