Search results for: Thanh N. Long

Authors: Ahmad Izani M. Ismail, Md. Fazlul Karim, Mai Duc Thanh

Abstract:

A well balanced numerical scheme based on stationary waves for shallow water flows with arbitrary topography has been introduced by Thanh et al. [18]. The scheme was constructed so that it maintains equilibrium states and tests indicate that it is stable and fast. Applying the well-balanced scheme for the one-dimensional shallow water equations, we study the early shock waves propagation towards the Phuket coast in Southern Thailand during a hypothetical tsunami. The initial tsunami wave is generated in the deep ocean with the strength that of Indonesian tsunami of 2004.

Keywords: Tsunami study, shallow water, conservation law, well-balanced scheme, topography. Subject classification: 86 A 05, 86 A 17.

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Authors: Ngo Thanh Xuan, Mai Thi Hang, Vu Nguyen Thanh

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A. niger XP isolated from Vietnam produces very low amount of acidic phytase with optimal pH at 2.5 and 5.5. The phytase production of this strain was successfully improved through gene cloning and expression. A 1.4 - kb DNA fragment containing the coding region of the phyA gene was amplified by PCR and inserted into the expression vector pPICZαA with a signal peptide α- factor, under the control of AOX1 promoter. The recombined plasmid was transformed into the host strain P. pastoris KM71H and X33 by electroporation. Both host strains could efficiently express and secret phytase. The multicopy strains were screened for over expression of phytase. All the selected multicopy strains of P. pastoris X33 were examined for phytase activity, the maximum phytase yield of 1329 IU/ml was obtained after 4 days of incubation in medium BMM. The recombinant protein with MW of 97.4 KW showed to be the only one protein secreted in the culture broth. Multicopy transformant P. pastoris X33 supposed to be potential candidate for producing the commercial preparation of phytase.

Keywords: Aspergillus niger XP, cloning, over expression, Pichia pastoris, phyA , phytase.

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Authors: Chatchai Pesee

Abstract:

This paper examines long-range dependence or longmemory of financial time series on the exchange rate data by the fractional Brownian motion (fBm). The principle of spectral density function in Section 2 is used to find the range of Hurst parameter (H) of the fBm. If 0< H <1/2, then it has a short-range dependence (SRD). It simulates long-memory or long-range dependence (LRD) if 1/2< H <1. The curve of exchange rate data is fBm because of the specific appearance of the Hurst parameter (H). Furthermore, some of the definitions of the fBm, long-range dependence and selfsimilarity are reviewed in Section II as well. Our results indicate that there exists a long-memory or a long-range dependence (LRD) for the exchange rate data in section III. Long-range dependence of the exchange rate data and estimation of the Hurst parameter (H) are discussed in Section IV, while a conclusion is discussed in Section V.

Keywords: Fractional Brownian motion, long-rangedependence, memory, short-range dependence.

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Authors: Gergely Treplan, Long Tran-Thanh, Janos Levendovszky

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In this paper, a reliable cooperative multipath routing algorithm is proposed for data forwarding in wireless sensor networks (WSNs). In this algorithm, data packets are forwarded towards the base station (BS) through a number of paths, using a set of relay nodes. In addition, the Rayleigh fading model is used to calculate the evaluation metric of links. Here, the quality of reliability is guaranteed by selecting optimal relay set with which the probability of correct packet reception at the BS will exceed a predefined threshold. Therefore, the proposed scheme ensures reliable packet transmission to the BS. Furthermore, in the proposed algorithm, energy efficiency is achieved by energy balancing (i.e. minimizing the energy consumption of the bottleneck node of the routing path) at the same time. This work also demonstrates that the proposed algorithm outperforms existing algorithms in extending longevity of the network, with respect to the quality of reliability. Given this, the obtained results make possible reliable path selection with minimum energy consumption in real time.

Keywords: wireless sensor networks, reliability, cooperativerouting, Rayleigh fading model, energy balancing

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Authors: Seung-Won Jung, Hye-Soo Kim, Le Thanh Ha, Seung-Jin Baek, Sung-Jea Ko

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In this paper, a novel deinterlacing algorithm is proposed. The proposed algorithm approximates the distribution of the luminance into a polynomial function. Instead of using one polynomial function for all pixels, different polynomial functions are used for the uniform, texture, and directional edge regions. The function coefficients for each region are computed by matrix multiplications. Experimental results demonstrate that the proposed method performs better than the conventional algorithms.

