Search results for: state equation

Authors: Mojtaba Hakimi-Moghaddam

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Routh-Hurwitz stability criterion is a powerful approach to determine stability of linear time invariant systems. On the other hand, applying this criterion to characteristic equation of a system, whose stability or marginal stability can be determined. Although the command roots (.) of MATLAB software can be easily used to determine the roots of a polynomial, the characteristic equation of closed loop system usually includes parameters, so software cannot handle it; however, Routh-Hurwitz stability criterion results the region of parameter changes where the stability is guaranteed. Moreover, this criterion has been extended to characterize the stability of interval polynomials as well as fractional-order polynomials. Furthermore, it can help us to design stable and minimum-phase controllers. In this paper, theory and application of this criterion will be reviewed. Also, several illustrative examples are given.

Keywords: Hurwitz polynomials, Routh-Hurwitz stability criterion, continued fraction expansion, pure imaginary roots

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Authors: Muslim Malik, Avadhesh Kumar

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A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings.

Keywords: Banach fixed point theorem, non-instantaneous impulses, strongly continuous cosine family, total controllability

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Authors: Jihye Jeon

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This paper analyzes the conceptual framework of three statistical methods, multiple regression, path analysis, and structural equation models. When establishing research model of the statistical modeling of complex social phenomenon, it is important to know the strengths and limitations of three statistical models. This study explored the character, strength, and limitation of each modeling and suggested some strategies for accurate explaining or predicting the causal relationships among variables. Especially, on the studying of depression or mental health, the common mistakes of research modeling were discussed.

Keywords: multiple regression, path analysis, structural equation models, statistical modeling, social and psychological phenomenon

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Authors: Tokuei Sako

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Laser-induced current in a quasi-one-dimensional nanostructure has been studied by a model of a few electrons confined in a 1D electrostatic potential coupled to electrodes at both ends and subjected to a pulsed laser field. The time-propagation of the one- and two-electron wave packets has been calculated by integrating the time-dependent Schrödinger equation directly by the symplectic integrator method with uniform Fourier grid. The temporal behavior of the resultant light-induced current in the studied systems has been discussed with respect to the lifetime of the quasi-bound states formed when the static bias voltage is applied.

Keywords: pulsed laser field, nanowire, electron wave packet, quantum dots, time-dependent Schrödinger equation

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Authors: T. Srinivasa Krishna, K. Narendra, K. Thomas, S. S. Raju, B. Munibhadrayya

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The densities, speeds of sound and refractive index of the binary mixture of ionic liquid (IL) 1-Butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([BMIM][Imide]) and Pyrrolidin-2-one(PY) was measured at atmospheric pressure, and over the range of temperatures T= (298.15 -323.15)K. The excess molar volume, excess isentropic compressibility, excess speed of sound, partial molar volumes, and isentropic partial molar compressibility were calculated from the values of the experimental density and speed of sound. From the experimental data excess thermal expansion coefficients and isothermal pressure coefficient of excess molar enthalpy at 298.15K were calculated. The results were analyzed and were discussed from the point of view of structural changes. Excess properties were calculated and correlated by the Redlich–Kister and the Legendre polynomial equation and binary coefficients were obtained. Values of excess partial volumes at infinite dilution for the binary system at different temperatures were calculated from the adjustable parameters obtained from Legendre polynomial and Redlich–Kister smoothing equation. Deviation in refractive indices ΔnD and deviation in molar refraction, ΔRm were calculated from the measured refractive index values. Equations of state and several mixing rules were used to predict refractive indices of the binary mixtures and compared with the experimental values by means of the standard deviation and found to be in excellent agreement. By using Prigogine–Flory–Patterson (PFP) theory, the above thermodynamic mixing functions have been calculated and the results obtained from this theory were compared with experimental results.

Keywords: density, refractive index, speeds of sound, Prigogine-Flory-Patterson theory

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Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

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Authors: Adamu Garba, Saidu Idi

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This study was conducted to determine the prevalence of Dermatophilosis in cattle in Bauchi State and suggest possible control measures. Data were obtained from the State Ministry of Agriculture and Natural Resources, Veterinary Division and monthly reports from Local Government Area Veterinary Offices for a period of three years ranging from 1996-1998. The result revealed that the disease is more prevalent in the rainy season which coincides with preponderance of the predisposing factors. Of the total 17,252 infected cattle in the State, Western zone had the highest cases with 8,298 (50.0%), followed by Central zone with 5,211 (30.0%) and the least was in the Northern zone with 3,753 (20.0%) cases. Rainfall pattern within the zones could be responsible for the variation in the prevalence rate. Analysis of variance revealed that there is no significant difference in the prevalence of Dermatophilosis between the years (P<0.212) while there is significant difference within the zones (P<0.012). Correlation analysis carried out showed that there is positive relationship between rainfall and Dermatophilosis (r<0.909). Since the disease is more prevalent during the rainy season, efforts should be exerted on thorough preventive measures during the period to control the disease in the State, particularly in the Western zone.

