Search results for: degree of bending (DoB)

Authors: Pankaj Kumar Srivastava

Abstract:

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

Abstract:

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: 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

Abstract:

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

Abstract:

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

Abstract:

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

Abstract:

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: 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: C. Malça, P. Gonçalves, N. Alves, A. Mateus

Abstract:

Regardless of the manufacturing process used, subtractive or additive, material, purpose and application, produced components are conventionally solid mass with more or less complex shape depending on the production technology selected. Aspects such as reducing the weight of components, associated with the low volume of material required and the almost non-existent material waste, speed and flexibility of production and, primarily, a high mechanical strength combined with high structural performance, are competitive advantages in any industrial sector, from automotive, molds, aviation, aerospace, construction, pharmaceuticals, medicine and more recently in human tissue engineering. Such features, properties and functionalities are attained in metal components produced using the additive technique of Rapid Prototyping from metal powders commonly known as Selective Laser Melting (SLM), with optimized internal topologies and varying densities. In order to produce components with high strength and high structural and functional performance, regardless of the type of application, three different internal topologies were developed and analyzed using numerical computational tools. The developed topologies were numerically submitted to mechanical compression and four point bending testing. Finite Element Analysis results demonstrate how different internal topologies can contribute to improve mechanical properties, even with a high degree of porosity relatively to fully dense components. Results are very promising not only from the point of view of mechanical resistance, but especially through the achievement of considerable variation in density without loss of structural and functional high performance.

Keywords: Additive Manufacturing, Internal topologies, Porosity, Rapid Prototyping, Selective Laser Melting.

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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: 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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Authors: Jan Cernohorsky

Abstract:

This article aims to assess the evolution of imperfect competition in selected banking markets, in particular in the banking markets of Slovakia, Poland, Hungary, Slovenia and Croatia. Another objective is to assess the evolution of the relationship of imperfect competition and profit development in the banking markets. The article first provides an overview of literature on the topic. It then measures the degree of imperfect competition in individual markets using the Herfindahl-Hirschman Index. The commonly used indicator of total assets was chosen as an indicator. Based on this measurement, the individual banking sectors are categorized into theoretical definitions of the various types of imperfect competition - namely all surveyed banking sectors falling within the theoretical definition of monopolistic competition. Subsequently, using correlation analysis, i.e., the Pearson correlation coefficient, or the Spearman correlation coefficient, the connection between the evolution of imperfect competition and the development of the gross profit on selected banking markets was surveyed. It was found that with the exception of the banking market in Slovenia, where there is a positive correlation; there is no correlation between the evolution of imperfect competition and profit development in the selected markets. This means a recommendation for the regulators that it is not appropriate to rationalize a higher degree of regulation in granting banking licenses on the size of the profits attained in the banking market, as the relationship between the degree of concentration in the banking market and the amount of profit according to our measurements does not exist.

Keywords: Banking system, imperfect competition, profitability.

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Authors: D. Zare, H. Naderi, A. A. Jafari

Abstract:

Drying characteristics of rough rice (variety of lenjan) with an initial moisture content of 25% dry basis (db) was studied in a hot air dryer assisted by infrared heating. Three arrival air temperatures (30, 40 and 500C) and four infrared radiation intensities (0, 0.2 , 0.4 and 0.6 W/cm2) and three arrival air speeds (0.1, 0.15 and 0.2 m.s-1) were studied. Bending strength of brown rice kernel, percentage of cracked kernels and time of drying were measured and evaluated. The results showed that increasing the drying arrival air temperature and radiation intensity of infrared resulted decrease in drying time. High bending strength and low percentage of cracked kernel was obtained when paddy was dried by hot air assisted infrared dryer. Between this factors and their interactive effect were a significant difference (p<0.01). An intensity level of 0.2 W/cm2 was found to be optimum for radiation drying. Furthermore, in the present study, the application of Artificial Neural Network (ANN) for predicting the moisture content during drying (output parameter for ANN modeling) was investigated. Infrared Radiation intensity, drying air temperature, arrival air speed and drying time were considered as input parameters for the model. An ANN model with two hidden layers with 8 and 14 neurons were selected for studying the influence of transfer functions and training algorithms. The results revealed that a network with the Tansig (hyperbolic tangent sigmoid) transfer function and trainlm (Levenberg-Marquardt) back propagation algorithm made the most accurate predictions for the paddy drying system. Mean square error (MSE) was calculated and found that the random errors were within and acceptable range of ±5% with coefficient of determination (R2) of 99%.

