Search results for: stationary bifurcation

Authors: Rahele Mosleh

Abstract:

This paper gives a survey of results on global stability of extended Ross model for malaria by constructing some elegant Lyapunov functions for two cases of epidemic, including disease-free and endemic occasions. The model is a nonlinear seven-dimensional system of ordinary differential equations that simulates this phenomenon in a more realistic fashion. We discuss the existence of positive disease-free and endemic equilibrium points of the model. It is stated that extended Ross model possesses invariant solutions for human and mosquito in a specific domain of the system.

Keywords: global stability, invariant solutions, Lyapunov function, stationary points

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Authors: Hamid Reza Pakzad

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In this paper, the properties of dust-ion-acoustic (DIA) shock waves in an unmagnetized dusty plasma, whose constituents are inertial ions, superthermal electrons, and stationary dust particles, are investigated by employing the reductive perturbation method. The dissipation is taken into account the kinematic viscosity among the plasma constituents. It is shown that the basic features of DIA shock waves are significantly modified by the effects of electron superthermality and ion kinematic viscosity.

Keywords: reductive perturbation method, dust ion acoustic shock wave, superthermal electron, dissipative plasmas

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Authors: Michaela Chovancova, Pavel Niedoba

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For the treatment of acute and chronic lung diseases it is preferred to deliver medicaments by inhalation. The drug is delivered directly to tracheobronchial tree. This way allows the given medicament to get directly into the place of action and it makes rapid onset of action and maximum efficiency. The transport of aerosol particles in the particular part of the lung is influenced by their size, anatomy of the lungs, breathing pattern and airway resistance. This article deals with calculation of airway resistance in the lung model of Horsfield. It solves the problem of determination of the pressure losses in bifurcation and thus defines the pressure drop at a given location in the bronchial tree. The obtained data will be used as boundary conditions for transport of aerosol particles in a central part of bronchial tree realized by Computational Fluid Dynamics (CFD) approach. The results obtained from CFD simulation will allow us to provide information on the required particle size and optimal inhalation technique for particle transport into particular part of the lung.

Keywords: human lungs, bronchial tree, pressure losses, airways resistance, flow, breathing

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Authors: F. Boudet, V. Galano, D. Gmira, L. Munoz, A. Reina

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Commodities pricing needs a specific approach as they are often linked to each other and so are expectedly doing their prices. They are called co-integrated when at least one stationary linear combination exists between them. Though widespread in economic literature, and even if many equilibrium relations and co-movements exist in the economy, this principle of co-movement is not developed in derivatives field. The present study focuses on the following problem: How can the price of a forward agreement on a commodity be simulated, when it is co-integrated with other ones? Theoretical analysis is developed from Gibson-Schwartz model and an analytical solution is given for short maturities contracts and under risk-neutral conditions. The application has been made to crude oil and heating oil energy commodities and result confirms the applicability of proposed method.

Keywords: co-integration, commodities, forward pricing, Gibson-Schwartz

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Authors: Heri Kuswanto, Philipp Sibbertsen, Irhamah

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A Wald type test to distinguish between long memory and ESTAR nonlinearity has been developed. The test uses a directed-Wald statistic to overcome the problem of restricted parameters under the alternative. The test is derived from a model specification i.e. allows the transition parameter to appear as a nuisance parameter in the transition function. A simulation study has been conducted and it indicates that the approach leads a test with good size and power properties to distinguish between stationary long memory and ESTAR.

Keywords: directed-Wald test, ESTAR, long memory, distinguish

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Authors: Goh Mingyuan Asher, Nurul Fadiah Johari, Neo Yu Wei, Kim Aryung, Ho Kong Chong, Irene Y. H. N. G.