Keywords: Deinterlacing, polynomial interpolation.

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Authors: D. Czurratis, Y. Beyl, S. Zinober, R. Zengerle, F. Lärmer

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A new concept for long-term reagent storage for Labon- a-Chip (LoC) devices is described. Here we present a polymer multilayer stack with integrated stick packs for long-term storage of several liquid reagents, which are necessary for many diagnostic applications. Stick packs are widely used in packaging industry for storing solids and liquids for long time. The storage concept fulfills two main requirements: First, a long-term storage of reagents in stick packs without significant losses and interaction with surroundings, second, on demand releasing of liquids, which is realized by pushing a membrane against the stick pack through pneumatic pressure. This concept enables long-term on-chip storage of liquid reagents at room temperature and allows an easy implementation in different LoC devices.

Keywords: Lab-on-a-Chip, long-term storage, reagent storage, stick pack.

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Authors: Tanvir Ahmed, Thanh N. Long, Phan T. Huong, Donald E. Stewart

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This paper presents views on condom use and the contexts of safe and unsafe sexual practices with different sexual partners and their relationships among Injecting Drug Users (IDUs) in Hai Phong, Vietnam. Fifteen IDUs participated and two local interviewers conducted qualitative semi-structured face-to-face interviews in September-October, 2012 in Vietnamese language. Data were analyzed thematically. Non-protective condom attitudes include negotiate or convince Female Sex Workers (FSW); not realizing risk, importance or necessity; partner doesn’t like, and having extra money/drug from clients. On the other hand, self-awareness, family-consciousness, suspicion of STI presence, fear of getting HIV, and client negotiation sometimes resulted in a safe-sex practice. A thematic diagram was developed to present the relationship (strong/weak) between condom attitude and sexual practice (safe/unsafe) by partner types. The experiences and views reflected in the qualitative information emphasize the heightened need for safe-sex education especially among young IDUs (male/female) highlighting sexual transmission risk.

Keywords: AIDS, HIV, injecting drug user, risk behaviors, Vietnam.

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Authors: Pham Thanh Trung, Huynh Quyet Thang

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Reliability is one of the most important quality attributes of software. Based on the approach of Reussner and the approach of Cheung, we proposed the reliability prediction model of component-based software architectures. Also, the value of the model is shown through the experimental evaluation on a web server system.

Keywords: component-based architecture, reliability prediction model, software reliability engineering.

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Authors: Y. Araki, M. Kim, S. Okayama, K. Ikago, K. Uetani

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We study dynamic instability in high-rise steel moment resisting frames (SMRFs) subjected to synthetic long-period ground motions caused by hypothetical huge subduction earthquakes. Since long duration as well as long dominant periods is a characteristic of long-period ground motions, interstory drifts may enter the negative postyield stiffness range many times when high-rise buildings are subjected to long-period ground motions. Through the case studies of 9 high-rise SMRFs designed in accordance with the Japanese design practice in 1980s, we demonstrate that drifting, or accumulation of interstory drifts in one direction, occurs at the lower stories of the SMRFs, if their natural periods are close to the dominant periods of the long-period ground motions. The drifting led to residual interstory drift ratio over 0.01, or to collapse if the design base shear was small.

Keywords: long-period ground motion, P-Delta effect, high-rise steel moment resisting frame (SMRF), subduction earthquake

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Authors: Jakyoung Kim, Sungwook Jang

