Search results for: mixing efficiency

Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: Coherent covering location problem, efficient frontier, Lagrangian relaxation, data envelopment analysis.

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Authors: Krishna S. Raghuwaiya, Shonal Singh, Jito Vanualailai

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In this paper, the trajectory tracking problem for carlike mobile robots have been studied. The system comprises of a leader and a follower robot. The purpose is to control the follower so that the leader-s trajectory is tracked with arbitrary desired clearance to avoid inter-robot collision while navigating in a terrain with obstacles. A set of artificial potential field functions is proposed using the Direct Method of Lyapunov for the avoidance of obstacles and attraction to their designated targets. Simulation results prove the efficiency of our control technique.

Keywords: Control, Trajectory Tracking, Lyapunov.

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Authors: O. Onal, O. Turan

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In this paper, some performance parameters of a selected turbofan engine (JT9D) are analyzed. The engine is a high bypass turbofan engine which powers a wide-body aircraft and it produces 206 kN thrust force (thrust/weight ratio is 5.4). The objective parameters for the engine include calculation of power, specific fuel consumption, specific thrust, engine propulsive, thermal and overall efficiencies according to the various definitions given in the literature. Furthermore, in the case study, wasted energy from the exhaust is calculated at the maximum power setting (i.e. take off phase) for the engine.

Keywords: Turbofan, power, efficiency, trust.

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Authors: S. N. Moghaddas Tafreshi, S. M. Amin Ghotbi

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This paper presents a numerical study for investigating the effectiveness of geocell reinforcement in reducing pressure and settlement over EPS geofoam blocks in road embankments. A 3-D FEM model of soil and geofoam was created in ABAQUS, and geocell was also modeled realistically using membrane elements. The accuracy of the model was tested by comparing its results with previous works. Sensitivity analyses showed that reinforcing the soil cover with geocell has a significant influence on the reduction of imposed stresses over geofoam and consequently decreasing its deformation.

Keywords: EPS geofoam, road embankments, geocell, reinforcement, lightweight fill.

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Authors: Leon Fu, Xiangyang Xue

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In this paper, we propose a new approach to query-by-humming, focusing on MP3 songs database. Since MP3 songs are much more difficult in melody representation than symbolic performance data, we adopt to extract feature descriptors from the vocal sounds part of the songs. Our approach is based on signal filtering, sub-band spectral processing, MDCT coefficients analysis and peak energy detection by ignorance of the background music as much as possible. Finally, we apply dual dynamic programming algorithm for feature similarity matching. Experiments will show us its online performance in precision and efficiency.

Keywords: DP, MDCT, MP3, QBH.

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Authors: Shiping Zhou, Minggen Cui

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This paper investigates the inverse problem of determining the unknown time-dependent leading coefficient in the parabolic equation using the usual conditions of the direct problem and an additional condition. An algorithm is developed for solving numerically the inverse problem using the technique of space decomposition in a reproducing kernel space. The leading coefficients can be solved by a lower triangular linear system. Numerical experiments are presented to show the efficiency of the proposed methods.

Keywords: parabolic equations, coefficient inverse problem, reproducing kernel.

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Authors: Milan Hladik

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The symmetric solution set Σ sym is the set of all solutions to the linear systems Ax = b, where A is symmetric and lies between some given bounds A and A, and b lies between b and b. We present a contractor for Σ sym, which is an iterative method that starts with some initial enclosure of Σ sym (by means of a cartesian product of intervals) and sequentially makes the enclosure tighter. Our contractor is based on polyhedral approximation and solving a series of linear programs. Even though it does not converge to the optimal bounds in general, it may significantly reduce the overestimation. The efficiency is discussed by a number of numerical experiments.

Keywords: Linear interval systems, solution set, interval matrix, symmetric matrix.

