Search results for: Discrete ill-posed problem

Authors: Carol B. Collins, M. H. N Tabrizi

Abstract:

The purposes of this paper are to (1) promote excellence in computer science by suggesting a cohesive innovative approach to fill well documented deficiencies in current computer science education, (2) justify (using the authors' and others anecdotal evidence from both the classroom and the real world) why this approach holds great potential to successfully eliminate the deficiencies, (3) invite other professionals to join the authors in proof of concept research. The authors' experiences, though anecdotal, strongly suggest that a new approach involving visual modeling technologies should allow computer science programs to retain a greater percentage of prospective and declared majors as students become more engaged learners, more successful problem-solvers, and better prepared as programmers. In addition, the graduates of such computer science programs will make greater contributions to the profession as skilled problem-solvers. Instead of wearily rememorizing code as they move to the next course, students will have the problem-solving skills to think and work in more sophisticated and creative ways.

Keywords: Algorithms, CASE, UML, Problem-solving.

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Authors: Veronica Diaz Quezada

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In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: Engineering education, errors, limits, mathematics competences, problem solving.

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Authors: Babak H. Tabrizi, Seyed Farid Ghaderi

Abstract:

Concurrent planning of project scheduling and material ordering has been increasingly addressed within last decades as an approach to improve the project execution costs. Therefore, we have taken the problem into consideration in this paper, aiming to maximize schedules quality robustness, in addition to minimize the relevant costs. In this regard, a bi-objective mathematical model is developed to formulate the problem. Moreover, it is possible to utilize the all-unit discount for materials purchasing. The problem is then solved by the E-constraint method, and the Pareto front is obtained for a variety of robustness values. The applicability and efficiency of the proposed model is tested by different numerical instances, finally.

Keywords: E-constraint method, material ordering, project management, project scheduling.

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Authors: Vesna Kirandziska, Nevena Ackovska, Ana Madevska Bogdanova

Abstract:

The problem of emotion recognition is a challenging problem. It is still an open problem from the aspect of both intelligent systems and psychology. In this paper, both voice features and facial features are used for building an emotion recognition system. A Support Vector Machine classifiers are built by using raw data from video recordings. In this paper, the results obtained for the emotion recognition are given, and a discussion about the validity and the expressiveness of different emotions is presented. A comparison between the classifiers build from facial data only, voice data only and from the combination of both data is made here. The need for a better combination of the information from facial expression and voice data is argued.

Keywords: Emotion recognition, facial recognition, signal processing, machine learning.

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Authors: Cha-Hwa Lin, Je-Wei Hu

Abstract:

The conventional GA combined with a local search algorithm, such as the 2-OPT, forms a hybrid genetic algorithm(HGA) for the traveling salesman problem (TSP). However, the geometric properties which are problem specific knowledge can be used to improve the search process of the HGA. Some tour segments (edges) of TSPs are fine while some maybe too long to appear in a short tour. This knowledge could constrain GAs to work out with fine tour segments without considering long tour segments as often. Consequently, a new algorithm is proposed, called intelligent-OPT hybrid genetic algorithm (IOHGA), to improve the GA and the 2-OPT algorithm in order to reduce the search time for the optimal solution. Based on the geometric properties, all the tour segments are assigned 2-level priorities to distinguish between good and bad genes. A simulation study was conducted to evaluate the performance of the IOHGA. The experimental results indicate that in general the IOHGA could obtain near-optimal solutions with less time and better accuracy than the hybrid genetic algorithm with simulated annealing algorithm (HGA(SA)).

Keywords: Traveling salesman problem, hybrid geneticalgorithm, priority selection, 2-OPT.

