Search results for: Capacity spectrum method

Authors: Nada Jasim Habeeb, Rana Saad Mohammed, Muntaha Khudair Abbass

Abstract:

For more efficient and fast video summarization, this paper presents a surveillance video summarization method. The presented method works to improve video summarization technique. This method depends on temporal differencing to extract most important data from large video stream. This method uses histogram differencing and Sum Conditional Variance which is robust against to illumination variations in order to extract motion objects. The experimental results showed that the presented method gives better output compared with temporal differencing based summarization techniques.

Keywords: Temporal differencing, video summarization, histogram differencing, sum conditional variance.

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Authors: Sachin Bhalekar, Varsha Daftardar-Gejji

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In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.

Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: Evapotranspiration, Hargreaves equation, FAOPenman method.

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, Hermite interpolating polynomial, initial value problem, local error.

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Authors: Qiang Niu, Linzhang Lu

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Restarted GMRES methods augmented with approximate eigenvectors are widely used for solving large sparse linear systems. Recently a new scheme of augmenting with error approximations is proposed. The main aim of this paper is to develop a restarted GMRES method augmented with the combination of harmonic Ritz vectors and error approximations. We demonstrate that the resulted combination method can gain the advantages of two approaches: (i) effectively deflate the small eigenvalues in magnitude that may hamper the convergence of the method and (ii) partially recover the global optimality lost due to restarting. The effectiveness and efficiency of the new method are demonstrated through various numerical examples.

Keywords: Arnoldi process, GMRES, Krylov subspace, systems of linear equations.

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Authors: Nur Nadiah Abd Hamid, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

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Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.

Keywords: two-point boundary value problem, B-spline, extendedcubic B-spline.

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, Decomposition Method, Generalized Thermoelasticity, algorithm, empirical parameter, lattice design.

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Authors: Reza Bazargan-Lari, Mohammad Ebrahim Bahrololoom, Afshin Nemati

Abstract:

Heavy metals have bad effects on environment and soils and it can uptake by natural HAP .natural Hap is an inexpensive material that uptake large amounts of various heavy metals like Zn (II) .Natural HAP (N-HAP), extracted from bovine cortical bone ash, is a good choice for substitution of commercial HAP. Several experiments were done to investigate the sorption capacity of Zn (II) to N-HAP in various particles sizes, temperatures, initial concentrations, pH and reaction times. In this study, the sorption of Zinc ions from a Zn solution onto HAP particles with sizes of 1537.6 nm and 47.6 nm at three initial pH values of 4.50, 6.00 and 7.50 was studied. The results showed that better performance was obtained through a 47.6 nm particle size and higher pH values. The experimental data were analyzed using Langmuir, Freundlich, and Arrhenius equations for equilibrium, kinetic and thermodynamic studies. The analysis showed a maximum adsorption capacity of NHAP as being 1.562 mmol/g at a pH of 7.5 and small particle size. Kinetically, the prepared N-HAP is a feasible sorbent that retains Zn (II) ions through a favorable and spontaneous sorption process.

Keywords: Natural Hydroxyapatite, Heavy metal ions, Adsorption, Zn removal, kinetic model, bone ash

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Authors: C. Ardil

Abstract:

This paper introduces the concept of neutral sets (NSs) and explores various operations on NSs, along with their associated properties. The foundation of the Neutral Set framework lies in ontological neutrality and the principles of logic, including the Law of Non-Contradiction. By encompassing components for possibility, indeterminacy, and necessity, the NS framework provides a flexible representation of truth, uncertainty, and necessity, accommodating diverse ontological perspectives without presupposing specific existential commitments. The inclusion of Possibility acknowledges the spectrum of potential states or propositions, promoting neutrality by accommodating various viewpoints. Indeterminacy reflects the inherent uncertainty in understanding reality, refraining from making definitive ontological commitments in uncertain situations. Necessity captures propositions that must hold true under all circumstances, aligning with the principle of logical consistency and implicitly supporting the Law of Non-Contradiction. Subsequently, a neutral set-TOPSIS approach is applied in the maintenance strategy selection problem, demonstrating the practical applicability of the NS framework. The paper further explores uncertainty relations and presents the fundamental preliminaries of NS theory, emphasizing its role in fostering ontological neutrality and logical coherence in reasoning.

