Search results for: relative degradation degree

Authors: Wongsakorn Charoenpanitseri

Abstract:

The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.

Keywords: Total colorings, the total chromatic number, 3-degenerated.

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Authors: Yingjeng James Li, Lung-Yu Sung, Andrew S. Lin, Huan-Jyun Ciou

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Durability of Membrane Electrode Assembly for Proton Exchange Membrane Fuel Cells was evaluated in both steady state and accelerated decay modes. Steady state mode was carried out at constant current of 800mA/cm2 for 2500 hours using air as cathode feed and pure hydrogen as anode feed. The degradation of the cell voltage was 0.015V after such 2500 hrs operation. The degradation rate was therefore calculated to be 6uV/hr. Continuously Vigorous fluctuation of the cell voltage, which was switched between OCV and 0.2V, was employed for the accelerated decay mode. No obvious change in performance of the MEA was observed after 10000 cycles of such operation.

Keywords: Durability, lifetime, membrane electrode assembly, proton exchange membrane fuel cells.

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Authors: A. G. Margaryan

Abstract:

Aims and Objectives: Assessment of health status and detection disorders of external respiration functions (ERF) during preventative medical examination among physicians of Armenia. Subjects and Methods: Overall, fifty-nine physicians (17 men and 42 women) were examined and spirometry was carried out. The average age of the physicians was 50 years old. The studies were conducted on the Micromedical MicroLab 3500 Spirometer. Results: 25.4% among 59 examined physicians are overweight; 22.0% of them suffer from obesity. Two physicians are currently smokers. About half of the examined physicians (50.8%) at the time of examination were diagnosed with some diseases and had different health-related problems (excluding the problems related to vision and hearing). FVC was 2.94±0.1, FEV1 – 2.64±0.1, PEF – 329.7±19.9, and FEV₁%/FVC – 89.7±1.3. Pathological changes of ERF are identified in 23 (39.0%) cases. 28.8% of physicians had first degree of restrictive disorders, 3.4% – first degree of combined obstructive/ restrictive disorders, 6.8% – second degree of combined obstructive/ restrictive disorders. Only three physicians with disorders of the ERF were diagnosed with chronic bronchitis and bronchial asthma. There were no statistically significant changes in ERF depending on the severity of obesity (P> 0.05). Conclusion: The study showed the prevalence of ERF among physicians, observing mainly mild and moderate changes in ERF parameters.

Keywords: Armenia, external respiration function, health status, physicians.

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Authors: Masoud Nasri, Ali Gholami, Ali Najafi

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In recent years, most of the regions in the world are exposed to degradation and erosion caused by increasing population and over use of land resources. The understanding of the most important factors on soil erosion and sediment yield are the main keys for decision making and planning. In this study, the sediment yield and soil erosion were estimated and the priority of different soil erosion factors used in the MPSIAC method of soil erosion estimation is evaluated in AliAbad watershed in southwest of Isfahan Province, Iran. Different information layers of the parameters were created using a GIS technique. Then, a multivariate procedure was applied to estimate sediment yield and to find the most important factors of soil erosion in the model. The results showed that land use, geology, land and soil cover are the most important factors describing the soil erosion estimated by MPSIAC model.

Keywords: land degradation, Soil erosion, Sediment yield, Aliabad, GIS technique, Land use.

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Authors: Yongkun Li, Erliang Xu

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In this paper, by using Mawhin-s continuation theorem of coincidence degree theory, we establish the existence of multiple positive periodic solutions of a competitor-competitor-mutualist Lotka-Volterra system with harvesting terms. Finally, an example is given to illustrate our results.

Keywords: Positive periodic solutions, competitor-competitor mutualist Lotka-Volterra systems, coincidence degree, harvesting term.

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Authors: Kaihong Zhao

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In this paper, the existence of 2n positive periodic solutions for n species non-autonomous Lotka-Volterra cooperative systems with harvesting terms is established by using Mawhin-s continuation theorem of coincidence degree theory and matrix inequality. An example is given to illustrate the effectiveness of our results.

