Search results for: Historical Square

Authors: B. Rebekka, B. Malarkodi

Abstract:

This paper describes an approach to detect the transmitted signals for 2×2 Multiple Input Multiple Output (MIMO) setup using roulette wheel based ant colony optimization technique. The results obtained are compared with classical zero forcing and least mean square techniques. The detection rates achieved using this technique are consistently larger than the one achieved using classical methods for 50 number of attempts with two different antennas transmitting the input stream from a user. This paves the path to use alternative techniques to improve the throughput achieved in advanced networks like Long Term Evolution (LTE) networks.

Keywords: MIMO, ant colony optimization, roulette wheel, soft computing, LTE.

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: Arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation.

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Authors: Hy Dang, Bo Mei

Abstract:

The development of machine learning methods and techniques has opened doors for investigation in many areas such as medicines, economics, finance, etc. One active research area involving machine learning is stock market prediction. This research paper tries to consider multiple techniques and methods for stock movement prediction using historical price or price factors. The paper explores the effectiveness of some deep learning frameworks for forecasting stock. Moreover, an architecture (TimeStock) is proposed which takes the representation of time into account apart from the price information itself. Our model achieves a promising result that shows a potential approach for the stock movement prediction problem.

Keywords: Classification, machine learning, time representation, stock prediction.

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Authors: Krishnamoorthy R, Rajavijayalakshmi K, Punidha R

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In this paper, a near lossless image coding scheme based on Orthogonal Polynomials Transform (OPT) has been presented. The polynomial operators and polynomials basis operators are obtained from set of orthogonal polynomials functions for the proposed transform coding. The image is partitioned into a number of distinct square blocks and the proposed transform coding is applied to each of these individually. After applying the proposed transform coding, the transformed coefficients are rearranged into a sub-band structure. The Embedded Zerotree (EZ) coding algorithm is then employed to quantize the coefficients. The proposed transform is implemented for various block sizes and the performance is compared with existing Discrete Cosine Transform (DCT) transform coding scheme.

Keywords: Near-lossless Coding, Orthogonal Polynomials Transform, Embedded Zerotree Coding

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Authors: Elteyeb Eljack, Takashi Ohta

Abstract:

Proper orthogonal decomposition (POD) is used to reconstruct spatio-temporal data of a fully developed turbulent channel flow with density variation at Reynolds number of 150, based on the friction velocity and the channel half-width, and Prandtl number of 0.71. To apply POD to the fully developed turbulent channel flow with density variation, the flow field (velocities, density, and temperature) is scaled by the corresponding root mean square values (rms) so that the flow field becomes dimensionless. A five-vector POD problem is solved numerically. The reconstructed second-order moments of velocity, temperature, and density from POD eigenfunctions compare favorably to the original Direct Numerical Simulation (DNS) data.

Keywords: Pattern Recognition, POD, Coherent Structures, Low dimensional modelling.

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Authors: Md. Sharif Imam Ibne Amir, Mohammad Masud Kamal khan, Mohammad Golam Rasul, Raj H Sharma, Fatema Akram

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Future flood can be predicted using the probable maximum flood (PMF). PMF is calculated using the historical discharge or rainfall data considering the other climatic parameters remaining stationary. However climate is changing globally and the key climatic variables are temperature, evaporation, rainfall and sea level rise are likely to change. To develop scenarios to a basin or catchment scale these important climatic variables should be considered. Nowadays scenario based on climatic variables is more suitable than PMF. Six scenarios were developed for a large Fitzroy basin and presented in this paper.

Keywords: Climate change, rainfall, potential evaporation, scenario, sea level rise (SLR), sub-catchment.

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Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In statistics parameter theory, usually the parameter estimations have two kinds, one is the least-square estimation (LSE), and the other is the best linear unbiased estimation (BLUE). Due to the determining theorem of minimum variance unbiased estimator (MVUE), the parameter estimation of BLUE in linear model is most ideal. But since the calculations are complicated or the covariance is not given, people are hardly to get the solution. Therefore, people prefer to use LSE rather than BLUE. And this substitution will take some losses. To quantize the losses, many scholars have presented many kinds of different relative efficiencies in different views. For the linear weighted regression model, this paper discusses the relative efficiencies of LSE of β to BLUE of β. It also defines two new relative efficiencies and gives their lower bounds.

