Search results for: Clustering functions

Authors: Sheetal Sharma

Abstract:

Runoff,decreasing water levels and recharge in urban areas have been a complex issue now a days pointing defective urban design and increasing demography as cause. Very less has been discussed or analysed for water sensitive Urban Master Plans or local area plans. Land use planning deals with land transformation from natural areas into developed ones, which lead to changes in natural environment. Elaborated knowledge of relationship between the existing patterns of land use-land cover and recharge with respect to prevailing soil below is less as compared to speed of development. The parameters of incompatibility between urban functions and the functions of the natural environment are becoming various. Changes in land patterns due to built up, pavements, roads and similar land cover affects surface water flow seriously. It also changes permeability and absorption characteristics of the soil. Urban planners need to know natural processes along with modern means and best technologies available,as there is a huge gap between basic knowledge of natural processes and its requirement for balanced development planning leading to minimum impact on water recharge. The present paper analyzes the variations in land use land cover and their impacts on surface flows and sub-surface recharge in study area. The methodology adopted was to analyse the changes in land use and land cover using GIS and Civil 3d auto cad. The variations were used in  computer modeling using Storm-water Management Model to find out the runoff for various soil groups and resulting recharge observing water levels in POW data for last 40 years of the study area. Results were anlayzed again to find best correlations for sustainable recharge in urban areas.

Keywords: Geology, runoff, urban planning, land use-land cover.

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Authors: H. Shayeghi, A. Jalili

Abstract:

This paper presents a new Hybrid Fuzzy (HF) PID type controller based on Genetic Algorithms (GA-s) for solution of the Automatic generation Control (AGC) problem in a deregulated electricity environment. In order for a fuzzy rule based control system to perform well, the fuzzy sets must be carefully designed. A major problem plaguing the effective use of this method is the difficulty of accurately constructing the membership functions, because it is a computationally expensive combinatorial optimization problem. On the other hand, GAs is a technique that emulates biological evolutionary theories to solve complex optimization problems by using directed random searches to derive a set of optimal solutions. For this reason, the membership functions are tuned automatically using a modified GA-s based on the hill climbing method. The motivation for using the modified GA-s is to reduce fuzzy system effort and take large parametric uncertainties into account. The global optimum value is guaranteed using the proposed method and the speed of the algorithm-s convergence is extremely improved, too. This newly developed control strategy combines the advantage of GA-s and fuzzy system control techniques and leads to a flexible controller with simple stricture that is easy to implement. The proposed GA based HF (GAHF) controller is tested on a threearea deregulated power system under different operating conditions and contract variations. The results of the proposed GAHF controller are compared with those of Multi Stage Fuzzy (MSF) controller, robust mixed H2/H∞ and classical PID controllers through some performance indices to illustrate its robust performance for a wide range of system parameters and load changes.

Keywords: AGC, Hybrid Fuzzy Controller, Deregulated Power System, Power System Control, GAs.

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Authors: M. Ben Slimene, M.-S. Ouali

Abstract:

Asset management of urban infrastructures faces a multitude of challenges that need to be overcome to obtain a reliable measurement of performances. Predicting the performance of slowly aging systems is one of those challenges, which helps the asset manager to investigate specific failure modes and to undertake the appropriate maintenance and rehabilitation interventions to avoid catastrophic failures as well as to optimize the maintenance costs. This article presents a methodology for modeling the deterioration of slowly degrading assets based on an operating history. It consists of extracting degradation profiles by grouping together assets that exhibit similar degradation sequences using an unsupervised classification technique derived from artificial intelligence. The obtained clusters are used to build the performance prediction models. This methodology is applied to a sample of a stormwater drainage culvert dataset.

Keywords: Artificial intelligence, clustering, culvert, regression model, slow degradation.

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Authors: Ali Nouri

Abstract:

Neuroeducation is one of the most exciting research fields which is continually evolving. However, there is a need to develop its theoretical bases in connection to practice. The present paper is a starting attempt in this regard to provide a space from which to think about neuroeducational theory and invoke more investigation in this area. Accordingly, a comprehensive theory of neuroeducation could be defined as grouping or clustering of concepts and propositions that describe and explain the nature of human learning to provide valid interpretations and implications useful for educational practice in relation to philosophical aspects or values. Whereas it should be originated from the philosophical foundations of the field and explain its normative significance, it needs to be testable in terms of rigorous evidence to fundamentally advance contemporary educational policy and practice. There is thus pragmatically a need to include a course on neuroeducational theory into the curriculum of the field. In addition, there is a need to articulate and disseminate considerable discussion over the subject within professional journals and academic societies.