Keywords: Multiple positive periodic solutions, Nonautonomous Lotka-Volterra cooperative system, Coincidence degree, Harvesting term.

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Authors: T. Li, J.Y. Zhang, W.H. Zhang, M.H. Zhu

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A numerical simulation of vortex-induced vibration of a 2-dimensional elastic circular cylinder with two degree of freedom under the uniform flow is calculated when Reynolds is 200. 2-dimensional incompressible Navier-Stokes equations are solved with the space-time finite element method, the equation of the cylinder motion is solved with the new explicit integral method and the mesh renew is achieved by the spring moving mesh technology. Considering vortex-induced vibration with the low reduced damping parameter, the variety trends of the lift coefficient, the drag coefficient, the displacement of cylinder are analyzed under different oscillating frequencies of cylinder. The phenomena of locked-in, beat and phases-witch were captured successfully. The evolution of vortex shedding from the cylinder with time is discussed. There are very similar trends in characteristics between the results of the one degree of freedom cylinder model and that of the two degree of freedom cylinder model. The streamwise vibrations have a certain effect on the lateral vibrations and their characteristics.

Keywords: Fluid-structure interaction, Navier-Stokes equation, Space-time finite element method, vortex-induced vibration.

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Authors: Kowit Suwannahong, Wipada Sanongra, Jittiporn Kruenate, Sarun Phibanchon, Siriuma Jawjit, Wipawee Khamwichit

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The photocatalytic activity efficiency of TiO2 for the degradation of Toluene in photoreactor can be enhanced by nano- TiO2/LDPE composite film. Since the amount of TiO2 affected the efficiency of the photocatalytic activity, this work was mainly concentrated on the effort to embed the high amount of TiO2 in the Polyethylene matrix. The developed photocatalyst was characterized by XRD, UV-Vis spectrophotometer and SEM. The SEM images revealed the high homogeneity of the deposition of TiO2 on the polyethylene matrix. The XRD patterns interpreted that TiO2 embedded in the PE matrix exhibited mainly in anatase form. In addition, the photocatalytic results show that the toluene removal efficiencies of 30±5%, 49±4%, 68±5%, 42±6% and 33±5% were obtained when using the catalyst loading at 0%, 10%, 15%, 25% and 50% (wt. cat./wt. film), respectively.

Keywords: Photocatalytic oxidation, Toluene, nano-TiO2/LDPE composite film.

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Authors: Ahmad Abubakar Sadiq, Mark N. Nwohu, Jacob Tsado, Ahmad A. Ashraf, Agbachi E. Okenna, Enesi E. Yahaya, Ambafi James Garba

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Transmission system performance analysis is vital to proper planning and operations of power systems in the presence of deregulation. Key performance indicators (KPIs) are often used as measure of degree of performance. This paper gives a novel method to determine the transmission efficiency by evaluating the ratio of real power losses incurred from a specified transfer direction. Available Transmission Transfer Efficiency (ATTE) expresses the percentage of real power received resulting from inter-area available power transfer. The Tie line (Rated system path) performance is seen to differ from system wide (Network response) performance and ATTE values obtained are transfer direction specific. The required sending end quantities with specified receiving end ATC and the receiving end power circle diagram are obtained for the tie line analysis. The amount of real power loss load relative to the available transfer capability gives a measure of the transmission grid efficiency.

Keywords: Available transfer capability, efficiency performance, real power, transmission system.

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Authors: D. Jakovčević, M. Mihelja Žaja

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The purpose of this paper is to analyze the influence and relative share of underwriting risks in explaining the variation in insurance cycles in subsequent periods. Through the insurance contracts they underwrite, insurance companies assume risks. Underwriting risks include pricing risk, reserve risk, reinsurance risk and occurrence risk. These risks pose major risks for property and liability insurers, and therefore their impact on the insurance cycle is important. The main goal of this paper is to determine the relative proportion of underwriting risks in explaining the variation of insurance cycle. In order to fulfill the main goal of the paper vector autoregressive model, VAR, will be applied.