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The COVID-19 pandemic represents an externally induced force as they face a combination of reduced work, dismissal, and job change for young precarious workers. The paper drew insights from two interview waves of the in-work poverty study in Singapore which were conducted a year apart. By analysing respondents’ job histories before and at the start of the pandemic as well as their job experiences over the two waves of interviews, the study found the presence of what scholars describe as trap and stepping stone trajectories. Trap trajectories refer to how the nature of precarious employment leads respondents to be in dead-end jobs with no room for progression while stepping stone trajectories refer to how poor work provides opportunities for the accumulation of work experiences. We also look at how structure, agency and biographical factors affect job trajectories and discuss the impacts of COVID-19 on work experiences and the implications of the bifurcation of trajectory outcomes on poverty and inequality among the young working poor in Singapore.

Keywords: working poor, precarity, young workers, COVID-19, work trajectories

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Authors: M. Sharif Imam Ibne Amir, Mohammad Masud Kamal Khan, Mohammad Golam Rasul, Raj H. Sharma, Fatema Akram

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Future flood can be predicted using the probable maximum flood (PMF). PMF is calculated using the historical discharge or rainfall data considering the other climatic parameter stationary. However, climate is changing globally and the key climatic variables are temperature, evaporation, rainfall and sea level rise (SLR). To develop scenarios to a basin or catchment scale these important climatic variables should be considered. Nowadays scenario based on climatic variables is more suitable than PMF. Six scenarios were developed for a large Fitzroy basin and presented in this paper.

Keywords: climate change, rainfall, potential evaporation, scenario, sea level rise (SLR), sub-catchment

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Authors: Somnath Mukhuti, Prem Kumar Ghosh

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Background and significance of the study Indian stock market has undergone sudden changes after the current China crisis in terms of turnover, market capitalization, share prices, etc. The average returns on equity investment in both markets have more than three and half times after global financial crisis owing to the development of industrial activity, corporate sectors development, enhancement in global consumption, change of global financial association and fewer imports from developed countries. But the economic policies of both the economies are far different, that is to say, where Indian economy maintaining a conservative policy, Chinese economy maintaining an aggressive policy. Besides this, Chinese economy recently lowering its currency for increasing mysterious growth but Indian does not. But on August 24, 2015 Indian stock market and world stock markets were fall down due to the reason of Chinese stock market. Keeping in view of the above, this study seeks to examine the influence of Chinese stock on Indian stock market. Methodology This research work is based on daily time series data obtained from yahoo finance database between 2009 (April 1) to 2015 (September 28). This study is based on two important stock markets, that is, Indian stock market (Bombay Stock Exchange) and Chinese stock market (Shanghai Stock Exchange). In the course of analysis, the daily raw data were converted into natural logarithm for minimizing the problem of heteroskedasticity. While tackling the issue, correlation statistics, ADF and PP unit root test, bivariate cointegration test and causality test were used. Major findings Correlation statistics show that both stock markets are associated positively. Both ADF and PP unit root test results demonstrate that the time series data were not normal and were not stationary at level however stationary at 1st difference. The bivariate cointegration test results indicate that the Indian stock market was associated with Chinese stock market in the long-run. The Granger causality test illustrates there was a unidirectional causality between Indian stock market and Chinese stock market. Concluding statement The empirical results recommend that India’s stock market was not very much dependent on Chinese stock market because of Indian economic conservative policies. Nevertheless, Indian stock market might be sturdy if Indian economic policies are changed slightly and if increases the portfolio investment with Chinese economy. Indian economy might be a third largest economy in 2030 if India increases its portfolio investment and trade relations with both Chinese economy and US economy.

Keywords: Indian stock market, China stock market, bivariate cointegration, causality test

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Authors: Mohamed El Morsy, Gabriela Achtenová

