Search results for: central limit theorem

Authors: Ping He, Heng-You Lan, Gong-Quan Tan

Abstract:

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.

Keywords: Linear system, Delay-independent stabilization, Lyapunovfunctional, Riccati algebra matrix equation.

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Authors: Pascal Mwenge, Jefrey Pilusa, Tumisang Seodigeng

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The current study investigated the effect of catalyst ratio and methanol to oil ratio on biodiesel production by using central composite design. Biodiesel was produced by transesterification using sodium hydroxide as a homogeneous catalyst, a laboratory scale reactor consisting of flat bottom flask mounts with a reflux condenser and a heating plate was used to produce biodiesel. Key parameters, including, time, temperature and mixing rate were kept constant at 60 minutes, 60 ^oC and 600 RPM, respectively. From the results obtained, it was observed that the biodiesel yield depends on catalyst ratio and methanol to oil ratio. The highest yield of 50.65% was obtained at catalyst ratio of 0.5 wt.% and methanol to oil mole ratio 10.5. The analysis of variances of biodiesel yield showed the R Squared value of 0.8387. A quadratic mathematical model was developed to predict the biodiesel yield in the specified parameters ranges.

Keywords: ANOVA, biodiesel, catalyst, CCD, transesterification.

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Authors: Chuanyun Gu

Abstract:

By using fixed point theorems for a class of generalized concave and convex operators, the positive solution of nonlinear fractional differential equation with integral boundary conditions is studied, where n ≥ 3 is an integer, μ is a parameter and 0 ≤ μ < α. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it. Finally, two examples are given to illustrate our results.

Keywords: Fractional differential equation, positive solution, existence and uniqueness, fixed point theorem, generalized concave and convex operator, integral boundary conditions.

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Authors: G. Saitova, A. Mashurova, F. Mashurova

Abstract:

In the national and professional music of oral tradition of many people in the East there is the metric formula called “ussuli", that is to say rhythmic constructions of different character and a composition. Ussuli in translation from Arabic means the law. The cultural contacts of the ancient and medieval inhabitants of the Central Asia, India, China, East Turkestan, Iraq, Afghanistan, Turkey, and Iran have played a certain role in formation of both musical and dancing heritage of each of these people. During theatrical shows many dances were performed under the accompaniment of percussion instruments as nagra, dayulpaz, doll. The abovementioned tools are used as the obligatory accompanying tool in an orchestra and at support of dancing acts as the solo tool. Dynamics of development of a dancing composition, at times execution of technique of movement depends on various combinations of ussuli and their receptions of execution.

Keywords: Dancing, plastic, rhythm, ussuli.

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Authors: M. Heck, H. Vettiger

Abstract:

Small and medium-sized enterprises (SME) are the backbone of central Europe’s economies and have a significant contribution to the gross domestic product. Production planning and scheduling (PPS) is still a crucial element in manufacturing industries of the 21^st century even though this area of research is more than a century old. The topic of PPS is well researched especially in the context of large enterprises in the manufacturing industry. However the implementation of PPS methodologies within SME is mostly unobserved. This work analyzes how PPS is implemented in SME with the geographical focus on Switzerland and its vicinity. Based on restricted resources compared to large enterprises, SME have to face different challenges. The real problem areas of selected enterprises in regards of PPS are identified and evaluated. For the identified real-life problem areas of SME clear and detailed recommendations are created, covering concepts and best practices and the efficient usage of PPS. Furthermore the economic and entrepreneurial value for companies is lined out and why the implementation of the introduced recommendations is advised.

Keywords: Central Europe, PPS, Production Planning, SME.