Keywords: Insurance cycle, insurance risks, combined ratio, Republic of Croatia.

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Authors: Pankaj Kumar Srivastava

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Bringing forth a survey on recent higher order spline techniques for solving boundary value problems in ordinary differential equations. Here we have discussed the summary of the articles since 2000 till date based on higher order splines like Septic, Octic, Nonic, Tenth, Eleventh, Twelfth and Thirteenth Degree splines. Comparisons of methods with own critical comments as remarks have been included.

Keywords: Septic spline, Octic spline, Nonic spline, Tenth, Eleventh, Twelfth and Thirteenth Degree spline, parametric and non-parametric splines, thermal instability, astrophysics.

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Authors: R. Ziaie Moayed, M. Mortezaee

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An important and influential factor in design and determining the safety factor in Soil Nailing is the ultimate pullout capacity, or, in other words, bond strength. This important parameter depends on several factors such as material and soil texture, method of implementation, excavation diameter, friction angle between the nail and the soil, grouting pressure, the nail depth (overburden pressure), the angle of drilling and the degree of saturation in soil. Federal Highway Administration (FHWA), a customary regulation in the design of nailing, is considered only the effect of the soil type (or rock) and the method of implementation in determining the bond strength, which results in non-economic design. The other regulations are each of a kind, some of the parameters affecting bond resistance are not taken into account. Therefore, in the present paper, at first the relationships and tables presented by several valid regulations are presented for estimating the ultimate pullout capacity, and then the effect of several important factors affecting on ultimate Pullout capacity are studied. Finally, it was determined, the effect of overburden pressure (in method of injection with pressure), soil dilatation and roughness of the drilling surface on pullout strength is incremental, and effect of degree of soil saturation on pullout strength to a certain degree of saturation is increasing and then decreasing. therefore it is better to get help from nail pullout-strength test results and numerical modeling to evaluate the effect of parameters such as overburden pressure, dilatation, and degree of soil saturation, and so on to reach an optimal and economical design.

Keywords: Soil nailing, pullout capacity, FHWA, grout.

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Authors: K. Broniszewski, J. Woźniak, K. Czechowski, P. Orłowski, A. Olszyna

Abstract:

Alumina matrix composites with addition of hexagonal boron nitride (hBN), acting as solid lubricant, were produced. Main purpose of solid lubricants is to dispose the necessity of using cooling lubricants in machining process. Hot pressing was used as a consolidating process for Al2O3-x%wt.hBN (x=1/ 2,5/ 5 /7,5 /10) composites. Properties of sinters such as relative density, hardness, Young-s modulus and fracture toughness were examined. Obtained samples characterize by high relative density. Hardness and fracture toughness values allow the use of alumina – hBN composites for machining steels even in hardened condition. However it was observed that high weight content of hBN can negatively influence the mechanical properties of composites.

Keywords: Alumina. Composites, Hexagonal boron nitride, Machining

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Authors: Yongkun Li, Tianwei Zhang, Shufa Bai

Abstract:

By using the method of coincidence degree theory and constructing suitable Lyapunov functional, several sufficient conditions are established for the existence and global exponential stability of anti-periodic solutions for Cohen-Grossberg shunting inhibitory neural networks with delays. An example is given to illustrate our feasible results.

Keywords: Anti-periodic solution, coincidence degree, global exponential stability, Cohen-Grossberg shunting inhibitory cellular neural networks.

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Authors: Goreti Botelho, Filomena Gomes, Fernanda M. Ferreira, Ilda Caldeira

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The strawberry tree (Arbutus unedo L.) is a small tree or shrub from botanical Ericaceae family that grows spontaneously nearby the Mediterranean basin and produce edible red fruits. A traditional processed fruit application, in Mediterranean countries, is the production of a spirit (known as aguardente de medronho, in Portugal) obtained from the fermented fruit. The main objective of our study was to contribute to the knowledge about the influence of the degree of maturation of fruits in the volatile composition and quality of arbutus spirit. The major volatiles in the three distillates fractions (head, heart and tail) obtained from fermentation of two different fruit maturation levels were quantified by GC-FID analysis and ANOVA one-way was performed. Additionally, the total antioxidant capacity and total phenolic compounds of both arbutus fruit spirits were determined, by ABTS and Folin-Ciocalteau method, respectively. The methanol concentration is higher (1022.39 g/hL a.a.) in the spirit made from fruits with highest total soluble solids, which is a value above the legal limit (1000 g/hL a.a.). Overall, our study emphasizes, for the first time, the influence of maturation degree of arbutus fruits in the spirit volatile composition and quality.

