Search results for: rational method

Authors: Azizakhanim Maharramli

Abstract:

The gradual transition from entrenched traditional technology and organization of construction production to innovative additive construction technology inevitably meets technological, technical, organizational, labour, and, finally, social difficulties. Therefore, the chosen nodal method will lead to the elimination of the above difficulties, combining some of the usual methods of construction and the myth in world practice that the labour force is subjected to a strong stream of reduction. The nodal method of additive technology will create favourable conditions for the optimal degree of distribution of labour across facilities due to the consistent performance of homogeneous work and the introduction of additive technology and traditional technology into construction production.

Keywords: parallel method, sequential method, stream method, combined method, nodal method

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Authors: Mahacine Amrani

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A simple and rapid method for the determination of alcohol in gasoline-alcohol mixtures using density measurements is described. The method can determine a minimum of 1% of alcohol by volume. The precision of the method is ± 3%.The method is more useful for field test in the quality assessment of alcohol blended fuels.

Keywords: gasoline-alcohol, mixture, alcohol determination, density, measurement, Morocco

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Authors: Kassahun Tilahun

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Most of the studies available on adult psychological well-being have been centered on Western countries. However, psychological well-being does not have the same meaning across the world. The Euro-American and African conceptions and experiences of psychological well-being differ systematically. As a result, questions like, how do people living in developing African countries, like Ethiopia, report their psychological well-being; what would the context-specific prominent determinants of their psychological well-being be, needs a definitive answer. This study was, therefore, aimed at developing a new theory that would address these socio-cultural issues of psychological well-being. Consequently, data were obtained through interview and open ended questionnaire. A total of 438 adults, working in governmental and non-governmental organizations situated in Addis Ababa, participated in the study. Appropriate qualitative method of data analysis, i.e. thematic content analysis, was employed for analyzing the data. The thematic analysis involves a type of abductive analysis, driven both by theoretical interest and the nature of the data. Reliability and credibility issues were addressed appropriately. The finding identified five major categories of themes, which are viewed as essential in determining the conceptions and experiences of psychological well-being of Ethiopian adults. These were; socio-cultural harmony, social cohesion, security, competence and accomplishment, and the self. Detailed discussion on the rational for including these themes was made and appropriate positive psychology interventions were proposed. Researchers are also encouraged to expand this qualitative research and in turn develop a suitable instrument taping the psychological well-being of adults with different sociocultural orientations.

Keywords: sociocultural, psychological, well-being Ethiopia, adults

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Authors: Sergey Chirun

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Using of a combination of institutional analysis and network access has allowed the author to identify the characteristics of the informal institutions of regional political power and political regimes. According to the author, ‘field’ of activity of post-Soviet regimes, formed under the influence of informal institutions, often contradicts democratic institutional regional changes which are aimed at creating of a legal-rational type of political domination and balanced model of separation of powers. This leads to the gap between the formal structure of institutions and the real nature of power, predetermining the specific character of the existing political regimes.

Keywords: authoritarianism, institutions, political regime, social networks, transformation

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Authors: Misbah Irshad, Faiza Sarfraz

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The problem of approximating surface to surface intersection is considered to be very important in computer aided geometric design and computer aided manufacturing. Although it is a complex problem to handle, its continuous need in the industry makes it an active topic in research. A technique for approximating intersection curves of two parametric surfaces is proposed, which extracts boundary points and turning points from a sequence of intersection points and interpolate them with the help of rational cubic spline functions. The proposed approach is demonstrated with the help of examples and analyzed by calculating error.

Keywords: approximation, parametric surface, spline function, surface intersection

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Michael G. Pantelyat

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Fundamental basics of pure and applied research in the area of magneto-thermo-mechanical numerical analysis and design of innovative electromagnetic devices (modern induction heaters, novel thermoelastic actuators, rotating electrical machines, induction cookers, electrophysical devices) are elaborated. Thus, mathematical models of magneto-thermo-mechanical processes in electromagnetic devices taking into account main interactions of interrelated phenomena are developed. In addition, graphical representation of coupled (multiphysics) phenomena under consideration is proposed. Besides, numerical techniques for nonlinear problems solution are developed. On this base, effective numerical algorithms for solution of actual problems of practical interest are proposed, validated and implemented in applied 2D and 3D computer codes developed. Many applied problems of practical interest regarding modern electrical engineering devices are numerically solved. Investigations of the influences of various interrelated physical phenomena (temperature dependences of material properties, thermal radiation, conditions of convective heat transfer, contact phenomena, etc.) on the accuracy of the electromagnetic, thermal and structural analyses are conducted. Important practical recommendations on the choice of rational structures, materials and operation modes of electromagnetic devices under consideration are proposed and implemented in industry.

