Search results for: Quality Index Method (QIM)

Authors: S. Balaji, N. Revathi

Abstract:

Connected dominating set (CDS) problem in unit disk graph has signi£cant impact on an ef£cient design of routing protocols in wireless sensor networks, where the searching space for a route is reduced to nodes in the set. A set is dominating if all the nodes in the system are either in the set or neighbors of nodes in the set. In this paper, a simple and ef£cient heuristic method is proposed for £nding a minimum connected dominating set (MCDS) in ad hoc wireless networks based on the new parameter support of vertices. With this parameter the proposed heuristic approach effectively £nds the MCDS of a graph. Extensive computational experiments show that the proposed approach outperforms the recently proposed heuristics found in the literature for the MCD

Keywords: ad hoc wireless networks, dominating sets, unit disk graphs, heuristic.

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Authors: Osama Terra, Mariesa Nel, Hatem Hussein

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Calibration of Optical Time Domain Reflectometer (OTDR) has a crucial role for the accurate determination of fault locations and the accurate calculation of loss budget of long-haul optical fibre links during installation and repair. A comparison has been made between the Egyptian National Institute for Standards (NIS-Egypt) and the National Metrology institute of South Africa (NMISA-South Africa) for the calibration of an OTDR. The distance and the attenuation scales of a transfer OTDR have been calibrated by both institutes using their standards according to the standard IEC 61746-1 (2009). The results of this comparison have been compiled in this report.

Keywords: OTDR calibration, recirculating loop, concatenated method, standard fibre.

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Authors: Hongji Tang, Yanbo Gao, Yue Yu

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This paper presents a new nonlinear integral-type sliding surface for synchronizing two different chaotic systems with parametric uncertainty. On the basis of Lyapunov theorem and average dwelling time method, we obtain the control gains of controllers which are derived to achieve chaos synchronization. In order to reduce the gains, the error system is modeled as a switching system. We obtain the sufficient condition drawn for the robust stability of the error dynamics by stability analysis. Then we apply it to guide the design of the controllers. Finally, numerical examples are used to show the robustness and effectiveness of the proposed control strategy.

Keywords: Chaos synchronization, Nonlinear sliding surface, Control gains, Sliding mode control.

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Authors: Dabyltayeva R. Y., Smatova K.B., Кabekenov G., Toleshova U., Shagyrbayeva M.

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In recent years in Kazakhstan, as well as in all countries, we have been talking not only about the professional stress, but also professional Burnout Syndrome of employees. Burnout is essentially a response to chronic emotional stress – manifests itself in the form of chronic fatigue, despondency, unmotivated aggression, anger, and others. This condition is due to mental fatigue among teachers as a sort of payment for overstrain when professional commitments include the impact of “heat your soul", emotional investment. The emergence of professional Burnout among teachers is due to the system of interrelated and mutually reinforcing factors relating to the various levels of the personality: individually-psychological level is psychodynamic special subject characteristics of valuemotivational sphere and formation of skills and habits of selfregulation; the socio-psychological level includes especially the Organization and interpersonal interaction of a teacher. Signs of the Burnout were observed in 15 testees, and virtually a symptom could be observed in every teacher. As a result of the diagnosis 48% of teachers had the signs of stress (phase syndrome), resulting in a sense of anxiety, mood, heightened emotional susceptibility. The following results have also been got:-the fall of General energy potential – 14 pers. -Psychosomatic and psycho vegetative syndrome – 26 pers. -emotional deficit-34 pers. -emotional Burnout Syndrome-6 pers. The problem of professional Burnout of teachers in the current conditions should become not only meaningful, but particularly relevant. The quality of education of the younger generation depends on professional development; teachers- training level, and how “healthy" teachers are. That is why the systematic maintenance of pedagogic-professional development for teachers (including disclosure of professional Burnout Syndrome factors) takes on a special meaning.

Keywords: Professional burnout syndrome, adaptive syndrome, stage of depletion syndrome, symptoms and characteristics of burnout, prophylactic of professional destruction techniques.