Keywords: Arbutus fruit, maturation, quality, spirit.

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Authors: Yung-Tan Lee, Ren-Yi Huang, Chih-Cheng Chen, You-Ting Liao

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The aim of this study is to discuss the relationship between tourist awareness of environmental issues and their own recreational behaviors in the Taipei Guandu Wetland. A total of 392 questionnaires were gathered for data analysis using descriptive statistics, t-testing, one-way analysis of variance (ANOVA) and least significant difference (LSD) post hoc comparisons. The results showed that most of the visitors there enjoying the beautiful scenery are 21 to 30 years old with a college education. The means and standard deviations indicate that tourists express a positive degree of cognition of environmental issues and recreational behaviors. They suggest that polluting the environment is harmful to the natural ecosystem and that the natural resources of ecotourism are fragile, as well as expressing a high degree of recognition of the need to protect wetlands. Most of respondents are cognizant of the regulations proposed by the Guandu Wetland administration which asks that users exercise self-control and follow recommended guidelines when traveling the wetland. There were significant differences in the degree of cognition related to the variables of age, number of visits and reasons for visiting. We found that most respondents with relatively high levels of education would like to learn more about the wetland and are supportive of its conservation.

Keywords: Guandu Wetland, environmental awareness, recreational behaviors, conservation.

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Authors: Junghan Kim, Wonkyu Chung, Sunyoung Bu, Philsu Kim

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In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower degree polynomial. The constructed algorithm controls both the error and the time step size simultaneously and further the errors at each integration step are embedded in the algorithm itself, which provides the efficiency of the computational cost. For the assessment of the effectiveness, numerical results obtained by the proposed method and the Radau IIA are presented and compared.

Keywords: Generalized Chebyshev Collocation method, Generalized Chebyshev Polynomial, Initial value problem.

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Authors: Ahmad T. Al-Taani, Noor Aldeen K. Al-Awad

Abstract:

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference approaches. These measures are applied and compared using 50 different Arabic web pages. Einstein measure was gave best performance among the other measures. An analysis of these measures and concluding remarks are drawn in this study.

Keywords: Text classification, HTML documents, Web pages, Machine learning, Fuzzy logic, Arabic Web pages.

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Authors: Serge B. Provost, Min Jiang

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The density estimates considered in this paper comprise a base density and an adjustment component consisting of a linear combination of orthogonal polynomials. It is shown that, in the context of density approximation, the coefficients of the linear combination can be determined either from a moment-matching technique or a weighted least-squares approach. A kernel representation of the corresponding density estimates is obtained. Additionally, two refinements of the Kronmal-Tarter stopping criterion are proposed for determining the degree of the polynomial adjustment. By way of illustration, the density estimation methodology advocated herein is applied to two data sets.

Keywords: kernel density estimation, orthogonal polynomials, moment-based methodologies, density approximation.

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Authors: Young-Seok Choi

Abstract:

This work assesses the cortical and the sub-cortical neural activity recorded from rodents using entropy and mutual information based approaches to study how hypothermia affects neural activity. By applying the multi-scale entropy and Shannon entropy, we quantify the degree of the regularity embedded in the cortical and sub-cortical neurons and characterize the dependency of entropy of these regions on temperature. We study also the degree of the mutual information on thalamocortical pathway depending on temperature. The latter is most likely an indicator of coupling between these highly connected structures in response to temperature manipulation leading to arousal after global cerebral ischemia.

Keywords: Spiking activity, entropy, mutual information, temperature modulation.