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Authors: Jin Xu, Albert Y.S. Lam, Victor O.K. Li

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Stock portfolio selection is a classic problem in finance, and it involves deciding how to allocate an institution-s or an individual-s wealth to a number of stocks, with certain investment objectives (return and risk). In this paper, we adopt the classical Markowitz mean-variance model and consider an additional common realistic constraint, namely, the cardinality constraint. Thus, stock portfolio optimization becomes a mixed-integer quadratic programming problem and it is difficult to be solved by exact optimization algorithms. Chemical Reaction Optimization (CRO), which mimics the molecular interactions in a chemical reaction process, is a population-based metaheuristic method. Two different types of CRO, named canonical CRO and Super Molecule-based CRO (S-CRO), are proposed to solve the stock portfolio selection problem. We test both canonical CRO and S-CRO on a benchmark and compare their performance under two criteria: Markowitz efficient frontier (Pareto frontier) and Sharpe ratio. Computational experiments suggest that S-CRO is promising in handling the stock portfolio optimization problem.

Keywords: Stock portfolio selection, Markowitz model, Chemical Reaction Optimization, Sharpe ratio

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Authors: Xiuyong Ding, Lan Shu

Abstract:

This paper addresses the stability of the switched systems with discrete and distributed time delays. By applying Lyapunov functional and function method, we show that, if the norm of system matrices Bi is small enough, the asymptotic stability is always achieved. Finally, a example is provided to verify technically feasibility and operability of the developed results.

Keywords: Switched system, stability, Lyapunov function, Lyapunov functional, delays.

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Authors: S. Balaji

Abstract:

An edge based local search algorithm, called ELS, is proposed for the maximum clique problem (MCP), a well-known combinatorial optimization problem. ELS is a two phased local search method effectively £nds the near optimal solutions for the MCP. A parameter ’support’ of vertices de£ned in the ELS greatly reduces the more number of random selections among vertices and also the number of iterations and running times. Computational results on BHOSLIB and DIMACS benchmark graphs indicate that ELS is capable of achieving state-of-the-art-performance for the maximum clique with reasonable average running times.

Keywords: Maximum clique, local search, heuristic, NP-complete.

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Authors: S. Pathomsiri, P. Sukaboon

Abstract:

The National Blood Center, Thai Red Cross Society is responsible for providing blood to hospitals all over the country. When any hospital needs blood, it will have to send the vehicle to pick up at the NBC. There are a lot of vehicles to pick up blood at the NBC every day. Each vehicle is usually empty for inbound trip and a little loaded for outbound. The NBC realized such waste or loss and there have been the third party offered to distribute blood and charge for fee. This paper proposes to apply the vehicle routing problem (VRP) for estimating the fair price. The idea is tested with the real data during seven-day period of 6 – 12 July 2010 to estimate the fair price for transporting blood in Bangkok Metropolitan Region.

Keywords: Blood Supply Chain, Vehicle Routing Problem, Heuristic, Saving Algorithm, Fair Price.

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Authors: M. Bouinoun, M. Bouhadef

Abstract:

The present study is concerned with the problem of determining the shape of the free surface flow in a hydraulic channel which has an uneven bottom. For the mathematical formulation of the problem, the fluid of the two-dimensional irrotational steady flow in water is assumed inviscid and incompressible. The solutions of the nonlinear problem are obtained by using the usual conformal mapping theory and Hilbert’s technique. An experimental study, for comparing the obtained results, has been conducted in a hydraulic channel (subcritical regime and supercritical regime). 

Keywords: Free-surface flow, experiments, numerical method, uneven bottom, supercritical regime, subcritical regime.

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Authors: V.Pavlika

Abstract:

In this paper a numerical algorithm is described for solving the boundary value problem associated with axisymmetric, inviscid, incompressible, rotational (and irrotational) flow in order to obtain duct wall shapes from prescribed wall velocity distributions. The governing equations are formulated in terms of the stream function ψ (x,y)and the function φ (x,y)as independent variables where for irrotational flow φ (x,y)can be recognized as the velocity potential function, for rotational flow φ (x,y)ceases being the velocity potential function but does remain orthogonal to the stream lines. A numerical method based on the finite difference scheme on a uniform mesh is employed. The technique described is capable of tackling the so-called inverse problem where the velocity wall distributions are prescribed from which the duct wall shape is calculated, as well as the direct problem where the velocity distribution on the duct walls are calculated from prescribed duct geometries. The two different cases as outlined in this paper are in fact boundary value problems with Neumann and Dirichlet boundary conditions respectively. Even though both approaches are discussed, only numerical results for the case of the Dirichlet boundary conditions are given. A downstream condition is prescribed such that cylindrical flow, that is flow which is independent of the axial coordinate, exists.