Keywords: Uncertainty sets, neutral sets, maintenance strategy selection multiple criteria decision-making analysis, MCDM, uncertainty decision analysis, distance function, multiple attribute, decision making, selection method, uncertainty, TOPSIS

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Authors: Roland Pusch, Richard Weston

Abstract:

The scale dependence of the strength of virtually homogeneous rock is usually considered to be insignificant but the spectrum of discontinuities plays a very important role for the strength of differently sized rock elements and also controls the rock creep strain. Large-scale load tests comprised recording of the creep strain rate that was found to be strongly retarded and negligible for stresses lower than about 1/3 of the failure load. For higher stresses creep took place according to a log time law representing secondary creep that ultimately changed to tertiary creep and failure.

Keywords: Impact of scale, rock strength.

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Authors: Yu-Chuan Chang, Chen Shi-Kai

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A water reuse system in wetland paddy was simulated to supply water for industrial in this paper. A two-tank model was employed to represent the return flow of the wetland paddy.Historical data were performed for parameter estimation and model verification. With parameters estimated from the data, the model was then used to simulate a reasonable return flow rate from the wetland paddy. The simulation results show that the return flow ratio was 11.56% in the first crop season and 35.66% in the second crop season individually; the difference may result from the heavy rainfall in the second crop season. Under the existent pond with surplus active capacity, the water reuse ratio was 17.14%, and the water supplementary ratio was 21.56%. However, the pattern of rainfall, the active capacity of the pond, and the rate of water treatment limit the volume of reuse water. Increasing the irrigation water, dredging the depth of pond before rainy season and enlarging the scale of module are help to develop water reuse system to support for the industrial water use around wetland paddy.

Keywords: Return flow, water reuse, wetland paddy, return flow ratio (RR), water reuse ratio (WRR), water supplementary ratio(WSR)

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Authors: Tibor Kulcsar, Gabor Sarossy, Gabor Bereznai, Robert Auer, Janos Abonyi

Abstract:

On-line (near infrared) spectroscopy is widely used to support the operation of complex process systems. Information extracted from spectral database can be used to estimate unmeasured product properties and monitor the operation of the process. These techniques are based on looking for similar spectra by nearest neighborhood algorithms and distance based searching methods. Search for nearest neighbors in the spectral space is an NP-hard problem, the computational complexity increases by the number of points in the discrete spectrum and the number of samples in the database. To reduce the calculation time some kind of indexing could be used. The main idea presented in this paper is to combine indexing and visualization techniques to reduce the computational requirement of estimation algorithms by providing a two dimensional indexing that can also be used to visualize the structure of the spectral database. This 2D visualization of spectral database does not only support application of distance and similarity based techniques but enables the utilization of advanced clustering and prediction algorithms based on the Delaunay tessellation of the mapped spectral space. This means the prediction has not to use the high dimension space but can be based on the mapped space too. The results illustrate that the proposed method is able to segment (cluster) spectral databases and detect outliers that are not suitable for instance based learning algorithms.

Keywords: indexing high dimensional databases, dimensional reduction, clustering, similarity, k-nn algorithm.

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Authors: Miloš Šeda

Abstract:

Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the well-known Quine-McCluskey method, which gives a unique procedure of computing and thus can be simply implemented, but, even for simple examples, does not guarantee an optimal solution. Since the Petrick extension of the Quine-McCluskey method does not give a generally usable method for finding an optimum for logical functions with a high number of values, we focus on interpretation of the result of the Quine-McCluskey method and show that it represents a set covering problem that, unfortunately, is an NP-hard combinatorial problem. Therefore it must be solved by heuristic or approximation methods. We propose an approach based on genetic algorithms and show suitable parameter settings.

Keywords: Boolean algebra, Karnaugh map, Quine-McCluskey method, set covering problem, genetic algorithm.

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Authors: Taro Matsuno, Yuta Otani, Ryo Tanaka, Kaori Ikezaki, Hitoshi Yamamoto, Masaru Fujieda, Yoshihisa Ishida

Abstract:

This paper presents an improvement method of the multiple pitch estimation algorithm using comb filters. Conventionally the pitch was estimated by using parallel -connected comb filters method (PCF). However, PCF has problems which often fail in the pitch estimation when there is the fundamental frequency of higher tone near harmonics of lower tone. Therefore the estimation is assigned to a wrong note when shared frequencies happen. This issue often occurs in estimating octave 3 or more. Proposed method, for solving the problem, estimates the pitch with every harmonic instead of every octave. As a result, our method reaches the accuracy of more than 80%.