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Authors: NattapongTecharattanased

Abstract:

The purpose of this research was to study the factors that influenced the success of mobile phone entrepreneurs at Central Plaza. The sample group included 187 entrepreneurs at Central Plaza. A questionnaire was utilized as a tool to collect data. Statistics used in this research included frequency, percentage, mean, and standard deviation. Independent- sample t- test, one way ANOVA, and multiple regression analysis. Data were analyzed by using Statistical Package for the Social Sciences.The findings disclosed that the majority of respondents were male between 25-40 years old, and held an undergraduate degree. The average income of respondents was between 15,001-25,000 baht. The majority of respondents had less than 5 years of working experience. In terms of personality, the findings revealed that expression and agreement were ranked at the highest level. Whereas, emotion stability, consciousness, open to new experience were ranked at high. From the hypotheses testing, the findings revealed that different genders had different success in their mobile phone business with different income from the last 6 months. However, difference in age, income, level of education, and experience affected the success in terms of income, number of customers, and overall success of business. Moreover, the factors of personalities included expression, agreement, emotion stability, consciousness, open to new experience, and competitive strategy. From the findings, these factors were able to predict mobile phone business success at 66.9 percent.

Keywords: Entrepreneur, Influencing Factors, Success, Mobile Phone Business.

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

Abstract:

In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: Conservation laws, diffusion equations, Cahn-Hilliard Equations, evolving surfaces.

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Authors: Meng Hu, Lili Wang

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In this paper, we investigate dynamics of 2n almost periodic attractors for Cohen-Grossberg neural networks (CGNNs) with variable and distribute time delays. By imposing some new assumptions on activation functions and system parameters, we split invariant basin of CGNNs into 2n compact convex subsets. Then the existence of 2n almost periodic solutions lying in compact convex subsets is attained due to employment of the theory of exponential dichotomy and Schauder-s fixed point theorem. Meanwhile, we derive some new criteria for the networks to converge toward these 2n almost periodic solutions and exponential attracting domains are also given correspondingly.

Keywords: CGNNs, almost periodic solution, invariant basins, attracting domains.

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Authors: Punit Kumar, Niraj Kumar

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The influence of transverse surface roughness on EHL characteristics has been investigated numerically using an extensive set of full EHL line contact simulations for shear-thinning lubricants under pure sliding condition. The shear-thinning behavior of lubricant is modeled using Carreau viscosity equation along with Doolittle-Tait equation for lubricant compressibility. The surface roughness is assumed to be sinusoidal and it is present on the stationary surface. It is found that surface roughness causes sharp pressure peaks along with reduction in central and minimum film thickness. With increasing amplitude of surface roughness, the minimum film thickness decreases much more rapidly as compared to the central film thickness.

Keywords: EHL, Carreau, Shear-thinning, Surface Roughness, Amplitude, Wavelength.

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Authors: Yuxuan Huang, Weixin Qian, Hongfang Ma, Haitao Zhang, Weiyong Ying

Abstract:

Light olefins are important building blocks for chemical industry. Direct conversion of syngas to light olefins has been investigated for decades. Meanwhile, the limit for light olefins selectivity described by Anderson-Schulz-Flory (ASF) distribution model is still a great challenge to conventional Fischer-Tropsch synthesis. The emerging strategy called oxide-zeolite concept (OX-ZEO) is a promising way to get rid of this limit. ZnCrO_x was prepared by co-precipitation method and (NH₄)₂CO₃ was used as precipitant. SAPO-34 was prepared by hydrothermal synthesis, and Tetraethylammonium hydroxide (TEAOH) was used as template, while silica sol, pseudo-boehmite, and phosphoric acid were Al, Si and P source, respectively. The bifunctional catalyst was prepared by mechanical mixing of ZnCrO_x and SAPO-34. Catalytic reactions were carried out under H₂/CO=2, 380 ℃, 1 MPa and 6000 mL·g_cat^-1·h^-1 in a fixed-bed reactor with a quartz lining. Catalysts were characterized by XRD, N₂ adsorption-desorption, NH₃-TPD, H₂-TPR, and CO-TPD. The addition of Al as structure promoter enhances CO conversion and selectivity to light olefins. Zn/Cr ratio, which decides the active component content and chemisorption property of the catalyst, influences CO conversion and selectivity to light olefins at the same time. C_2-4⁼ distribution of 86% among hydrocarbons at CO conversion of 14% was reached when Zn/Cr=1.5.