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The purpose of this study is to examine the research trends of life-long education for people with disabilities using a keyword network analysis. For this purpose, 151 papers were selected from 594 papers retrieved using keywords such as 'people with disabilities' and 'life-long education' in the Korean Education and Research Information Service. The Keyword network analysis was constructed by extracting and coding the keyword used in the title of the selected papers. The frequency of the extracted keywords, the centrality of degree, and betweenness was analyzed by the keyword network. The results of the keyword network analysis are as follows. First, the main keywords that appeared frequently in the study of life-long education for people with disabilities were 'people with disabilities', 'life-long education', 'developmental disabilities', 'current situations', 'development'. The research trends of life-long education for people with disabilities are focused on the current status of the life-long education and the program development. Second, the keyword network analysis and visualization showed that the keywords with high frequency of occurrences also generally have high degree centrality and betweenness centrality. In terms of the keyword network diagram, it was confirmed that research trends of life-long education for people with disabilities are centered on six prominent keywords. Based on these results, it was discussed that life-long education for people with disabilities in the future needs to expand the subjects and the supporting areas of the life-long education, and the research needs to be further expanded into more detailed and specific areas. 

Keywords: Life-long education, people with disabilities, research trends, keyword network analysis.

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Authors: Abriak Nor Edine, Zentar Rachid, Achour Raouf, Tran Ngoc Thanh

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This work is undertaken to develop a methodology to enhance the management of dredged marine and river sediments in the North of France. The main objective of this study is to determine the main characteristics of these sediments. In this order, physical, mineralogical and chemical properties of both types of sediments are measured. Moreover, their potential impacts on the environment are assessed throughout leaching tests. From the obtained results, the potential of their use in road engineering is discussed.

Keywords: Marine sediments, River sediments, Physicochemical characterizations, Environmental characterizations.

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Authors: Yilun Shang

Abstract:

We study a long-range percolation model in the hierarchical lattice ΩN of order N where probability of connection between two nodes separated by distance k is of the form min{αβ−k, 1}, α ≥ 0 and β > 0. The parameter α is the percolation parameter, while β describes the long-range nature of the model. The ΩN is an example of so called ultrametric space, which has remarkable qualitative difference between Euclidean-type lattices. In this paper, we characterize the sizes of large clusters for this model along the line of some prior work. The proof involves a stationary embedding of ΩN into Z. The phase diagram of this long-range percolation is well understood.

Keywords: percolation, component, hierarchical lattice, phase transition.

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Authors: S. Noor, M. W. Siddiqi

Abstract:

This study examines causal link between energy use and economic growth for five South Asian countries over period 1971-2006. Panel cointegration, ECM and FMOLS are applied for short and long run estimates. In short run unidirectional causality from per capita GDP to per capita energy consumption is found, but not vice versa. In long run one percent increase in per capita energy consumption tend to decrease 0.13 percent per capita GDP. i.e. Energy use discourage economic growth. This short and long run relationship indicate energy shortage crisis in South Asia due to increased energy use coupled with insufficient energy supply. Beside this long run estimated coefficient of error term suggest that short term adjustment to equilibrium are driven by adjustment back to long run equilibrium. Moreover, per capita energy consumption is responsive to adjustment back to equilibrium and it takes 59 years approximately. It specifies long run feedback between both variables.

Keywords: Energy consumption, Income, Panel co-integration, Causality.

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Authors: Le Thanh Ha, Hye-Soo Kim, Chun-Su Park, Seung-Won Jung, Sung-Jea Ko

Abstract:

Flexible macroblock ordering (FMO), adopted in the H.264 standard, allows to partition all macroblocks (MBs) in a frame into separate groups of MBs called Slice Groups (SGs). FMO can not only support error-resilience, but also control the size of video packets for different network types. However, it is well-known that the number of bits required for encoding the frame is increased by adopting FMO. In this paper, we propose a novel algorithm that can reduce the bitrate overhead caused by utilizing FMO. In the proposed algorithm, all MBs are grouped in SGs based on the similarity of the transform coefficients. Experimental results show that our algorithm can reduce the bitrate as compared with conventional FMO.

Keywords: Data Partition, Entropy Coding, Greedy Algorithm, H.264/AVC, Slice Group.

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Authors: M. Olmedilla, M. R. Martinez-Torres, S. L. Toral

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Electronic Word-Of-Mouth (eWOM) communities represent today an important source of information in which more and more customers base their purchasing decisions. They include thousands of reviews concerning very different products and services posted by many individuals geographically distributed all over the world. Due to their massive audience, eWOM communities can help users to find the product they are looking for even if they are less popular or rare. This is known as the long tail effect, which leads to a larger number of lower-selling niche products. This paper analyzes the long tail effect in a well-known eWOM community and defines a tool for finding niche products unavailable through conventional channels.

