Search results for: Case study research

Authors: Mohammad H. Fattahi

Abstract:

Chaotic analysis has been performed on the river flow time series before and after applying the wavelet based de-noising techniques in order to investigate the noise content effects on chaotic nature of flow series. In this study, 38 years of monthly runoff data of three gauging stations were used. Gauging stations were located in Ghar-e-Aghaj river basin, Fars province, Iran. Noise level of time series was estimated with the aid of Gaussian kernel algorithm. This step was found to be crucial in preventing removal of the vital data such as memory, correlation and trend from the time series in addition to the noise during de-noising process.

Keywords: Chaotic behavior, wavelet, noise reduction, river flow.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical parameter, functionally graded index and piezoelectric thickness on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Stability, Functionally graded beam, First order shear deformation theory, Piezoelectric layer.

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Authors: Ilze Beitane, Inga Ciprovica

Abstract:

The influence of lactulose and inulin on rheological properties of fermented milk during storage was studied.Pasteurized milk, freeze-dried starter culture Bb-12 (Bifidobacterium lactis, Chr. Hansen, Denmark), inulin – RAFTILINE®HP (ORAFI, Belgium) and syrup of lactulose (Duphalac®, the Netherlands) were used for experiments. The fermentation process was realized at 37 oC for 16 hours and the storage of products was provided at 4 oC for 7 days. Measurements were carried out by BROOKFIELD standard methods and the flow curves were described by Herschel-Bulkley model. The results of dispersion analysis have shown that both the concentration of prebiotics (p=0.04<0.05) and shelf life (p=0.003<0.05) have a significant influence on the apparent viscosity of the product.

Keywords: Apparent viscosity, B.lactis, consistency coefficient, flow behavior index, prebiotics.

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Authors: Velid Demir, Mesut Akgün

Abstract:

The lanthanum and zinc oxide were synthesized and then loaded with 6 wt% over γ-Al2O3 using the wet impregnation method. The samples were calcined at 900 °C to ensure a coherent structure with high catalytic performance. Characterization of the catalysts was verified by X-ray diffraction (XRD) and Fourier-transform infrared spectroscopy (FTIR). The effect of catalysts on biodiesel content from jatropha oil was studied under supercritical conditions. The results showed that ZnO/γ-Al2O3 was the superior catalyst for jatropha oil with 98.05% biodiesel under reaction conditions of 7 min reaction time, 1:40 oil to methanol molar ratio, 6 wt% of catalyst loading, 90 bar of reaction pressure, and 300 °C of reaction temperature, compared to 95.50% with La2O3/γ-Al2O3 at the same parameters. For this study, ZnO/γ-Al2O3 was the most suitable catalyst due to performance and cost considerations.

Keywords: Biodiesel, heterogeneous catalyst, Jatropha oil, supercritical methanol, transesterification.

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Authors: Jung-Ho Moon, Tae Kwon Ha

Abstract:

In the present study, the effect of Si, Al, Ti, Zr, and Nb addition on the microstructure and hot workability of cast M42 tool steels, basically consisting of 1.0C, 0.2Mn, 3.8Cr, 1.5W, 8.5Co, 9.2Mo, and 1.0V in weight percent has been investigated. Tool steels containing Si of 0.25 and 0.5wt.%, Al of 0.06 and 0.12wt.%, Ti of 0.3wt.%, Zr of 0.3wt.%, and Nb of 0.3wt.% were cast into ingots of 140mm ´ 140mm ´ 330mm by vacuum induction melting. After solution treatment at 1150^oC for 1.5hr followed by furnace cooling, hot rolling at 1180^oC was conducted on the ingots. Addition of titanium, zirconium and niobium was found to retard the decomposition of the eutectic carbides and result in the deterioration of hot workability of the tool steels, while addition of aluminum and silicon showed relatively well decomposed carbide structure and resulted in sound hot rolled plates.

Keywords: High speed steels, alloying elements, eutectic carbides, microstructure, hot workability.