Keywords: Light olefins, OX-ZEO, syngas, ZnCrOx.

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Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

Abstract:

The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: Arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation.

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Authors: S. Aghainajafi Zadeh, M.R. Hemami., F. Heydari

Abstract:

Knowledge of food resource of the houbara which an endangered species would be a important step toward the preservation of this bird. Adequate study has not been done in this field and therefore the food sources of the houbara during the brooding season was studied in the central steppe of Iran. In order to determine the density of insect in plant communities the pitfall trap was used , positioned in five linear transects divided between plant communities and in two repetitions. The results showed that the among communities there was a significant difference in term of the number beetles and ants ( p= 0.01, F2, 29= 4.66) collectively. Also bush steppe habitat had a higher arthropoda density in comparison with the shrub steppe habitat. Considering that most houbara nests were found in the bush steppe habitat .It seems this habitat provides the most available food supply for the houbara chicks.

Keywords: Asiatic houbara bustard, Brooding season, Food resource

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Authors: Dongdong Zhang, Deran Zhang

Abstract:

In this paper, a Markovian risk model with two-type claims is considered. In such a risk model, the occurrences of the two type claims are described by two point processes {Ni(t), t ¸ 0}, i = 1, 2, where {Ni(t), t ¸ 0} is the number of jumps during the interval (0, t] for the Markov jump process {Xi(t), t ¸ 0} . The ruin probability ª(u) of a company facing such a risk model is mainly discussed. An integral equation satisfied by the ruin probability ª(u) is obtained and the bounds for the convergence rate of the ruin probability ª(u) are given by using key-renewal theorem.

Keywords: Risk model, ruin probability, Markov jump process, integral equation.

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Authors: Tatyana Boikova

Abstract:

The strong international competition as the factor of rising economic development efficiency should not turn into destructive force for models of social orientation. What result Europe received from the accelerated integration without a long transition period of the accepted countries. Correlative relationship between the research and development expenditure and labor productivity, inflation and the rate economy's growth of the USA and the euro zone, employment and gross value added between Old and New Europe is analyzed in this article. The article estimates the differences in economic growth of Old and New Europe. Correlation rate between cycles of the euro area and the countries of Central and the Eastern Europe very much differs, though some of these countries have high correlation as members of the Economic and Monetary Union. Besides, the majority of the countries of Central and the Eastern Europe does not correspond to criteria of an optimum currency area.

Keywords: endogenous economic growth, sustainability, competitiveness, economic development

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Authors: Shuimiao Wan, Chao Yuan, Baoguang Tian

Abstract:

In statistics parameter theory, usually the parameter estimations have two kinds, one is the least-square estimation (LSE), and the other is the best linear unbiased estimation (BLUE). Due to the determining theorem of minimum variance unbiased estimator (MVUE), the parameter estimation of BLUE in linear model is most ideal. But since the calculations are complicated or the covariance is not given, people are hardly to get the solution. Therefore, people prefer to use LSE rather than BLUE. And this substitution will take some losses. To quantize the losses, many scholars have presented many kinds of different relative efficiencies in different views. For the linear weighted regression model, this paper discusses the relative efficiencies of LSE of β to BLUE of β. It also defines two new relative efficiencies and gives their lower bounds.

Keywords: Linear weighted regression, Relative efficiency, Lower bound, Parameter estimation.

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Authors: Rashid S. S., Alam M. Z.