Keywords: eWOM, Online user reviews, Long tail theory, Product categorization, Social Network Analysis.

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Authors: Thang V. Kieu, Long P. Nguyen

Abstract:

Kernelized Correlation Filter (KCF) based trackers have gained a lot of attention recently because of their accuracy and fast calculation speed. However, this algorithm is not robust in cases where the object is lost by a sudden change of direction, being obscured or going out of view. In order to improve KCF performance in long-term tracking, this paper proposes an anomaly detection method for target loss warning by analyzing the response map of each frame, and a classification algorithm for reliable target re-locating mechanism by using Random fern. Being tested with Visual Tracker Benchmark and Visual Object Tracking datasets, the experimental results indicated that the precision and success rate of the proposed algorithm were 2.92 and 2.61 times higher than that of the original KCF algorithm, respectively. Moreover, the proposed tracker handles occlusion better than many state-of-the-art long-term tracking methods while running at 60 frames per second.

Keywords: Correlation filter, long-term tracking, random fern, real-time tracking.

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Authors: Ariane Lazaridès, Claude Bélanger, Stéphane Sabourin

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In this longitudinal study, we examined the moderating role of personality in the relationship between communication behaviors and long-term dyadic adjustment. A sample of 82 couples completed the NEO Five-Factor Inventory and the Dyadic Adjustment Scale. These couples were also videotaped during a 15-minute problem-solving discussion. Approximately 2.5 years later, these couples completed again the Dyadic Adjustment Scale. Results show that personality of both men and women moderates the relationship between communication behaviors of the partner and long-term dyadic adjustment of the individual. Women-s openness and men-s extraversion moderate the relationship between some communication behaviors and long-term dyadic adjustment

Keywords: Communication Behavior, Couples, Dyadic Adjustment, Personality.

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Authors: O. Miraliyari, M.M. Najafizadeh, A.R. Rahmani, A. Momeni Hezaveh

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This paper presents the buckling analysis of short and long functionally graded cylindrical shells under thermal and mechanical loads. The shell properties are assumed to vary continuously from the inner surface to the outer surface of the shell. The equilibrium and stability equations are derived using the total potential energy equations, Euler equations and first order shear deformation theory assumptions. The resulting equations are solved for simply supported boundary conditions. The critical temperature and pressure loads are calculated for both short and long cylindrical shells. Comparison studies show the effects of functionally graded index, loading type and shell geometry on critical buckling loads of short and long functionally graded cylindrical shells.

Keywords: Buckling, Functionally graded materials, Short and long cylindrical shell, Thermal and mechanical loads.

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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. Ilyas, M. W. Siddiqi

Abstract:

This study employs auto-regressive distributed lag (ARDL) bounds approach to cointegration for long run and errorcorrection modeling (ECM) for short run analysis to examine the relationship between revenue gap and economic growth for Pakistan using annual time series data over the period 1980 to 2008. The short and long run results indicate that revenue gap is statistical significant and negatively effect economic growth. The significant and negative coefficient of error correction term in ECM indicates that after a shock, the long rum equilibrium will again converge towards equilibrium about 10.406 percent within a year.

Keywords: ARDL cointegration, Economic Growth, RevenueGap, Pakistan.

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Authors: B. Skrabic, N. Tomic-Plazibat

Abstract:

In this paper real money demand function is analyzed within multivariate time-series framework. Cointegration approach is used (Johansen procedure) assuming interdependence between money demand determinants, which are nonstationary variables. This will help us to understand the behavior of money demand in Croatia, revealing the significant influence between endogenous variables in vector autoregrression system (VAR), i.e. vector error correction model (VECM). Exogeneity of the explanatory variables is tested. Long-run money demand function is estimated indicating slow speed of adjustment of removing the disequilibrium. Empirical results provide the evidence that real industrial production and exchange rate explains the most variations of money demand in the long-run, while interest rate is significant only in short-run.

Keywords: Cointegration, Long-run equilibrium, Money demand function, Vector error correction model.