Keywords: Inverse problem, irrotational incompressible flow, Boundary value problem.

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Authors: S. Khamsawang, S. Jiriwibhakorn

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This paper proposes an improved approach based on conventional particle swarm optimization (PSO) for solving an economic dispatch(ED) problem with considering the generator constraints. The mutation operators of the differential evolution (DE) are used for improving diversity exploration of PSO, which called particle swarm optimization with mutation operators (PSOM). The mutation operators are activated if velocity values of PSO nearly to zero or violated from the boundaries. Four scenarios of mutation operators are implemented for PSOM. The simulation results of all scenarios of the PSOM outperform over the PSO and other existing approaches which appeared in literatures.

Keywords: Novel particle swarm optimization, Economic dispatch problem, Mutation operator, Prohibited operating zones, Differential Evolution.

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Authors: Yu-Jen Chang, Shih-Chieh Chen, Yu-Wei Kuo

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In this study, we are interested in the economic lot scheduling problem (ELSP) that considers manufacturing of the serviceable products and remanufacturing of the reworked products. In this paper, we formulate a mathematical model for the ELSP with reworks using the basic period approach. In order to solve this problem, we propose a search algorithm to find the cyclic multiplier ki of each product that can be cyclically produced for every ki basic periods. This research also uses two heuristics to search for the optimal production sequence of all lots and the optimal time length of the basic period so as to minimize the average total cost. This research uses a numerical example to show the effectiveness of our approach.

Keywords: Economic lot, reworks, inventory, basic period.

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Authors: U. Prasopchingchana

Abstract:

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

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

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Authors: Loay A. Al-Zu'be, Asma A. Al-Tamimi, Thakir D. Al-Momani, Ayat J. Alkarala, Maryam A. Alzawahreh

Abstract:

A two dimensional three segments coupled pendulum system that mathematically models human arm configuration was developed along with constructing and solving the equations of motions for this model using the energy (work) based approach of Lagrange. The equations of motion of the model were solved iteratively both as an initial value problem and as a two point boundary value problem. In the initial value problem solutions, both the initial system configuration (segment angles) and initial system velocity (segment angular velocities) were used as inputs, whereas, in the two point boundary value problem solutions initial and final configurations and time were used as inputs to solve for the trajectory of motion. The results suggest that the model solutions are sensitive to small changes in the dynamic forces applied to the system as well as to the initial and boundary conditions used. To overcome the system sensitivity a new approach is suggested.

Keywords: Body Configurations, Equations of Motion, Mathematical Modeling, Movement Trajectories.

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Authors: V. Kahya, A. Birinci, R. Erdol

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A frictionless contact problem for a two-layer orthotropic elastic medium loaded through a rigid flat stamp is considered. It is assumed that tensile tractions are not allowed and only compressive tractions can be transmitted across the interface. In the solution, effect of gravity is taken into consideration. If the external load on the rigid stamp is less than or equal to a critical value, continuous contact between the layers is maintained. The problem is expressed in terms of a singular integral equation by using the theory of elasticity and the Fourier transforms. Numerical results for initial separation point, critical separation load and contact stress distribution are presented.

Keywords: Frictionless contact, Initial separation, Orthotropicmaterial, Singular integral equation.

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Authors: Soottipoom Yaowiwat, Manoj Lohatepanont, Proadpran Punyabukkana

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Several approaches such as linear programming, network modeling, greedy heuristic and decision support system are well-known approaches in solving irregular airline operation problem. This paper presents an alternative approach based on Multi Objective Micro Genetic Algorithm. The aim of this research is to introduce the concept of Multi Objective Micro Genetic Algorithm as a tool to solve irregular airline operation, combine and reroute problem. The experiment result indicated that the model could obtain optimal solutions within a few second.

Keywords: Irregular Airline Operation, Combine and RerouteRoutine, Genetic Algorithm, Micro Genetic Algorithm, Multi ObjectiveOptimization, Evolutionary Algorithm.