Abstract:

A statistical optimization of the saccharification process of EFB was studied. The statistical analysis was done by applying faced centered central composite design (FCCCD) under response surface methodology (RSM). In this investigation, EFB dose, enzyme dose and saccharification period was examined, and the maximum 53.45% (w/w) yield of reducing sugar was found with 4% (w/v) of EFB, 10% (v/v) of enzyme after 120 hours of incubation. It can be calculated that the conversion rate of cellulose content of the substrate is more than 75% (w/w) which can be considered as a remarkable achievement. All the variables, linear, quadratic and interaction coefficient, were found to be highly significant, other than two coefficients, one quadratic and another interaction coefficient. The coefficient of determination (R2) is 0.9898 that confirms a satisfactory data and indicated that approximately 98.98% of the variability in the dependent variable, saccharification of EFB, could be explained by this model.

Keywords: Face centered central composite design (FCCCD), Liquid state bioconversion (LSB), Palm oil mill effluent, Trichoderma reesei RUT C-30.

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Authors: Cristian Păuna

Abstract:

In the first decades of the 21st century, in the electronic trading environment, algorithmic capital investments became the primary tool to make a profit by speculations in financial markets. A significant number of traders, private or institutional investors are participating in the capital markets every day using automated algorithms. The autonomous trading software is today a considerable part in the business intelligence system of any modern financial activity. The trading decisions and orders are made automatically by computers using different mathematical models. This paper will present one of these models called Price Prediction Line. A mathematical algorithm will be revealed to build a reliable trend line, which is the base for limit conditions and automated investment signals, the core for a computerized investment system. The paper will guide how to apply these tools to generate entry and exit investment signals, limit conditions to build a mathematical filter for the investment opportunities, and the methodology to integrate all of these in automated investment software. The paper will also present trading results obtained for the leading German financial market index with the presented methods to analyze and to compare different automated investment algorithms. It was found that a specific mathematical algorithm can be optimized and integrated into an automated trading system with good and sustained results for the leading German Market. Investment results will be compared in order to qualify the presented model. In conclusion, a 1:6.12 risk was obtained to reward ratio applying the trigonometric method to the DAX Deutscher Aktienindex on 24 months investment. These results are superior to those obtained with other similar models as this paper reveal. The general idea sustained by this paper is that the Price Prediction Line model presented is a reliable capital investment methodology that can be successfully applied to build an automated investment system with excellent results.

Keywords: Algorithmic trading, automated investment system, DAX Deutscher Aktienindex.

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Authors: Kaihong Zhao, Jiuqing Liu

Abstract:

In this letter, we considers a delayed predatory-prey system with Holling type II functional response. Under some sufficient conditions, the existence of multiple positive periodic solutions is obtained by using Mawhin’s continuation theorem of coincidence degree theory. An example is given to illustrate the effectiveness of our results.

Keywords: Multiple positive periodic solutions, Predatory-prey system, Coincidence degree, Holling type II functional response.

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Authors: S. E. Musa, N. E. Mohamed, N. A. Ahmed

Abstract:

In this study, several crossplots of the P-impedance with the lithology logs (gamma ray, neutron porosity, deep resistivity, water saturation and Vp/Vs curves) were made in three available wells, which were drilled in central part of the Blue Nile basin in depths varies from 1460m to 1600m. These crossplots were successful to discriminate between sand and shale when using PImpedance values, and between the wet sand and the pay sand when using both P-impedance and Vp/Vs together. Also some impedance sections were converted to porosity sections using linear formula to characterize the reservoir in terms of porosity. The used crossplots were created on log resolution, while the seismic resolution can identify only the reservoir, unless a 3D seismic angle stacks were available; then it would be easier to identify the pay sand with great confidence; through high resolution seismic inversion and geostatistical approach when using P-impedance and Vp/Vs volumes.

Keywords: Basin, Blue Nile, Inversion, Seismic.