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Condition monitoring is used to increase machinery availability and machinery performance, whilst reducing consequential damage, increasing machine life, reducing spare parts inventories, and reducing breakdown maintenance. An efficient condition monitoring system provides early warning of faults by predicting them at an early stage. When a localized fault occurs in gears, the vibration signals always exhibit non-stationary behavior. The periodic impulsive feature of the vibration signal appears in the time domain and the corresponding gear mesh frequency (GMF) emerges in the frequency domain. However, one limitation of frequency-domain analysis is its inability to handle non-stationary waveform signals, which are very common when machinery faults occur. Particularly at the early stage of gear failure, the GMF contains very little energy and is often overwhelmed by noise and higher-level macro-structural vibrations. An effective signal processing method would be necessary to remove such corrupting noise and interference. In this paper, a new hybrid method based on optimal Morlet wavelet filter and autocorrelation enhancement is presented. First, to eliminate the frequency associated with interferential vibrations, the vibration signal is filtered with a band-pass filter determined by a Morlet wavelet whose parameters are selected or optimized based on maximum Kurtosis. Then, to further reduce the residual in-band noise and highlight the periodic impulsive feature, an autocorrelation enhancement algorithm is applied to the filtered signal. The test stand is equipped with three dynamometers; the input dynamometer serves as the internal combustion engine, the output dynamometers induce a load on the output joint shaft flanges. The pitting defect is manufactured on the tooth side of a gear of the fifth speed on the secondary shaft. The gearbox used for experimental measurements is of the type most commonly used in modern small to mid-sized passenger cars with transversely mounted powertrain and front wheel drive: a five-speed gearbox with final drive gear and front wheel differential. The results obtained from practical experiments prove that the proposed method is very effective for gear fault diagnosis.

Keywords: wavelet analysis, pitted gear, autocorrelation, gear fault diagnosis

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Authors: Ramachandran Manivannan, B. Sakthi Swaroop, Selvam Noyel Victoria

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Microbial corrosion of brass gauze by the aerobic film forming bacteria Arthrobacter sulfurous in neutral media was investigated using gravimetric studies. Maximum weight loss of 166.98 mg was observed for a period of 28 days of exposure to the bacterial medium as against the weight loss of 13.69 mg for control. The optical density studies for the bacterial culture was found to show attainment of stationary phase in 48 h. Scanning electron microscopy analysis of the samples shows the presence of pitting corrosion. The energy dispersive X-ray analysis of the samples showed increased oxygen and phosphorus content in the sample due to bacterial activity.

Keywords: Arthrobacter sulfureus, biocorrosion, brass, neutral medium

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Authors: Adel Yasky, Waseem Al-Talalwah, Shorok Al Dorazi, Roger Soames

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The internal pudendal artery is a standard branch of the anterior division of the internal iliac artery. The current study includes 41 cadavers to investigate the origin and branches of the internal pudendal artery and its clinical significances. The internal pudendal artery arose directly from the anterior division of the internal iliac artery in 48.3% while it arose indirectly in 48.5%. However, the internal pudendal artery arose from the posterior division of internal iliac artery in 1.6%. Moreover, it arose internal iliac artery bifurcation site in 1.6%. Further, the internal pudendal artery supplied the urinary bladder in 17.1%. Also, the internal pudendal artery supplied the rectum 33.5% respectively. It gave uterine and vaginal arteries in 9.4% and 7.8% respectively. Finally, it supplied the sciatic nerve via giving lateral sacral branch in 1.6%. Internists, surgeons and radiologists have to be aware of the variability to decrease iatrogenic injury. Therefore, unnecessary proximal ligation should be avoided at the site of indirect origin of the internal pudendal artery to prevent sciatic neuropathy. Further, intrapelvic bleeding as result of laceration of internal pudendal branches during hysterectomy, prostatectomy or proctectomy should be expected. Therefore, this study increases the awareness of surgeons leading to minimize iatrogenic faults,

Keywords: internal pudendal artery, inferior gluteal artery, superior gluteal artery, internal iliac artery, impotence, decreased libido

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Authors: M. Osman Gani, M. Ferdows, Toshiyuki Ogawa

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In this work, we proposed a modified FHN-type reaction-diffusion system for a bistable excitable system by adding a scaled function obtained from a given function. We study the existence and the stability of the periodic traveling waves (or wavetrains) for the FitzHugh-Nagumo (FHN) system and the modified one and compare the results. The stability results of the periodic traveling waves (PTWs) indicate that most of the solutions in the fast family of the PTWs are stable for the FitzHugh-Nagumo equations. The instability occurs only in the waves having smaller periods. However, the smaller period waves are always unstable. The fast family with sufficiently large periods is always stable in FHN model. We find that the oscillation of pulse widths is absent in the standard FHN model. That motivates us to study the PTWs in the proposed FHN-type reaction-diffusion system for the bistable excitable media. A good agreement is found between the solutions of the traveling wave ODEs and the corresponding whole PDE simulation.