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Authors: N. Choosri, N. Swadchaipong, T. Utistham, U. W. Hartley

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Performance of a cobalt doped sol-gel derived silica (Co/SiO2) catalyst for Fischer–Tropsch synthesis (FTS) in slurryphase reactor was studied using paraffin wax as initial liquid media. The reactive mixed gas, hydrogen (H2) and carbon monoxide (CO) in a molar ratio of 2:1, was flowed at 50 ml/min. Braunauer-Emmett- Teller (BET) surface area and X-ray diffraction (XRD) techniques were employed to characterize both the specific surface area and crystallinity of the catalyst, respectively. The reduction behavior of Co/SiO2 catalyst was investigated using the Temperature Programmmed Reduction (TPR) method. Operating temperatures were varied from 493 to 533K to find the optimum conditions to maximize liquid fuels production, gasoline and diesel.

Keywords: Fischer Tropsch synthesis, slurry phase, Co/SiO2, operating temperature.

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Authors: Christopher Spiewak, M. R. Islam, Mohammad Arifur Rahaman, Mohammad H. Rahman, Roger Smith, Maarouf Saad

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For those who have lost the ability to move their hand, going through repetitious motions with the assistance of a therapist is the main method of recovery. We have been developed a robotic assistive device to rehabilitate the hand motions in place of the traditional therapy. The developed assistive device (RAD-HR) is comprised of four degrees of freedom enabling basic movements, hand function, and assists in supporting the hand during rehabilitation. We used a nonlinear computed torque control technique to control the RAD-HR. The accuracy of the controller was evaluated in simulations (MATLAB/Simulink environment). To see the robustness of the controller external disturbance as modelling uncertainty (±10% of joint torques) were added in each joints.

Keywords: Biorobotics, rehabilitation, nonlinear control, robotic assistive device, exoskeleton.

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Authors: K. Suganya Devi, P. Srinivasan, M. P. Vaishnave, G. Arutperumjothi

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Today’s internet world is highly prone to various online attacks, of which the most harmful attack is phishing. The attackers host the fake websites which are very similar and look alike. We propose an image based authentication using steganography and visual cryptography to prevent phishing. This paper presents a secure steganographic technique for true color (RGB) images and uses Discrete Cosine Transform to compress the images. The proposed method hides the secret data inside the cover image. The use of visual cryptography is to preserve the privacy of an image by decomposing the original image into two shares. Original image can be identified only when both qualified shares are simultaneously available. Individual share does not reveal the identity of the original image. Thus, the existence of the secret message is hard to be detected by the RS steganalysis.

Keywords: Image security, random LSB, steganography, visual cryptography.

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Authors: Fatima Akhmedova, Simon Liao

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One of the most critical decision points in the design of a face recognition system is the choice of an appropriate face representation. Effective feature descriptors are expected to convey sufficient, invariant and non-redundant facial information. In this work we propose a set of Hahn moments as a new approach for feature description. Hahn moments have been widely used in image analysis due to their invariance, nonredundancy and the ability to extract features either globally and locally. To assess the applicability of Hahn moments to Face Recognition we conduct two experiments on the Olivetti Research Laboratory (ORL) database and University of Notre-Dame (UND) X1 biometric collection. Fusion of the global features along with the features from local facial regions are used as an input for the conventional k-NN classifier. The method reaches an accuracy of 93% of correctly recognized subjects for the ORL database and 94% for the UND database.

Keywords: Face Recognition, Hahn moments, Recognition-by-parts, Time-lapse.

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Authors: F. Fernandes, C. Poleto

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This paper aims at assessing the concentrations of heavy metals and the isotopic composition of lead ²¹⁰Pb in different fractions of sediment produced in the watershed that makes up the Mãe d'água dam and thus characterizing the distribution of metals along the sedimentary column and inferencing in the urbanization of the same process. Sample collection was carried out in June 2014; eight sediment cores were sampled in the lake of the dam. For extraction of the sediments core, a core sampler “Piston Core” was used. The trace metal concentrations were determined by conventional atomic absorption spectrophotometric methods. The samples were subjected to radiochemical analysis of ²¹⁰Po. ²¹⁰Pb activity was obtained by measuring ²¹⁰Po activity. The chronology was calculated using the constant rate of supply (CRS). ²¹⁰Pb is used to estimate the sedimentation rate.