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Authors: Zahra Ghiabaklou

Abstract:

This paper presents the climatic range calculations for comfort evaporative cooling for Tehran. In this study the minimum climatic conditions required to achieve an appropriate comfort zone will be presented. Physiologically uncomfortable conditions in arid climates are mainly caused by the extreme heat and dryness. Direct evaporative cooling adds moisture to the air stream until the air stream is close to saturation. The dry bulb temperature is reduced, while the wet bulb temperature stays the same. Evaporative cooling is economical, effective, environmentally friendly, and healthy. Comfort cooling by direct evaporative cooling (passive or fan forced) in the 35. 41 N (such as Tehran) latitude requires design wet-bulb temperature not over 25.4 C. Evaporative cooling outside this limit cannot achieve the required 26.7 ET, and is recommended for relief cooling only.

Keywords: Evaporative cooling, Comfort temperature, Climaticdesign, Comfort cooling

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Authors: Norwati Mustapha, Manijeh Jalali, Abolghasem Bozorgniya, Mehrdad Jalali

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Web usage mining algorithms have been widely utilized for modeling user web navigation behavior. In this study we advance a model for mining of user-s navigation pattern. The model makes user model based on expectation-maximization (EM) algorithm.An EM algorithm is used in statistics for finding maximum likelihood estimates of parameters in probabilistic models, where the model depends on unobserved latent variables. The experimental results represent that by decreasing the number of clusters, the log likelihood converges toward lower values and probability of the largest cluster will be decreased while the number of the clusters increases in each treatment.

Keywords: Web Usage Mining, Expectation maximization, navigation pattern mining.

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Authors: Jian Zheng, Yoshiyasu Takahashi, Yuichi Kobayashi, Tatsuhiro Sato

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In the study, we present a conceptual framework for developing a scheduling system that can generate self-explanatory and easy-understanding schedules. To this end, a user interface is conceived to help planners record factors that are considered crucial in scheduling, as well as internal and external sources relating to such factors. A hybrid approach combining machine learning and constraint programming is developed to generate schedules and the corresponding factors, and accordingly display them on the user interface. Effects of the proposed system on scheduling are discussed, and it is expected that scheduling efficiency and system understandability will be improved, compared with previous scheduling systems.

Keywords: Constraint programming, Factors considered in scheduling, machine learning, scheduling system.

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Authors: Mostafa.A. Fellani, Daw .E. Abaid

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This paper deals with stability analysis for synchronous reluctance motors drive. Special attention is paid to the transient performance with variations in motor's parameters such as Ld and Rs. A study of the dynamic control using d-q model is presented first in order to clarify the stability of the motor drive system. Based on the experimental parameters of the synchronous reluctance motor, this paper gives some simulation results using MATLAB/SIMULINK software packages. It is concluded that the motor parameters, especially Ld, affect the estimator stability and hence the whole drive system.

Keywords: Dynamic Simulation, MATLAB, PWM-inverter, Reluctance Machine, Sensorless Control

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Authors: F. Habibi Tirtash, M. Keshavarzi, F. Fazeli

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The genus Fumaria L. (Papaveraceae) in Iran comprises 8 species with a vast medicinal use in Asian folk medicine. These herbs are considered to be useful in the treatment of gastrointestinal disease and skin disorders. Antioxidant activities of alkaloids and phenolic extracts of these species had been studied previously. These species are: F. officinalis, F. parviflora, F. asepala, F. densiflora, F. schleicheri, F. vaillantii and F. indica. More than 50 populations of Fumaria species were sampled from nature. In this study different fatty acids are extracted. Their picks were recorded by GC technique. This species contain some kind of fatty acids with antioxidant effects. A part of these lipids are phospholipids. As these are unsaturated fatty acids they may have industrial use as natural additive to cosmetics, dermal and oral medicines. The presences of different materials are discussed. Our studies for antioxidant effects of these substances are continued.

Keywords: Fumaria, Papaveraceae, fatty acid, antioxidant, Iran

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Authors: Chiung-Ju Huang

Abstract:

This study utilizes the panel vector error correction model (PVECM) to examine the relationship among corruption, economic growth, and income inequality experienced within ten Asian countries over the 1995 to 2010 period. According to the empirical results, we do not support the common perception that corruption decreases economic growth. On the contrary, we found that corruption increases economic growth. Meanwhile, an increase in economic growth will cause an increase in income inequality, although the effect is insignificant. Similarly, an increase in income inequality will cause an increase in economic growth but a decrease in corruption, although the effect is also insignificant.