Keywords: Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation.

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Authors: Alexander J. Severinsky

Abstract:

Radiative forces of greenhouse gases (GHG) increase the temperature of the Earth's surface, more on land, and less in oceans, due to their thermal capacities. Given this inertia, the temperature increase is delayed over time. Air temperature, however, is not delayed as air thermal capacity is much lower. In this study, through analysis and synthesis of multidisciplinary science and data, an estimate of atmospheric temperature increase is made. Then, this estimate is used to shed light on current observations of ice and snow loss, desertification and forest fires, and increased extreme air disturbances. The reason for this inquiry is due to the author’s skepticism that current changes cannot be explained by a "~1 ^oC" global average surface temperature rise within the last 50-60 years. The only other plausible cause to explore for understanding is that of atmospheric temperature rise. The study utilizes an analysis of air temperature rise from three different scientific disciplines: thermodynamics, climate science experiments, and climactic historical studies. The results coming from these diverse disciplines are nearly the same, within ± 1.6%. The direct radiative force of GHGs with a high level of scientific understanding is near 4.7 W/m² on average over the Earth’s entire surface in 2018, as compared to one in pre-Industrial time in the mid-1700s. The additional radiative force of fast feedbacks coming from various forms of water gives approximately an additional ~15 W/m². In 2018, these radiative forces heated the atmosphere by approximately 5.1 ^oC, which will create a thermal equilibrium average ground surface temperature increase of 4.6 ^oC to 4.8 ^oC by the end of this century. After 2018, the temperature will continue to rise without any additional increases in the concentration of the GHGs, primarily of carbon dioxide and methane. These findings of the radiative force of GHGs in 2018 were applied to estimates of effects on major Earth ecosystems. This additional force of nearly 20 W/m² causes an increase in ice melting by an additional rate of over 90 cm/year, green leaves temperature increase by nearly 5 ^oC, and a work energy increase of air by approximately 40 Joules/mole. This explains the observed high rates of ice melting at all altitudes and latitudes, the spread of deserts and increases in forest fires, as well as increased energy of tornadoes, typhoons, hurricanes, and extreme weather, much more plausibly than the 1.5 ^oC increase in average global surface temperature in the same time interval. Planned mitigation and adaptation measures might prove to be much more effective when directed toward the reduction of existing GHGs in the atmosphere.

Keywords: GHG radiative forces, GHG air temperature, GHG thermodynamics, GHG historical, GHG experimental, GHG radiative force on ice, GHG radiative force on plants, GHG radiative force in air.

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Authors: Noor Atinah Ahmad, Shazia Javed

Abstract:

We present a discussion of three adaptive filtering algorithms well known for their one-step termination property, in terms of their relationship with the minimal residual method. These algorithms are the normalized least mean square (NLMS), Affine Projection algorithm (APA) and the recursive least squares algorithm (RLS). The NLMS is shown to be a result of the orthogonality condition imposed on the instantaneous approximation of the Wiener equation, while APA and RLS algorithm result from orthogonality condition in multi-dimensional minimal residual formulation. Further analysis of the minimal residual formulation for the RLS leads to a triangular system which also possesses the one-step termination property (in exact arithmetic)

Keywords: Adaptive filtering, minimal residual method, projection method.

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Authors: Shih-Ching Lo

Abstract:

Discrete choice model is the most used methodology for studying traveler-s mode choice and demand. However, to calibrate the discrete choice model needs to have plenty of questionnaire survey. In this study, an aggregative model is proposed. The historical data of passenger volumes for high speed rail and domestic civil aviation are employed to calibrate and validate the model. In this study, different models are compared so as to propose the best one. From the results, systematic equations forecast better than single equation do. Models with the external variable, which is oil price, are better than models based on closed system assumption.