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Authors: S. R. Hosseini, N. Choupani, A. R. M. Gharabaghi

Abstract:

The modified Arcan fixture was used in order to investigate the mixed mode fracture properties of high strength steel butt weld through experimental and numerical analysis. The fixture consisted of a central section with "butterfly-shaped" specimen that had central crack. The specimens were under pure mode I (opening), pure mode II (shearing) and all in plane mixed mode loading angles starting from 0 to 90 degrees. The geometric calibration factors were calculated with the aid of finite element analysis for various loading mode and different crack length (0.45≤ a/w ≤0.55) and the critical fracture loads obtained experimentally. The critical fracture toughness (KIC & KIIC) estimated with experimental and numerical analysis under mixed mode loading conditions.

Keywords: Arcan specimen, fracture toughness, mixed mode, steel weld.

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Authors: Karakulov Y., Baizakova K.

Abstract:

Kazakhstan attaches the great importance to cooperation with European countries within the framework of multilateral security organizations such as NATO. Cooperation of Kazakhstan with the NATO is a prominent aspect of strengthening of regional security of republic. It covers a wide spectrum of areas, such as reform of sector of defense and security, military operative compatibility of armed forces of NATO member-countries and Kazakhstan, civil emergency planning and scientific cooperation. The cooperation between Kazakhstan and NATO is based on the mutual interests of neighboring republics in the region so that the existing forms of cooperation between Kazakhstan and NATO will not be negatively perceived both in Asia as well as among CIS countries. Kazakhstan tailors its participation in the PfP programme through an annual Individual Partnership Programme, selecting those activities that will help achieve the goals it has set in the IPAP. Level of cooperation within the limits of PfP essentially differs on each republic. Cooperation with Kazakhstan progressed most of all since has been signed IPAP from the NATO

Keywords: Central Asia, Kazakhstan, NATO cooperation, regional security

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Authors: T. Aldeeb, M. Abduelmula

Abstract:

This study examines the fatigue life of S275 mild steel at room temperature. Mechanical components can fail under cyclic loading during period of time, known as the fatigue phenomenon. In order to prevent fatigue induced failures, material behavior should be investigated to determine the endurance limit of the material for safe design and infinite life, thus leading to reducing the economic cost and loss in human lives. The fatigue behavior of S275 mild steel was studied and investigated. Specimens were prepared in accordance with ASTM E3-11, and fatigue tests of the specimen were conducted in accordance with ASTM E466-07 on a smooth plate, with a continuous radius between ends (hourglass-shaped plate). The method of fatigue testing was applied with constant load amplitude and constant frequency of 4 Hz with load ratio (Fully Reversal R= -1). Surface fractures of specimens were investigated using Scanning Electron Microscope (SEM). The experimental results were compared with the results of a Finite Element Analysis (FEA), using simulation software. The experiment results indicated that the endurance fatigue limit of S275 mild steel was 195.47 MPa.

Keywords: Fatigue life, fatigue strength, finite element analysis, S275 mild steel, scanning electron microscope.

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Authors: I. Zamani, M. H. Zarif

Abstract:

In this paper a method for designing of nonlinear controller for a fuzzy model of Double Inverted Pendulum is proposed. This system can be considered as a fuzzy large-scale system that includes offset terms and disturbance in each subsystem. Offset terms are deterministic and disturbances are satisfied a matching condition that is mentioned in the paper. Based on Lyapunov theorem, a nonlinear controller is designed for this fuzzy system (as a model reference base) which is simple in computation and guarantees stability. This idea can be used for other fuzzy large- scale systems that include more subsystems Finally, the results are shown.

Keywords: Controller, Fuzzy Double Inverted Pendulums, Fuzzy Large-Scale Systems, Lyapunov Stability.

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Authors: Hongji Tang, Yanbo Gao, Yue Yu

Abstract:

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: Saulius Minkevicius, Genadijus Kulvietis

Abstract:

The modern queueing theory is one of the powerful tools for a quantitative and qualitative analysis of communication systems, computer networks, transportation systems, and many other technical systems. The paper is designated to the analysis of queueing systems, arising in the networks theory and communications theory (called open queueing network). The authors of this research in the sphere of queueing theory present the theorem about the law of the iterated logarithm (LIL) for the queue length of a customers in open queueing network and its application to the mathematical model of the open message switching system.