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Authors: Eugene Kindler

Abstract:

The present paper is oriented to classification and application of agent technique in simulation of anticipatory systems, namely those that use simulation models for the aid of anticipation. The main ideas root in the fact that the best way for description of computer simulation models is the technique of describing the simulated system itself (and the translation into the computer code is provided as automatic), and that the anticipation itself is often nested.

Keywords: Agents, Anticipatory systems, Discrete eventsimulation, Simula, Taxonomy.

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Authors: Farooq Ahmad, Hejiao Huang, Xiaolong Wang

Abstract:

Reachability graph (RG) generation suffers from the problem of exponential space and time complexity. To alleviate the more critical problem of time complexity, this paper presents the new approach for RG generation for the Petri net (PN) models of parallel processes. Independent RGs for each parallel process in the PN structure are generated in parallel and cross-product of these RGs turns into the exhaustive state space from which the RG of given parallel system is determined. The complexity analysis of the presented algorithm illuminates significant decrease in the time complexity cost of RG generation. The proposed technique is applicable to parallel programs having multiple threads with the synchronization problem.

Keywords: Parallel processes, Petri net, reachability graph, time complexity.

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Authors: Marco Antonio Cruz-Chávez, Juan Frausto-Solís, Fernando Ramos-Quintana

Abstract:

A procedure commonly used in Job Shop Scheduling Problem (JSSP) to evaluate the neighborhoods functions that use the non-deterministic algorithms is the calculation of the critical path in a digraph. This paper presents an experimental study of the cost of computation that exists when the calculation of the critical path in the solution for instances in which a JSSP of large size is involved. The results indicate that if the critical path is use in order to generate neighborhoods in the meta-heuristics that are used in JSSP, an elevated cost of computation exists in spite of the fact that the calculation of the critical path in any digraph is of polynomial complexity.

Keywords: Job Shop, CPM, critical path, neighborhood, meta-heuristic.

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Authors: M. T. Yazdani Sabouni, Rasaratnam Logendran

Abstract:

We consider a typical problem in the assembly of printed circuit boards (PCBs) in a two-machine flow shop system to simultaneously minimize the weighted sum of weighted tardiness and weighted flow time. The investigated problem is a group scheduling problem in which PCBs are assembled in groups and the interest is to find the best sequence of groups as well as the boards within each group to minimize the objective function value. The type of setup operation between any two board groups is characterized as carryover sequence-dependent setup time, which exactly matches with the real application of this problem. As a technical constraint, all of the boards must be kitted before the assembly operation starts (kitting operation) and by kitting staff. The main idea developed in this paper is to completely eliminate the role of kitting staff by assigning the task of kitting to the machine operator during the time he is idle which is referred to as integration of internal (machine) and external (kitting) setup times. Performing the kitting operation, which is a preparation process of the next set of boards while the other boards are currently being assembled, results in the boards to continuously enter the system or have dynamic arrival times. Consequently, a dynamic PCB assembly system is introduced for the first time in the assembly of PCBs, which also has characteristics similar to that of just-in-time manufacturing. The problem investigated is computationally very complex, meaning that finding the optimal solutions especially when the problem size gets larger is impossible. Thus, a heuristic based on Genetic Algorithm (GA) is employed. An example problem on the application of the GA developed is demonstrated and also numerical results of applying the GA on solving several instances are provided.

Keywords: Genetic algorithm, Dynamic PCB assembly, Carryover sequence-dependent setup times, Multi-objective.

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Authors: Hamed Rafiei, Masoud Rabbani

Abstract:

This paper deals with the project selection problem. Project selection problem is one of the problems arose firstly in the field of operations research following some production concepts from primary product mix problem. Afterward, introduction of managerial considerations into the project selection problem have emerged qualitative factors and criteria to be regarded as well as quantitative ones. To overcome both kinds of criteria, an analytic network process is developed in this paper enhanced with fuzzy sets theory to tackle the vagueness of experts- comments to evaluate the alternatives. Additionally, a modified version of Least-Square method through a non-linear programming model is augmented to the developed group decision making structure in order to elicit the final weights from comparison matrices. Finally, a case study is considered by which developed structure in this paper is validated. Moreover, a sensitivity analysis is performed to validate the response of the model with respect to the condition alteration.