Keywords: incidence, dermatophilosis, cattle, Bauchi State

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Authors: Vinay Choudhary, Ibakordor Patlong

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This study investigates and evaluates pre and post competitive anxiety, self-confidence, and performance of the athletes. The Cognitive State Anxiety Inventory-2 was administered to collect data from 73 athletes, both men, and women, before and after the competition, who participated in the Reliance Foundation Youth Sports (RFYS)-Athletics, held at Gachibowli Stadium, Hyderabad. A paired t-test was used to find the significant difference between the pre and post-competition. Results showed that the levels of cognitive state anxiety before the competition was low as compared after the competition and the levels of somatic state anxiety before the competition was high as compared after the competition whereas the levels of self-confidence before the competition was high as compared after the competition. This study concludes that the levels of cognitive state anxiety increases after the competition as athletes could not perform according to the performance expectations, on the contrary, the levels of somatic anxiety decrease as there was no pressure of performance on the athletes after the competition and the levels of self-confidence decreases after the competition as athletes could not reach their desired performance levels.

Keywords: anxiety, athletes, pre and post, CSAI-2, self-confidence, performance

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Authors: Essa Njie

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One of the challenges that Africa needs to overcome for the sustenance of its democratic gains is to separate the state from the ruling party to avoid the latter’s attempt in monopolizing the former’s resources and institutions for political supremacy. But this separation must go along with the process of depoliticizing the civil services (separation from partisan politics) which have been politicized by incumbents to register electoral successes. While researches conducted on the Gambia’s democratic reality tend to have looked at a wide range of challenges confronting the country’s democratic progress, this paper focuses on state power monopolization and its impediment to democratic governance in the country. The paper explores the involvement of civil/public servants in partisan politics in the Gambia. It looks at the intertwined nature of the state and the ruling party as state resources could not be separated from that of the ruling party (lack of separation between political and non-political resources) in both Dawda Jawara and Yahya Jammeh eras, and how such affected the country’s democratic credential. The paper in particular addresses the need for the current government to depoliticize the country’s civil service and concomitantly separate the state from the ruling party by not monopolizing the former’s resources and institutions to galvanize political support.

Keywords: civil service, democratic consolidation, monopolisation, multi-party elections, public institutions, ruling party, state resources

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Authors: Collen Maseloane, Chris Cloete

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The study investigated the status of building condition assessments of state-owned immovable assets in South Africa. A stratified random sample of 200 (out of 372) personnel was drawn from the eight rele-vant business units of the Department of Public Works (DPW). A questionnaire comprising open-ended questions was distributed to the sampled participants and a total of 139 completed questionnaires were received. A significant number of state asset properties were found to be in poor condition owing to the asset managers’ inability to access automated information on the conditions of assets. It is recommended that the immovable asset register of the Department requires constant enhancement to update information on the condition of each state-owned immovable asset under its custodianship. Implementation of the proposals should contribute to the maintenance of the value of state assets in South Africa.

Keywords: building condition assessment, immovable asset register, life cycle asset management, public works, South Africa

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Authors: H. Ben Khlifa, W. Cheikhrouhou-Koubaa, A. Cheikhrouhou

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The orthorhombic Pr₀.₈Na₀.₂−ₓKₓMnO₃ (x = 0.10 and 0.15) manganites are prepared by using the solid-state reaction at high temperatures. The critical exponents (β, γ, δ) are investigated through various techniques such as modified Arrott plot, Kouvel-Fisher method, and critical isotherm analysis based on the data of the magnetic measurements recorded around the Curie temperature. The critical exponents are derived from the magnetization data using the Kouvel-Fisher method, are found to be β = 0.32(4) and γ = 1.29(2) at TC ~ 123 K for x = 0.10 and β = 0.31(1) and γ = 1.25(2) at TC ~ 133 K for x = 0.15. The critical exponent values obtained for both samples are comparable to the values predicted by the 3D-Ising model and have also been verified by the scaling equation of state. Such results demonstrate the existence of ferromagnetic short-range order in our materials. The magnetic entropy changes of polycrystalline samples with a second-order phase transition are investigated. A large magnetic entropy change deduced from isothermal magnetization curves, is observed in our samples with a peak centered on their respective Curie temperatures (TC). The field dependence of the magnetic entropy changes are analyzed, which shows power-law dependence ΔSmax ≈ a(μ0 H)n at the transition temperature. The values of n obey the Curie Weiss law above the transition temperature. It is shown that for the investigated materials, the magnetic entropy change follows a master curve behavior. The rescaled magnetic entropy change curves for different applied fields collapse onto a single curve for both samples.