Keywords: Models of information systems, open message switching system, open queueing network, queue length of a customers, heavy traffic, a law of the iterated logarithm.

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

Abstract:

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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Authors: P. Siriarchawatana, K. Leungchavaphongse, N. Covavisaruch, K. Rojananuangnit, P. Boondaeng, N. Panyayingyong

Abstract:

Glaucoma is a disease that causes visual loss in adults. Glaucoma causes damage to the optic nerve and its overall pathophysiology is still not fully understood. Vasculopathy may be one of the possible causes of nerve damage. Photographic imaging of retinal vessels by fundus camera during eye examination may complement clinical management. This paper presents an innovation for measuring central light reflex width-to-retinal vessel diameter ratio (CRR) from digital retinal photographs. Using our edge detection technique, CRRs from glaucoma and normal eyes were compared to examine differences and associations. CRRs were evaluated on fundus photographs of participants from Mettapracharak (Wat Raikhing) Hospital in Nakhon Pathom, Thailand. Fifty-five photographs from normal eyes and twenty-one photographs from glaucoma eyes were included. Participants with hypertension were excluded. In each photograph, CRRs from four retinal vessels, including arteries and veins in the inferotemporal and superotemporal regions, were quantified using edge detection technique. From our finding, mean CRRs of all four retinal arteries and veins were significantly higher in persons with glaucoma than in those without glaucoma (0.34 vs. 0.32, p < 0.05 for inferotemporal vein, 0.33 vs. 0.30, p < 0.01 for inferotemporal artery, 0.34 vs. 0.31, p < 0.01 for superotemporal vein, and 0.33 vs. 0.30, p < 0.05 for superotemporal artery). From these results, an increase in CRRs of retinal vessels, as quantitatively measured from fundus photographs, could be associated with glaucoma.

Keywords: Glaucoma, retinal vessel, central light reflex, image processing, fundus photograph, edge detection.

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Authors: M. Khal, Ab. Algouti, A. Algouti

Abstract:

Water erosion is the major cause of the erosion that shapes the earth's surface. Modeling water erosion requires the use of software and GIS programs, commercial or closed source. The very high prices for commercial GIS licenses, motivates users and researchers to find open source software as relevant and applicable as the proprietary GIS. The objective of this study is the modeling of water erosion and the hydrogeological and morphophysical characterization of the Oued M'Goun watershed (southern flank of the Central High Atlas) developed by free programs of GIS. The very pertinent results are obtained by executing tasks and algorithms in a simple and easy way. Thus, the various geoscientific and geostatistical analyzes of a digital elevation model (SRTM 30 m resolution) and their combination with the treatments and interpretation of satellite imagery information allowed us to characterize the region studied and to map the area most vulnerable to water erosion.

Keywords: Central High-Atlas, hydrogeology, M’Goun watershed, OpenGIS, water erosion.

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

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Authors: Ademeso, Odunyemi Anthony

Abstract:

The charnockitic and associated granitic rocks of Akure area were studied for their field and petrographic relationship's. The outcrops locations were plotted in Surfer 8. The granitic rock exhibits a porphyritic texture and outcrops in the north-eastern side of the study area while the charnockitics outcrop in the central/western part. An essentially dark coloured and fine grained intrusive exhibiting xenoliths and xenocrysts (plagioclase phenocrysts) of the granite outcrops between the granitic and charnockitic rocks. Mineralogically, the central rock combines the content of the other two indicating that it is most likely a product of their hybridization. The charnockitic magma is believed to have intruded and assimilated the granite substantially thereby contaminating itself and consequently emplacing the hybrid. The presented model of emplacement elucidates the hybridization proposal. Conclusively, the charnockitics are believed to be (a) younger than the granite, (b) of Pan-African age and (c) of igneous origin.

Keywords: Charnockitic rock, Hybrid rock, ImageJ, Xenocryst

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