Keywords: 210Pb dating method, heavy metal, lakes urban, pollution history.

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Authors: Liu-Chao Qiu

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The damage caused by surge waves generated in water bodies by flow-like landslides can be very high in terms of human lives and economic losses. The complicated phenomena occurred in this highly unsteady process are difficult to model because three interacting phases: air, water and sediment are involved. The problem therefore is challenging since the effects of non-Newtonian fluid describing the rheology of the flow-like landslides, multi-phase flow and free surface have to be included in the simulation. In this work, the commercial computational fluid dynamics (CFD) package FLUENT is used to model the surge waves due to flow-like landslides. The comparison between the numerical results and experimental data reported in the literature confirms the accuracy of the method.

Keywords: Flow-like landslide, surge wave, VOF, non-Newtonian fluids, multi-phase flows, free surface flow.

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Authors: H. Jusoh, N. Sapari, R.Z. Raja Azie

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Iron in groundwater is one of the problems that render the water unsuitable for drinking. The concentration above 0.3 mg/L is common in groundwater. The conventional method of removal is by precipitation under oxic condition. In this study, iron removal under anaerobic conditions was examined by batch experiment as a main purpose. The process involved by purging of groundwater samples with H2S to form iron sulfide. Removal up to 83% for 1 mg/L iron solution was achieved. The removal efficiency dropped to 82% and 75% for the higher initial iron concentrations 3.55 and 5.01 mg/L, respectively. The average residual sulfide concentration in water after the process was 25*g/L. The Eh level during the process was -272 mV. The removal process was found to follow the first order reaction with average rate constant of 4.52 x 10-3. The half-life for the concentrations to reduce from initial values was 157 minutes.

Keywords: Anaerobic, chemical kinetics, hydrogen sulfide, iron, rate constant

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Authors: J. Shah, M. Rasul Jan, Adnan

Abstract:

The aluminum impregnated catalysts of Al-alumina (Al-Al2O3), Al-montmorillonite (Al-Mmn) and Al-activated charcoal (Al-AC) of various percent loadings were prepared by wet impregnation method and characterized by SEM, XRD and N2 adsorption/desorption (BET). The catalytic properties were investigated in the degradation of waste polystyrene (WPS). The results of catalytic degradation of Al metal, 20% Al-Al2O3, 5% Al-Mmn and 20% Al-AC were compared with each other for optimum conditions. Among the catalyst used 20% Al-Al2O3 was found the most effective catalyst. The BET surface area of 20% Al-Al2O3 determined was 70.2 m2/g. The SEM data revealed the catalyst with porous structure throughout the frame work with small nanosized crystallites. The yield of liquid products with 20% Al-Al2O3 (91.53 ± 2.27 wt%) was the same as compared to Al metal (91.20 ± 0.35 wt%) but the selectivity of hydrocarbons and yield of styrene monomer (56.32 wt%) was higher with 20% Al-Al2O3 catalyst.

 

Keywords: Impregnation, catalytic degradation, waste polystyrene, styrene.

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Authors: Khalid Salhi, El Miloud Jaara, Mohammed Talibi Alaoui

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In this paper, we present a neural approach for unsupervised natural color-texture image segmentation, which is based on both Kohonen maps and mathematical morphology, using a combination of the texture and the image color information of the image, namely, the fractal features based on fractal dimension are selected to present the information texture, and the color features presented in RGB color space. These features are then used to train the network Kohonen, which will be represented by the underlying probability density function, the segmentation of this map is made by morphological watershed transformation. The performance of our color-texture segmentation approach is compared first, to color-based methods or texture-based methods only, and then to k-means method.

Keywords: Segmentation, color-texture, neural networks, fractal, watershed.

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Authors: Md. Fazlul Karim, Esa Al-Islam

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This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. We develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons of water surface elevation obtained from numerical simulations and field measurements are made.

