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Numerical Simulation of the Phase Space of Jupiter-Europa System Including the Effect of Oblateness
Get PDFWe have numerically investigated the phase space of the Jupiter-Europa system in the framework of a Circular Restricted Three-Body Problem. In our model, Jupiter is taken as oblate primary. We have considered time-frequency analysis (TFA) based on wavelets and the Poincare Surface of Section (PSS) for the characterization of orbits in the Jupiter-Europa model. We have exploited both cases: a system with and without considering the effect of oblateness. Graphs (ridge-plots) explaining the phenomenon of resonance trapping, a difference between chaotic sticky orbit and the non-sticky orbit, and periodic and quasi-periodic orbit are presented. Our results of Poincare surfaces of the section of the Jupiter-Europa system (with and without the effect of oblateness) reveal the impact of oblateness of Jupiter as reducing parameter for regular and chaotic regions. Time-frequency analysis based on wavelets is comparatively fast and is suitable for the identification and characterization of the different type of trajectories in the nonlinear dynamical system
Farlie-Gumbel-Morgenstern Family: Equivalence of Uncorrelation and Independence
Get PDFConsidering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this problem in other distributions. In other words, whether the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. In this paper, we answer to this question and establish generalized Farlie-Gumbel-Morgenstern (FGM) family is another family of distributions under which uncorrelation is equivalent to independence
Fitting Skew Distributions to Iranian Auto Insurance Claim Data
Get PDFIn actuary, the derivation of loss distributions from insurance data is of great interest. Fitting an adequate distribution to real insurance data is not an easy task, mainly due to the nature of the data, which shows several features to be accounted for. Although, because of its stochastic and numerical simplicity, it is often assumed that the involved financial risk factors are normally distributed, but empirical studies indicate that most of financial risk factors have distributions with high peaks and heavy tails. Thus, it is important in the actuarial science to model insurance risks with skewed distributions. Claims size data in non-life insurance policies are very skewed and exhibit high kurtosis and extreme tails. Skew distributions are reasonable models for describing claims in property-liability insurance. We fit several well-known skew distributions (skew-normal, skew-Laplace, generalized logistic, generalized hyperbolic, variance gamma, normal inverse Gaussian, Marshal-Olkin Log-Logistic and Kumaraswamy Marshal-Olkin Log-Logistic distributions) to the amount of automobile accident claims for property damage to a third party. The data are from financial records of a state-owned major general insurance company in Iran. The fitted models are compared using AIC (Akaike information criterion), BIC (Bayesian information criterion) and Kolmogorov-Smirnov goodness-of-fit test statistics. We find that the Kumarasamy Marshal-Olkin Log-Logistic distribution is better than other considered distributions in describing the features of the observed data. This distribution is a very perfect distribution to describe the skew data. The value at risk and conditional tail expectation, as most common risk measures in insurance, are estimated for the data under consideration
A new hybrid method for solving nonlinear fractional differential equations
Get PDFIn this paper, numerical solution of initial and boundary value problems for nonlinear fractional differential equations is considered by pseudospectral method. In order to avoid solving systems of nonlinear equations resulting from the method, the residual function of the problem is constructed, as well as a suggested unconstrained optimization model solved by PSOGSA algorithm. Furthermore, the research inspects and discusses the spectral accuracy of Chebyshev polynomials in the approximation theory. The following scheme is tested for a number of prominent examples, and the obtained results demonstrate the accuracy and efficiency of the proposed method
The TRI-AG Academics Research Extension College Of Agriculture Sciences - Vol. 2 No.2 - 2017
Get PDFhttps://digitalcommons.pvamu.edu/pv-magazine/1017/thumbnail.jp
Equilibrium charge distribution on a finite straight one-dimensional wire