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Authors: A. Md. Harunur Rashid B. Md. Keramat Ali Molla C. Tarif Uddin Ahmed

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This paper represents the results of long term strength of mortar incorporating Rice Husk Ash (RHA). For these work mortar samples were made according to ASTM standard C 109/C. OPC cement was partially replaced by RHA at 0, 10, 15, 20, 25 and 30 percent replacement level. After casting all samples were kept in controlled environment and curing was done up to 90 days. Test of mortar was performed on 3, 7, 28, 90, 365 and 700 days. It is noticed that OPC mortar shows better strength at early age than mortar having RHA but at 90 days and onward the picture is different. At 700 days it is observed that mortar containing 20% RHA shows better result than any other samples.

Keywords: OPC, RHA, replacement level, long term, strength.

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Authors: Viet Dzung Nguyen, Duc Thuan Nguyen, Tien Dzung Nguyen, Van Thanh Pham

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Mammography is the most effective procedure for an early diagnosis of the breast cancer. Nowadays, people are trying to find a way or method to support as much as possible to the radiologists in diagnosis process. The most popular way is now being developed is using Computer-Aided Detection (CAD) system to process the digital mammograms and prompt the suspicious region to radiologist. In this paper, an automated CAD system for detection and classification of massive lesions in mammographic images is presented. The system consists of three processing steps: Regions-Of- Interest detection, feature extraction and classification. Our CAD system was evaluated on Mini-MIAS database consisting 322 digitalized mammograms. The CAD system-s performance is evaluated using Receiver Operating Characteristics (ROC) and Freeresponse ROC (FROC) curves. The archived results are 3.47 false positives per image (FPpI) and sensitivity of 85%.

Keywords: classification, computer-aided detection, featureextraction, mass detection.

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Authors: Samra Bajwa, Muhammad W. Siddiqi

Abstract:

The study investigates the causal link between trade openness and economic growth for four South Asian countries for period 1972-1985 and 1986-2007 to examine the scenario before and after the implementation of SAARC. Panel cointegration and FMOLS techniques are employed for short run and long run estimates. In 1972-85 short run unidirectional causality from GDP to openness is found whereas, in 1986-2007 there exists bi-directional causality between GDP and openness. The long run elasticity magnitude between GDP and openness contains negative sign in 1972-85 which shows that there exists long run negative relationship. While in time period 1986-2007 the elasticity magnitude has positive sign that indicates positive causation between GDP and openness. So it can be concluded that after the implementation of SAARC overall situation of selected countries got better. Also long run coefficient of error term suggests that short term equilibrium adjustments are driven by adjustment back to long run equilibrium.

Keywords: Causality, Economic Growth, Panel Co-integration, SAARC, Trade Openness.

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Authors: Augustine C. Azubogu, Victor E. Idigo, Schola U. Nnebe, Obinna S. Oguejiofor, Simon E.

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The main goal of this seminal paper is to introduce the application of Wireless Sensor Networks (WSN) in long distance infrastructure monitoring (in particular in pipeline infrastructure monitoring) – one of the on-going research projects by the Wireless Communication Research Group at the department of Electronic and Computer Engineering, Nnamdi Azikiwe University, Awka. The current sensor network architectures for monitoring long distance pipeline infrastructures are previewed. These are wired sensor networks, RF wireless sensor networks, integrated wired and wireless sensor networks. The reliability of these architectures is discussed. Three reliability factors are used to compare the architectures in terms of network connectivity, continuity of power supply for the network, and the maintainability of the network. The constraints and challenges of wireless sensor networks for monitoring and protecting long distance pipeline infrastructure are discussed.

Keywords: Connectivity, maintainability, reliability, wireless sensor networks.

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Authors: Serge Provost, Yishan Zang

Abstract:

Following a review of various approaches that are utilized for classifying the tail behavior of a distribution, an easily implementable methodology that relies on an arctangent transformation is presented. The classification criterion is actually based on the difference between two specific quantiles of the transformed distribution. The resulting categories enable one to classify distributional tails as distinctly short, short, nearly medium, medium, extended medium and somewhat long, providing that at least two moments exist. Distributions possessing a single moment are said to be long tailed while those failing to have any finite moments are classified as having an extremely long tail. Several illustrative examples will be presented.