Keywords: Rough rice, Infrared-hot air, Artificial Neural Network

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Authors: Jian Zheng, Xinhua Ni, Xiequan Liu

Abstract:

According to isotropy of parallel fiber eutectic, the no- damage strain field in parallel fiber eutectic is obtained from the flexibility tensor of parallel fiber eutectic. Considering the damage behavior of parallel fiber eutectic, damage variables are introduced to determine the strain field of parallel fiber eutectic. The damage strains in the matrix, interphase, and fiber of parallel fiber eutectic are quantitatively analyzed. Results show that damage strains are not only associated with the fiber volume fraction of parallel fiber eutectic, but also with the damage degree.

Keywords: Parallel fiber eutectic, no-damage strain, damage strain, fiber volume fraction, damage degree.

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Authors: Chaiwat Waree

Abstract:

The purposes of the research were to develop online lessons to strengthen the learning process of Master's degree students majoring in Curriculum and Instruction at Suan Sunandha Rajabhat University; to achieve the efficiency criteria of 80/80; and to study the satisfaction of students who use online lessons to strengthen the learning process of Master’s degree students majoring in Curriculum and Instruction at Suan Sunandha Rajabhat University. The sample consisted of 40 university students studying in semester 1, academic year 2012. The sample was determined by Purposive Sampling. Selected students were from the class which the researcher was the homeroom tutor. The tutor was responsible for the teaching of learning process. Tools used in the study were online lessons, 60-point performance test, and evaluation test of satisfaction of students on online lessons. Data analysis yielded the following results; 83.66/88.29 efficiency of online lessons measured against the criteria; the comparison of performance before and after taking online lessons using t-test yielded 29.67. The statistical significance was at 0.05; the average satisfaction level of forty students on online lessons was 4.46 with standard deviation of 0.68.

Keywords: Online Lessons, Curriculum and Instruction.

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Authors: Elsayed A. Habib Elamir

Abstract:

In social network analysis the mean nodal degree and density of the graph can be considered as a measure of the activity of all actors in the network and this is an important property of a graph and for making comparisons among networks. Since subjects in a family or organization are subject to common environment factors, it is prime interest to study the association between responses. Therefore, we study the distribution of the mean nodal degree and density of the graph under correlated binary units. The cross product ratio is used to capture the intra-units association among subjects. Computer program and an application are given to show the benefits of the method.

Keywords: Correlated Binary data, cross product ratio, densityof the graph, multiplicative binomial distribution.

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Authors: Angelo Thurairajah

Abstract:

Sufficient ultimate deformation is necessary to demonstrate the member ductility, which is dependent on the section and the material ductility. The concrete cracking phase of softening prior to the plastic hinge formation is an essential feature as well. The nature of the overload behaviour is studied using the order of the ultimate deflection. The ultimate deflection is primarily dependent on the slenderness (span to depth ratio), the ductility of the reinforcing steel, the degree of moment redistribution, the type of loading, and the support conditions. The ultimate deflection and the degree of moment redistribution from the analytical study are in good agreement with the experimental results and the moment redistribution provisions of the Australian Standards AS3600 Concrete Structures Code.

Keywords: Ductility, softening, ultimate deflection, overload behaviour, moment redistribution.

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Authors: Satish Kolli, Adriana Ferancova, David Porter, Jukka Kömi

Abstract:

Electrochemical impedance spectroscopy (EIS) has been used to detect sensitization in austenitic stainless steels that are heat treated in the temperature regime 600-820 °C to produce different degrees of sensitization in the material. The tests were conducted at five different DC potentials in the transpassive region. The quantitative determination of degree of sensitization has been done using double loop electrochemical potentiokinetic reactivation tests (DL-EPR). The correlation between EIS Nyquist diagrams and DL-EPR degree of sensitization values has been studied. The EIS technique can be used as a qualitative tool in determining the intergranular corrosion in austenitic stainless steels that are heat treated at a given temperature.

Keywords: Electrochemical impedance spectroscopy, intergranular corrosion, sensitization, stainless steel.

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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: Jerome G. Chandraseelan, Samuel M. D. Oliveira, Antti Häkkinen, Sofia Startceva, Andre S. Ribeiro

Abstract:

We used live E. coli containing synthetic genetic oscillators to study how the degree of synchrony between the genetic circuits of sister cells changes with temperature. We found that both the mean and the variability of the degree of synchrony between the fluorescence signals from sister cells are affected by temperature. Also, while most pairs of sister cells were found to be highly synchronous in each condition, the number of asynchronous pairs increased with increasing temperature, which was found to be due to disruptions in the oscillations. Finally we provide evidence that these disruptions tend to affect multiple generations as opposed to individual cells. These findings provide insight in how to design more robust synthetic circuits and in how cell division can affect their dynamics.