Keywords: bistable system, Eckhaus bifurcation, excitable media, FitzHugh-Nagumo model, periodic traveling waves

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Authors: M.R Asghari Bejestani, Gh. R. Mohammad Khani, V.R. Nafisi

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Imagined speech recognition is one of the most interesting approaches to BCI development and a lot of works have been done in this area. Many different experiments have been designed and hundreds of combinations of feature extraction methods and classifiers have been examined. Reported classification accuracies range from the chance level to more than 90%. Based on non-stationary nature of brain signals, we have introduced 3 classification modes according to time difference in inter and intra-class samples. The modes can explain the diversity of reported results and predict the range of expected classification accuracies from the brain signal accusation procedure. In this paper, a few samples are illustrated by inspecting results of some previous works.

Keywords: brain computer interface, silent talk, imagined speech, classification, signal processing

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Authors: Najwa Mimouni, Omar Rahli, Rachid Bennacer, Salah Chikh

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In the present work 2D and 3D numerical simulations of double diffusion natural convection in an elongated enclosure filled with a binary fluid saturating a porous medium are carried out. In the formulation of the problem, the Boussinesq approximation is considered and cross Neumann boundary conditions are specified for heat and mass walls conditions. The numerical method is based on the control volume approach with the third order QUICK scheme. Full approximation storage (FAS) with full multigrid (FMG) method is used to solve the problem. For the explored large range of the controlling parameters, we clearly evidenced that the increase in the depth of the cavity i.e. the lateral aspect ratio has an important effect on the flow patterns. The 2D perfect parallel flows obtained for a small lateral aspect ratio are drastically destabilized by increasing the cavity lateral dimension. This yields a 3D fluid motion with a much more complicated flow pattern and the classically studied 2D parallel flows are impossible.

Keywords: bifurcation, natural convection, heat and mass transfer, parallel flow, porous media

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Authors: Ekaterina Artiukhina, Panagiotis Grammelis

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Torrefaction of biomass pellets is considered as a useful pretreatment technology in order to convert them into a high quality solid biofuel that is more suitable for pyrolysis, gasification, combustion and co-firing applications. In the course of torrefaction the temperature varies across the pellet, and therefore chemical reactions proceed unevenly within the pellet. However, the uniformity of the thermal distribution along the pellet is generally assumed. The torrefaction process of a single cylindrical pellet is modeled here, accounting for heat transfer coupled with chemical kinetics. The drying sub-model was also introduced. The non-stationary process of wood pellet decomposition is described by the system of non-linear partial differential equations over the temperature and mass. The model captures well the main features of the experimental data.

Keywords: torrefaction, biomass pellets, model, heat, mass transfer

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Authors: J. Berčík, A. Mravcová, A. Rusková, P. Jurčišin, R. Virágh

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The online world is changing every day. With this comes the emergence and development of new business models. One of them is the sale of several types of products in one place. This type of sales in the form of online marketplaces has undergone a positive development in recent years and represents a kind of alternative to brick-and-mortar shopping centres. The main philosophy is to buy several products under one roof. Examples of popular e-commerce marketplaces are Amazon, eBay, and Allegro. Their share of total e-commerce turnover is expected to even double in the coming years. The paper highlights possibilities for testing web applications and online marketplace using emerging methods like stationary eye cameras (eye tracking) and facial analysis (FaceReading).