Keywords: manganites, critical exponents, magnetization, magnetocaloric, master curve

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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: Maszlee Malik

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If the contemporary notion of welfare arises from the horizontal material needs and to be structured by the vertical framework of the state, Islamic societal-based welfare is to be shaped by moral based and faith inspired ihsan (benevolence) culture in producing the ‘Ihsani’ version of the enhancement of the political participation, democratic culture, good governance and self-realisation, which eventually culminating towards the bigger picture of ‘development’. This paper will analytically investigate on how the over-arching principle of ‘ihsan’ could be an essential tool in harmonizing the social-based welfare instrument as another conceptual framework to formulate a conceptual approach towards development and poverty elevation beyond the state. Essentially, this research will employ the inductive method of exploration on Islamic epistemological sources and historical evidence, to formulate the discursive concept of non-state societal-based welfare based on the ‘ihsani’ framework.

Keywords: benevolent society, development, Hisbah, HomoIslamicus, Ihsani, islamic epistemology, state, social capital, societal-based welfare, zakat

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Authors: Iniye Irene Wodi, Allen A. Agih

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Goal theory perspective as an emerging trend in students’ motivation explores reasons why students engage in achievement related behaviour. While previous research typifies students’ goal orientations into two dimensions of mastery and performance orientations in various other parts of the world, not much has been done in this regard in Nigeria and specifically in Bayelsa state to the best of the researcher’s knowledge. To this end, the study explores the achievement goal orientations of schooling adolescents in Bayelsa State. The sample of the study consists of 220 schooling adolescents drawn from four urban schools in the state. A modified form of the Patterns of Adaptive learning survey (PALS) questionnaire was used to elicit data. Results indicated that schooling adolescents in Bayelsa state are mastery as well as performance oriented. The students also did not differ in goal orientations by gender. The implications of this for sustainable development were highlighted.

Keywords: achievement goals, goal orientations, schooling adolescents, sustainable development

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Authors: Hyun-Ji Choi

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This paper aims to examine the meaning of ‘state’ as a monopoly of violence, in regard with South Korean democratic transition. Since institutional democratization in 1987, it is conventionally known that governmental authority has exercised its power through law and police force, rather than inclusive or private violence. In other words, 1987 pro-democracy movement has been a critical juncture for a step towards democratic consolidation. However, state coercion may continually be exerted despite institutional specification by law in South Korean context. Explicit case would be amendment of ‘the Law on Assembly and Demonstration’ which determines citizens’ right to take collective action mostly against government actions. This paper investigates amendment process of the law along with social reality since 1987 until 2015 to see how effectively institutionalization has progressed.

Keywords: democratic transition, historical institutionalism, state coercion, the law on Assembly and Demonstration

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Authors: Ralpian Randolian

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Eighty-five Romanian teachers and principals participated on this study to examine their perspectives of different leadership styles. Demographic variables such as the source of degree (Romania, Europe institutes, USA institutes, etc.), gender, region, level taught, years of experience, and specialty were identified. The researcher developed a questionnaire that consisted of 4 leadership styles. The data were analyzed using structural equation modeling (SEM) to identify which of the variables best predict the leadership styles. Results indicated that the democracy style was the most preferred leadership style by Jordanian parents, while the authoritarian styles ranked second. The results also found statistically significant differences were found related to the study variables. This study ends by putting forward a number of suggestions and recommendation.

Keywords: teachers’ perspectives, leadership styles, gender, structural equation modeling

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Authors: N. Reichbach, A. Kuperman

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The paper describes a design of a monitoring system for super capacitor packs in propulsion systems, allowing determining the instantaneous energy capacity under power loading. The system contains real-time recursive-least-squares identification mechanism, estimating the values of pack capacitance and equivalent series resistance. These values are required for accurate calculation of the state-of-energy.