Keywords: Neuroeducation studies, neuroeducational theory, theory building, neuroeducation research.

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Authors: Shamim Ahmed Koichi Nishigaki

Abstract:

Genome profiling (GP), a genotype based technology, which exploits random PCR and temperature gradient gel electrophoresis, has been successful in identification/classification of organisms. In this technology, spiddos (Species identification dots) and PaSS (Pattern similarity score) were employed for measuring the closeness (or distance) between genomes. Based on the closeness (PaSS), we can buildup phylogenetic trees of the organisms. We noticed that the topology of the tree is rather robust against the experimental fluctuation conveyed by spiddos. This fact was confirmed quantitatively in this study by computer-simulation, providing the limit of the reliability of this highly powerful methodology. As a result, we could demonstrate the effectiveness of the GP approach for identification/classification of organisms.

Keywords: Fluctuation, Genome profiling (GP), Pattern similarity score (PaSS), Robustness, Spiddos-shift.

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Authors: T. S. Chou, K. K. Yen, J. Luo

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The network traffic data provided for the design of intrusion detection always are large with ineffective information and enclose limited and ambiguous information about users- activities. We study the problems and propose a two phases approach in our intrusion detection design. In the first phase, we develop a correlation-based feature selection algorithm to remove the worthless information from the original high dimensional database. Next, we design an intrusion detection method to solve the problems of uncertainty caused by limited and ambiguous information. In the experiments, we choose six UCI databases and DARPA KDD99 intrusion detection data set as our evaluation tools. Empirical studies indicate that our feature selection algorithm is capable of reducing the size of data set. Our intrusion detection method achieves a better performance than those of participating intrusion detectors.

Keywords: Intrusion detection, feature selection, k-nearest neighbors, fuzzy clustering, Dempster-Shafer theory

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Authors: Ruigang Zhang, Wuyungaowa, Xingchen Ma

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In this paper, we present some formulas of symbolic operator summation, which involving Generalization well-know number sequences or polynomial sequences, and mean while we obtain some identities about the sequences by employing M-R‘s substitution rule.

Keywords: Generating functions, operators sequence group, Riordan arrays, R. G operator group, combinatorial identities.

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Authors: S. Sowmyayani

Abstract:

The advancement of computer-aided design helps the medical force and security force. Some applications include biometric recognition, elderly fall detection, face recognition, cancer recognition, tumor recognition, etc. This paper deals with different machine learning algorithms that are more generically used for any health care system. The most focused problems are classification and regression. With the rise of big data, machine learning has become particularly important for solving problems. Machine learning uses two types of techniques: supervised learning and unsupervised learning. The former trains a model on known input and output data and predicts future outputs. Classification and regression are supervised learning techniques. Unsupervised learning finds hidden patterns in input data. Clustering is one such unsupervised learning technique. The above-mentioned models are discussed briefly in this paper.

Keywords: Supervised learning, unsupervised learning, regression, neural network.

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Authors: Norlyda Mohamed, Daud Mohamad, Shaharuddin Cik Soh

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Let Gα ,β (γ ,δ ) denote the class of function f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) , β ∈ı and γ ∈ı (0 ≤γ <α ) where δ ≤ π and α cosδ −γ > 0 . In this paper, we determine some extremal properties including distortion theorem and argument of f ′( z ) .

Keywords: Argument of f ′(z) , Carathéodory Function, Closeto- convex Function, Distortion Theorem, Extremal Properties

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Authors: Yan-Fang Niu

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In view of current IT integration development of SOA, this paper examines AIS design based on SOA, including information sources collection, accounting business process integration and real-time financial reports. The main objective of this exploratory paper is to facilitate AIS research combing the Web Service, which is often ignored in accounting and computer research. It provides a conceptual framework that clarifies the interdependency between SOA and AIS, and also presents the major SOA functions in different areas of AIS

Keywords: AIS, SOA, Web Service

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Authors: Yasuhito Tanaka

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We examine the maximum theorem by Berge from the point of view of Bishop style constructive mathematics. We will show an approximate version of the maximum theorem and the maximum theorem for functions with sequentially locally at most one maximum.