Keywords: Repressilator, robustness, synchrony, synthetic biology.

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Authors: Chiu-Wen Chen, Chih-Feng Chen, Cheng-Di Dong

Abstract:

This study was conducted using the data collected at the mouth of Jen-Gen River to investigate and analyze chromium (Cr) contained in the sediments, and to evaluate the accumulation of Cr and the degree of its potential risk. The results show that samples collected at all monitoring stations near the mouth of Jen-Gen River contain 92–567 mg/kg of Cr with average of 366±166 mg/kg. The spatial distribution of Cr reveals that the Cr concentration is relatively high in the river mouth region, and gradually diminishes toward the harbor region. This indicates that upstream industrial and municipal wastewater discharges along the river bank are major sources of pollution. The accumulation factor and potential ecological risk index indicate that the sedimentation at Jen-Gen River mouth has the most serious degree of Cr accumulation and the highest ecological potential risk.

Keywords: chromium, sediment, river mouth, enrichment factor

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Authors: Patrick M. Stanton, William R. McCumber

Abstract:

Using a large dataset of more than 2,400 individual microfinance institutions (MFIs) from 120 countries from 1999 to 2016, this study finds that nearly half of the international MFIs operate as for-profit institutions. Formal institutions (business regulatory environment, property rights, social protection, and a developed financial sector) impact the likelihood of MFIs being for-profit across countries. Cultural differences across countries (power distance, individualism, masculinity, and indulgence) seem to be a factor in the legal status of the MFI (non-profit or for-profit). MFIs in countries with stronger formal institutions, a greater degree of power distance, and a higher degree of collectivism experience better financial and social performance.

Keywords: Hofstede cultural dimensions, international finance, microfinance institutions, non-profit.

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Authors: Walter Hussak, Heiko Schröder

Abstract:

Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoint Hamiltonian cycles, and therefore a simple routing can be found in the case of an edge failure. The existence of Hamiltonian cycles in Cayley graphs has been known for some time. So far, there are no published results on the much stronger condition of the existence of Hamiltonian decompositions. In this paper, we give a construction of a Hamiltonian decomposition of the star graph 5-star of degree 4, by defining an automorphism for 5-star and a Hamiltonian cycle which is edge-disjoint with its image under the automorphism.

Keywords: interconnection networks, paths and cycles, graphs andgroups.

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Authors: Akiko Kondo, Akio Kondo

Abstract:

We are facing serious problems related to long-term depopulation and an aging society with a falling birth rate in Japan. In this situation, we are suffering from a shortfall in human resources as well as a shortage of workforce in rural regions. In addition, we are struggling with a protracted economic slump and excess concentration of population in the Tokyo Metropolitan area. It is an urgent national issue to consider how to live in this country and what kind of structure of society and administration policy is needed. It is necessary to clarify people’s desire for their way of living and social assistance to be provided. The aim of this study is to clarify the characteristics of regional issues and the degree of their seriousness in local municipalities of Japan. We conducted a questionnaire survey about regional agenda in all local municipalities in Japan. We obtained responses concerning the degree of seriousness of regional issues and degree of importance of policies. Based on the data gathered from the survey, it is apparent that many local municipalities are facing an aging population and declining population. We constructed a model to analyze factors for declining population. Using the model, it was clarified that a population’s age structure, job opportunities and income level affect the decline of population. In addition, we showed the way of the evaluation of state of local municipality.

Keywords: Evaluation, Local municipality, Regional analysis, Regional issue.

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Authors: Hossein Kabir, Mojtaba Sadeghi

Abstract:

Finding the linear and nonlinear responses of a typical single-degree-of-freedom system (SDOF) is always being regarded as a time-consuming process. This study attempts to provide modifications in the renowned Newmark method in order to make it more time efficient than it used to be and make it more accurate by modifying the system in its own non-linear state. The efficacy of the presented method is demonstrated by assigning three base excitations such as Tabas 1978, El Centro 1940, and MEXICO CITY/SCT 1985 earthquakes to a SDOF system, that is, SDOF, to compute the strength reduction factor, yield pseudo acceleration, and ductility factor.

Keywords: Single-degree-of-freedom system, linear acceleration method, nonlinear excited system, equivalent displacement method.

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