Keywords: music transcription, pitch estimation, comb filter, fractional delay

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Authors: Ou Xie, Zhenyu Zhao

Abstract:

In this paper, we consider the problem for identifying the unknown source in the Poisson equation. A modified Tikhonov regularization method is presented to deal with illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical examples show that the proposed method is effective and stable.

Keywords: Ill-posed problem, Unknown source, Poisson equation, Tikhonov regularization method, Discrepancy principle

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Authors: Alexander B. Bichkov, Valery V. Smirnov

Abstract:

Total cross section of helium atom photo-ionization by weak short pulse is calculated using the variant of trajectory method, developed in our earlier work. The method enables simple estimation of total ionization probability (or cross section) without integration of differential one.

Keywords: Evaluation of Photo-Ionization, Helium, Trajectory Method

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Authors: Gülnihal Meral

Abstract:

In this study, the density dependent nonlinear reactiondiffusion equation, which arises in the insect dispersal models, is solved using the combined application of differential quadrature method(DQM) and implicit Euler method. The polynomial based DQM is used to discretize the spatial derivatives of the problem. The resulting time-dependent nonlinear system of ordinary differential equations(ODE-s) is solved by using implicit Euler method. The computations are carried out for a Cauchy problem defined by a onedimensional density dependent nonlinear reaction-diffusion equation which has an exact solution. The DQM solution is found to be in a very good agreement with the exact solution in terms of maximum absolute error. The DQM solution exhibits superior accuracy at large time levels tending to steady-state. Furthermore, using an implicit method in the solution procedure leads to stable solutions and larger time steps could be used.

Keywords: Density Dependent Nonlinear Reaction-Diffusion Equation, Differential Quadrature Method, Implicit Euler Method.

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Authors: F. S. Eguakun, P. O. Adesoye

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One of the major problems being faced by human society is that the global temperature is believed to be rising due to human activity that releases carbon IV Oxide (CO2) to the atmosphere. Carbon IV Oxide is the most important greenhouse gas influencing global warming and possible climate change. With climate change becoming alarming, reducing CO2 in our atmosphere has become a primary goal of international efforts. Forest lands are major sink and could absorb large quantities of carbon if the trees are judiciously managed. The study aims at estimating the carbon sequestration capacity of Pinus caribaea (pine) and Tectona grandis (Teak) under the prevailing environmental conditions and exploring tree growth variables that influences the carbon sequestration capacity in Omo Forest Reserve, Ogun State, Nigeria. Improving forest management by manipulating growth characteristics that influences carbon sequestration could be an adaptive strategy of forestry to climate change. Random sampling was used to select Temporary Sample Plots (TSPs) in the study area from where complete enumeration of growth variables was carried out within the plots. The data collected were subjected to descriptive and correlational analyses. The results showed that average carbon stored by Pine and Teak are 994.4±188.3 Kg and 1350.7±180.6 Kg respectively. The difference in carbon stored in the species is significant enough to consider choice of species relevant in climate change adaptation strategy. Tree growth variables influence the capacity of the tree to sequester carbon. Height, diameter, volume, wood density and age are positively correlated to carbon sequestration. These tree growth variables could be manipulated by the forest manager as an adaptive strategy for climate change while plantations of high wood density species could be relevant for management strategy to increase carbon storage.

Keywords: Adaptation, carbon sequestration, climate change, growth variables, wood density.

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Authors: Geng Xiangren, Liu Lei, Gui Ye-Wei, Tang Wei, Wang An-ling

Abstract:

The malfunction of thermal protection system (TPS) caused by aerodynamic heating is a latent trouble to aircraft structure safety. Accurately predicting the structure temperature field is quite important for the TPS design of hypersonic vehicle. Since Thornton’s work in 1988, the coupled method of aerodynamic heating and heat transfer has developed rapidly. However, little attention has been paid to the influence of structural deformation on aerodynamic heating and structural temperature field. In the flight, especially the long-endurance flight, the structural deformation, caused by the aerodynamic heating and temperature rise, has a direct impact on the aerodynamic heating and structural temperature field. Thus, the coupled interaction cannot be neglected. In this paper, based on the method of static aero-thermo-elasticity, considering the influence of aero-thermo-elasticity deformation, the aerodynamic heating and heat transfer coupled results of hypersonic vehicle wing model were calculated. The results show that, for the low-curvature region, such as fuselage or center-section wing, structure deformation has little effect on temperature field. However, for the stagnation region with high curvature, the coupled effect is not negligible. Thus, it is quite important for the structure temperature prediction to take into account the effect of elastic deformation. This work has laid a solid foundation for improving the prediction accuracy of the temperature distribution of aircraft structures and the evaluation capacity of structural performance.