Keywords: forecasting, passenger volume, dynamic competition model, external variable, oil price

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Authors: Nikou Javadi, Uğur Dağlı

Abstract:

The importance of culture and tourism in the attractiveness and competitiveness of the countries is central, and many regions are evidencing their cultural assets, tangible and intangible, as a means to create comparative advantages in tourism and produce a distinctive place in response to the pressures of globalization. Culture and tourism are interlinked because of their obvious combination and growth potential. Cultural tourism is a crucial global tourism market with fast growing. Regions can develop significant relations between culture and tourism to increase their attractiveness as places to visit, live and invest, increasing their competitiveness. Accordingly, having new and creative approach to historical areas as cultural value-based destinations can improve their conditions to promote tourism. Furthermore, in 21st century, media become the most important factor affecting the development of urban cities, including public places. As a result of the digital revolution, re-imaging and re-linkage public places by media are essential to create more interactions between public spaces and users, interaction media display, and urban screens, one of the most important defined media. This interaction can transform the urban space from being neglected to be more interactive space with users, especially the pedestrians. The paper focuses on The Walled City of Famagusta. As many other historic quarters elsewhere in the world, is in a process, of decay and deterioration, and its functionally distinctive areas are severely threatened by physical, functional, locational, and image obsolescence at varying degrees. So the focus on the future development of this area through tourism promotion can be an appropriate decision for the monument enhancement of the spatial quality in Walled City of Famagusta. In this paper, it is aimed to identify the effects of these new digital factors to transform public spaces especially in historic urban areas to promote creative tourism. Accordingly, two different analysis methods are used as well as a theoretical review. The first is case study on site and the second is Close ended questionnaire, test many concepts raised in this paper. The physical analysis on site carried out in order to evaluate the walled city restoration for touristic purpose. Besides, theoretical review is done in order to provide background to the subject and cleared Factors to attract tourists.

Keywords: Historical areas, Media Facade, Sustainable tourism, Walled city of Famagusta.

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Authors: Carla E. O. de Moraes, Gladson O. Antunes, Mauro A. Rincon

Abstract:

The aim of this paper is to study the internal stabilization of the Bernoulli-Euler equation numerically. For this, we consider a square plate subjected to a feedback/damping force distributed only in a subdomain. An algorithm for obtaining an approximate solution to this problem was proposed and implemented. The numerical method used was the Finite Difference Method. Numerical simulations were performed and showed the behavior of the solution, confirming the theoretical results that have already been proved in the literature. In addition, we studied the validation of the numerical scheme proposed, followed by an analysis of the numerical error; and we conducted a study on the decay of the energy associated.

Keywords: Bernoulli-Euler Plate Equation, Numerical Simulations, Stability, Energy Decay, Finite Difference Method.

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Authors: Hasan.O. Farahneh, Ayman A. Issa

Abstract:

Software development is moving towards agility with use cases and scenarios being used for requirements stories. Estimates of software costs are becoming even more important than before as effects of delays is much larger in successive short releases context of agile development. Thus, this paper reports on the development of new linear use case based software cost estimation model applicable in the very early stages of software development being based on simple metric. Evaluation showed that accuracy of estimates varies between 43% and 55% of actual effort of historical test projects. These results outperformed those of wellknown models when applied in the same context. Further work is being carried out to improve the performance of the proposed model when considering the effect of non-functional requirements.

Keywords: Metrics, Software Cost Estimation, Use Cases

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Authors: Sajjad Seifoori

Abstract:

Impact behavior of striker on graphene sheet and carbon nanotube is investigated based on molecular dynamics (MD) simulations. A MD simulation is conducted to obtain the maximum dynamic deflections of a square and rectangular single-layered graphene sheets (SLGSs) with various values of side-length and striker parameter. Effect of (i) chirality, (ii) graphene side-length and nanotube length, (iii) striker mass on the maximum dynamic deflections of graphene and nanotube are investigated. The effect of different types of boundary condition on the maximum dynamic deflections is studied for zigzag and armchair SWCNTs with various aspect ratios (Length/Diameter).

Keywords: Impact, molecular dynamic, graphene, nanotube.