Keywords: Corruption, economic growth, income inequality, panel vector error correction model

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Authors: E. Kam, Z. U. Yümün, D. Kurt

Abstract:

In this study, sediment samples were collected from four sampling sites located on the shores of the Gulf of İzmir. In the samples, Cd, Co, Cr, Cu, Mn, Ni, Pb and Zn concentrations were determined using inductively coupled, plasma-optical emission spectrometry (ICP-OES). The average heavy metal concentrations were: Cd < LOD (limit of detection); Co 14.145 ± 0.13 μg g⁻¹; Cr 112.868 ± 0.89 μg g⁻¹; Cu 34.045 ± 0.53 μg g⁻¹; Mn 481.43 ± 7.65 μg g⁻¹; Ni 76.538 ± 3.81 μg g⁻¹; Pb 11.059 ± 0.53 μg g⁻¹ and Zn 140.133 ± 1.37 μg g⁻¹, respectively. The results were compared with the average abundances of these elements in the Earth’s crust. The measured heavy metal concentrations can serve as reference values for further studies carried out on the shores of the Aegean Sea.

Keywords: Heavy metal, Aegean Sea, ICP-OES, sediment.

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Authors: U.K.Ghosh, M.K.Ghosh

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The present experimental investigation brings about a comparative study of lactic acid production by pure strains of Lactobacilli (1) L. delbreuckii (NCIM2025), (2) L. pentosus (NCIM 2912), (3) Lactobacillus sp.(NCIM 2734, (4) Lactobacillus sp. (NCIM2084) and coculture of strain-1 and Stain-2 in solid bed of wheat bran, under the influence of different nitrogen sources such as baker-s yeast, meat extract and proteose peptone. Among the pure cultures, strain-3 attained lowest pH value of 3.44, hence highest acid formation 46.41 g/L, while the coculture attained an overall maximum value 47.56 g/L lactic acid (pH 3.38) at 15 g/L and 20 g/L level of baker-s yeast, respectively.

Keywords: Eco-friendly, lactic acid, lactobacilli, wheat bran

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Authors: Guojia Ma, Guoqiang Lin, Shuili Gong, Gang Sun, Dawang Wang

Abstract:

A diamond-like carbon (DLC) based solid-lubricant film was designed and DLC films were successfully prepared using a microwave plasma enhanced magnetron sputtering deposition technology. Post-test characterizations including Raman spectrometry, X-ray diffraction, nano-indentation test, adhesion test, friction coefficient test were performed to study the influence of substrate bias voltage on the mechanical properties of the W- and S-doped DLC films. The results indicated that the W- and S-doped DLC films also had the typical structure of DLC films and a better mechanical performance achieved by the application of a substrate bias of -200V.

Keywords: Adhesive Strength, Coefficient of Friction, Substrate Bias, W- and S-doped DLC film

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Authors: H. Sezgin, S. Kursun Bahadır, Y. E. Boke, F. Kalaoğlu

Abstract:

By textile science incorporating with electronic industry, developed textile products start to take part in different areas such as industry, military, space, medical etc. for health, protection, defense, communication and automation. Electronic textiles (e-textiles) are fabrics that contain electronics and interconnections with them. In this study, two types of base yarns (cotton and acrylic) and three types of conductive steel yarns with different linear resistance values (14Ω/m, 30Ω/m, 70Ω/m) were used to investigate the effect of base yarn type and linear resistance of conductive yarns on thermal behavior of e-textile structures. Thermal behavior of samples was examined by thermal camera.

Keywords: Conductive yarn, e-textiles, smart textiles, thermal analysis.

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Authors: J. Zach, J. Hroudova, J. Brozovsky

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Thermal insulation materials based on natural fibers represent a very promising area of materials based on natural easy renewable row sources. These materials may be in terms of the properties of most competing synthetic insulations, but show somewhat higher moisture sensitivity and thermal insulation properties are strongly influenced by the density and orientation of fibers. The paper described the problem of hygrothermal behavior of thermal insulation materials based on natural plant and animal fibers. This is especially the dependence of the thermal properties of these materials on the type of fiber, bulk density, temperature, moisture and the fiber orientation.

Keywords: Thermal insulating materials, hemp fibers, sheep wool fibers, thermal conductivity, moisture.

