Search results for: positive solution
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 3763

Search results for: positive solution

2473 Solving SPDEs by a Least Squares Method

Authors: Hassan Manouzi

Abstract:

We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: Least squares, Wick product, SPDEs, finite element, Wiener chaos expansion, gradient method.

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2472 Fuzzy Boundary Layer Solution to Nonlinear Hydraulic Position Control Problem

Authors: Mustafa Resa Becan

Abstract:

Sliding mode control with a fuzzy boundary layer is presented to hydraulic position control problem in this paper. A nonlinear hydraulic servomechanism which has an asymmetric cylinder is modeled and simulated first, then the proposed control scheme is applied to this model versus the conventional sliding mode control. Simulation results proved that the chattering free position control is achieved by tuning the fuzzy scaling factors properly.

Keywords: Hydraulic servomechanism, position control, sliding mode control, chattering, fuzzy boundary layer.

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2471 A Study of Thermal Convection in Two Porous Layers Governed by Brinkman's Model in Upper Layer and Darcy's Model in Lower Layer

Authors: M. S. Al-Qurashi

Abstract:

This work examines thermal convection in two porous layers. Flow in the upper layer is governed by Brinkman-s equations model and in the lower layer is governed by Darcy-s model. Legendre polynomials are used to obtain numerical solution when the lower layer is heated from below.

Keywords: Brinkman's law, Darcy's law, porous layers, Legendre polynomials, the Oberbeck-Boussineq approximation.

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2470 Adsorption Kinetics of Alcohols over MCM-41 Materials

Authors: Farouq Twaiq, Mustafa Nasser, Siham Al-Hajri, Mansoor Al-Hasani

Abstract:

Adsorption of methanol and ethanol over mesoporous siliceous material are studied in the current paper. The pure mesoporous silica is prepared using tetraethylorthosilicate (TEOS) as silica source and dodecylamine as template at low pH. The prepared material was characterized using nitrogen adsorption,nX-ray diffraction (XRD) and scanning electron microscopy (SEM). The adsorption kinetics of methanol and ethanol from aqueous solution were studied over the prepared mesoporous silica material. The percent removal of alcohol was calculated per unit mass of adsorbent used. The 1st order model is found to be in agreement with both adsorbates while the 2nd order model fit the adsorption of methanol only.

Keywords: Adsorption, Kinetics, Mesoprous silica, Methanol

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2469 Formation of Nanosize Phases under Thermomechanical Strengthening of Low Carbon Steel

Authors: Victor E. Gromov, Yurii F. Ivanov, Vadim B. Kosterev, Sergey V. Konovalov, Veronica I. Myasnikova, Guoyi Tang

Abstract:

A study of the H-beam's nanosize structure phase states after thermomechanical strengthening was carried out by TEM. The following processes were analyzed. 1. The dispersing of the cementite plates by cutting them by moving dislocations. 2. The dissolution of cementite plates and repeated precipitation of the cementite particles on the dislocations, the boundaries, subgrains and grains. 3. The decay of solid solution of carbon in the α-iron after "self-tempering" of martensite. 4. The final transformation of the retained austenite in beinite with α-iron particles and cementite formation. 5. The implementation of the diffusion mechanism of γ ⇒ α transformation.

Keywords: nanosize, phase, steel, strengthening

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2468 Depth-Averaged Modelling of Erosion and Sediment Transport in Free-Surface Flows

Authors: Thomas Rowan, Mohammed Seaid

Abstract:

A fast finite volume solver for multi-layered shallow water flows with mass exchange and an erodible bed is developed. This enables the user to solve a number of complex sediment-based problems including (but not limited to), dam-break over an erodible bed, recirculation currents and bed evolution as well as levy and dyke failure. This research develops methodologies crucial to the under-standing of multi-sediment fluvial mechanics and waterway design. In this model mass exchange between the layers is allowed and, in contrast to previous models, sediment and fluid are able to transfer between layers. In the current study we use a two-step finite volume method to avoid the solution of the Riemann problem. Entrainment and deposition rates are calculated for the first time in a model of this nature. In the first step the governing equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the method of characteristics. In the second stage, the numerical fluxes are reconstructed in conservative form and are used to calculate a solution that satisfies the conservation property. This method is found to be considerably faster than other comparative finite volume methods, it also exhibits good shock capturing. For most entrainment and deposition equations a bed level concentration factor is used. This leads to inaccuracies in both near bed level concentration and total scour. To account for diffusion, as no vertical velocities are calculated, a capacity limited diffusion coefficient is used. The additional advantage of this multilayer approach is that there is a variation (from single layer models) in bottom layer fluid velocity: this dramatically reduces erosion, which is often overestimated in simulations of this nature using single layer flows. The model is used to simulate a standard dam break. In the dam break simulation, as expected, the number of fluid layers utilised creates variation in the resultant bed profile, with more layers offering a higher deviation in fluid velocity . These results showed a marked variation in erosion profiles from standard models. The overall the model provides new insight into the problems presented at minimal computational cost.

Keywords: Erosion, finite volume method, sediment transport, shallow water equations.

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2467 An Interval-Based Multi-Attribute Decision Making Approach for Electric Utility Resource Planning

Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

This paper presents an interval-based multi-attribute decision making (MADM) approach in support of the decision process with imprecise information. The proposed decision methodology is based on the model of linear additive utility function but extends the problem formulation with the measure of composite utility variance. A sample study concerning with the evaluation of electric generation expansion strategies is provided showing how the imprecise data may affect the choice toward the best solution and how a set of alternatives, acceptable to the decision maker (DM), may be identified with certain confidence.

Keywords: Decision Making, Power Generation, ElectricUtilities, Resource Planning.

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2466 Constructing Approximate and Exact Solutions for Boussinesq Equations using Homotopy Perturbation Padé Technique

Authors: Mohamed M. Mousa, Aidarkhan Kaltayev

Abstract:

Based on the homotopy perturbation method (HPM) and Padé approximants (PA), approximate and exact solutions are obtained for cubic Boussinesq and modified Boussinesq equations. The obtained solutions contain solitary waves, rational solutions. HPM is used for analytic treatment to those equations and PA for increasing the convergence region of the HPM analytical solution. The results reveal that the HPM with the enhancement of PA is a very effective, convenient and quite accurate to such types of partial differential equations.

Keywords: Homotopy perturbation method, Padé approximants, cubic Boussinesq equation, modified Boussinesq equation.

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2465 Seat Assignment Problem Optimization

Authors: Mohammed Salem Alzahrani

Abstract:

In this paper the optimality of the solution of an existing real word assignment problem known as the seat assignment problem using Seat Assignment Method (SAM) is discussed. SAM is the newly driven method from three existing methods, Hungarian Method, Northwest Corner Method and Least Cost Method in a special way that produces the easiness & fairness among all methods that solve the seat assignment problem.

Keywords: Assignment Problem, Hungarian Method, Least Cost Method, Northwest Corner Method, Seat Assignment Method (SAM), A Real Word Assignment Problem.

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2464 Distributed e-Learning System with Client-Server and P2P Hybrid Architecture

Authors: Kazunari Meguro, Shinichi Motomura, Takao Kawamura, Kazunori Sugahara

Abstract:

We have developed a distributed asynchronous Web based training system. In order to improve the scalability and robustness of this system, all contents and a function are realized on mobile agents. These agents are distributed to computers, and they can use a Peer to Peer network that modified Content-Addressable Network. In this system, all computers offer the function and exercise by themselves. However, the system that all computers do the same behavior is not realistic. In this paper, as a solution of this issue, we present an e-Learning system that is composed of computers of different participation types. Enabling the computer of different participation types will improve the convenience of the system.