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Authors: Sutthawee Suwannarat, Thanate Khaorapapong, Mitchai Chongcheawchamnan

Abstract:

In this paper, an ultrasonic technique is proposed to predict oil content in a fresh palm fruit. This is accomplished by measuring the attenuation based on ultrasonic transmission mode. Several palm fruit samples with known oil content by Soxhlet extraction (ISO9001:2008) were tested with our ultrasonic measurement. Amplitude attenuation data results for all palm samples were collected. The Feedforward Neural Networks (FNNs) are applied to predict the oil content for the samples. The Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) of the FNN model for predicting oil content percentage are 7.6186 and 5.2287 with the correlation coefficient (R) of 0.9193.

Keywords: Non-destructive, ultrasonic testing, oil content, fresh palm fruit, neural network.

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Authors: A. Daftari, W. Kudla

Abstract:

Liquefaction is a phenomenon in which the strength  and stiffness of a soil is reduced by earthquake shaking or other rapid  cyclic loading. Liquefaction and related phenomena have been  responsible for huge amounts of damage in historical earthquakes  around the world.  Modeling of soil behavior is the main step in soil liquefaction  prediction process. Nowadays, several constitutive models for sand  have been presented. Nevertheless, only some of them can satisfy this  mechanism. One of the most useful models in this term is  UBCSAND model. In this research, the capability of this model is  considered by using PLAXIS software. The real data of superstition  hills earthquake 1987 in the Imperial Valley was used. The results of  the simulation have shown resembling trend of the UBC3D-PLM  model. 

Keywords: Liquefaction, Plaxis, Pore-Water pressure, UBC3D-PLM.

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Authors: Kargarnovin M.H., Faghidian S. A, Arghavani J.

Abstract:

The limit load carrying capacity of functionally graded materials (FGM) circular plates subjected to an arbitrary rotationally symmetric loading has been computed. It is provided that the plate material behaves rigid perfectly plastic and obeys either the Square or the Tresca yield criterion. To this end the upper and lower bound principles of limit analysis are employed to determine the exact value for the limiting load. The correctness of the result are verified and finally limiting loads for two examples namely; through radius and through thickness FGM circular plates with simply supported edges are calculated, respectively and moreover, the values of critical loading factor are determined.

Keywords: Circular plate, FGM circular plate, Limit analysis, Lower and Upper bound theorems.

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Authors: Norashikin Ahmad, Damminda Alahakoon

Abstract:

Self-organizing map (SOM) provides both clustering and visualization capabilities in mining data. Dynamic self-organizing maps such as Growing Self-organizing Map (GSOM) has been developed to overcome the problem of fixed structure in SOM to enable better representation of the discovered patterns. However, in mining large datasets or historical data the hierarchical structure of the data is also useful to view the cluster formation at different levels of abstraction. In this paper, we present a technique to generate concept trees from the GSOM. The formation of tree from different spread factor values of GSOM is also investigated and the quality of the trees analyzed. The results show that concept trees can be generated from GSOM, thus, eliminating the need for re-clustering of the data from scratch to obtain a hierarchical view of the data under study.

Keywords: dynamic self-organizing map, concept formation, clustering.

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Authors: Abhijit Mitra

Abstract:

we propose a new normalized LMS (NLMS) algorithm, which gives satisfactory performance in certain applications in comaprison with con-ventional NLMS recursion. This new algorithm can be treated as a block based simplification of NLMS algorithm with significantly reduced number of multi¬ply and accumulate as well as division operations. It is also shown that such a recursion can be easily implemented in block floating point (BFP) arithmetic, treating the implementational issues much efficiently. In particular, the core challenges of a BFP realization to such adaptive filters are mainly considered in this regard. A global upper bound on the step size control parameter of the new algorithm due to BFP implementation is also proposed to prevent overflow in filtering as well as weight updating operations jointly.

Keywords: Adaptive algorithm, Block floating point arithmetic, Implementation issues, Normalized least mean square methods

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Authors: Z. Masoumi, B. Moaveni

Abstract:

This article is about first step of structural health monitoring by identifying structural system in the presence of unknown input. In the structural system identification, identification of structural parameters such as stiffness and damping are considered. In this study, the Kalman filter (KF) design for structural systems with unknown excitation is expressed. External excitations, such as earthquakes, wind or any other forces are not measured or not available. The purpose of this filter is its strengths to estimate the state variables of the system in the presence of unknown input. Also least squares estimation (LSE) method with unknown input is studied. Estimates of parameters have been adopted. Finally, using two examples advantages and drawbacks of both methods are studied.