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Authors: Antonis Sideris, Elias Chlis Kalogeropoulos, Konstantia Moirogiorgou

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The present study proposes a methodology for the efficient daily management of fleet vehicles and construction machinery. The application covers the area of remote monitoring of heavy-duty vehicles operation parameters, where specific sensor data are stored and examined in order to provide information about the vehicle’s health. The vehicle diagnostics allow the user to inspect whether maintenance tasks need to be performed before a fault occurs. A properly designed machine learning model is proposed for the detection of two different types of faults through classification. Cross validation is used and the accuracy of the trained model is checked with the confusion matrix.

Keywords: Fault detection, feature selection, machine learning, predictive maintenance.

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Authors: M. Anandhavalli Gauthaman

Abstract:

DNA microarrays allow the measurement of expression levels for a large number of genes, perhaps all genes of an organism, within a number of different experimental samples. It is very much important to extract biologically meaningful information from this huge amount of expression data to know the current state of the cell because most cellular processes are regulated by changes in gene expression. Association rule mining techniques are helpful to find association relationship between genes. Numerous association rule mining algorithms have been developed to analyze and associate this huge amount of gene expression data. This paper focuses on some of the popular association rule mining algorithms developed to analyze gene expression data.

Keywords: DNA microarray, gene expression, association rule mining.

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Authors: Dnyandip K. Bhamare, Manish K Rathod, Jyotirmay Banerjee

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This paper aims to study performance of a thermosiphon solar water heating system with the help of the proposed analytical model. This proposed model predicts the temperature and mass flow rate in a thermosiphon solar water heating system depending on radiation intensity and ambient temperature. The performance of the thermosiphon solar water heating system is evaluated in the Indian context. For this, eight cities in India are selected considering radiation intensity and geographical positions. Predicted performance at various cities reveals the potential for thermosiphon solar water in India.

Keywords: Collector outlet temperature, India, solar water heater, thermosiphon.

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Authors: L. Petrovičová, Ž. Balážová, Z. Gálová, M. Wójcik-Jagła, M. Rapacz

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In the present study, RAPD-PCR was used to assess genetic diversity of the rye including landrances and new rye cultivars coming from Central Europe and the Union of Soviet Socialist Republics (SUN). Five arbitrary random primers were used to determine RAPD polymorphism in the set of 38 rye genotypes. These primers amplified altogether 43 different DNA fragments with an average number of 8.6 fragments per genotypes. The number of fragments ranged from 7 (RLZ 8, RLZ 9 and RLZ 10) to 12 (RLZ 6). DI and PIC values of all RAPD markers were higher than 0.8 that generally means high level of polymorphism detected between rye genotypes. The dendrogram based on hierarchical cluster analysis using UPGMA algorithm was prepared. The cultivars were grouped into two main clusters. In this experiment, RAPD proved to be a rapid, reliable and practicable method for revealing of polymorphism in the rye cultivars.

Keywords: Genetic diversity, polymorphism, RAPD markers, Secalecereale L.

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Authors: B. R. Tapas Bapu, K. Thanigaivelu, A. Rajkumar

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Wireless Sensor Networks (WSNs) have wide variety of applications and provide limitless future potentials. Nodes in WSNs are prone to failure due to energy depletion, hardware failure, communication link errors, malicious attacks, and so on. Therefore, fault tolerance is one of the critical issues in WSNs. We study how fault tolerance is addressed in different applications of WSNs. Fault tolerant routing is a critical task for sensor networks operating in dynamic environments. Many routing, power management, and data dissemination protocols have been specifically designed for WSNs where energy awareness is an essential design issue. The focus, however, has been given to the routing protocols which might differ depending on the application and network architecture.

Keywords: Resiliency, Self-diagnosis, Smart Grid, TinyOS, WSANs.

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Authors: Muhaimin Bin Sulam, Abdul Mutalib Embong, Azelin Mohamed Noor

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This paper presents the reinvention of the role of education (tarbiyyah) in the social influence of organizations focusing on the sustainability of a specific religio-political organization. The objective of the paper is to describe how the position secured by education could transform the organization while maintaining its objective and vision. The study employed the qualitative approach that involves data from conducted interviews. An analysis on the role political leaders play in educating the organization in the context of ideological struggle is also analyzed. The process description also evaluates how education could intellectualize its followers and members which inspires them to submit to their leaders and the organization. This extensive cultivation of religio-political doctrine could offer a new interpretation on politics.