Keywords: Aero-thermo-elasticity, elastic deformation, structural temperature, multi-field coupling.

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Authors: J. Hassan

Abstract:

Water 2H NMR signal on the surface of nano-silica material, MCM-41, consists of two overlapping resonances. The 2H water spectrum shows a superposition of a Lorentzian line shape and the familiar NMR powder pattern line shape, indicating the existence of two spin components. Chemical exchange occurs between these two groups. Decomposition of the two signals is a crucial starting point for study the exchange process. In this article we have determined these spin component populations along with other important parameters for the 2H water NMR signal over a temperature range between 223 K and 343 K.

Keywords: Nano-Silica, surface water, NMR

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Authors: Swadhin Kumar Mishra, Sidhartha Panda, C. Ardil

Abstract:

Multiple-Input-Multiple-Output (MIMO) is one of the most important communication techniques that allow wireless systems to achieve higher data rate. To overcome the practical difficulties in implementing Dirty Paper Coding (DPC), various suboptimal MIMO Broadcast (MIMO-BC) scheduling algorithms are employed which choose the best set of users among all the users. In this paper we discuss such a sub-optimal MIMO-BC scheduling algorithm which employs antenna selection at the receiver side. The channels for the users considered here are not Identical and Independent Distributed (IID) so that users at the receiver side do not get equal opportunity for communication. So we introduce a method of applying weights to channels of the users which are not IID in such a way that each of the users gets equal opportunity for communication. The effect of weights on overall sum-rate achieved by the system has been investigated and presented.

Keywords: Antenna selection, Identical and Independent Distributed (IID), Sum-rate capacity, Weighted sum rate.

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Authors: Amal Elmzabi, Mostafa Bellafkih, Mohammed Ramdani

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The Chiu-s method which generates a Takagi-Sugeno Fuzzy Inference System (FIS) is a method of fuzzy rules extraction. The rules output is a linear function of inputs. In addition, these rules are not explicit for the expert. In this paper, we develop a method which generates Mamdani FIS, where the rules output is fuzzy. The method proceeds in two steps: first, it uses the subtractive clustering principle to estimate both the number of clusters and the initial locations of a cluster centers. Each obtained cluster corresponds to a Mamdani fuzzy rule. Then, it optimizes the fuzzy model parameters by applying a genetic algorithm. This method is illustrated on a traffic network management application. We suggest also a Mamdani fuzzy rules generation method, where the expert wants to classify the output variables in some fuzzy predefined classes.

Keywords: Fuzzy entropy, fuzzy inference systems, genetic algorithms, network management, subtractive clustering.

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Authors: Essam S. Altubaishi

Abstract:

The motivation for adaptive modulation and coding is to adjust the method of transmission to ensure that the maximum efficiency is achieved over the link at all times. The receiver estimates the channel quality and reports it back to the transmitter. The transmitter then maps the reported quality into a link mode. This mapping however, is not a one-to-one mapping. In this paper we investigate a method for selecting the proper modulation scheme. This method can dynamically adapt the mapping of the Signal-to- Noise Ratio (SNR) into a link mode. It enables the use of the right modulation scheme irrespective of changes in the channel conditions by incorporating errors in the received data. We propose a Markov model for this method, and use it to derive the average switching thresholds and the average throughput. We show that the average throughput of this method outperforms the conventional threshold method.

Keywords: Adaptive modulation and coding, CDMA, Markov model.

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Authors: A. M. Sagir

Abstract:

Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVP­s­) in ordinary differential equations (ODE­s­) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: Block Method, First Order Ordinary Differential Equations, Hybrid, Self starting.

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Authors: Jalal Soleimannejad, Mohammad Asadizeidabadi, Mahmoud Koorki, Mojtaba Azarpira

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A significant percentage of production costs is the maintenance costs, and analysis of maintenance costs could to achieve greater productivity and competitiveness. With this is mind, the maintenance of machines and installations is considered as an essential part of organizational functions and applying effective strategies causes significant added value in manufacturing activities. Organizations are trying to achieve performance levels on a global scale with emphasis on creating competitive advantage by different methods consist of RCM (Reliability-Center-Maintenance), TPM (Total Productivity Maintenance) etc. In this study, increasing the capacity of Concentration Plant of Golgohar Iron Ore Mining & Industrial Company (GEG) was examined by using of reliability and maintainability analyses. The results of this research showed that instead of increasing the number of machines (in order to solve the bottleneck problems), the improving of reliability and maintainability would solve bottleneck problems in the best way. It should be mention that in the abovementioned study, the data set of Concentration Plant of GEG as a case study, was applied and analyzed.