Keywords: Structural health monitoring, Kalman filter, Least square estimation, structural system identification.

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Authors: Neha Khanduja

Abstract:

This paper presents a comparative analysis of continuously stirred tank reactor (CSTR) control based on adaptive control and optimal tuning of PID control based on particle swarm optimization. In the design of adaptive control, Model reference adaptive control (MRAC) scheme is used, in which the adaptation law have been developed by MIT rule & Lyapunov’s rule. In PSO control parameters of PID controller is tuned by using the concept of particle swarm optimization to get optimized operating point for minimum integral square error (ISE) condition. The results show the adjustment of PID parameters converting into the optimal operating point and the good control response can be obtained by the PSO technique.

Keywords: Model reference adaptive control (MRAC), optimal control, particle swarm optimization (PSO).

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Authors: R. Nouri, M.R. Jafari, M. Arain., F. Feizi

Abstract:

The Mahin area is a part of Tarom- Hashtjin zone that located in west of Qazvin province in northwest of Iran. Many copper and base metals ore deposits are hosted by this zone. High potential localities identification in this area is very necessary. The objective of this research, is finding hydrothermal alteration zones by remote sensing methods and best processing technique of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data. Different methods such as band ratio, Principal Component Analysis (PCA), Minimum Noise Fraction (MNF) and Least Square Fit (LS-Fit) were used for mapping hydrothermal alteration zones.

Keywords: Hydrothermal alteration, Iran, Mahin, Remote sensing

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Authors: R. Nandikeswari, M. Sambasivam, V. Anandan

Abstract:

In the present study fecundity of Terapon jarbua was estimated for 41 matured females from the Bay of Bengal, Pondicherry. The fecundity (F) was found to range from 13,475 to 115,920 in fishes between 173-278mm Total length (TL) and 65- 298 gm weight respectively. The co-efficient of correlation for F/TL (log F = - 4.821 + 4.146 log TL), F/SL (log F = -3.936 + 3.867 log SL), F/WF (log F = 1.229 + 0.730 log TW) and F/GW (log F = 0.724 + 1.113 log GW) were obtained as 0.474, 0.537, 0.641 and 0.908 respectively. The regression line for the TL, SL, WF and GW of the fishes were found to be linear when they were plotted against their fecundity on logarithmic scales. Highly significant (P<0.01) relationship was obtained for all the variables. Hence Total Length, Standard Length, Weight of Fish and Gonad Weight were found to be the best indicators of the fecundity of Terapon jarbua. Gonadosomatic indices of Terapon jarbua showed that the spawning took place in February to July. The overall sex ratio of male to female is 1.28:1 with chi-square value 5.719, significant at 5% level.

Keywords: Fecundity, Gonadosomatic index, Reproductive biology, spawning, Terapon jarbua.

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Authors: M. Arja, G. Sauce, B. Souyri

Abstract:

Overall cost is a significant consideration in any decision-making process. Although many studies were carried out on overall cost in construction, little has treated the uncertainties of real life cycle development. On the basis of several case studies, a feedback process was performed on the historical data of studied buildings. This process enabled to identify some factors causing uncertainty during the operational period. As a result, the research proposes a new method for assessing the overall cost during a part of the building-s life cycle taking account of the building actual value, its end-of-life value and the influence of the identified life cycle uncertainty factors. The findings are a step towards a higher level of reliability in overall cost evaluation taking account of some usually unexpected uncertainty factors.

Keywords: Asset management, building life cycle uncertainty, building value, overall cost.

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Authors: Edem K. Bankas, Kazeem A. Gbolagade

Abstract:

In this paper, we propose a new efficient reverse converter for the 4-moduli set {2ⁿ, 2ⁿ + 1, 2ⁿ − 1, 2²ⁿ⁺¹ – 1} based on a modified Chinese Remainder Theorem and Mixed Radix Conversion. Additionally, the resulting architecture is further reduced to obtain a reverse converter that utilizes only carry save adders, a multiplexer and carry propagate adders. The proposed converter has an area cost of (12n + 2) FAs and (5n + 1) HAs with a delay of (9n + 6)t_FA + t_MUX. When compared with state of the art, our proposal demonstrates to be faster, at the expense of slightly more hardware resources. Further, the Area-Time square metric was computed which indicated that our proposed scheme outperforms the state of the art reverse converter.