Keywords: emerging methods, consumer neuroscience, e-commerce, marketplace, user experience, user interface

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Authors: Mohamed M. A. Abumandour, Neveen E. R. El-Bakary

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The present work performed on the six tongues of African Beauty snake (Psammophis sibilans) that were obtained immediately after their catching, from agricultural fields, Desouk city, Kafrelsheikh Governorate, Egypt. These collected snakes should be from any oral abnormalities or injuries. The lingual surface of the Psammophis sibilans was studied by scanning electron microscopy (SEM). The surface of the bifurcated apex was smoother than the lingual body. The median lingual sulcus was deep and contained a number of the taste pores. By the high magnification of SEM of each part of a bifurcated area of the lingual apex have numerous taste buds and no lingual papillae were observed. A few numbers of papillae were observed in the lingual body. The microridges and microvilli distributed in the lingual body helped in spreading of mucus over the epithelial surface. Taste pores and papillae in the tongue indicate the presence of a direct chemo-sensory function for the tongue of these snakes as the chemicals dissolved in the mucus then transferred to Jacobson organ. To conclude, the bifurcation appearance of the snake lingual tip act as a chemical or edge detector help in the process named chemo-mechano-reception.

Keywords: African beauty snake, taste buds, taste pores, tongue, papillae

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Authors: Zahra Sadeghian

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This paper reports on the geometrical parameters optimized of the stationary point for the 2,3-Bis(furan-2-yl)pyrazino[2,3-f][1,10]phenanthroline. The calculations are performed using density functional theory (DFT) method at the B3LYP/LanL2DZ level. We determined bond lengths and bond angles values for the compound and calculate the amount of bond hybridization according to the natural bond orbital theory (NBO) too. The energy of frontier orbital (HOMO and LUMO) are computed. In addition, calculated data are accurately compared with the experimental result. This comparison show that the our theoretical data are in reasonable agreement with the experimental values.

Keywords: 2, 3-Bis(furan-2-yl)pyrazino[2, 3-f][1, 10]phenanthroline, density functional theory, theorical calculations, LanL2DZ level, B3LYP level

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Authors: N. F. M. Mokhtar, N. Z. A. Hamid

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This paper reports an analytical investigation of the stability and thermal convection in a horizontal anisotropic porous medium in the presence of Coriolis force and magnetic field. The Darcy model is used in the momentum equation and Boussinesq approximation is considered for the density variation of the porous medium. The upper and lower boundaries of the porous medium are assumed to be conducting to temperature perturbation and we used first order Chebyshev polynomial Tau method to solve the resulting eigenvalue problem. Analytical solution is obtained for the case of stationary convection. It is found that the porous layer system becomes unstable when the mechanical anisotropy parameter elevated and increasing the Coriolis force and magnetic field help to stabilize the anisotropy porous medium.

Keywords: anisotropic, Chebyshev tau method, Coriolis force, Magnetic field

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Authors: Karen Cilliers, Benedict John Page

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The middle cerebral artery (MCA) is the most complex cerebral artery although few anomalies are found compared to the other cerebral arteries. The branches of the MCA cover a large part of each hemisphere, therefore it is exposed in various operations. Although the segments of the MCA are similarly described by most authors, there is some disagreement on the branching pattern of the MCA. The aim of this study was to review the available literature on the anatomy and variations of the MCA, and to compare this to a pilot study. For the pilot study, 20 hemispheres were perfused with coloured silicone and the MCA was dissected. According to the literature, the two most common branching configurations are the bifurcating and trifurcating patterns. In the pilot study, bifurcation was observed in 19 hemispheres, and in one hemisphere there was no branching (monofurcation). No trifurcation was observed. The most commonly duplicated branch was the anterior parietal artery in 30%, and most commonly absent was the common temporal artery in 65% and the temporal polar artery in 40%. Very few studies describe the origins of the branches of the MCA, therefore a detailed description is given. Middle cerebral artery variations that are occasionally reported in the literature include fenestration, and a duplicated or accessory MCA, although no variations were observed in the pilot study. Aneurysms can frequently be observed at the branching of cerebral vessels, therefore a thorough knowledge of the vascular anatomy is vital. Furthermore, knowledge of possible variations is important since variations can have serious clinical implications.