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Authors: Theingi Shwe, Riken Homma, Kazuhisa Iki, Juko Ito

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The growing cities of the developing country are characterized by rapid growth and poor infrastructure management inviting and accelerating relative environmental problems. Even though the movements of the sustainability had already been developed around the world, it is still increasing in the developing countries to plant sustainable practices. Aligned with the sustainable development actions, many sustainable assessment tools are also developed to rate and evaluate the sustainability performances through the building to community level. Among them, CASBEE is developed by Japanese organizations and is recognized as one of the international well-known assessment tools. The main purpose of the study is to find out the potential of CASBEE tool reflecting sustainability city level performances in developing countries. The research framework was designed with three major phases: Quantitative Approach, Qualitative Approach and Evaluation Reflection. The first two approaches were based on the investigation of tool’s contents and indicators by means of three sustainable dimensions and sustainability categories. To know the reality and reflection on developing country, Pathein City from Myanmar was selected and evaluated by 2012 version of CASBEE for Cities. The evaluation practices went through assigned indicators and the evaluation outcome presents the performances of Pathein city’s environmental efficiency as a very good in current conditions. The results of this study indicate that the indicators of this tool have balance coverage among three dimensions of sustainability but it has not yet counted enough for some indicators like location, infrastructure and institution which are relative to society dimension. In the developing countries’ cities, the most critical issues on development such as affordable housing and heritage preservation which are already planted in Pathein City but the tool does not account for those issues. Moreover, in some of the indicators, the benchmark and the weighting coefficient are strongly linked to the system birth region. By means of this study, it can be stated that CASBEE for Cities would be potential for delivering sustainable city level development in developing country especially in Myanmar along with further inclusion of the indicators.

Keywords: Assessment tool, CASBEE, developing country, Myanmar, Pathein city, sustainable development.

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Authors: R. Manaffar, R. Maleki, S. Zare, N. Agh, S. Soltanian, B. Sehatnia, P. Sorgeloos, P. Bossier, G. Van Stappen

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Artemia is one of the most conspicuous invertebrates associated with aquaculture. It can be considered as a model organism, offering numerous advantages for comprehensive and multidisciplinary studies using morphologic or molecular methods. Since DNA extraction is an important step of any molecular experiment, a new and a rapid method of DNA extraction from adult Artemia was described in this study. Besides, the efficiency of this technique was compared with two widely used alternative techniques, namely Chelex® 100 resin and SDS-chloroform methods. Data analysis revealed that the new method is the easiest and the most cost effective method among the other methods which allows a quick and efficient extraction of DNA from the adult animal.

Keywords: APD, Artemia, DNA extraction, Molecularexperiments

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Authors: Julian Becker, Wiebke Hartmann, Sebastian Bertsch, Johannes Nywlt, Matthias Schmidt

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In order to ensure a high service level industrial enterprises have to maintain safety-stock that directly influences the economic efficiency at the same time. This paper analyses established mathematical methods to calculate safety-stock. Therefore, the performance measured in stock and service level is appraised and the limits of several methods are depicted. Afterwards, a new dynamic approach is presented to gain an extensive method to calculate safety-stock that also takes the knowledge of future volatility into account.

Keywords: Inventory dimensioning, material requirement planning, safety-stock calculation.

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Authors: Jose J.CarreñoZagarra, Rodolfo Villamizar Mejía

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This work describes a CACSD tool for automatic design of robust controllers for hydraulic turbines. The tool calculates the optimal
 controller using the MATLAB hinfopt function and it serves as a practical and effective solution for the laborious task of designing a different controller for each type of turbine and generator, and different parameters and conditions of the plant. Results of the simulation of a generating unit subject to parameters variation show the accuracy and efficiency of the obtained robust controllers.

Keywords: Robust Control, Hydroelectric System Turbine, Control H∞, CACSD

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Authors: Zhenyu Zhao, Lei You

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The numerical analytic continuation of a function f(z) = f(x + iy) on a strip is discussed in this paper. The data are only given approximately on the real axis. The periodicity of given data is assumed. A truncated Fourier spectral method has been introduced to deal with the ill-posedness of the problem. The theoretic results show that the discrepancy principle can work well for this problem. Some numerical results are also given to show the efficiency of the method.

Keywords: Analytic continuation, ill-posed problem, regularization method Fourier spectral method, the discrepancy principle.

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Authors: Rahib H. Abiyev

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In this paper the application of neuro-fuzzy system for equalization of channel distortion is considered. The structure and operation algorithm of neuro-fuzzy equalizer are described. The use of neuro-fuzzy equalizer in digital signal transmission allows to decrease training time of parameters and decrease the complexity of the network. The simulation of neuro-fuzzy equalizer is performed. The obtained result satisfies the efficiency of application of neurofuzzy technology in channel equalization.

Keywords: Neuro-fuzzy system, noise equalization, neuro-fuzzy equalizer, neural system.