Keywords: Maximum theorem, Constructive mathematics, Sequentially locally at most one maximum.

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Authors: Yee Ling Boo, Damminda Alahakoon

Abstract:

Biologically human brain processes information in both unimodal and multimodal approaches. In fact, information is progressively abstracted and seamlessly fused. Subsequently, the fusion of multimodal inputs allows a holistic understanding of a problem. The proliferation of technology has exponentially produced various sources of data, which could be likened to being the state of multimodality in human brain. Therefore, this is an inspiration to develop a methodology for exploring multimodal data and further identifying multi-view patterns. Specifically, we propose a brain inspired conceptual model that allows exploration and identification of patterns at different levels of granularity, different types of hierarchies and different types of modalities. A structurally adaptive neural network is deployed to implement the proposed model. Furthermore, the acquisition of multi-view patterns with the proposed model is demonstrated and discussed with some experimental results.

Keywords: Multimodal, Granularity, Hierarchical Clustering, Growing Self Organising Maps, Data Mining

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Authors: Abder-Rahman Ali, Adélaïde Albouy-Kissi, Manuel Grand-Brochier, Viviane Ladan-Marcus, Christine Hoeffl, Claude Marcus, Antoine Vacavant, Jean-Yves Boire

Abstract:

In this paper, we present a new segmentation approach for focal liver lesions in contrast enhanced ultrasound imaging. This approach, based on a two-cluster Fuzzy C-Means methodology, considers type-II fuzzy sets to handle uncertainty due to the image modality (presence of speckle noise, low contrast, etc.), and to calculate the optimum inter-cluster threshold. Fine boundaries are detected by a local recursive merging of ambiguous pixels. The method has been tested on a representative database. Compared to both Otsu and type-I Fuzzy C-Means techniques, the proposed method significantly reduces the segmentation errors.

Keywords: Defuzzification, fuzzy clustering, image segmentation, type-II fuzzy sets.

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Authors: Cheng-Lung Huang, Han-Yu Chien, Michael Conyette

Abstract:

Social bookmarking is an environment in which the user gradually changes interests over time so that the tag data associated with the current temporal period is usually more important than tag data temporally far from the current period. This implies that in the social tagging system, the newly tagged items by the user are more relevant than older items. This study proposes a novel recommender system that considers the users- recent tag preferences. The proposed system includes the following stages: grouping similar users into clusters using an E-M clustering algorithm, finding similar resources based on the user-s bookmarks, and recommending the top-N items to the target user. The study examines the system-s information retrieval performance using a dataset from del.icio.us, which is a famous social bookmarking web site. Experimental results show that the proposed system is better and more effective than traditional approaches.

Keywords: Recommender systems, Social bookmarking, Tag

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Authors: Surender Kumar Soni, Dhirendra Pratap Singh

Abstract:

Wireless Sensor Networks can be used to monitor the physical phenomenon in such areas where human approach is nearly impossible. Hence the limited power supply is the major constraint of the WSNs due to the use of non-rechargeable batteries in sensor nodes. A lot of researches are going on to reduce the energy consumption of sensor nodes. Energy map can be used with clustering, data dissemination and routing techniques to reduce the power consumption of WSNs. Energy map can also be used to know which part of the network is going to fail in near future. In this paper, Energy map is constructed using the prediction based approach. Adaptive alpha GM(1,1) model is used as the prediction model. GM(1,1) is being used worldwide in many applications for predicting future values of time series using some past values due to its high computational efficiency and accuracy.

Keywords: Adaptive Alpha GM(1, 1) Model, Energy Map, Prediction Based Data Reduction, Wireless Sensor Networks

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Authors: Iqbal Hossain, Dr. Monzur Imteaz, Dr. Shirley Gato-Trinidad, Prof. Abdallah Shanableh

Abstract:

Estimation of runoff water quality parameters is required to determine appropriate water quality management options. Various models are used to estimate runoff water quality parameters. However, most models provide event-based estimates of water quality parameters for specific sites. The work presented in this paper describes the development of a model that continuously simulates the accumulation and wash-off of water quality pollutants in a catchment. The model allows estimation of pollutants build-up during dry periods and pollutants wash-off during storm events. The model was developed by integrating two individual models; rainfall-runoff model, and catchment water quality model. The rainfall-runoff model is based on the time-area runoff estimation method. The model allows users to estimate the time of concentration using a range of established methods. The model also allows estimation of the continuing runoff losses using any of the available estimation methods (i.e., constant, linearly varying or exponentially varying). Pollutants build-up in a catchment was represented by one of three pre-defined functions; power, exponential, or saturation. Similarly, pollutants wash-off was represented by one of three different functions; power, rating-curve, or exponential. The developed runoff water quality model was set-up to simulate the build-up and wash-off of total suspended solids (TSS), total phosphorus (TP) and total nitrogen (TN). The application of the model was demonstrated using available runoff and TSS field data from road and roof surfaces in the Gold Coast, Australia. The model provided excellent representation of the field data demonstrating the simplicity yet effectiveness of the proposed model.

Keywords: Catchment, continuous pollutants build-up, pollutants wash-off, runoff, runoff water quality model.

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Authors: Jinhwan Yu, Jooyeon Yook

Abstract:

After Apple's first introduction its smart phone, iPhone in the end of 2009 in Korea, the number of Korean smarphone users had been rapidly increasing so that the half of Korean population became smart phone users as of February, 2012. Currently, smart phones are positioned as a major digital media with powerful influences in Korea. And, now, Koreans are leaning new information, enjoying games and communicating other people every time and everywhere. As smart phone devices' performances increased, the number of usable services became more while adequate GUI developments are required to implement various functions with smart phones. The strategy to provide similar experiences on smart phones through familiar features based on employment of existing media's functions mostly contributed to smart phones' popularization in connection with smart phone devices' iconic GUIs. The spread of Smart phone increased mobile web accesses. Therefore, the attempts to implement PC's web in the smart phone's web are continuously made. The mobile web GUI provides familiar experiences to users through designs adequately utilizing the smart phone's GUIs. As the number of users familiarized to smart phones and mobile web GUIs, opposite to reversed remediation from many parts of PCs, PCs are starting to adapt smart phone GUIs. This study defines this phenomenon as the reversed remediation, and reviews the reversed remediation cases of Smart phone GUI' characteristics of PCs. For this purpose, the established study issues are as under: · what is the reversed remediation? · what are the smart phone GUI's characteristics? · what kind of interrelationship exist s between the smart phone and PC's web site? It is meaningful in the forecast of the future GUI's change by understanding of characteristics in the paradigm changes of PC and smart phone's GUI designs. This also will be helpful to establish strategies for digital devices' development and design.

Keywords: Graphic User Interface, Remediation, Smart Phone, South Korea, Web Site

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Authors: Bhanu Gupta, Sanjay K. Srivastava

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In this paper, we shall present sufficient conditions for the ψ-exponential stability of a class of nonlinear impulsive differential equations. We use the Lyapunov method with functions that are not necessarily differentiable. In the last section, we give some examples to support our theoretical results.

Keywords: Exponential stability, globally exponential stability, impulsive differential equations, Lyapunov function, ψ-stability.

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Authors: Ali E. Abbas

Abstract:

This paper highlights some of the normative issues that might result by setting independent thresholds in risk analyses and particularly with safety regions. A second objective is to explain how such regions can be specified appropriately in a meaningful way. We start with a review of the importance of setting deterministic trade-offs among target requirements. We then show how to determine safety regions for risk analysis appropriately using utility functions.

Keywords: Decision analysis, thresholds, risk, reliability.

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Authors: Hager Kammoun, Jean Charles Lamirel, Mohamed Ben Ahmed

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In this paper, a model for an information retrieval system is proposed which takes into account that knowledge about documents and information need of users are dynamic. Two methods are combined, one qualitative or symbolic and the other quantitative or numeric, which are deemed suitable for many clustering contexts, data analysis, concept exploring and knowledge discovery. These two methods may be classified as inductive learning techniques. In this model, they are introduced to build “long term" knowledge about past queries and concepts in a collection of documents. The “long term" knowledge can guide and assist the user to formulate an initial query and can be exploited in the process of retrieving relevant information. The different kinds of knowledge are organized in different points of view. This may be considered an enrichment of the exploration level which is coherent with the concept of document/query structure.

Keywords: Information Retrieval Systems, machine learning, classification, Galois lattices, Self Organizing Map.