Keywords: Boundary-fitted nested grid model, finite difference method, Indonesian tsunami of 2004, Southern Thailand.

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Authors: Thang Manh Hoang

Abstract:

Recent research result has shown that two multidelay feedback systems can synchronize each other under different schemes, i.e. lag, projective-lag, anticipating, or projectiveanticipating synchronization. There, the driving signal is significantly complex due that it is constituted by multiple nonlinear transformations of delayed state variable. In this paper, a secure communication model is proposed based on synchronization of coupled multidelay feedback systems, in which the plain signal is mixed with a complex signal at the transmitter side and it is precisely retrieved at the receiver side. The effectiveness of the proposed model is demonstrated and verified in the specific example, where the message signal is masked directly by the complex signal and security is examined under the breaking method of power spectrum analysis.

Keywords: chaos synchronization, time-delayed system, chaosbasedsecure communications

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Authors: Sara Kamalisiahroudi, Jun Huang, Zhe Li, Jianbo Zhang

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Two types of commercial cylindrical lithium ion batteries (Panasonic 3.4 Ah NCR-18650B and Samsung 2.9 Ah INR-18650), were investigated experimentally. The capacities of these samples were individually measured using constant current-constant voltage (CC-CV) method at different ambient temperatures (-10°C, 0°C, 25°C). Their internal resistance was determined by electrochemical impedance spectroscopy (EIS) and pulse discharge methods. The cells with different configurations of parallel connection NCR-NCR, INR-INR and NCR-INR were charged/discharged at the aforementioned ambient temperatures. The results showed that the difference of internal resistance between cells much more evident at low temperatures. Furthermore, the parallel connection of NCR-NCR exhibits the most uniform temperature distribution in cells at -10°C, this feature is quite favorable for the safety of the battery pack.

Keywords: Batteries in parallel connection, internal resistance, low temperature, temperature difference, current distribution.

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Authors: H. K. Hwang, Zekeriya Aliyazicioglu, Solomon Wu, Hung Lu, Nick Wilkins, Daniel Kerr

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Multiple-input multiple-output (MIMO) radar has received increasing attention in recent years. MIMO radar has many advantages over conventional phased array radar such as target detection,resolution enhancement, and interference suppression. In this paper, the results are presented from a simulation study of MIMO uniformly-spaced linear array (ULA) antennas. The performance is investigated under varied parameters, including varied array size, pseudo random (PN) sequence length, number of snapshots, and signal to noise ratio (SNR). The results of MIMO are compared to a traditional array antenna.

Keywords: Multiple-input multiple-output (MIMO) radar, phased array antenna, target detection, radar signal processing.

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Authors: Chun-Wei Tung, Chyn Liaw, Shinn-Jang Ho, Shinn-Ying Ho

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Protein subchloroplast locations are correlated with its functions. In contrast to the large amount of available protein sequences, the information of their locations and functions is less known. The experiment works for identification of protein locations and functions are costly and time consuming. The accurate prediction of protein subchloroplast locations can accelerate the study of functions of proteins in chloroplast. This study proposes a Random Forest based method, ChloroRF, to predict protein subchloroplast locations using interpretable physicochemical properties. In addition to high prediction accuracy, the ChloroRF is able to select important physicochemical properties. The important physicochemical properties are also analyzed to provide insights into the underlying mechanism.

Keywords: Chloroplast, Physicochemical properties, Proteinlocations, Random Forests.

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Authors: A. Salmanpour, Sh. Mohammad Nejad

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One of the methods for detecting the target position error in the laser tracking systems is using Four Quadrant (4Q) detectors. If the coordinates of the target center is yielded through the usual relations of the detector outputs, the results will be nonlinear, dependent on the shape, target size and its position on the detector screen. In this paper we have designed an algorithm with using neural network that coordinates of the target center in laser tracking systems is calculated by using detector outputs obtained from visual modeling. With this method, the results except from the part related to the detector intrinsic limitation, are linear and dependent from the shape and target size.