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Authors: Keke Gao, Tao Lin, Yonghui Xie, Di Zhang

Abstract:

Complicated unsteady flow in axial turbines produces high-frequency unsteady aerodynamic exciting force, which threatens the safe operation of turbines. This paper illustrates how negative-bowed stator reduces the rotor unsteady aerodynamic exciting force by unsteady flow field. With the support of three-dimensional viscous compressible Navier-Stokes equation, the single axial turbines with 0, -10 and -20 degree bowed stator are comparably investigated, aiming to identify the flow field structure difference caused by various negative-bowed degrees. The results show that negative-bowed stator strengthens the turbulence kinetic energy, which is further strengthened with the increase of negative-bowed degree. Meanwhile, the flow phenomenon including stator wakes and passage vortex is shown. In addition, the interaction of upstream negative-bowed wakes contributes to the reduction of unsteady blade load fluctuation. Furthermore, the aerodynamic exciting force decreases with the increasing negative bowed degree, while the efficiency is correspondingly reduced. This paper provides the reference for the alleviation of the harmful impact caused by unsteady interaction with the method of wake control.

Keywords: Unsteady flow, axial turbine, wake, aerodynamic force, loss.

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Authors: Yanling Zhu, Kai Wang

Abstract:

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.

Keywords: Predator-prey model, Holling II type functional response, positive periodic solution, coincidence degree theorem.

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Authors: Ahmad T. Al-Taani, Noor Aldeen K. Al-Awad

Abstract:

In this study, a fuzzy similarity approach for Arabic web pages classification is presented. The approach uses a fuzzy term-category relation by manipulating membership degree for the training data and the degree value for a test web page. Six measures are used and compared in this study. These measures include: Einstein, Algebraic, Hamacher, MinMax, Special case fuzzy and Bounded Difference approaches. These measures are applied and compared using 50 different Arabic web-pages. Einstein measure was gave best performance among the other measures. An analysis of these measures and concluding remarks are drawn in this study.

Keywords: Text classification, HTML, web pages, machine learning, fuzzy logic, Arabic web pages.

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Authors: Glauber Cruz, Patrícia A. S. Monteiro, Carlos E. M. Braz, Paulo Seleghin Jr., Igor Polikarpov, Paula M.Crnkovic

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Enzymatic hydrolysis is one of the major steps involved in the conversion from sugarcane bagasse to yield ethanol. This process offers potential for yields and selectivity higher, lower energy costs and milder operating conditions than chemical processes. However, the presence of some factors such as lignin content, crystallinity degree of the cellulose, and particle sizes, limits the digestibility of the cellulose present in the lignocellulosic biomasses. Pretreatment aims to improve the access of the enzyme to the substrate. In this study sugarcane bagasse was submitted chemical pretreatment that consisted of two consecutive steps, the first with dilute sulfuric acid (1 % (v/v) H2SO4), and the second with alkaline solutions with different concentrations of NaOH (1, 2, 3 and 4 % (w/v)). Thermal Analysis (TG/ DTG and DTA) was used to evaluate hemicellulose, cellulose and lignin contents in the samples. Scanning Electron Microscopy (SEM) was used to evaluate the morphological structures of the in natura and chemically treated samples. Results showed that pretreatments were effective in chemical degradation of lignocellulosic materials of the samples, and also was possible to observe the morphological changes occurring in the biomasses after pretreatments.

Keywords: Alkaline solutions, bioethanol production, dilute acid, enzymatic hydrolysis, lignocellulosic biomass.

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Authors: Pu Duan, Shi Cui, Choong Wah Chan

Abstract:

Finding suitable non-supersingular elliptic curves for pairing-based cryptosystems becomes an important issue for the modern public-key cryptography after the proposition of id-based encryption scheme and short signature scheme. In previous work different algorithms have been proposed for finding such elliptic curves when embedding degree k ∈ {3, 4, 6} and cofactor h ∈ {1, 2, 3, 4, 5}. In this paper a new method is presented to find more non-supersingular elliptic curves for pairing-based cryptosystems with general embedding degree k and large values of cofactor h. In addition, some effective parameters of these non-supersingular elliptic curves are provided in this paper.