No full textThe electrostatic properties of uniformly charged regular bodies are prominently discussed on college-level electromagnetism courses. However, one of the most basic problems of electrostatics that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this level. In this work we revisit the problem of equilibrium charge distribution on a straight one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated analytically for a Coulomb interaction potential between point charges. Surprisingly, different models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate limit. Instead, our starting point is the obvious one, a finite straight 1D wire that contains charge. However, the new tweak in the model is the assumption that point charges interact with each other via a non-Coulomb power-law interaction potential. This potential is well-behaved, allows exact analytical results and approaches the standard Coulomb interaction potential as a limit. The results originating from this approach suggest that the equilibrium charge distribution for a finite straight 1D wire is a uniform charge density when the power-law interaction potential approaches the Coulomb interaction potential as a suitable limit. We contrast such a finding to results obtained using a different regularised logarithmic interaction potential which allows exact treatment in 1D. The present self-contained material may be of interest to instructors teaching electromagnetism as well as students who will discover that simple-looking problems may sometimes pose important scientific challenges
Interplay of Dzyaloshinsky-Moriya and dipole-dipole interactions and their joint effects upon vortical structures on nanodisks
No full textIn transition metal oxides, magnetic dipole-dipole (DD) and chiral Dzyaloshinsky-Moriya (DM) interactions between nearest neighboring spins are comparable in magnitude. In particular, the effects of the DD interaction on the physical properties of magnetic nanosystems cannot be simply neglected due to its long-range character. For these reasons, we employed here a new quantum simulation approach in order to investigate the interplay of these two interactions and study their combined effects upon the magnetic vortical structures of monolayer nanodisks. Consequently, we found out from our computational results that, in the presence of Heisenberg exchange interaction, a sufficiently strong DD interaction is also able to induce a single magnetic vortex on a small nanodisk; a strong DM interaction usually gives rise to a multi-domain structure which evolves with changing temperature; In this circumstance, if a weak DD interaction is further considered, the multi-domains merge to form a single vortex in the whole magnetic phase. Moreover, if only the Heisenberg exchange and chiral DM interactions are considered in simulations, our results from calculations with different spin values show that the transition temperature TM is simply proportional to S(S+1); if the temperature is scaled with TM, and the calculated magnetizations are divided by the spin value S, their curves exhibit very similar features in the whole temperature region below TM
Comparison of Helplessness and Hopelessness as Sources of Cognitive Vulnerability Among Black and White College Students
No full textThe Cognitive Style Questionnaire (CSQ), an expansion of the Attributional Style Questionnaire (ASQ), was created as an enhanced measure of cognitive vulnerability to depression using a hopelessness theory framework. However, the CSQ’s development emphasized facets of cognitive vulnerability consistent with a Eurocentric worldview. Consequently, the CSQ may inadvertently degrade rather than enhance assessment of cognitive vulnerability to depression for Black participants whose vulnerability may be shaped by a different sociopolitical context. Participants were 259 White and 180 Black college students. As predicted, cognitive vulnerability to depression assessed via the reformulated learned helplessness (ASQ) but not hopelessness theory (CSQ) was associated with increased symptoms of depression for Black participants. The opposite pattern of results was found for White participants for whom hopelessness (CSQ), but not helplessness (ASQ) was associated with higher levels of depression symptoms. The current findings support the need for more extensive examination of social context and race in assessing cognitive vulnerability to depression
Numerical solution of fractional elliptic PDE\u27s by the collocation method
Get PDFIn this presentation a numerical solution for the solution of fractional order of elliptic partial differential equation in R2 is proposed. In this method we use the Radial basis functions (RBFs) method to benefit the desired properties of mesh free techniques such as no need to generate any mesh and easily applied to multi dimensions. In the numerical solution approach the RBF collocation method is used to discrete fractional derivative terms with the Gaussian basis function. Two dimensional numerical examples are presented and discussed, which conform well with the corresponding exact solutions
Exponentiated Weibull-Exponential Distribution with Applications
Get PDFIn this article, a new four-parameter continuous model, called the exponentiated Weibull exponential distribution, is introduced based on exponentiated Weibull-G family (Hassan and Elgarhy, 2016). The new model contains some new distributions as well as some former distributions. Various mathematical properties of this distribution are studied. General explicit expressions for the quantile function, expansion of distribution and density functions, moments, generating function, Rényi and q – entropies, and order statistics are obtained. The estimation of the model parameters is discussed using maximum likelihood method. The practical importance of the new distribution is demonstrated through real data set where we compare it with several lifetime distributions