Keywords: electromagnetic devices, multiphysics, numerical analysis, simulation and design

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Authors: Jiankang Wang, Hongyang Yu

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This paper proposes a portable online 3D modeling method. The method first utilizes a depth camera to collect data and compresses the depth data using a frame-by-frame lossless data compression method. The color image is encoded using the H.264 encoding format. After the cloud obtains the color image and depth image, a 3D modeling method based on bundlefusion is used to complete the 3D modeling. The results of this study indicate that this method has the characteristics of portability, online, and high efficiency and has a wide range of application prospects.

Keywords: 3D reconstruction, bundlefusion, lossless compression, depth image

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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Authors: J. Trarbach, S. Schosser, B. Vogt

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Decision-makers tend to prefer the first alternative over subsequent alternatives which is called the primacy effect. To reliably measure this effect, we conducted an experiment with real consequences for preference statements. Therefore, we elicit preferences of subjects using a rating scale, i.e. hypothetical preferences, and willingness to pay, i.e. real preferences, for two sequences of pain. Within these sequences, both overall intensity and duration of pain are identical. Hence, a rational decision-maker should be indifferent, whereas the primacy effect predicts a stronger preference for the first sequence. What we see is a primacy effect only for hypothetical preferences. This effect vanishes for real preferences.

Keywords: decision making, primacy effect, real incentives, willingness to pay

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Authors: Marco Sewald

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Comparing present to past the numbers of Americans expatriating U. S. citizenship have risen. Even though these numbers are small compared to the immigrants, U. S. citizens expatriations have historically been much lower, making the uptick worrisome. In addition, the published lists and numbers from the U.S. government seems incomplete, with many not counted. Different branches of the U. S. government report different numbers and no one seems to know exactly how big the real number is, even though the IRS and the FBI both track and/or publish numbers of Americans who renounce. Since there is no single explanation, anecdotal evidence suggests this uptick is caused by global tax law and increased compliance burdens imposed by the U.S. lawmakers on U.S. citizens abroad. Within a research project the question arose about the reasons why a constant growing number of U.S. citizens are expatriating – the answers are believed helping to explain the underlying governmental policy rational, leading to such activities. While it is impossible to locate former U.S. citizens to conduct a survey on the reasons and the U.S. government is not commenting on the reasons given within the process of expatriation, the chosen methodology is Structural Equation Modeling (SEM), in the first step by re-using current surveys conducted by different researchers within the population of U. S. citizens residing abroad during the last years. Surveys questioning the personal situation in the context of tax, compliance, citizenship and likelihood to repatriate to the U. S. In general SEM allows: (1) Representing, estimating and validating a theoretical model with linear (unidirectional or not) relationships. (2) Modeling causal relationships between multiple predictors (exogenous) and multiple dependent variables (endogenous). (3) Including unobservable latent variables. (4) Modeling measurement error: the degree to which observable variables describe latent variables. Moreover SEM seems very appealing since the results can be represented either by matrix equations or graphically. Results: the observed variables (items) of the construct are caused by various latent variables. The given surveys delivered a high correlation and it is therefore impossible to identify the distinct effect of each indicator on the latent variable – which was one desired result. Since every SEM comprises two parts: (1) measurement model (outer model) and (2) structural model (inner model), it seems necessary to extend the given data by conducting additional research and surveys to validate the outer model to gain the desired results.

Keywords: expatriation of U. S. citizens, SEM, structural equation modeling, validating

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Authors: Mojtaba Hakimi-Moghaddam

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Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.

Keywords: real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof

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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.

Keywords: image stitching, direct based method, panoramic image, X-ray

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Authors: S. B. Provost, Hossein Zareamoghaddam

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A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

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Authors: Monika Zalewska

Abstract:

Hans Kelsen was a versatile legal thinker whose achievements in the fields of legal theory, international law, and the theory of democracy are remarkable. All of the fields tackled by Kelsen are regarded as part of his “pure theory of law.” While the link between international law and Kelsen’s pure theory of law is apparent, the same cannot be said about the link between the theory of democracy and his pure theory of law. On the contrary, the general thinking concerning Kelsen’s thought is that it can be used to legitimize authoritarian regimes. The aim of this presentation is to address this concern by identifying the common ground between Kelsen’s pure theory of law and his theory of democracy and to show that they are compatible in a way that his pure theory of law and authoritarianism cannot be. The conceptual analysis of the purity of Kelsen’s theory and his goal of creating ideology-free legal science hints at how Kelsen’s pure theory of law and the theory of democracy are brought together. The presentation will first demonstrate that these two conceptions have common underlying values and meta-ethical convictions. Both are founded on relativism and a rational worldview, and the aim of both is peaceful co-existence. Second, it will be demonstrated that the separation of law and morality provides the maximum space for deliberation within democratic processes. The conclusion of this analysis is that striking similarities exist between Kelsen’s legal theory and his theory of democracy. These similarities are grounded in the Enlightenment tradition and its values, including rationality, a scientific worldview, tolerance, and equality. This observation supports the claim that, for Kelsen, legal positivism and the theory of democracy are not two separate theories but rather stem from the same set of values and from Kelsen’s relativistic worldview. Furthermore, three main issues determine Kelsen’s orientation toward a positivistic and democratic outlook. The first, which is associated with personality type, is the distinction between absolutism and relativism. The second, which is associated with the values that Kelsen favors in the social order, is peace. The third is legality, which creates the necessary condition for democracy to thrive and reveals that democracy is capable of fulfilling Kelsen’s ideal of law at its fullest. The first two categories exist in the background of Kelsen’s pure theory of law, while the latter is an inherent part of Kelsen’s concept of law. The analysis of the text concerning natural law doctrine and democracy indicates that behind the technical language of Kelsen’s pure theory of law is a strong concern with the trends that appeared after World War I. Despite his rigorous scientific mind, Kelsen was deeply humanistic. He tried to create a powerful intellectual weapon to provide strong arguments for peaceful coexistence and a rational outlook in Europe. The analysis provided by this presentation facilitates a broad theoretical, philosophical, and political understanding of Kelsen’s perspectives and, consequently, urges a strong endorsement of Kelsen’s approach to constitutional democracy.

Keywords: hans kelsen, democracy, legal positivism, pure theory of law

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Abdulaziz Omar Alsadhan, Mohd Mudasir Shafi

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Performance testing is done to prove the reliability of any software product. There are a number of tools available in the markets that are used to perform performance testing. In this paper we present a comparative study of the three most commonly used performance testing tools. These tools cover the major share of the performance testing market and are widely used. In this paper we compared the tools on five evaluation parameters which are; User friendliness, portability, tool support, compatibility and cost. The conclusion provided at the end of the paper is based on our study and does not support any tool or company.

Keywords: software development, software testing, quality assurance, performance testing, load runner, rational testing, silk performer

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Alkaben Patel

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The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.

Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation

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Authors: Mikel Alonso López

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This paper explores, in depth, the idea that emotions are present in all consumer decision making processes, meaning that purchase decisions have never been purely cognitive or as they traditionally have been defined, rational. Human beings, in all kinds of decisions, has "always" used neural systems related to emotions along with neural systems related to cognition, regardless of the type of purchase or the product or service in question. Therefore, all purchase decisions are, at the same time, cognitive and emotional. This paper presents an analysis of the main contributions of researchers in this regard.

Keywords: emotions, decision making, consumer behaviour, emotional behaviour

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Authors: Divyansh Goel, Varun Jain

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Classical economics works on the principle that people are rational and analytical in their decision making and their choices fall in line with the most suitable option according to the dominant strategy in a standard game theory model. This model has failed at many occasions in estimating the behavior and dealings of rational people, giving proof of some other underlying heuristics and cognitive biases at work. This paper probes into the study of these factors, which fall under the umbrella of behavioral economics and through their medium explore the solution to a problem which a lot of nations presently face. There has long been a wide disparity in the number of people holding favorable views on organ donation and the actual number of people signing up for the same. This paper, in its entirety, is an attempt to shape the public policy which leads to an increase the number of organ donations that take place and close the gap in the statistics of the people who believe in signing up for organ donation and the ones who actually do. The key assumption here is that in cases of cognitive dissonance, where people have an inconsistency due to conflicting views, people have a tendency to go with the default choice. This tendency is a well-documented cognitive bias known as the status quo bias. The research in this project involves an assay of mandated choice models of organ donation with two case studies. The first of an opt-in system of Germany (where people have to explicitly sign up for organ donation) and the second of an opt-out system of Austria (every citizen at the time of their birth is an organ donor and has to explicitly sign up for refusal). Additionally, there has also been presented a detailed analysis of the experiment performed by Eric J. Johnson and Daniel G. Goldstein. Their research as well as many other independent experiments such as that by Tsvetelina Yordanova of the University of Sofia, both of which yield similar results. The conclusion being that the general population has by and large no rigid stand on organ donation and are gullible to status quo bias, which in turn can determine whether a large majority of people will consent to organ donation or not. Thus, in our paper, we throw light on how governments can use status quo bias to drive positive social change by making policies in which everyone by default is marked an organ donor, which will, in turn, save the lives of people who succumb on organ transplantation waitlists and save the economy countless hours of economic productivity.