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Authors: Payman Davoodi-Nasab, Ahmad Rahbar-Kelishami, Jaber Safdari, Hossein Abolghasemi

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The high purity rare earth elements (REEs) have been vastly used in the field of chemical engineering, metallurgy, nuclear energy, optical, magnetic, luminescence and laser materials, superconductors, ceramics, alloys, catalysts, and etc. Neodymium is one of the most abundant rare earths. By development of a neodymium–iron–boron (Nd–Fe–B) permanent magnet, the importance of neodymium has dramatically increased. Solvent extraction processes have many operational limitations such as large inventory of extractants, loss of solvent due to the organic solubility in aqueous solutions, volatilization of diluents, etc. One of the promising methods of liquid membrane processes is emulsion liquid membrane (ELM) which offers an alternative method to the solvent extraction processes. In this work, a study on Nd extraction through multi-walled carbon nanotubes (MWCNTs) assisted ELM using response surface methodology (RSM) has been performed. The ELM composed of diisooctylphosphinic acid (CYANEX 272) as carrier, MWCNTs as nanoparticles, Span-85 (sorbitan triooleate) as surfactant, kerosene as organic diluent and nitric acid as internal phase. The effects of important operating variables namely, surfactant concentration, MWCNTs concentration, and treatment ratio were investigated. Results were optimized using a central composite design (CCD) and a regression model for extraction percentage was developed. The 3D response surfaces of Nd(III) extraction efficiency were achieved and significance of three important variables and their interactions on the Nd extraction efficiency were found out. Results indicated that introducing the MWCNTs to the ELM process led to increasing the Nd extraction due to higher stability of membrane and mass transfer enhancement. MWCNTs concentration of 407 ppm, Span-85 concentration of 2.1 (%v/v) and treatment ratio of 10 were achieved as the optimum conditions. At the optimum condition, the extraction of Nd(III) reached the maximum of 99.03%.

Keywords: Emulsion liquid membrane, extraction of neodymium, multi-walled carbon nanotubes, response surface method.

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Authors: S.G.Venkatesh, S.K.Ayyaswamy, G.Hariharan

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In this paper, we present a framework to determine Haar solutions of Bratu-type equations that are widely applicable in fuel ignition of the combustion theory and heat transfer. The method is proposed by applying Haar series for the highest derivatives and integrate the series. Several examples are given to confirm the efficiency and the accuracy of the proposed algorithm. The results show that the proposed way is quite reasonable when compared to exact solution.

Keywords: Haar wavelet method, Bratu's problem, boundary value problems, initial value problems, adomain decomposition method.

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Authors: C. Kocatepe, E. Taslak, C. F. Kumru, O. Arıkan

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While choosing insulating oil, characteristic features such as thermal cooling, endurance, efficiency and being environment-friendly should be considered. Mineral oils are referred as petroleum-based oil. In this study, vegetable oils investigated as an alternative insulating liquid to mineral oil. Dissipation factor, breakdown voltage, relative dielectric constant and resistivity changes with the frequency and voltage of mineral, rapeseed and nut oils were measured. Experimental studies were performed according to ASTM D924 and IEC 60156 standards.

Keywords: Breakdown voltage, dielectric dissipation factor, mineral oil, vegetable oils.

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Authors: Shazia Javed, Noor Atinah Ahmad

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In this paper an efficient incomplete factorization preconditioner is proposed for the Least Mean Squares (LMS) adaptive filter. The proposed preconditioner is approximated from a priori knowledge of the factors of input correlation matrix with an incomplete strategy, motivated by the sparsity patter of the upper triangular factor in the QRD-RLS algorithm. The convergence properties of IPLMS algorithm are comparable with those of transform domain LMS(TDLMS) algorithm. Simulation results show efficiency and robustness of the proposed algorithm with reduced computational complexity.

Keywords: Autocorrelation matrix, Cholesky's factor, eigenvalue spread, Markov input.

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Authors: Bashar Al-Shboul, Sung-Hyon Myaeng

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K-Means (KM) is considered one of the major algorithms widely used in clustering. However, it still has some problems, and one of them is in its initialization step where it is normally done randomly. Another problem for KM is that it converges to local minima. Genetic algorithms are one of the evolutionary algorithms inspired from nature and utilized in the field of clustering. In this paper, we propose two algorithms to solve the initialization problem, Genetic Algorithm Initializes KM (GAIK) and KM Initializes Genetic Algorithm (KIGA). To show the effectiveness and efficiency of our algorithms, a comparative study was done among GAIK, KIGA, Genetic-based Clustering Algorithm (GCA), and FCM [19].