Keywords: Distributed Multimedia Systems, e-Learning, P2P, Mobile Agen

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2463 Technological Innovation Persistence Organizational Innovation Matters

Authors: H. Naciba, C. Le Bas, C. Mothe, T.U. Nguyen-Thi

Abstract:

Organizational innovation favors technological innovation, but does it also influence technological innovation persistence? This article investigates empirically the pattern of technological innovation persistence and tests the potential impact of organizational innovation using firm-level data from three waves of the French Community Innovation Surveys. Evidence shows a positive effect of organizational innovation on technological innovation persistence, according to various measures of organizational innovation. Moreover, this impact is more significant for complex innovators (i.e., those who innovate in both products and processes). These results highlight the complexity of managing organizational practices with regard to the firm-s technological innovation. They also add to comprehension of the drivers of innovation persistence, through a focus on an often forgotten dimension of innovation in a broader sense.

Keywords: Organizational Innovation, Technological Innovation, Persistence

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2462 The Multi-scenario Knapsack Problem: An Adaptive Search Algorithm

Authors: Mhand Hifi, Hedi Mhalla, Mustapha Michaphy

Abstract:

In this paper, we study the multi-scenario knapsack problem, a variant of the well-known NP-Hard single knapsack problem. We investigate the use of an adaptive algorithm for solving heuristically the problem. The used method combines two complementary phases: a size reduction phase and a dynamic 2- opt procedure one. First, the reduction phase applies a polynomial reduction strategy; that is used for reducing the size problem. Second, the adaptive search procedure is applied in order to attain a feasible solution Finally, the performances of two versions of the proposed algorithm are evaluated on a set of randomly generated instances.

Keywords: combinatorial optimization, max-min optimization, knapsack, heuristics, problem reduction

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2461 Contributions to Differential Geometry of Pseudo Null Curves in Semi-Euclidean Space

Authors: Melih Turgut, Süha Yılmaz

Abstract:

In this paper, first, a characterization of spherical Pseudo null curves in Semi-Euclidean space is given. Then, to investigate position vector of a pseudo null curve, a system of differential equation whose solution gives the components of the position vector of a pseudo null curve on the Frenet axis is established by means of Frenet equations. Additionally, in view of some special solutions of mentioned system, characterizations of some special pseudo null curves are presented.

Keywords: Semi-Euclidean Space, Pseudo Null Curves, Position Vectors.

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2460 A New Evolutionary Algorithm for Cluster Analysis

Authors: B.Bahmani Firouzi, T. Niknam, M. Nayeripour

Abstract:

Clustering is a very well known technique in data mining. One of the most widely used clustering techniques is the kmeans algorithm. Solutions obtained from this technique depend on the initialization of cluster centers and the final solution converges to local minima. In order to overcome K-means algorithm shortcomings, this paper proposes a hybrid evolutionary algorithm based on the combination of PSO, SA and K-means algorithms, called PSO-SA-K, which can find better cluster partition. The performance is evaluated through several benchmark data sets. The simulation results show that the proposed algorithm outperforms previous approaches, such as PSO, SA and K-means for partitional clustering problem.

Keywords: Data clustering, Hybrid evolutionary optimization algorithm, K-means algorithm, Simulated Annealing (SA), Particle Swarm Optimization (PSO).

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2459 The Investigations of Water-ethanol Mixture by Monte Carlo Method

Authors: Atamas N. A., Atamas A. A.

Abstract:

Energetic and structural results for ethanol-water mixtures as a function of the mole fraction were calculated using Monte Carlo methodology. Energy partitioning results obtained for equimolar water-ethanol mixture and ether organic liquids are compared. It has been shown that at xet=0.22 the RDFs for waterethanol and ethanol-ethanol interactions indicated strong hydrophobic interactions between ethanol molecules and the local structure of solution is less structured at this concentration as at ether ones. Results obtained for ethanol-water mixture as a function of concentration are in good agreement with the experimental data.

Keywords: Ethanol, molecular liquids, Monte Carlo, water, thermodynamics.

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2458 Methodologies for Management of Sustainable Tourism: A Case Study in Jalapão/Tocantins/Brazil

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

Abstract:

The study is in application and analysis of two tourism management tools that can contribute to making public managers decision: the Barometer of Tourism Sustainability (BTS) and the Ecological Footprint (EF). The results have shown that BTS allows you to have an integrated view of the tourism system, awakening to the need for planning of appropriate actions so that it can achieve the positive scale proposed (potentially sustainable). Already the methodology of ecological tourism footprint is an important tool to measure potential impacts generated by tourism to tourist reality.