Keywords: Religio-political organization. Malaysia, education (tarbiyyah), followers, political movement.

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Authors: M. Challal, F. Labu, M. Dehmas, A. Azrar

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In this paper, three types of defected ground structure (DGS) units which are triangular-head (TH), rectangular-head (RH) and U-shape (US) are investigated. They are further used to low-pass and band-pass filters designs (LPF and BPF) and the obtained performances are examined. The LPF employing RH-DGS geometry presents the advantages of compact size, low-insertion loss and wide stopband compared to the other filters. It provides cutoff frequency of 2.5 GHz, largest rejection band width of 20 dB from 2.98 to 8.76 GHz, smallest transition region and smallest sharpness of the cutoff frequency. The BPF based on RH-DGS has the highest bandwidth (BW) of about 0.74 GHz and the lowest center frequency of 3.24 GHz, whereas the other BPFs have BWs less than 0.7 GHz.

Keywords: Defected ground structure (DGS), triangular-head(TH) DGS, rectangular-head (RH) DGS, U-shape (US) DGS, lowpassfilter (LPF) and band-pass filter (BPF).

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Authors: Rajendra K. Ray, H. V. R. Mittal

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A numerical study is made of laminar, unsteady flow behind a rotationally oscillating circular cylinder using a recently developed higher order compact (HOC) scheme. The stream function vorticity formulation of Navier-Stokes (N-S) equations in cylindrical polar coordinates are considered as the governing equations. The temporal behaviour of vortex formation and relevant streamline patterns of the flow are scrutinized over broad ranges of two externally specified parameters namely dimensionless forced oscillating frequency Sf and dimensionless peak rotation rate αm for the Reynolds-s number Re = 200. Excellent agreements are found both qualitatively and quantitatively with the existing experimental and standard numerical results.

Keywords: HOC, Navier-Stokes, non-uniform polar grids, rotationally oscillating cylinder.

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Authors: Chutima Prommak, Airisa Jantaweetip

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This paper presents a hybrid association control scheme that can maintain load balancing among access points in the wireless LANs and can satisfy the quality of service requirements of the multimedia traffic applications. The proposed model is mathematically described as a linear programming model. Simulation study and analysis were conducted in order to demonstrate the performance of the proposed hybrid load balancing and association control scheme. Simulation results shows that the proposed scheme outperforms the other schemes in term of the percentage of blocking and the quality of the data transfer rate providing to the multimedia and real-time applications.

Keywords: Association control, Load balancing, Wireless LANs

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Authors: Y. Saylan, F. Yılmaz, A. Denizli

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In this study, we have focused our attention on combining of molecular imprinting into nanofilms and QCM nanosensor approaches and producing QCM nanosensor for anti- CCP, chosen as model protein, using anti-CCP imprinted nanofilms. The nonimprinted nanosensor was also prepared to evaluate the selectivity of the imprinted nanosensor. Anti-CCP imprinted QCM nanosensor was tested for real time detection of anti-CCP from aqueous solution. The kinetic and affinity studies were determined by using anti-CCP solutions with different concentrations. The responses related with mass shifts (%m) and frequency shifts (%f) were used to evaluate adsorption properties. To show the selectivity of the anti-CCP imprinted QCM nanosensor, competitive adsorption of anti-CCP and IgM was investigated. The results indicate that anti- CCP imprinted QCM nanosensor has higher adsorption capabilities for anti-CCP than for IgM, due to selective cavities in the polymer structure.

Keywords: Anti-CCP, molecular imprinting, QCM nanosensor, rheumatoid arthritis.

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Authors: Dimitris Georgoutsos, Petros M. Migiakis

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The concurrent era is characterised by strengthened interactions among financial markets and increased capital mobility globally. In this frames we examine the effects the international financial integration process has on the European bond markets. We perform a comparative study of the interactions of the European and international bond markets and exploit Cointegration analysis results on the elimination of stochastic trends and the decomposition of the underlying long run equilibria and short run causal relations. Our investigation provides evidence on the relation between the European integration process and that of globalisation, viewed through the bond markets- sector. Additionally the structural formulation applied, offers significant implications of the findings. All in all our analysis offers a number of answers on crucial queries towards the European bond markets integration process.