Keywords: Clustering, Genetic Algorithms, K-means.

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Authors: M. A. Putera, N. Yasufuku, A. Alowaisy, R. Ishikura, J. G. Hussary, A. Rifa’i

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Indonesia’s government has planned a project for a high-speed railway connecting the capital cities, Jakarta and Surabaya, about 700 km. Based on that location, it has been planning construction above the lowland soil region. The lowland soil region comprises cohesive soil with high water content and high compressibility index, which in fact, led to a settlement problem. Among the variety of railway track structures, the adoption of the ballastless track was used effectively to reduce the settlement; it provided a lightweight structure and minimized workspace. Contradictorily, deploying this thin layer structure above the lowland area was compensated with several problems, such as lack of bearing capacity and deflection behavior during traffic loading. It is necessary to combine with ground improvement to assure a settlement behavior on the clayey soil. Reflecting on the assurance of strength increment and working period, those were convinced by adopting methods such as cement-treated soil as the substructure of railway track. Particularly, evaluating mechanical properties in the field has been well known by using the plate load test and cone penetration test. However, observing an increment of mechanical properties has uncertainty, especially for evaluating cement-treated soil on the substructure. The current quality control of cement-treated soils was established by laboratory tests. Moreover, using small strain devices measurement in the laboratory can predict more reliable results that are identical to field measurement tests. Aims of this research are to show an intercorrelation of confining pressure with the initial condition of the Young’s modulus (E0), Poisson ratio (υ0) and Shear modulus (G0) within small strain ranges. Furthermore, discrepancies between those parameters were also investigated. Experimental result confirmed the intercorrelation between cement content and confining pressure with a power function. In addition, higher cement ratios have discrepancies, conversely with low mixing ratios.

Keywords: Cement content, confining pressure, high-speed railway, small strain ranges.

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Authors: Achim Kampker, Heiner H. Heimes, Mathias Ordung, Christoph Lienemann, Ansgar Hollah, Nemanja Sarovic

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Electric cars with their fast innovation cycles and their disruptive character offer a high degree of freedom regarding innovative design for remanufacturing. Remanufacturing increases not only the resource but also the economic efficiency by a prolonged product life time. The reduced power train wear of electric cars combined with high manufacturing costs for batteries allow new business models and even second life applications. Modular and intermountable designed battery packs enable the replacement of defective or outdated battery cells, allow additional cost savings and a prolongation of life time. This paper discusses opportunities for future remanufacturing value chains of electric cars and their battery components and how to address their potentials with elaborate designs. Based on a brief overview of implemented remanufacturing structures in different industries, opportunities of transferability are evaluated. In addition to an analysis of current and upcoming challenges, promising perspectives for a sustainable electric car circular economy enabled by design for remanufacturing are deduced. Two mathematical models describe the feasibility of pursuing a circular economy of lithium ion batteries and evaluate remanufacturing in terms of sustainability and economic efficiency. Taking into consideration not only labor and material cost but also capital costs for equipment and factory facilities to support the remanufacturing process, cost benefit analysis prognosticate that a remanufacturing battery can be produced more cost-efficiently. The ecological benefits were calculated on a broad database from different research projects which focus on the recycling, the second use and the assembly of lithium ion batteries. The results of this calculations show a significant improvement by remanufacturing in all relevant factors especially in the consumption of resources and greenhouse warming potential. Exemplarily suitable design guidelines for future remanufacturing lithium ion batteries, which consider modularity, interfaces and disassembly, are used to illustrate the findings. For one guideline, potential cost improvements were calculated and upcoming challenges are pointed out.

Keywords: Circular economy, electric mobility, lithium ion batteries, remanufacturing.

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Authors: Essam Al Daoud

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Gradient boosting methods have been proven to be a very important strategy. Many successful machine learning solutions were developed using the XGBoost and its derivatives. The aim of this study is to investigate and compare the efficiency of three gradient methods. Home credit dataset is used in this work which contains 219 features and 356251 records. However, new features are generated and several techniques are used to rank and select the best features. The implementation indicates that the LightGBM is faster and more accurate than CatBoost and XGBoost using variant number of features and records.

Keywords: Gradient boosting, XGBoost, LightGBM, CatBoost, home credit.