Keywords: Barometer of tourism sustainability, ecological footprint of tourism, Jalapão/Brazil, sustainable tourism.

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2457 Anti-periodic Solutions for Cohen-Grossberg Shunting Inhibitory Neural Networks with Delays

Authors: Yongkun Li, Tianwei Zhang, Shufa Bai

Abstract:

By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.

Keywords: Anti-periodic solution, coincidence degree, global exponential stability, Cohen-Grossberg shunting inhibitory cellular neural networks.

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2456 Noise Analysis of Single-Ended Input Differential Amplifier using Stochastic Differential Equation

Authors: Tarun Kumar Rawat, Abhirup Lahiri, Ashish Gupta

Abstract:

In this paper, we analyze the effect of noise in a single- ended input differential amplifier working at high frequencies. Both extrinsic and intrinsic noise are analyzed using time domain method employing techniques from stochastic calculus. Stochastic differential equations are used to obtain autocorrelation functions of the output noise voltage and other solution statistics like mean and variance. The analysis leads to important design implications and suggests changes in the device parameters for improved noise characteristics of the differential amplifier.

Keywords: Single-ended input differential amplifier, Noise, stochastic differential equation, mean and variance.

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2455 New Stabilization for Switched Neutral Systems with Perturbations

Authors: Lianglin Xiong, Shouming Zhong, Mao Ye

Abstract:

This paper addresses the stabilization issues for a class of uncertain switched neutral systems with nonlinear perturbations. Based on new classes of piecewise Lyapunov functionals, the stability assumption on all the main operators or the convex combination of coefficient matrices is avoid, and a new switching rule is introduced to stabilize the neutral systems. The switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. Finally, three simulation examples are given to demonstrate the significant improvements over the existing results.

Keywords: Switched neutral system, piecewise Lyapunov functional, nonlinear perturbation, Lyapunov-Metzler linear matrix inequality.

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2454 The Relationship between Value-Added and Energy Consumption in Iran’s Industry Sector

Authors: Morteza Raei Dehaghi, Mojtaba Molaahmadi, Seyed Mohammad Mirhashemi

Abstract:

This study aimed to explore the relationship between energy consumption and value-added in Iran’s industry sector during the time period 1973-2011. Annual data related to energy consumption and value added in the industry sector were used. The results of the study revealed a positive relationship between energy consumption and value-added of the industry sector. Similarly, the results showed that there is one-way causality between energy consumption and value-added in the industry sector.

Keywords: Energy consumption, economic growth, industry sector.

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2453 Model Reference Adaptive Approach for Power System Stabilizer for Damping of Power Oscillations

Authors: Jožef Ritonja, Bojan Grčar, Boštjan Polajžer

Abstract:

In recent years, electricity trade between neighboring countries has become increasingly intense. Increasing power transmission over long distances has resulted in an increase in the oscillations of the transmitted power. The damping of the oscillations can be carried out with the reconfiguration of the network or the replacement of generators, but such solution is not economically reasonable. The only cost-effective solution to improve the damping of power oscillations is to use power system stabilizers. Power system stabilizer represents a part of synchronous generator control system. It utilizes semiconductor’s excitation system connected to the rotor field excitation winding to increase the damping of the power system. The majority of the synchronous generators are equipped with the conventional power system stabilizers with fixed parameters. The control structure of the conventional power system stabilizers and the tuning procedure are based on the linear control theory. Conventional power system stabilizers are simple to realize, but they show non-sufficient damping improvement in the entire operating conditions. This is the reason that advanced control theories are used for development of better power system stabilizers. In this paper, the adaptive control theory for power system stabilizers design and synthesis is studied. The presented work is focused on the use of model reference adaptive control approach. Control signal, which assures that the controlled plant output will follow the reference model output, is generated by the adaptive algorithm. Adaptive gains are obtained as a combination of the "proportional" term and with the σ-term extended "integral" term. The σ-term is introduced to avoid divergence of the integral gains. The necessary condition for asymptotic tracking is derived by means of hyperstability theory. The benefits of the proposed model reference adaptive power system stabilizer were evaluated as objectively as possible by means of a theoretical analysis, numerical simulations and laboratory realizations. Damping of the synchronous generator oscillations in the entire operating range was investigated. Obtained results show the improved damping in the entire operating area and the increase of the power system stability. The results of the presented work will help by the development of the model reference power system stabilizer which should be able to replace the conventional stabilizers in power systems.