Keywords: Family of group order, kth root of unity, non-supersingular elliptic curves polynomial field.

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Authors: HoYoung Son, DongHoon Shin, WooYoung Jung

Abstract:

This study presented the seismic fragility framework of concrete weir structure subjected to strong seismic ground motions and in particular, concrete aging condition of the weir structure was taken into account in this study. In order to understand the influence of concrete aging on the weir structure, by using probabilistic risk assessment, the analytical seismic fragility of the weir structure was derived for pre- and post-deterioration of concrete. The performance of concrete weir structure after five years was assumed for the concrete aging or deterioration, and according to after five years’ condition, the elastic modulus was simply reduced about one–tenth compared with initial condition of weir structures. A 2D nonlinear finite element analysis was performed considering the deterioration of concrete in weir structures using ABAQUS platform, a commercial structural analysis program. Simplified concrete degradation was resulted in the increase of almost 45% of the probability of failure at Limit State 3, in comparison to initial construction stage, by analyzing the seismic fragility.

Keywords: Weir, FEM, concrete, fragility, aging

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Authors: M. S. Meon, M. N. Rao, K-U. Schröder

Abstract:

Mechanical fasteners especially bolting is commonly used in joining carbon-fiber reinforced polymer (CFRP) composite structures due to their good joinability and easy for maintenance characteristics. Since this approach involves with notching, a proper progressive damage model (PDM) need to be implemented and verified to capture existence of damages in the structure. A three dimensional (3D) failure criteria of Puck is established to predict the ultimate bearing failure of such joint. The failure criteria incorporated with degradation scheme are coded based on user subroutine executed in Abaqus. Single lap joint (SLJ) of composite bolted joint is used as target configuration. The results revealed that the PDM adopted here could sufficiently predict the behaviour of composite bolted joint up to ultimate bearing failure. In addition, mesh refinement near holes increased the accuracy of predicted strength as well as computational effort.

Keywords: Bearing strength, bolted joint, degradation scheme, progressive damage model.

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Authors: Yilun Shang

Abstract:

In this paper we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process. The transition probability matrix and stationary distribution are derived for the Markov chains concerning connectivity and the number of components. We analyze the algorithm for hitting time regarding disconnectivity. In addition to dynamical properties, we also study topological properties for static snapshots. We obtain the degree distributions as well as asymptotic precise bounds and strong law of large numbers for connectivity threshold distance and the largest nearest neighbor distance amongst others. Both exact results and limit theorems are provided in this paper.

Keywords: random geometric graph, autoregressive process, degree, connectivity, Markovian, wireless network.

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Authors: M. A. Basunia

Abstract:

Thirty three re-wetting tests were conducted at different combinations of temperatures (5.7- 46.30C) and relative humidites (48.2-88.6%) with barley. Two most commonly used thinlayer drying and rewetting models i.e. Page and Diffusion were compared for their ability to the fit the experimental re-wetting data based on the standard error of estimate (SEE) of the measured and simulated moisture contents. The comparison shows both the Page and Diffusion models fit the re-wetting experimental data of barley well. The average SEE values for the Page and Diffusion models were 0.176 % d.b. and 0.199 % d.b., respectively. The Page and Diffusion models were found to be most suitable equations, to describe the thin-layer re-wetting characteristics of barley over a typically five day re-wetting. These two models can be used for the simulation of deep-bed re-wetting of barley occurring during ventilated storage and deep bed drying.

Keywords: Thin-layer, barley, re-wetting parameters, temperature, relative humidity.

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Authors: Daiming Wang

Abstract:

In this paper, by using Mawhin-s continuation theorem of coincidence degree and a method based on delay differential inequality, some sufficient conditions are obtained for the existence and global exponential stability of periodic solutions of cellular neural networks with distributed delays and impulses on time scales. The results of this paper generalized previously known results.

Keywords: Periodic solutions, global exponential stability, coincidence degree, M-matrix.

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