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Authors: L. Belkhiri, L. Mouni, A. Tiri, T.S. Narany

Abstract:

In the present study, the self-organizing map (SOM) clustering technique was applied to identify homogeneous clusters of hydrochemical parameters in El Milia plain, Algeria, to assess the quality of groundwater for potable and agricultural purposes. The visualization of SOM-analysis indicated that 35 groundwater samples collected in the study area were classified into three clusters, which showed progressive increase in electrical conductivity from cluster one to cluster three. Samples belonging to cluster one are mostly located in the recharge zone showing hard fresh water type, however, water type gradually changed to hard-brackish type in the discharge zone, including clusters two and three. Ionic ratio studies indicated the role of carbonate rock dissolution in increases on groundwater hardness, especially in cluster one. However, evaporation and evapotranspiration are the main processes increasing salinity in cluster two and three.

Keywords: Drinking water, groundwater quality, irrigation water, self-organizing maps.

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Authors: G. Van Dijck, M. M. Van Hulle, M. Wevers

Abstract:

A genetic algorithm (GA) based feature subset selection algorithm is proposed in which the correlation structure of the features is exploited. The subset of features is validated according to the classification performance. Features derived from the continuous wavelet transform are potentially strongly correlated. GA-s that do not take the correlation structure of features into account are inefficient. The proposed algorithm forms clusters of correlated features and searches for a good candidate set of clusters. Secondly a search within the clusters is performed. Different simulations of the algorithm on a real-case data set with strong correlations between features show the increased classification performance. Comparison is performed with a standard GA without use of the correlation structure.

Keywords: Classification, genetic algorithm, hierarchicalagglomerative clustering, wavelet transform.

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Authors: Ramin Javadzadeh., Zahra Afsahi, MohammadReza Meybodi

Abstract:

The Artificial immune systems algorithms are Meta heuristic optimization method, which are used for clustering and pattern recognition applications are abundantly. These algorithms in multimodal optimization problems are more efficient than genetic algorithms. A major drawback in these algorithms is their slow convergence to global optimum and their weak stability can be considered in various running of these algorithms. In this paper, improved Artificial Immune System Algorithm is introduced for the first time to overcome its problems of artificial immune system. That use of the small size of a local search around the memory antibodies is used for improving the algorithm efficiently. The credibility of the proposed approach is evaluated by simulations, and it is shown that the proposed approach achieves better results can be achieved compared to the standard artificial immune system algorithms

Keywords: Artificial immune system, Cellular Automata, Cellular learning automata, Cellular learning automata, , Local search, Optimization.

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Authors: Rudolf Csikja, Janos Toth

Abstract:

Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.

Keywords: blow up, finite escape time, polynomial ODE, singularity, Lotka–Volterra equation, Painleve analysis, Ψ-series, global existence

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Authors: Mustafa M. Donma, Orkide Donma

Abstract:

The impact of metabolic syndrome (MetS) on cognition and functions of the brain is being investigated. Iron deficiency and deficiencies of B9 (folate) as well as B12 (cobalamin) vitamins are best-known nutritional anemias. They are associated with cognitive disorders and learning difficulties. The antidepressant effects of vitamin D are known and the deficiency state affects mental functions negatively. The aim of this study is to investigate possible correlations of MetS with serum brain-derived neurotrophic factor (BDNF), iron, folate, cobalamin and vitamin D in pediatric patients. 30 children, whose age- and sex-dependent body mass index (BMI) percentiles vary between 85 and 15, 60 morbid obese children with above 99^th percentiles constituted the study population. Anthropometric measurements were taken. BMI values were calculated. Age- and sex-dependent BMI percentile values were obtained using the appropriate tables prepared by the World Health Organization (WHO). Obesity classification was performed according to WHO criteria. Those with MetS were evaluated according to MetS criteria. Serum BDNF was determined by enzyme-linked immunosorbent assay. Serum folate was analyzed by an immunoassay analyzer. Serum cobalamin concentrations were measured using electrochemiluminescence immunoassay. Vitamin D status was determined by the measurement of 25-hydroxycholecalciferol [25-hydroxy vitamin D3, 25(OH)D] using high performance liquid chromatography. Statistical evaluations were performed using SPSS for Windows, version 16. The p values less than 0.05 were accepted as statistically significant. Although statistically insignificant, lower folate and cobalamin values were found in MO children compared to those observed for children with normal BMI. For iron and BDNF values, no alterations were detected among the groups. Significantly decreased vitamin D concentrations were noted in MO children with MetS in comparison with those in children with normal BMI (p ≤ 0.05). The positive correlation observed between iron and BDNF in normal-BMI group was not found in two MO groups. In THE MetS group, the partial correlation among iron, BDNF, folate, cobalamin, vitamin D controlling for waist circumference and BMI was r = -0.501; p ≤ 0.05. None was calculated in MO and normal BMI groups. In conclusion, vitamin D should also be considered during the assessment of pediatric MetS. Waist circumference and BMI should collectively be evaluated during the evaluation of MetS in children. Within this context, BDNF appears to be a key biochemical parameter during the examination of obesity degree in terms of mental functions, cognition and learning capacity. The association observed between iron and BDNF in children with normal BMI was not detected in MO groups possibly due to development of inflammation and other obesity-related pathologies. It was suggested that this finding may contribute to mental function impairments commonly observed among obese children.