Keywords: Power system, stability, oscillations, power system stabilizer, model reference adaptive control.

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2452 Two Stage Fuzzy Methodology to Evaluate the Credit Risks of Investment Projects

Authors: O. Badagadze, G. Sirbiladze, I. Khutsishvili

Abstract:

The work proposes a decision support methodology for the credit risk minimization in selection of investment projects. The methodology provides two stages of projects’ evaluation. Preliminary selection of projects with minor credit risks is made using the Expertons Method. The second stage makes ranking of chosen projects using the Possibilistic Discrimination Analysis Method. The latter is a new modification of a well-known Method of Fuzzy Discrimination Analysis.

Keywords: Expert valuations, expertons, investment project risks, positive and negative discriminations, possibility distribution.

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2451 Military Families’ Attachment to the Royal Guards Community of Dusit District, Bangkok Metropolitan

Authors: Kaniknun Photchong, Phusit Phukamchanoad

Abstract:

The objective of this research is to study the people’s level of participation in activities of the community, their satisfaction towards the community, the attachment they have to the community, factors that influence the attachment, as well as the characteristics of the relationships of military families’ of the Royal Guards community of Dusit District. The method used was non-probability sampling by quota sampling according to people’s age. The determined age group was 18 years or older.

One set of a sample group was done per family. The questionnaires were conducted by 287 people. Snowball sampling was also used by interviewing people of the community, starting from the Royal Guards Community’s leader, then by 20 of the community’s well-respected persons. The data was analyzed by using descriptive statistics, such as arithmetic mean and standard deviation, as well as by inferential statistics, such as Independent - Samples T test (T-test), One-Way ANOVA (F-test), Chi-Square. Descriptive analysis according to the structure of the interview content was also used. The results of the research is that the participation of the population in the Royal Guards Community in various activities is at a medium level, with the average participation level during Mother’s and Father’s Days. The people’s general level of satisfaction towards the premises of the Royal Guards Community is at the highest level.

The people were most satisfied with the transportation within the community and in contacting with people from outside the premises. The access to the community is convenient and there are various entrances. The attachment of the people to the Royal Guards Community in general and by each category is at a high level. The feeling that the community is their home rated the highest average. Factors that influence the attachment of the people of the Royal Guards Community are age, status, profession, income, length of stay in the community, membership of social groups, having neighbors they feel close and familiar with, and as well as the benefits they receive from the community. In addition, it was found that people that participate in activities have a high level of positive relationship towards the attachment of the people to the Royal Guards Community. The satisfaction of the community has a very high level of positive relationship with the attachment of the people to the Royal Guards Community.

The characteristics of the attachment of military families’ is that they live in big houses that everyone has to protect and care for, starting from the leader of the family as well as all members. Therefore, they all love the community they live in. The characteristics that show the participation of activities within the community and the high level of satisfaction towards the premises of the community will enable the people to be more attached to the community. The people feel that everyone is close neighbors within the community, as if they are one big family.

Keywords: Activities, Attachment, Community, Royal Guards, Satisfaction.

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2450 An Approximation Method for Exact Boundary Controllability of Euler-Bernoulli System

Authors: Abdelaziz Khernane, Naceur Khelil, Leila Djerou

Abstract:

The aim of this work is to study the numerical implementation of the Hilbert Uniqueness Method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step, the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T.

Keywords: Boundary control, exact controllability, finite difference methods, functional optimization.