Keywords: Bottleneck, Golgohar Iron Ore Mining and Industrial Company, maintainability, maintenance costs, reliability.

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Authors: Yong-Gyu Lee, Gilwon Yoon

Abstract:

Automatic detection of bleeding is of practical importance since capsule endoscopy produces an extremely large number of images. Algorithm development of bleeding detection in the digestive tract is difficult due to different contrasts among the images, food dregs, secretion and others. In this study, were assigned weighting factors derived from the independent features of the contrast and brightness between bleeding and normality. Spectral analysis based on weighting factors was fast and accurate. Results were a sensitivity of 87% and a specificity of 90% when the accuracy was determined for each pixel out of 42 endoscope images.

Keywords: bleeding, capsule endoscopy, image analysis, weighted spectrum

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Authors: Mohammad Hadi Zohdi, Mohamad Reza Dalvand, Maryam Zohdi

Abstract:

In this research relationship between to be smooth the interest and output of accepted companies stock at negotiable paper exchange of Tehran is studied. Static community capacity included 363 companies member of negotiable paper exchange of Tehran that 54 companies were, by considering research limitation, selected from 2004 to 2009. Needed data for model test in librarian method was chosen from RAH AVARDE NOVIN informative banks, TADBIR and collecting needed data was selected from Tehran negotiable paper exchange archive. Given results show that in spite of belief among people based on companies have more smooth interest have more output, but resulted outcomes of test-done reveals that there is no relation between smooth interest and stock output.

Keywords: Smooth interest, interest fluctuation, interest level, output average, cost capital

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Authors: Nighat Mir, Sayed Afaq Hussain

Abstract:

Advent enhancements in the field of computing have increased massive use of web based electronic documents. Current Copyright protection laws are inadequate to prove the ownership for electronic documents and do not provide strong features against copying and manipulating information from the web. This has opened many channels for securing information and significant evolutions have been made in the area of information security. Digital Watermarking has developed into a very dynamic area of research and has addressed challenging issues for digital content. Watermarking can be visible (logos or signatures) and invisible (encoding and decoding). Many visible watermarking techniques have been studied for text documents but there are very few for web based text. XML files are used to trade information on the internet and contain important information. In this paper, two invisible watermarking techniques using Synonyms and Acronyms are proposed for XML files to prove the intellectual ownership and to achieve the security. Analysis is made for different attacks and amount of capacity to be embedded in the XML file is also noticed. A comparative analysis for capacity is also made for both methods. The system has been implemented using C# language and all tests are made practically to get the results.

Keywords: Watermarking, Extensible Markup Language (XML), Synonyms, Acronyms, Copyright protection.

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Authors: Mazin Z. Othman, Maan M. Shaker, Mohammed F. Abdullah

Abstract:

This study introduces a new method for detecting, sorting, and localizing spikes from multiunit EEG recordings. The method combines the wavelet transform, which localizes distinctive spike features, with Super-Paramagnetic Clustering (SPC) algorithm, which allows automatic classification of the data without assumptions such as low variance or Gaussian distributions. Moreover, the method is capable of setting amplitude thresholds for spike detection. The method makes use of several real EEG data sets, and accordingly the spikes are detected, clustered and their times were detected.

Keywords: EEG time localizations, EEG spike detection, superparamagnetic algorithm, wavelet transform.

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Authors: A. O. Salami

Abstract:

The transportation problems are primarily concerned with the optimal way in which products produced at different plants (supply origins) are transported to a number of warehouses or customers (demand destinations). The objective in a transportation problem is to fully satisfy the destination requirements within the operating production capacity constraints at the minimum possible cost. The objective of this study is to determine ways of minimizing transportation cost in order to maximum profit. Data were sourced from the records of the Distribution Department of 7-Up Bottling Company Plc., Ilorin, Kwara State, Nigeria. The data were computed and analyzed using the three methods of solving transportation problem. The result shows that the three methods produced the same total transportation costs amounting to N1, 358, 019, implying that any of the method can be adopted by the company in transporting its final products to the wholesale dealers in order to minimize total production cost. 

Keywords: Allocation problem, Cost Minimization, Distribution system, Resources utilization.

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