Keywords: Brain-derived neurotrophic factor, iron, Vitamin B9, Vitamin B12, Vitamin D.

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Authors: A. S. Issa, S. K. Q. AL-Omari

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In this paper, we investigate certain spaces of generalized functions for the Fourier and Fourier type integral transforms. We discuss convolution theorems and establish certain spaces of distributions for the considered integrals. The new Fourier type integral is well-defined, linear, one-to-one and continuous with respect to certain types of convergences. Many properties and an inverse problem are also discussed in some details.

Keywords: Fourier type integral, Fourier integral, generalized quotient, Boehmian, distribution.

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Authors: Bakhtiar Ul Haq, R. Ahmed, A. Shaari, Mazmira Binti Mohamed, Nisar Ali

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The capability of exploiting the electronic charge and spin properties simultaneously in a single material has made diluted magnetic semiconductors (DMS) remarkable in the field of spintronics. We report the designing of DMS based on zinc-blend ZnO doped with Cr impurity. The full potential linearized augmented plane wave plus local orbital FP-L(APW+lo) method in density functional theory (DFT) has been adapted to carry out these investigations. For treatment of exchange and correlation energy, generalized gradient approximations have been used. Introducing Cr atoms in the matrix of ZnO has induced strong magnetic moment with ferromagnetic ordering at stable ground state. Cr:ZnO was found to favor the short range magnetic interaction that reflect tendency of Cr clustering. The electronic structure of ZnO is strongly influenced in the presence of Cr impurity atoms where impurity bands appear in the band gap.

Keywords: ZnO, Density functional theory, Diluted magnetic semiconductors, Ferromagnetic materials, FP-L(APW+lo).

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Authors: Om Parkash, C.P.Gandhi

Abstract:

Probabilistic measures of uncertainty have been obtained as functions of time and birth and death rates in a queuing process. The variation of different entropy measures has been studied in steady and non-steady processes of queuing theory.

Keywords: Uncertainty, steady state, non-steady state, trafficintensity, monotonocity

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Authors: Mat Syai'in, Adi Soeprijanto

Abstract:

An Optimal Power Flow based on Improved Particle Swarm Optimization (OPF-IPSO) with Generator Capability Curve Constraint is used by NN-OPF as a reference to get pattern of generator scheduling. There are three stages in Designing NN-OPF. The first stage is design of OPF-IPSO with generator capability curve constraint. The second stage is clustering load to specific range and calculating its index. The third stage is training NN-OPF using constructive back propagation method. In training process total load and load index used as input, and pattern of generator scheduling used as output. Data used in this paper is power system of Java-Bali. Software used in this simulation is MATLAB.

Keywords: Optimal Power Flow, Generator Capability Curve, Improved Particle Swarm Optimization, Neural Network

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Authors: Valentina Koliskina

Abstract:

Change in impedance of an encircling coil is obtained in the present paper for the case where the electric conductivity and magnetic permeability of a metal cylindrical tube depend on the radial coordinate. The system of equations for the vector potential is solved by means of the Fourier cosine transform. The solution is expressed in terms of improper integral containing modified Bessel functions of complex order.

Keywords: Eddy currents, magnetic permeability, Besselfunctions

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