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Authors: N. M. Kamoh, M. C. Soomiyol

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In this work, a five step continuous method for the solution of third order ordinary differential equations was developed in block form using collocation and interpolation techniques of the shifted Legendre polynomial basis function. The method was found to be zero-stable, consistent and convergent. The application of the method in solving third order initial value problem of ordinary differential equations revealed that the method compared favorably with existing methods.

Keywords: Shifted Legendre polynomials, third order block method, discrete method, convergent.

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Authors: Pavel Y. Tabakov

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An accurate optimal design of laminated composite structures may present considerable difficulties due to the complexity and multi-modality of the functional design space. The Big Bang – Big Crunch (BB-BC) optimization method is a relatively new technique and has already proved to be a valuable tool for structural optimization. In the present study the exceptional efficiency of the method is demonstrated by an example of the lay-up optimization of multilayered anisotropic cylinders based on a three-dimensional elasticity solution. It is shown that, due to its simplicity and speed, the BB-BC is much more efficient for this class of problems when compared to the genetic algorithms.

Keywords: Big Bang – Big Crunch method, optimization, composite laminates, pressure vessel.

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Authors: Ali Salem Bin Samma, Rosalina Abdul Salam

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Representation and description of object shapes by the slopes of their contours or borders are proposed. The idea is to capture the essence of the features that make it easier for a shape to be stored, transmitted, compared and recognized. These features must be independent of translation, rotation and scaling of the shape. A approach is proposed to obtain high performance, efficiency and to merge the boundaries into sequence of straight line segments with the fewest possible segments. Evaluation on the performance of the proposed method is based on its comparison with established method of object shape description.

Keywords: Shape description, Shape representation and Slope.

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Authors: Meng-Cong Zheng, Yu-Sheng Chen

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The meeting behavior is a pervasive kind of interaction, which often occurs between the passenger and the shuttle. However, the meeting point set up at the Taoyuan International Airport is too far from the entry-exit, often causing passengers to stop searching near the entry-exit. When the number of people waiting for the rush hour increases, it often results in chaos in the waiting area. This study tried to find out what is the key factor to promote the rapid finding of each other between the passengers and the pick-ups. Then we implemented several design proposals to improve the meeting behavior of passengers and pick-ups based on behavior mapping and post-occupancy evaluation to enhance their meeting efficiency in unfamiliar environments. The research base is the reception hall of the second terminal of Taoyuan International Airport. Behavioral observation and mapping are implemented on the entry of inbound passengers into the welcome space, including the crowd distribution of the people who rely on the separation wall in the waiting area, the behavior of meeting and the interaction between the inbound passengers and the pick-ups. Then we redesign the space planning and signage design based on post-occupancy evaluation to verify the effectiveness of space plan and signage design. This study found that passengers ignore existing meeting-point designs which are placed on distant pillars at both ends. The position of the screen affects the area where the receiver is stranded, causing the pick-ups to block the passenger's moving line. The pick-ups prefer to wait where it is easy to watch incoming passengers and where it is closest to the mode of transport they take when leaving. Large visitors tend to gather next to landmarks, and smaller groups have a wide waiting area in the lobby. The location of the meeting point chosen by the pick-ups is related to the view of the incoming passenger. Finally, this study proposes an improved design of the meeting point, setting the traffic information in it, so that most passengers can see the traffic information when they enter the country. At the same time, we also redesigned the pick-ups desk to improve the efficiency of passenger meeting.

Keywords: Meeting point design, post-occupancy evaluation, behavioral mapping, international airport.

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Authors: A. Hadi-Vencheh, N. Shayesteh Moghadam

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Data envelopment analysis (DEA) has gained great popularity in environmental performance measurement because it can provide a synthetic standardized environmental performance index when pollutants are suitably incorporated into the traditional DEA framework. Since some of the environmental performance indicators cannot be controlled by companies managers, it is necessary to develop the model in a way that it could be applied when discretionary and/or non-discretionary factors were involved. In this paper, we present a semi-radial DEA approach to measuring environmental performance, which consists of non-discretionary factors. The model, then, has been applied on a real case.

Keywords: Environmental performance, efficiency, non-discretionary variables, data envelopment analysis.