Keywords: Arctangent transformation, change of variables, heavy-tailed distributions, tail classification.

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Authors: Viet-Hoang Vu, Nhan Le-Thanh

Abstract:

Recently the usefulness of Concept Abduction, a novel non-monotonic inference service for Description Logics (DLs), has been argued in the context of ontology-based applications such as semantic matchmaking and resource retrieval. Based on tableau calculus, a method has been proposed to realize this reasoning task in ALN, a description logic that supports simple cardinality restrictions as well as other basic constructors. However, in many ontology-based systems, the representation of ontology would require expressive formalisms for capturing domain-specific constraints, this language is not sufficient. In order to increase the applicability of the abductive reasoning method in such contexts, we would like to present in the scope of this paper an extension of the tableaux-based algorithm for dealing with concepts represented inALCQ, the description logic that extends ALN with full concept negation and quantified number restrictions.

Keywords: Abductive reasoning, description logics, semantic matchmaking, non-monotonic inference, tableaux-based method.

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Authors: Atisthan Wuttimanop, Suchada Rianmora, Mahint Mahattanakorn

Abstract:

Feet and ankles are parts of human body that receive high-pressure in every day. Feet disorders such as ankle sprain, achilles tendonitis, heel pain, and plantar fasciitis are very common. There are many causes for these feet disorders such as wearing high heels, obesity, sports activity, and standing for a long time. There are many reliefs for feet disorders such as heel insert. However, they come in various shapes and use different materials. There are no specifications in which type is suitable for specific user. This has led to the proposed research to provide guidelines for selecting the appropriate heel insert for ladies who face with long-standing carriers. This research uses contact-measuring techniques to test forces, contact area, and pressure acting on a person’s feet in various standing positions with different insert materials and shapes. The proper material for making insert will be presented and discussed.

Keywords: Heel inserts, Long-standing person, Contact-data acquisition, Finite element analysis, Ethylene-vinyl acetate (EVA).

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Authors: Hicham Benamirouche, Oum Elkheir Moussi

Abstract:

The purpose of the study is to examine the dynamics of Algeria’s natural gas exports through the Autoregressive Distributed Lag (ARDL) bounds testing approach with break points. The analysis was carried out for the period from 1967 to 2015. Based on imperfect substitution specification, the ARDL approach reveals a long-run equilibrium relationship between Algeria’s Natural gas exports and their determinant factors (Algeria’s gas reserves, Domestic gas consumption, Europe’s GDP per capita, relative prices, the European gas production and the market share of competitors). All the long-run elasticities estimated are statistically significant with a large impact of domestic factors, which constitute the supply constraints. In short term, the elasticities are statistically significant, and almost comparable to those of the long term. Furthermore, the speed of adjustment towards long-run equilibrium is less than one year because of the little flexibility of the long term export contracts. Two break points have been estimated when we employ the domestic gas consumption as a break variable; 1984 and 2010, which reflect the arbitration policy between the domestic gas market and gas exports.

Keywords: Natural gas exports, elasticity, ARDL bounds testing, break points, Algeria.

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Authors: Nguyen Thi Thanh Truc, Chi-Hyeon Lee, Byeong-Kyu Lee, Srinivasa Reddy Mallampati

Abstract:

This study evaluated to facilitate separation of ABS plastics from other waste plastics by froth flotation after surface hydrophilization of ABS with heat treatment. The mild heat treatment at 100oC for 60s could selectively increase the hydrophilicity of the ABS plastics surface (i.e., ABS contact angle decreased from 79o to 65.8o) among other plastics mixture. The SEM and XPS results of plastic samples sufficiently supported the increase in hydrophilic functional groups and decrease contact angle on ABS surface, after heat treatment. As a result of the froth flotation (at mixing speed 150 rpm and airflow rate 0.3 L/min) after heat treatment, about 85% of ABS was selectively separated from other heavy plastics with 100% of purity. The effect of optimum treatment condition and detailed mechanism onto separation efficiency in the froth floatation was also investigated. This research is successful in giving a simple, effective, and inexpensive method for ABS separation from waste plastics.

Keywords: ABS, hydrophilic, heat treatment, froth flotation, contact angle.

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