Keywords: four quadrant detector, laser tracking system, rangefinder, tracking sensor

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Authors: O. H. Colak, T. C. Destici, S. Ozen, H. Arman, O. Cerezci

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The wavelet transform is one of the most important method used in signal processing. In this study, we have introduced frequency-energy characteristics of local earthquakes using discrete wavelet transform. Frequency-energy characteristic was analyzed depend on difference between P and S wave arrival time and noise within records. We have found that local earthquakes have similar characteristics. If frequency-energy characteristics can be found accurately, this gives us a hint to calculate P and S wave arrival time. It can be seen that wavelet transform provides successful approximation for this. In this study, 100 earthquakes with 500 records were analyzed approximately.

Keywords: Discrete Wavelet Transform, Frequency-EnergyCharacteristics, P and S waves arrival time.

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Authors: Guclu Insel, Efe Gumuslu, Gulten Yuksek, Nilay Sayi Ucar, Emine Ubay Cokgor, Tugba Olmez Hanci, Didem Okutman Tas, Fatos Germirli Babuna, Derya Firat Ertem, Okmen Yildirim, Ozge Erturan, Betul Kirci

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In order to eliminate water scarcity problems, effective precautions must be taken. Growing competition for water is increasingly forcing facilities to tackle their own water scarcity problems. At this point, application of wastewater reclamation and reuse results in considerable economic advantageous. In this study, an enamel coating facility, which is one of the high water consumed facilities, is evaluated in terms of its wastewater reuse potential. Wastewater reclamation and reuse can be defined as one of the best available techniques for this sector. Hence, process and pollution profiles together with detailed characterization of segregated wastewater sources are appraised in a way to find out the recoverable effluent streams arising from enamel coating operations. Daily, 170 m³ of process water is required and 160 m³ of wastewater is generated. The segregated streams generated by two enamel coating processes are characterized in terms of conventional parameters. Relatively clean segregated wastewater streams (reusable wastewaters) are separately collected and experimental treatability studies are conducted on it. The results reflected that the reusable wastewater fraction has an approximate amount of 110 m³/day that accounts for 68% of the total wastewaters. The need for treatment applicable on reusable wastewaters is determined by considering water quality requirements of various operations and characterization of reusable wastewater streams. Ultra-filtration (UF), Nano-filtration (NF) and Reverse Osmosis (RO) membranes are subsequently applied on reusable effluent fraction. Adequate organic matter removal is not obtained with the mentioned treatment sequence.

Keywords: enamel coating, membrane, reuse, wastewater

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Authors: Pan Cheng, Jin Huang, Guang Zeng

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Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The methods possess high accuracy O(h3) and low computing complexity. The convergence and stability are proved based on Anselone-s collective compact theory. Bases on the asymptotic error expansion with odd powers, we can greatly improve the accuracy of the approximation, and also derive a posteriori error estimate which can be used for constructing self-adaptive algorithms. The efficiency of the algorithms are illustrated by numerical examples.

Keywords: boundary integral equation, extrapolation algorithm, aposteriori error estimate, elasticity.

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Authors: Duy Cuong Nguyen, Ali Makke, Guillaume Montay

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This work presents an improved single fiber pull-out test for fiber/matrix interface characterization. This test has been used to study the Inter-Facial Shear Strength ‘IFSS’ of hemp fibers reinforced polypropylene (PP). For this aim, the fiber diameter has been carefully measured using a tomography inspired method. The fiber section contour can then be approximated by a circle or a polygon. The results show that the IFSS is overestimated if the circular approximation is used. The Influence of the molding temperature on the IFSS has also been studied. We find that a molding temperature of 183◦C leads to better interfacial properties. Above or below this temperature the interface strength is reduced.

Keywords: Interface, pull-out, processing, temperature, hemp, polypropylene, composite.