Keywords: real-time monitoring, RLS identification algorithm, state-of-energy, super capacitor

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Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

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For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

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Authors: Neslihan Cetin

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In this study, we will aim to analyze how the period of the state of emergency in Turkey lead to gaps in law and the formation of areas in which there was a complete lack of supervision. The state of emergency that was proclaimed following the coup attempt of July 15, 2016, continued until July 18, 2018, that is to say, 2 years, without taking into account whether the initial circumstances persisted. As part of this work, we claim that the state of emergency provided the executive power with important tools for governing, which it took constant use. We can highlight how the concern for security at the center of the basic considerations of the people in a city was exploited as a foundation by the military power in Turkey to interfere in the political, legal, and social spheres. The constitutions of 1924, 1961, and 1982 entrusted the army with the role of protector of the integrity of the state. This became an instrument at the hands of the military to legitimize their interventions in the name of public security. Its interventions in the political field are indeed politically motivated. The constitution, the legislative, and regulatory systems are modified and monopolized by the military power that dominates the legislative, regulatory, and judicial power, leading to a state of exception. With the political convulsions over a decade, the government was able to usurp the instrument called the state of exception. In particular, the decree-laws of the state of emergency, which the executive makes frequent and generally abusive use, became instruments in the hands of the government to take measures that it wishes to escape from the rules and the pre-established control mechanisms. Thus the struggle against the political opposition becomes more unbalanced and destructive. To this must also be added the ineffectiveness of ex-post controls and domestic remedies. This research allows us to stress how a legal concept, such as ‘the state of emergency’ can be politically exploited to make it a legal weapon that continues to produce victims.

Keywords: constitutional law, state of emergency, rule of law, instrumentalization of law

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Authors: Ghzlan Mahmoud Abdel Aziz

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This case study aims to identify the intrastate conflicts between the nation state and armed groups. Nowadays, most wars weaken states against armed groups. Thus, it is very important to negotiate with such groups in order to reinforce the law for the protection of victims. These armed groups are the cause of conflicts and they are related with many of humanitarian issues that result out of conflicts. In this age of rivalry; terrorists, insurgents, or transnational criminal parties have surfaced to the top as a reaction to these armed groups in an effort to set up a new world order. Moreover, the intra state conflicts became increasingly treacherous than the interstate conflicts, particularly when nation state systems deal with armed groups which try to influence the state. The unexpected upraising of the Arab Spring during 2011 in parts of the Middle East and North Africa formed various patterns of conflicts. The events of the Arab Spring resulted in current and long term change across the region. Significant modifications in the level, strength and period of armed conflict around the world have been made. Egypt was in the center of these events. It has fought back the armed groups under the name of terrorism and spread common disorder and violence among civilians. On this note, this study focuses on the problem of the transformation in the methods of organized violence within one state rather than between two state or more and analyzes the objectives, strategies, and internal composition of armed groups and the environments that foster them, with a focus on the Egyptian case.

Keywords: armed groups, conflicts, Egyptian armed forces, intrastate conflicts

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Authors: Yi Yu, Vu Xuan Nguyen, Gaoxi Xiao

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Opinion formation in complex social networks may exhibit complex system dynamics even when based on some simplest system evolution models. An interesting and important issue is the effects of the initial state on the final steady-state opinion distribution. By carrying out extensive simulations and providing necessary discussions, we show that, while different initial opinion distributions certainly make differences to opinion evolution in social systems without noises, in systems with noises, given enough time, different initial states basically do not contribute to making any significant differences in the final steady state. Instead, it is the basal distribution of the preferred opinions that contributes to deciding the final state of the systems. We briefly explain the reasons leading to the observed conclusions. Such an observation contradicts with a long-term belief on the roles of system initial state in opinion formation, demonstrating the dominating role that opinion mutation can play in opinion formation given enough time. The observation may help to better understand certain observations of opinion evolution dynamics in real-life social networks.

Keywords: opinion formation, Deffuant model, opinion mutation, consensus making

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Authors: Khalil H. Al-Bayati, G. Nasma, Hussein Ban H. Adel

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The purpose of the present work is to calculate the expectation value of potential energy for different spin states (ααα ≡ βββ, αβα ≡ βαβ) and compare it with spin states (αββ, ααβ ) for lithium excited state (1s2s3s) and Li-like ions (Be+, B+2) using Hartree-Fock wave function by partitioning technique. The result of inter particle expectation value shows linear behaviour with atomic number and for each atom and ion the shows the trend ααα < ααβ < αββ < αβα.

Keywords: lithium excited state, potential energy, 1s2s3s, mathematical physics

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Authors: I. Muslih, A. Alkhalailah, A. Merdji

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Photovoltaic efficiency is highly affected by dust accumulation; the dust particles prevent direct solar radiation from reaching the panel surface; therefore a reduction in output power will occur. A study of dust and soiling accumulation effect on the output power of PV panels was conducted for different periods of time from May to October in three countries of the MENA region, Jordan, Egypt, and Algeria, under local weather conditions. This study leads to build a more realistic equation to estimate the power reduction as a function of time. This logarithmic function shows the high reduction in power in the first days with 10% reduction in output power compared to the reference system, where it reaches a steady state value after 60 days to reach a maximum value of 30%.