Keywords: anatomy, anomaly, description, middle cerebral artery, origin, variation

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Authors: O. Hanita, S. A. Ainnul Hamidah, A. H. Yang Zalila, M. R. Siti Nadiah, M. H. Najihah, M. A. Hapipah

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The crude extract of the leaves of Actinodaphne sesquipedalis Hook. F. Var. Glabra (Kochummen), was taken under phytochemical investigation. The crude methanolic extract was partitioned with a different solvent system by increasing their polarities (n-hexane, dichloromethane, and methanol). The compounds were fractionated and isolated from n-hexane partition by using column chromatography with silica gel 60 or Sephadex LH-20 as a stationary phase and preparative thin layer chromatographic technique. Isolates were characterized using TLC, FTIR, UV spectrophotometer and NMR spectroscopy. The n-hexane fractionates yielded a total of four compounds namely N-methyllaurotetanine (1), dicentrine (2), β-sitosterol (3), and stigmasterol (4). The result indicates that the leaves of Actinodaphne sesquipedalis may provide a rich source of alkaloids and triterpenoids.

Keywords: actinodaphne sesquipedalis, alkaloids, phytochemical investigation, triterpenoids

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Authors: Niloofar Ashktorab, Negar Ashktorab

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Oil exports fund nearly half of Iran’s government expenditures, since many years other countries have been imposed different sanctions against Iran. Sanctions that primarily target Iran’s key energy sector have harmed Iran’s economy. The strategic effects of sanctions might be reduction as Iran adjusts to them economically. In this study, we evaluate the impact of oil price and sanctions against Iran on food commodity prices by using panel data method. Here, we find that the food commodity prices, the oil price and real exchange rate are stationary. The results show positive effect of oil price changes, real exchange rate and sanctions on food commodity prices.

Keywords: oil price, food basket, sanctions, panel data, Iran

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Authors: Meriem Hamla, Mohamed Benaicha, Sabrine Derbal

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In the present work, several materials such as M/glass (M = Pt, Mo) were investigated to test their suitability for studying the early nucleation stages and growth of copper-tin clusters. It was found that most of these materials stand as good substrates to be used in the study of the nucleation and growth of electrodeposited Cu-Sn alloys from aqueous solution containing CuCl2, SnCl2 as electroactive species and Na3C6H5O7 as complexing agent. Among these substrates, Pt shows instantaneous models followed by 3D diffusion-limited growth. On the other hand, the electrodeposited copper-tin thin films onto Mo substrate followed progressive nucleation. The deposition mechanism of the Cu-Sn films has been studied using stationary electrochemical techniques (cyclic voltammetery (CV) and chronoamperometry (CA). The structural, morphological and compositional of characterization have been studied using X-ray diffraction (XRD), scanning electron microscopy (SEM) and EDAX techniques respectively.

Keywords: electrodeposition, CuSn, nucleation, mechanism

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Authors: Kay Thinzar Phu, Lwin Lwin Oo

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In an intelligent transport system and advanced driver assistance system, the developing of real-time traffic sign detection and recognition (TSDR) system plays an important part in recent research field. There are many challenges for developing real-time TSDR system due to motion artifacts, variable lighting and weather conditions and situations of traffic signs. Researchers have already proposed various methods to minimize the challenges problem. The aim of the proposed research is to develop an efficient and effective TSDR in real time. This system proposes an adaptive thresholding method based on RGB color for traffic signs detection and new features for traffic signs recognition. In this system, the RGB color thresholding is used to detect the blue and yellow color traffic signs regions. The system performs the shape identify to decide whether the output candidate region is traffic sign or not. Lastly, new features such as termination points, bifurcation points, and 90’ angles are extracted from validated image. This system uses Myanmar Traffic Sign dataset.