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Authors: Thanh-Phong Dao, Shyh-Chour Huang

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This study presents a quasi-zero stiffness (QZS) vibration isolator using flexure-based spring mechanisms which afford both negative and positive stiffness elements, which enable self-adjustment. The QZS property of the isolator is achieved at the equilibrium position. A nonlinear mathematical model is then developed, based on the pre-compression of the flexure-based spring mechanisms. The dynamics are further analyzed using the Harmonic Balance method. The vibration attention efficiency is illustrated using displacement transmissibility, which is then compared with the corresponding linear isolator. The effects of parameters on performance are also investigated by numerical solutions. The flexure-based spring mechanisms are subsequently designed using the concept of compliant mechanisms, with evaluation by ANSYS software, and simulations of the QZS isolator.

Keywords: Vibration isolator, quasi-zero stiffness, flexure-based spring mechanisms, compliant mechanism.

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Authors: M. C. Arcuri, L. Gai, F. Ielasi

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Italian Central Guarantee Fund (CGF) has the purpose to facilitate Small and Medium-sized Enterprises (SMEs)’ access to credit. The aim of the paper is to study the evaluation method adopted by the CGF with regard to SMEs requiring its intervention. This is even more important in the light of the recent CGF reform. We analyse an initial sample of more than 500.000 guarantees from 2012 to 2018. We distinguish between a counter-guarantee delivered to a mutual guarantee institution and a guarantee directly delivered to a bank. We investigate the impact of variables related to the operations and the SMEs on Altman Z’’-score and the score consistent with CGF methodology. We verify that the type of intervention affects the scores and the initial condition changes with the new assessment criterions. 

Keywords: Banks, default risk, Italian Guarantee Fund, mutual guarantee institutions.

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Authors: F. Z. Doğru, O. Arslan

Abstract:

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

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

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Authors: Ş. Aksoy, A. Kurşun, E. Çetin, M. R. Haboğlu

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In this study, thermo elastic stress analysis is  performed on a cylinder made of laminated isotropic materials under  thermomechanical loads. Laminated cylinders have many  applications such as aerospace, automotive and nuclear plant in the  industry. These cylinders generally performed under  thermomechanical loads. Stress and displacement distribution of the  laminated cylinders are determined using by analytical method both  thermal and mechanical loads. Based on the results, materials  combination plays an important role on the stresses distribution along  the radius. Variation of the stresses and displacements along the  radius are presented as graphs. Calculations program are prepared  using MATLAB® by authors.

 

Keywords: Isotropic materials, laminated cylinders, thermoelastic stress, thermomechanical load.

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Authors: Zane Turner, Kevin Labille, Susan Gauch

Abstract:

Sentiment analysis is a broad and expanding field that aims to extract and classify opinions from textual data. Lexicon-based approaches are based on the use of a sentiment lexicon, i.e., a list of words each mapped to a sentiment score, to rate the sentiment of a text chunk. Our work focuses on predicting stock price change using a sentiment lexicon built from financial conference call logs. We present a method to generate a sentiment lexicon based upon an existing probabilistic approach. By using a domain-specific lexicon, we outperform traditional techniques and demonstrate that domain-specific sentiment lexicons provide higher accuracy than generic sentiment lexicons when predicting stock price change.

Keywords: Lexicon, sentiment analysis, stock movement prediction., computational finance.

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Authors: Somi Nah, Timothy Yoonsuk Lee, Jinhwan Yu

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In films, visual effects have played the role of expressing realities more realistically or describing imaginations as if they are real. Such images are immediated images representing realism, and the logic of immediation for the reality of images has been perceived dominant in visual effects. In order for immediation to have an identity as immediation, there should be the opposite concept hypermediation. In the mid 2000s, hypermediated images were settled as a code of mass culture in Asia. Thus, among Asian films highly popular in those days, this study selected five displaying hypermediated images – 2 Korean, 2 Japanese, and 1 Thailand movies – and examined the semiotic meanings of such images using Roland Barthes- directional and implicated meaning analysis and Metz-s paradigmatic analysis method, focusing on how hypermediated images work in the general context of the films, how they are associated with spaces, and what meanings they try to carry.

Keywords: Asian Films, Hypermediated Images, Semiotics, Visual Effects

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Option price valuation, Partial Differential Equations, Black-Scholes PDEs, Ito process.

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