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On the Hyper-Order of Solutions of Some Second-Order Linear Differential Equations
Acta Mathematica Sinica, English Series, 2002Consider the second-order linear differential equation \[ f'' + A(z)f' + B(z)f = 0 \tag{1} \] with entire functions \(A\) and \(B\). It is well known that all solutions are entire functions, and if \(A\) or \(B\) are transcendental, then there exists a solution \(f\) with \(\sigma(f)=\infty\), where \[ \sigma(f) = \varlimsup_{r\to\infty}{\frac{\log{T(r,
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Hyper-order and order of meromorphic functions sharing functions
Annales Polonici Mathematici, 2015The authors obtain results on the hyper-order and the order of meromorphic functions sharing a function with its derivatives.
Qi, Jianming, Yuan, Wenjun, Yi, Hongxun
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On the hyper-order of meromorphic solutions of linear differential equations
Applied Mathematics-A Journal of Chinese Universities, 1998This paper contains some order considerations for solutions to the linear differential equation \[ f^{(k)} + A_{k-1}(z) f^{(k-1)} + ... + A_0(z) f = 0 \] with entire coefficients in the complex plane, related to a recent paper by \textit{K.-H. Kwon} [Bull. Korean Math. Soc. 33, No. 3, 487-496 (1996; Zbl 0863.34007)].
Li, Yezhou, Chen, Zongxuan
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Training and making calculations with mixed order hyper-networks
Neurocomputing, 2014A neural network with mixed order weights, n neurons and a modified Hebbian learning rule can learn any function f:{−1,1}n→R and reproduce its output as the network׳s energy function. The network weights are equal to Walsh coefficients, the fixed point attractors are local maxima in the function, and partial sums across the weights of the network ...
Kevin Swingler, Leslie S. Smith
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Hyper-relations, choice functions, and orderings of opportunity sets
Social Choice and Welfare, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vladimir I. Danilov +2 more
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ANTICIPATING SYNCHRONIZATION OF INTEGER ORDER AND FRACTIONAL ORDER HYPER-CHAOTIC CHEN SYSTEM
International Journal of Modern Physics B, 2012Such a problem, how to resolve the problem of long-term unpredictability of chaotic systems, has puzzled researchers in nonlinear research fields for a long time during the last decades. Recently, Voss et al. had proposed a new scheme to research the anticipating synchronization of integral-order nonlinear systems for arbitrary initial values and ...
Dong, Pengzhen, Shang, Gang, Liu, Jie
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Generalized transitivity and preferences modelling: The concept of Hyper-Order
European Journal of Operational Research, 1988zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Comparison of Learning Rules for Mixed Order Hyper Networks
Proceedings of the 7th International Joint Conference on Computational Intelligence, 2015A mixed order hyper network (MOHN) is a neural network in which weights can connect any number of neurons, rather than the usual two. MOHNs can be used as content addressable memories with higher capacity than standard Hopfield networks. They can also be used for regression, clustering, classification, and as fitness models for use in heuristic ...
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The Modern State and the Society of Hyper-Order to 1939
2020Abstract For the past 200 years the defining feature of most domestic contests between Western governments and armed opponents has tended to be their lopsided asymmetry. Since the later nineteenth century a recurrent phenomenon of Western societies have been hopeless micro-insurrections mounted against stable societies: the armed ...
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