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1.
S. Y. Slavyanov 《Constructive Approximation》2014,39(1):75-83
Painlevé equations are studied on the basis of linear equations, which are generic for them. Different possible approaches are compared to each other. Formulas binding these approaches are derived. Symmetries demonstrated in the equations are also a subject of discussion. 相似文献
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We establish a new sufficient condition for avoiding a generalized Anscombe’s paradox. In a situation where votes describe positions regarding finitely many yes-or-no issues, the Anscombe’s α-paradox holds if more than α% of the voters disagree on a majority of issues with the outcome of issue-wise majority voting. We define the level of unanimity of a set of votes as the number of issues minus the maximal Hamming distance between two votes. We compute for the case of large electorates the exact level of unanimity above which the Anscombe’s α-paradox never holds, whatever the distribution of individuals among votes. 相似文献
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J.M. McDonald 《Discrete Mathematics》2010,310(15-16):2212-2214
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Model selection bias and Freedman’s paradox 总被引:2,自引:0,他引:2
Paul M. Lukacs Kenneth P. Burnham David R. Anderson 《Annals of the Institute of Statistical Mathematics》2010,62(1):117-125
In situations where limited knowledge of a system exists and the ratio of data points to variables is small, variable selection
methods can often be misleading. Freedman (Am Stat 37:152–155, 1983) demonstrated how common it is to select completely unrelated
variables as highly “significant” when the number of data points is similar in magnitude to the number of variables. A new
type of model averaging estimator based on model selection with Akaike’s AIC is used with linear regression to investigate
the problems of likely inclusion of spurious effects and model selection bias, the bias introduced while using the data to
select a single seemingly “best” model from a (often large) set of models employing many predictor variables. The new model
averaging estimator helps reduce these problems and provides confidence interval coverage at the nominal level while traditional
stepwise selection has poor inferential properties. 相似文献
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Muhamed Borogovac 《Journal of Difference Equations and Applications》2016,22(6):727-744
In the first part of the article, a new interesting system of difference equations is introduced. It is developed for re-rating purposes in general insurance. A nonlinear transformation φ of a d-dimensional (d ≥ 2) Euclidean space is introduced that enables us to express the system in the form ft+1:=φ( ft), t = 0, 1, 2,. …. Under typical actuarial assumptions, existence of solutions of that system is proven by means of Brouwer’s fixed point theorem in normed spaces. In addition, conditions that guarantee uniqueness of a solution are given. The second, smaller part of the article is about Leslie–Gower’s system of d ≥ 2 difference equations. We focus on the system that satisfies conditions consistent with weak inter-specific competition. We prove existence and uniqueness of the equilibrium of the model under surprisingly simple and very general conditions. Even though the two parts of this article have applications in two different sciences, they are connected with similar mathematics, in particular by our use of Brouwer’s fixed point theorem. 相似文献
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We study the solutions of the second Painlevé equation (P II) in the space of initial conditions first constructed by Okamoto, in the limit as the independent variable, x, goes to infinity. Simultaneously, we study solutions of the related equation known as the thirty-fourth Painlevé equation (P 34). By considering degenerate cases of the autonomous flow, we recover the known special solutions, which are either rational functions or expressible in terms of Airy functions. We show that the solutions that do not vanish at infinity possess an infinite number of poles. An essential element of our construction is the proof that the union of exceptional lines is a repeller for the dynamics in Okamoto’s space. Moreover, we show that the limit set of the solutions exists and is compact and connected. 相似文献
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Sirous Moradi 《Annali dell'Universita di Ferrara》2012,58(1):119-125
In this paper we provide a simple proof of the existence coupled fixed point theorem in complete cone metric spaces due to Sabetghadam et al. (Fixed Point Theory Appl 2009:8, 2009) and due to Olatinwo (Annali Dell’Universita’Di Ferrara 57:173–180, 2011). In particular we prove that these results are spacial cases of Rezapour and Hamlbarani’s theorems (J Math Anal Appl 345(2):719–724, 2008). 相似文献
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《The Journal of Mathematical Behavior》2001,20(3):337-361
Developing a view of functions as systematic processes involving co-variation among variables has been identified as a goal for mathematics learners at the pre-university level. In this investigation I examined the processes used by an eighth-grade student to interpret linear functions originating in dynamic physical models and the processed he used to link his interpretations to tables, equations, and graphs. The student deepened his understanding of functions by generalizing his view of multiplication beyond that of products resulting from the multiplication of individual factors or from repeated addition. He was enabled to do this by building links between graphic and tabular representations of the functions generated from his exploration with dynamic physical models and by comparing tables of different linear functions. This paper suggests that the development of a student’s reasoning about functions originating in dynamic physical models can be interpreted in terms of generalized multiplicative processes that may occur thorough mapping variations and that a student who interprets such functions as generalized multiplicative processes may use notational variations to generate representing equations. 相似文献
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LIU Jixue & CHEN Xiru Department of Statistics Finance University of Science Technology of China Hefei China Department of Mathematics Graduate School of Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2005,48(7):915-928
It is well known that for one-dimensional normal EV regression model X = x u,Y =α βx e, where x, u, e are mutually independent normal variables and Eu=Ee=0, the regression parameters a and βare not identifiable without some restriction imposed on the parameters. This paper discusses the problem of existence of unbiased estimate for a and βunder some restrictions commonly used in practice. It is proved that the unbiased estimate does not exist under many such restrictions. We also point out one important case in which the unbiased estimates of a and βexist, and the form of the MVUE of a and βare also given. 相似文献
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In this study, a new nonlinear mathematical model is developed to describe the conversion of glycerol to 1,3- propanediol by Klebsiella pneumoniae and the changes of concentrations of intracellular substances are taken into consideration. We consider the cases that glycerol passes the membrane by active transport and 1,3-propanediol passes the membrane by passive transport. We firstly study the solution’s existence and uniqueness and prove that the solution is bounded in a positive quadrant. Secondly, we discuss the existence of equilibrium solutions and calculate them, dependent on some given steady accuracy by Newton’s Method. Lastly, we analyze the asymptotical behavior and the global stability of the mathematical model. 相似文献
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In this article we present a simple and elegant algebraic proof of Pascal’s hexagon theorem which requires only knowledge of basics on conic sections without theory of projective transformations. Also, we provide an efficient algorithm for finding an equation of the conic containing five given points and a criterion for verification whether a set of points is a subset of the conic. 相似文献
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V. I. Danchenko E. N. Kondakova 《Proceedings of the Steklov Institute of Mathematics》2010,270(1):80-90
Uniform approximation of real constants by simple partial fractions on a closed interval of the real axis is studied. It is proved that a simple partial fraction of best approximation of degree n for a constant is unique and coincides with this constant at n nodes lying on the interval; moreover, there is a Chebyshev alternance consisting of n + 1 points. 相似文献
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We obtain weighted algebra analogues of the classical theorems of Weiner and Lévy on absolutely convergent Fourier series. 相似文献
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Timothy H. McNicholl 《复变函数与椭圆型方程》2016,61(1):76-85
We give a quantitative proof of the Carathéodory Theorem by means of the concept of a modulus of local connectivity and the extremal distance of the separating curves of an annulus. 相似文献