Keywords: Analytic network process, Fuzzy sets theory, Nonlinear programming, Project selection.

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Authors: Mehmet Nefes, Selman Demirel, Hasan H. Ertok, Cenk Sen

Abstract:

A typical reliability engineering problem regarding communication satellites has been considered to determine redundancy allocation scheme of power amplifiers within payload transponder module, whose dominant function is to amplify power levels of the received signals from the Earth, through maximizing reliability against mass, power, and other technical limitations. Adding each redundant power amplifier component increases not only reliability but also hardware, testing, and launch cost of a satellite. This study investigates a multi-objective approach used in order to solve Redundancy Allocation Problem (RAP) for a communication satellite payload transponder, focusing on design cost due to redundancy and reliability factors. The main purpose is to find the optimum power amplifier redundancy configuration satisfying reliability and capacity thresholds simultaneously instead of analyzing respectively or independently. A mathematical model and calculation approach are instituted including objective function definitions, and then, the problem is solved analytically with different input parameters in MATLAB environment. Example results showed that payload capacity and failure rate of power amplifiers have remarkable effects on the solution and also processing time.

Keywords: Communication satellite payload, multi-objective optimization, redundancy allocation problem, reliability, transponder.

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Authors: Eylem Koç, Hasan Arda Burhan

Abstract:

Location selection presents a crucial decision problem in today’s business world where strategic decision making processes have critical importance. Thus, location selection has strategic importance for companies in boosting their strength regarding competition, increasing corporate performances and efficiency in addition to lowering production and transportation costs. A right choice in location selection has a direct impact on companies’ commercial success. In this study, a store location selection problem of Carglass Turkey which operates in vehicle glass branch is handled. As this problem includes both tangible and intangible criteria, Analytic Network Process (ANP) was accepted as the main methodology. The model consists of control hierarchy and BOCR subnetworks which include clusters of actors, alternatives and criteria. In accordance with the management’s choices, five different locations were selected. In addition to the literature review, a strict cooperation with the actor group was ensured and maintained while determining the criteria and during whole process. Obtained results were presented to the management as a report and its feasibility was confirmed accordingly.

Keywords: Analytic Network Process, BOCR, location selection, multi-actor decision making, multi-criteria decision making, real life problem.

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Authors: M. Rodionov, Z. Dedovets

Abstract:

This article discusses plausible reasoning use for solution to practical problems. Such reasoning is the major driver of motivation and implementation of mathematical, scientific and educational research activity. A general, practical problem solving algorithm is presented which includes an analysis of specific problem content to build, solve and interpret the underlying mathematical model. The author explores the role of practical problems such as the stimulation of students' interest, the development of their world outlook and their orientation in the modern world at the different stages of learning mathematics in secondary school. Particular attention is paid to the characteristics of those problems which were systematized and presented in the conclusions.

Keywords: Mathematics, motivation, secondary school, student, practical problem.

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Authors: Ahmed Elrewainy

Abstract:

Mixing in the hyperspectral imaging occurs due to the low spatial resolutions of the used cameras. The existing pure materials “endmembers” in the scene share the spectra pixels with different amounts called “abundances”. Unmixing of the data cube is an important task to know the present endmembers in the cube for the analysis of these images. Unsupervised unmixing is done with no information about the given data cube. Sparsity is one of the recent approaches used in the source recovery or unmixing techniques. The l₁-norm optimization problem “basis pursuit” could be used as a sparsity-based approach to solve this unmixing problem where the endmembers is assumed to be sparse in an appropriate domain known as dictionary. This optimization problem is solved using proximal method “iterative thresholding”. The l₁-norm basis pursuit optimization problem as a sparsity-based unmixing technique was used to unmix real and synthetic hyperspectral data cubes.

Keywords: Basis pursuit, blind source separation, hyperspectral imaging, spectral unmixing, wavelets.