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Authors: Zhengsheng Wang, Xiangyong Ji, Yong Du

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The projection methods, usually viewed as the methods for computing eigenvalues, can also be used to estimate pseudospectra. This paper proposes a kind of projection methods for computing the pseudospectra of large scale matrices, including orthogonalization projection method and oblique projection method respectively. This possibility may be of practical importance in applications involving large scale highly nonnormal matrices. Numerical algorithms are given and some numerical experiments illustrate the efficiency of the new algorithms.

Keywords: Pseudospectra, eigenvalue, projection method, Arnoldi, IOM(q)

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Authors: Ireneusz Majsterek, Anna Merecz, Agnieszka Sliwinska, Marcin Kosmalski, Jacek Kasznicki, Jozef Drzewoski

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Oxidative stress is considered to be the cause for onset and the progression of type 2 diabetes mellitus (T2DM) and complications including neuropathy. It is a deleterious process that can be an important mediator of damage to cell structures: protein, lipids and DNA. Data suggest that in patients with diabetes and diabetic neuropathy DNA repair is impaired, which prevents effective removal of lesions. Objective: The aim of our study was to evaluate the association of the hOGG1 (326 Ser/Cys) and XRCC1 (194 Arg/Trp, 399 Arg/Gln) gene polymorphisms whose protein is involved in the BER pathway with DNA repair efficiency in patients with diabetes type 2 and diabetic neuropathy compared to the healthy subjects. Genotypes were determined by PCR-RFLP analysis in 385 subjects, including 117 with type 2 diabetes, 56 with diabetic neuropathy and 212 with normal glucose metabolism. The polymorphisms studied include codon 326 of hOGG1 and 194, 399 of XRCC1 in the base excision repair (BER) genes. Comet assay was carried out using peripheral blood lymphocytes from the patients and controls. This test enabled the evaluation of DNA damage in cells exposed to hydrogen peroxide alone and in the combination with the endonuclease III (Nth). The results of the analysis of polymorphism were statistically examination by calculating the odds ratio (OR) and their 95% confidence intervals (95% CI) using the ¤ç2-tests. Our data indicate that patients with diabetes mellitus type 2 (including those with neuropathy) had higher frequencies of the XRCC1 399Arg/Gln polymorphism in homozygote (GG) (OR: 1.85 [95% CI: 1.07-3.22], P=0.3) and also increased frequency of 399Gln (G) allele (OR: 1.38 [95% CI: 1.03-1.83], P=0.3). No relation to other polymorphisms with increased risk of diabetes or diabetic neuropathy. In T2DM patients complicated by neuropathy, there was less efficient repair of oxidative DNA damage induced by hydrogen peroxide in both the presence and absence of the Nth enzyme. The results of our study suggest that the XRCC1 399 Arg/Gln polymorphism is a significant risk factor of T2DM in Polish population. Obtained data suggest a decreased efficiency of DNA repair in cells from patients with diabetes and neuropathy may be associated with oxidative stress. Additionally, patients with neuropathy are characterized by even greater sensitivity to oxidative damage than patients with diabetes, which suggests participation of free radicals in the pathogenesis of neuropathy.

Keywords: Diabetic neuropathy, oxidative stress, gene polymorphisms, oxidative DNA damage.

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Authors: Wang Xingbo

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Computation of determinant in the form |I-X| is primary and fundamental because it can help to compute many other determinants. This article puts forward a time-reducible approach to compute determinant |I-X|. The approach is derived from the Newton’s identity and its time complexity is no more than that to compute the eigenvalues of the square matrix X. Mathematical deductions and numerical example are presented in detail for the approach. By comparison with classical approaches the new approach is proved to be superior to the classical ones and it can naturally reduce the computational time with the improvement of efficiency to compute eigenvalues of the square matrix.

Keywords: Algorithm, determinant, computation, eigenvalue, time complexity.

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Authors: V. Tereshchenko, D. Taran

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In this paper we propose a new approach to constructing the Delaunay Triangulation and the optimum algorithm for the case of multidimensional spaces (d ≥ 2). Analysing the modern state, it is possible to draw a conclusion, that the ideas for the existing effective algorithms developed for the case of d ≥ 2 are not simple to generalize on a multidimensional case, without the loss of efficiency. We offer for the solving this problem an effective algorithm that satisfies all the given requirements. But theoretical complexity of the problem it is impossible to improve as the Worst - Case Optimality for algorithms of solving such a problem is proved.

Keywords: Delaunay triangulation, multidimensional space, Voronoi Diagram, optimal algorithm.

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