Keywords: dust effect, MENA, solar energy, PV system

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Authors: Pavel E. Golosov, Vladimir I. Gorelov, Oksana L. Karelova

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There are visible changes in the world organization, environment and health of national conscience that create a background for discussion on possible redefinition of global, state and regional management goals. Authors apply the sustainable development criteria to a hierarchical management scheme that is to lead the world community to non-contradictory growth. Concrete definitions are discussed in respect of decision-making process representing the state mostly. With the help of system analysis it is highlighted how to understand who would carry the distinctive sign of world leadership in the nearest future.

Keywords: decision-making, information technology, public administration

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Authors: Abdurrahim Dal, Tuncay Karaçay

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Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.

Keywords: air bearing, internal pressure, Reynold’s equation, rotor

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Authors: G. Mattia, A. Di Leo, L. Principato

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The purchase impulsiveness is preceded by a lack of self-control: consequently, it is legitimate to believe that a consumer with a low level of self-control can result in a higher probability of cognitive dissonance. Moreover, the process of purchase is influenced by the pre-existing affective state in a considerable way. With reference to on-line purchases, digital behavior cannot be merely ascribed to the rational sphere, given the speed and ease of transactions and the hedonistic dimension of purchases. To our knowledge, this research is among the first cases of verification of the effect of moderation exerted by the positive affective state in the on-line impulse purchase of products with a high expressive value such as a smartphone on the occurrence of cognitive dissonance. To this aim, a moderation analysis was conducted on a sample of 212 impulsive millennials buyers. Three scales were adopted to measure the constructs of interest: IBTS for impulsivity, PANAS for the affective state, Sweeney for cognitive dissonance. The analysis revealed that positive affective state does not affect the onset of cognitive dissonance.

Keywords: cognitive dissonance, impulsive buying, online shopping, online consumer behavior

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Authors: Wanhyun Cho, Seongchae Seo, Soonja Kang

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In this work, we propose a variational technique for image contrast enhancement which utilizes global and local information around each pixel. The energy functional is defined by a weighted linear combination of three terms which are called on a local, a global contrast term and dispersion term. The first one is a local contrast term that can lead to improve the contrast of an input image by increasing the grey-level differences between each pixel and its neighboring to utilize contextual information around each pixel. The second one is global contrast term, which can lead to enhance a contrast of image by minimizing the difference between its empirical distribution function and a cumulative distribution function to make the probability distribution of pixel values becoming a symmetric distribution about median. The third one is a dispersion term that controls the departure between new pixel value and pixel value of original image while preserving original image characteristics as well as possible. Second, we derive the Euler-Lagrange equation for true image that can achieve the minimum of a proposed functional by using the fundamental lemma for the calculus of variations. And, we considered the procedure that this equation can be solved by using a gradient decent method, which is one of the dynamic approximation techniques. Finally, by conducting various experiments, we can demonstrate that the proposed method can enhance the contrast of colour images better than existing techniques.

Keywords: color image, contrast enhancement technique, variational approach, Euler-Lagrang equation, dynamic approximation method, EME measure

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Nurul A. Hamzah, Tony Morris, Dan Van Der Westhuizen

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Music listening can potentially promote the achievement of flow state during exercise. Selecting music for exercise should consider the motivational factors-internal factors (music tempo and musicality) and external factors (cultural impact and association). This study was a cross-over study which was designed to examine the motivational qualities of music (participant-selected music and researcher-selected music) and flow state responses during exercise accompanying with music. 17 healthy participants (M=30.2, SD=6.3 years old) were among low physical activity individuals. Participants completed two separate sessions of 30 minutes of moderate intensity exercise (40-60% of Heart Rate Reserve) while listening to music. Half the participants at random were assigned to exercise with participant-selected music first, and half were assigned to exercise with researcher-selected music first. Parameters including flow state responses (Flow State Scale-2) and motivational music rating (Brunel Music Rating Inventory-2) were administered immediately after the exercise. Results from this study showed that there were no significant differences for both flow state t(32)=0.00, p>0.05 and motivational music rating t(32)= .393, p>0.05 between exercise with participant-selected music and exercise with researcher-selected music. Listening to music either participant or researcher selected music could promote flow experience during exercise when music is perceived as motivational. Music tempo and music preference are factors that could influence individuals to enjoy exercise and improve the exercise performance.

Keywords: motivational music, flow state, researcher-selected music, participant-selected music

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations

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