Keywords: adaptive thresholding based on RGB color, blue color detection, feature extraction, yellow color detection

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Authors: Omar Farahat Hassanein, A. Samer Ezeldin

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The construction industry is a very dynamic field. Every day new technologies and methods are developing to fasten the process and increase its efficiency. Hence, if a project uses fewer resources, it will be more efficient. This paper examines the recycling of concrete construction and demolition (C&D) waste to reuse it as aggregates in on-site applications for construction projects in Egypt and possibly in the Middle East. The study focuses on a stationary plant setting. The machinery set-up used in the plant is analyzed technically and financially. The findings are gathered and grouped to obtain a comprehensive cost-benefit financial model to demonstrate the feasibility of establishing and operating a concrete recycling plant. Furthermore, a detailed business plan including the time and hierarchy is proposed.

Keywords: construction wastes, recycling, sustainability, financial model, concrete recycling, concrete life cycle

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Authors: Zina Benouaret, Djamil Aissani

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In this work, we introduce the qualitative and quantitative concept of the strong stability method in the risk process modeling two lines of business of the same insurance company or an insurance and re-insurance companies that divide between them both claims and premiums with a certain proportion. The approach proposed is based on the identification of the ruin probability associate to the model considered, with a stationary distribution of a Markov random process called a reversed process. Our objective, after clarifying the condition and the perturbation domain of parameters, is to obtain the stability inequality of the ruin probability which is applied to estimate the approximation error of a model with disturbance parameters by the considered model. In the stability bound obtained, all constants are explicitly written.

Keywords: Markov chain, risk models, ruin probabilities, strong stability analysis

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Authors: Abdallah Benaissa

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In this paper, we consider the problem of asymptotics of double oscillatory integrals in the case of critical points of the second kind, the order of contact between the boundary and a level curve of the phase being even, the situation when the order of contact is odd will be studied in other occasions. Complete asymptotic expansions will be derived and the coefficient of the leading term will be computed in terms of the original data of the problem. A multitude of people have studied this problem using a variety of methods, but only in a special case when the order of contact is minimal: the more cited papers are a paper of Jones and Kline and an other one of Chako. These integrals are encountered in many areas of science, especially in problems of diffraction of optics.

Keywords: asymptotic expansion, double oscillatory integral, critical point of the second kind, optics diffraction

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Authors: Sadia Arshad, Yifa Tang, Dumitru Baleanu

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A fractional order mathematical model is proposed that incorporate CD8+ cells, natural killer cells, cytokines and tumor cells. The tumor cells growth in the absence of an immune response is modeled by logistic law as it was the simplest form for which predictions also agreed with the experimental data. Natural Killer Cells are our first line of defense. NK cells directly kill tumor cells through several mechanisms, including the release of cytoplasmic granules containing perforin and granzyme, expression of tumor necrosis factor (TNF) family members. The effect of the NK cells on the tumor cell population is expressed with the product term. Rational form is used to describe interaction between CD8+ cells and tumor cells. A number of cytokines are produced by NKs, including tumor necrosis factor TNF, IFN, and interleukin (IL-10). Source term for cytokines is modeled by Michaelis-Menten form to indicate the saturated effects of the immune response. Stability of the equilibrium points is discussed for biologically significant values of bifurcation parameters. We studied the treatment of fractional order system by investigating analytical conditions of tumor eradication. Numerical simulations are presented to illustrate the analytical results.

Keywords: cancer model, fractional calculus, numerical simulations, stability analysis

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Authors: Mamyrbek A. Beisenbi, Nurgul M. Kissikova, Saltanat E. Beisembina, Salamat T. Suleimenova, Samal A. Kaliyeva

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The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability

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Authors: F. Calderón-Vega, A. D. García-Soto, C. Mösso

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Recorded significant wave heights sometimes exhibit large uncommon values (outliers) that can be associated with extreme phenomena such as hurricanes and cold fronts. In this study, some extremely large wave heights recorded in NOAA buoys (National Data Buoy Center, noaa.gov) are used to investigate their effect in the prediction of future wave heights associated with given return periods. Extreme waves are predicted through a time-dependent model based on the so-called generalized extreme value distribution. It is found that the outliers do affect the estimated wave heights. It is concluded that a detailed inspection of outliers is envisaged to determine whether they are real recorded values since this will impact defining design wave heights for coastal protection purposes.

Keywords: GEV model, non-stationary, seasonality, outliers

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