Keywords: behavioral economics, game theory, organ donation, status quo bias

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Authors: Gaosheng Ju

Abstract:

Our empirical evidence supports a model of consumption planning behaviors with the following two characteristics. First, households formulate a rational consumption target based on their desired target, displaying a diminishing sensitivity to the discrepancy between them. Second, the established target is a reference point for their planned consumption. The diminishing sensitivity leads to opposite reactions in higher and lower quantiles of both consumption targets and consumption growth to changes in economic conditions. This phenomenon accounts for the perplexingly low correlation between consumption and other macroeconomic variables. Furthermore, the opposing movements of consumption targets offer new insights into consumption-based asset pricing.

Keywords: consumption planning, reference point, diminishing sensitivity, quantile regression, asset pricing puzzles

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Authors: Fatih Topaloğlu

Abstract:

Although philosophy is inherently a theoretical and intellectual activity, it should not be denied that environmental conditions influence the formation and shaping of philosophical thought. In this context, it should be noted that the Philosophy of Religion has been influential in the debates in the West, especially since the beginning of the 20th century, and that this influence has dimensions that cannot be limited to academic or intellectual fields. The issues and problems that fall within the field of interest of Philosophy of Religion are followed with interest by a significant proportion of society through popular publications. Philosophy of Religion has its share in many social, economic, cultural, scientific, political and ethical developments. Philosophy of Religion, in the most general sense, can be defined as a philosophical approach to religion or a philosophical way of thinking and discussing religion. Philosophy of Religion tries to explain the epistemological foundations of concepts such as belief and faith that shape religious life by revealing their meaning for the individual. Thus, Philosophy of Religion tries to evaluate the effect of beliefs on the individual's values, judgments and behaviours with a comprehensive and critical eye. The Philosophy of Religion, which tries to create new solutions and perspectives by applying the methods of philosophy to religious problems, tries to solve these problems not by referring to the holy book or religious teachings but by logical proofs obtained through the possibilities of reason and evidence filtered through the filter of criticism. Although there is no standard method for doing Philosophy of Religion, it can be said that an approach that can be expressed as thinking about religion in a rational, objective, and consistent way is generally accepted. The evaluations made within the scope of Philosophy of Religion have two stages. The first is the definition stage, and the second is the evaluation stage. In the first stage, the data of different scientific disciplines, especially other religious sciences, are utilized to define the issues objectively. In the second stage, philosophical evaluations are made based on this foundation. During these evaluations, the issue of how the relationship between religion and philosophy should be established is extremely sensitive. The main thesis of this paper is that the Philosophy of Religion, as a branch of philosophy, has been affected by the conditions caused by the historical experience through which it has passed and has differentiated its subjects and the methods it uses to realize its philosophical acts over time under the influence of these conditions. This study will attempt to evaluate the validity of this study based on the "Introduction to Philosophy of Religion" literature, which we assume reflects this differentiation. As a result of this examination will aim to reach some factual conclusions about the nature of both philosophical and religious thought, to determine the phases that the Philosophy of Religion as a discipline has gone through since the day it emerged, and to investigate the possibilities of a holistic view of the field.

Keywords: content analysis, culture, history, philosophy of religion, method

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Authors: Amir Alani, Mojtaba Mahmoodian, Anna Romanova, Asaad Faramarzi

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Pipelines are extensively used engineering structures which convey fluid from one place to another. Most of the time, pipelines are placed underground and are encumbered by soil weight and traffic loads. Corrosion of pipe material is the most common form of pipeline deterioration and should be considered in both the strength and serviceability analysis of pipes. The study in this research focuses on concrete pipes in sewage systems (concrete sewers). This research firstly investigates how to involve the effect of corrosion as a time dependent process of deterioration in the structural and failure analysis of this type of pipe. Then three probabilistic time dependent reliability analysis methods including the first passage probability theory, the gamma distributed degradation model and the Monte Carlo simulation technique are discussed and developed. Sensitivity analysis indexes which can be used to identify the most important parameters that affect pipe failure are also discussed. The reliability analysis methods developed in this paper contribute as rational tools for decision makers with regard to the strengthening and rehabilitation of existing pipelines. The results can be used to obtain a cost-effective strategy for the management of the sewer system.

Keywords: reliability analysis, service life prediction, Monte Carlo simulation method, first passage probability theory, gamma distributed degradation model

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: apportionment, bias, divisor, fair, measurement

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Authors: Tea Poklepović, Zdravka Aljinović, Mario Matković

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Modern Portfolio Theory (MPT) according to Markowitz states that investors form mean-variance efficient portfolios which maximizes their utility. Markowitz proposed the standard deviation as a simple measure for portfolio risk and the lower semi-variance as the only risk measure of interest to rational investors. This paper uses a third volatility estimator based on intraday data and compares three efficient frontiers on the Croatian Stock Market. The results show that range-based volatility estimator outperforms both mean-variance and lower semi-variance model.

Keywords: variance, lower semi-variance, range-based volatility, MPT

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Authors: Mei-Jie Xu, Yang Zhong

Abstract:

Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

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