Keywords: Modified Chinese Remainder Theorem, Mixed Radix Conversion, Reverse Converter, Carry Save Adder, Carry Propagate Adder.

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Authors: Siraa Ben Ftima, Mourad Talbi, Tahar Ezzedine

Abstract:

In this paper, we present a technique of secure watermarking of grayscale and color images. This technique consists in applying the Singular Value Decomposition (SVD) in LWT (Lifting Wavelet Transform) domain in order to insert the watermark image (grayscale) in the host image (grayscale or color image). It also uses signature in the embedding and extraction steps. The technique is applied on a number of grayscale and color images. The performance of this technique is proved by the PSNR (Pick Signal to Noise Ratio), the MSE (Mean Square Error) and the SSIM (structural similarity) computations.

Keywords: Color image, grayscale image, singular values decomposition, lifting wavelet transform, image watermarking, watermark, secure.

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Authors: Anna Romanova, Morteza A. Alani

Abstract:

Corrosion of concrete sewer pipes induced by sulfuric acid is an acknowledged problem and a ticking time-bomb to sewer operators. Whilst the chemical reaction of the corrosion process is well-understood, the indirect roles of other parameters in the corrosion process which are found in sewer environment are not highly reflected on. This paper reports on a field studies undertaken in Austria and United Kingdom, where the parameters of temperature, pH, H2S and CO2 were monitored over a period of time. The study establishes that (i) effluent temperature and pH have similar daily pattern and peak times, when examined in minutes scale; (ii) H2S and CO2 have an identical hourly pattern; (iii) H2S instant or shifted relation to effluent temperature is governed by the root mean square value of CO2.

Keywords: Concrete corrosion, carbon dioxide, hydrogen sulphide, sewer pipe, sulfuric acid.

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Authors: Tomáš Seidler, Marek Mihola, Denisa Cihlarova

Abstract:

The article presents analysis results of maps of expected subsidence in undermined areas for road repair management. The analysis was done in the area of Karvina district in the Czech Republic, including undermined areas with ongoing deep mining activities or finished deep mining in years 2003 - 2009. The article discusses the possibilities of local road maintenance authorities to determine areas that will need most repairs in the future with limited data available. Using the expected subsidence maps new map of surface curvature was calculated. Combined with road maps and historical data about repairs the result came for five main categories of undermined areas, proving very simple tool for management.

Keywords: GIS, Map of Subsidence, Road, Undermined Area

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Authors: F. Z. Doğru, O. Arslan

Abstract:

In general, classical methods such as maximum likelihood (ML) and least squares (LS) estimation methods are used to estimate the shape parameters of the Burr XII distribution. However, these estimators are very sensitive to the outliers. To overcome this problem we propose alternative robust estimators based on the M-estimation method for the shape parameters of the Burr XII distribution. We provide a small simulation study and a real data example to illustrate the performance of the proposed estimators over the ML and the LS estimators. The simulation results show that the proposed robust estimators generally outperform the classical estimators in terms of bias and root mean square errors when there are outliers in data.

Keywords: Burr XII distribution, robust estimator, M-estimator, maximum likelihood, least squares.

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Authors: Samia Salah, M’hamed Hadj Sadok, Abderrezak Guessoum

Abstract:

In this paper, we propose a new modular approach called neuroglial consisting of two neural networks slow and fast which emulates a biological reality recently discovered. The implementation is based on complex multi-time scale systems; validation is performed on the model of the asynchronous machine. We applied the geometric approach based on the Gerschgorin circles for the decoupling of fast and slow variables, and the method of singular perturbations for the development of reductions models.

This new architecture allows for smaller networks with less complexity and better performance in terms of mean square error and convergence than the single network model.

Keywords: Gerschgorin’s Circles, Neuroglial Network, Multi time scales systems, Singular perturbation method.

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