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2449 Decision Making under Strict Uncertainty: Case Study in Sewer Network Planning

Authors: Zhen Wu, David Lupien St-Pierre, Georges Abdul-Nour

Abstract:

In decision making under strict uncertainty, decision makers have to choose a decision without any information about the states of nature. The classic criteria of Laplace, Wald, Savage, Hurwicz and Starr are introduced and compared in a case study of sewer network planning. Furthermore, results from different criteria are discussed and analyzed. Moreover, this paper discusses the idea that decision making under strict uncertainty (DMUSU) can be viewed as a two-player game and thus be solved by a solution concept in game theory: Nash equilibrium.

Keywords: Decision criteria, decision making, sewer network planning, strict uncertainty.

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2448 Analytical Approach of the In-Pipe Robot on Branched Pipe Navigation and Its Solution

Authors: Yoon Koo Kang, Jung wan Park, Hyun Seok Yang

Abstract:

This paper determines most common model of in-pipe robots to derive its degree of freedom in order to compare with the necessary degree of freedom required for a system to move inside pipelines freely in order to derive analytical reason for losing control of in-pipe robots at branched pipe. DOF of most common mechanism in in-pipe robots can be calculated by considering the robot as a parallel manipulator. A new design based on previously researched in-pipe robot PAROYS has been suggested, and its possibility to overcome branched section has been simulated.

Keywords: Branched pipe, Degree of freedom, In-pipe robot, Parallel manipulator.

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2447 On the Way to the European Research Area: Programmes of the European Union as Factor of the Innovation Development the Scientific Organization in Ukraine

Authors: Yuri Nikitin, Veronika Rukas

Abstract:

Within the framework of the FP7 project "START" the cooperation with European research centres has had a positive impact on raising the level of innovation researches and the introduction of innovations Institute for Superhard Materials of the National Academy of Sciences (ISM NAS) of Ukraine in the economy of Europe and Ukraine, which in turn permits to speeds up the way for Ukrainian science to the European research area through the creation in Ukraine the scientific organizations of innovative type.

Keywords: Programs of the EU, innovative scientific results, innovation competence of the staff, commercialization in business of industry of the Europe and Ukraine.

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2446 A New Time Discontinuous Expanded Mixed Element Method for Convection-dominated Diffusion Equation

Authors: Jinfeng Wang, Yuanhong Bi, Hong Li, Yang Liu, Meng Zhao

Abstract:

In this paper, a new time discontinuous expanded mixed finite element method is proposed and analyzed for two-order convection-dominated diffusion problem. The proofs of the stability of the proposed scheme and the uniqueness of the discrete solution are given. Moreover, the error estimates of the scalar unknown, its gradient and its flux in the L1( ¯ J,L2( )-norm are obtained.

Keywords: Convection-dominated diffusion equation, expanded mixed method, time discontinuous scheme, stability, error estimates.

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2445 Theoretical Investigation of Steel Plated Girder Resistance

Authors: J. Kala, J. Melcher, M. Škaloud, Z. Kala

Abstract:

In the paper, the results of sensitivity analysis of the influence of initial imperfections on the web stress state of a thinwalled girder are presented. The results of the study corroborate a very good and effective agreement of experiments with theory. Most input random quantities were found experimentally. The change of sensitivity coefficients in dependence on working load value is analysed. The stress was analysed by means of a geometrically and materially non-linear solution by applying the program ANSYS. This research study offers important background for theoretical studies of stability problems, post-critical effects and limit states of thin-walled steel structures.

Keywords: Buckling, Fatigue, Imperfection, Steel, Sensitivity analysis.

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2444 A Scenario-Based Approach for the Air Traffic Flow Management Problem with Stochastic Capacities

Authors: Soumia Ichoua

Abstract:

In this paper, we investigate the strategic stochastic air traffic flow management problem which seeks to balance airspace capacity and demand under weather disruptions. The goal is to reduce the need for myopic tactical decisions that do not account for probabilistic knowledge about the NAS near-future states. We present and discuss a scenario-based modeling approach based on a time-space stochastic process to depict weather disruption occurrences in the NAS. A solution framework is also proposed along with a distributed implementation aimed at overcoming scalability problems. Issues related to this implementation are also discussed.

Keywords: Air traffic management, sample average approximation, scenario-based approach, stochastic capacity.

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