Keywords: financial integration, bond markets, cointegration

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Authors: Mustafa M. Donma, Orkide Donma

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Obesity is a clinical state associated with low-grade inflammation. It is also a major risk factor for insulin resistance (IR). In its advanced stages, metabolic syndrome (MetS), a much more complicated disease which may lead to life-threatening problems, may develop. Obesity-mediated IR seems to correlate with the inflammation. Human studies performed particularly on pediatric population are scarce. The aim of this study is to detect possible associations between inflammation and IR in terms of some related ratios. 549 children were grouped according to their age- and sex-based body mass index (BMI) percentile tables of WHO. MetS components were determined. Informed consent and approval from the Ethics Committee for Clinical Investigations were obtained. The principles of the Declaration of Helsinki were followed. The exclusion criteria were infection, inflammation, chronic diseases and those under drug treatment. Anthropometric measurements were obtained. Complete blood cell, fasting blood glucose, insulin, and C-reactive protein (CRP) analyses were performed. Homeostasis model assessment of insulin resistance (HOMA-IR), systemic immune inflammation (SII) index, tense index, alanine aminotransferase to aspartate aminotransferase ratio (ALT/AST), neutrophils to lymphocyte (NLR), platelet to lymphocyte, and lymphocyte to monocyte ratios were calculated. Data were evaluated by statistical analyses. The degree for statistical significance was 0.05. Statistically significant differences were found among the BMI values of the groups (p < 0.001). Strong correlations were detected between the BMI and waist circumference (WC) values in all groups. Tense index values were also correlated with both BMI and WC values in all groups except overweight (OW) children. SII index values of children with normal BMI were significantly different from the values obtained in OW, obese, morbid obese and MetS groups. Among all the other lymphocyte ratios, NLR exhibited a similar profile. Both HOMA-IR and ALT/AST values displayed an increasing profile from N towards MetS3 group. BMI and WC values were correlated with HOMA-IR and ALT/AST. Both in morbid obese and MetS groups, significant correlations between CRP versus SII index as well as HOMA-IR versus ALT/AST were found. ALT/AST and HOMA-IR values were correlated with NLR in morbid obese group and with SII index in MetS group, (p < 0.05), respectively. In conclusion, these findings showed that some parameters may exhibit informative differences between the early and late stages of obesity. Important associations among HOMA-IR, ALT/AST, NLR and SII index have come to light in the morbid obese and MetS groups. This study introduced the SII index and NLR as important inflammatory markers for the discrimination of normal and obese children. Interesting links were observed between inflammation and IR in morbid obese children and those with MetS, both being late stages of obesity.

Keywords: Children, inflammation, insulin resistance, metabolic syndrome, obesity.

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Authors: Poo Bee Tin, Rahmah Ismail, Norasmah Othman

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Globalisation is a phenomenon that cannot be avoided. As globalisation allowed free flow of inputs including labour, it may affect job opportunities for the locals. Therefore, investigate the determinants of labour supply is essential in understanding the structure of labour market in the new era of globalization. The objective of this article is to examine labour supply by taking into account the globalisation effect. The study covers 3885 households in Peninsular Malaysia who are chosen using stratified random sampling. The labour supply model will be the basis for the analysis. The basic labour supply determinants are own wage and non-labour income. However, the extended labour supply model incorporates other variables like spouse wage，number of children and individuals characteristics like education level and age. Besides, the globalization indicator will also be incorporated as another independent variable.

Keywords: globalization, head of households, labour supply, wage

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Authors: Lianglin Xiong, Yun Zhao, Tao Jiang

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In this paper, we study the stability of n-dimensional linear fractional neutral differential equation with time delays. By using the Laplace transform, we introduce a characteristic equation for the above system with multiple time delays. We discover that if all roots of the characteristic equation have negative parts, then the equilibrium of the above linear system with fractional order is Lyapunov globally asymptotical stable if the equilibrium exist that is almost the same as that of classical differential equations. An example is provided to show the effectiveness of the approach presented in this paper.

Keywords: Fractional neutral differential equation, Laplace transform, characteristic equation.

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