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Authors: Muhammed Yousoof, Mohd Sapiyan, Khaja Kamaluddin

Abstract:

Learning programming is difficult for many learners. Some researches have found that the main difficulty relates to cognitive load. Cognitive overload happens in programming due to the nature of the subject which is intrinisicly over-bearing on the working memory. It happens due to the complexity of the subject itself. The problem is made worse by the poor instructional design methodology used in the teaching and learning process. Various efforts have been proposed to reduce the cognitive load, e.g. visualization softwares, part-program method etc. Use of many computer based systems have also been tried to tackle the problem. However, little success has been made to alleviate the problem. More has to be done to overcome this hurdle. This research attempts at understanding how cognitive load can be managed so as to reduce the problem of overloading. We propose a mechanism to measure the cognitive load during pre instruction, post instruction and in instructional stages of learning. This mechanism is used to help the instruction. As the load changes the instruction is made to adapt itself to ensure cognitive viability. This mechanism could be incorporated as a sub domain in the student model of various computer based instructional systems to facilitate the learning of programming.

Keywords: Cognitive load, Working memory, Cognitive Loadmeasurement.

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Authors: Gionata Carmignani, Mario G. C. A. Cimino, Franco Failli

Abstract:

Business Processes (BPs) are the key instrument to understand how companies operate at an organizational level, taking an as-is view of the workflow, and how to address their issues by identifying a to-be model. In last year’s, the BP Model and Notation (BPMN) has become a de-facto standard for modeling processes. However, this standard does not incorporate explicitly the Problem- Solving (PS) knowledge in the Process Modeling (PM) results. Thus, such knowledge cannot be shared or reused. To narrow this gap is today a challenging research area. In this paper we present a framework able to capture the PS knowledge and to improve a workflow. This framework extends the BPMN specification by incorporating new general-purpose elements. A pilot scenario is also presented and discussed.

Keywords: Business Process Management, BPMN, Problem Solving, Process mapping.

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Authors: Yousef Abu Nahleh, Alhasan Hakami, Arun Kumar, Fugen Daver

Abstract:

This study considers the problem of calculating safety stocks in disaster situations inventory systems that face demand uncertainties. Safety stocks are essential to make the supply chain, which is controlled by forecasts of customer needs, in response to demand uncertainties and to reach predefined goal service levels. To solve the problem of uncertainties due to the disaster situations affecting the industry sector, the concept of Emergency Safety Stock (ESS) was proposed. While there exists a huge body of literature on determining safety stock levels, this literature does not address the problem arising due to the disaster and dealing with the situations. In this paper, the problem of improving the Order Quantity Model to deal with uncertainty of demand due to disasters is managed by incorporating a new idea called ESS which is based on the probability of disaster occurrence and uses probability matrix calculated from the historical data. 

Keywords: Emergency Safety Stocks, Safety stocks, Order Quantity Model, Supply chain.

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Authors: Praveen Kumar, Nitin Kumar, Hemant Kumar

Abstract:

The modernization of computer technology and commercial computational fluid dynamic (CFD) simulation has given better detailed results as compared to experimental investigation techniques. CFD techniques are widely used in different field due to its flexibility and performance. Evaluation of pipeline erosion is complex phenomenon to solve by numerical arithmetic technique, whereas CFD simulation is an easy tool to resolve that type of problem. Erosion wear behaviour due to solid–liquid mixture in the slurry pipeline has been investigated using commercial CFD code in FLUENT. Multi-phase Euler-Lagrange model was adopted to predict the solid particle erosion wear in 22.5° pipe bend for the flow of bottom ash-water suspension. The present study addresses erosion prediction in three dimensional 22.5° pipe bend for two-phase (solid and liquid) flow using finite volume method with standard k-ε turbulence, discrete phase model and evaluation of erosion wear rate with varying velocity 2-4 m/s. The result shows that velocity of solid-liquid mixture found to be highly dominating parameter as compared to solid concentration, density, and particle size. At low velocity, settling takes place in the pipe bend due to low inertia and gravitational effect on solid particulate which leads to high erosion at bottom side of pipeline.

Keywords: Computational fluid dynamics, erosion, slurry transportation, k-ε Model.

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