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On the Order of Growth of Lerch Zeta Functions
Mathematics, 2023 We extend Bourgain’s bound for the order of growth of the Riemann zeta function on the critical line to Lerch zeta functions. More precisely, we prove L(λ, α, 1/2 + it) ≪ t13/84+ϵ as t → ∞.
Jörn Steuding, Janyarak Tongsomporn
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ORDERS OF GROWTH AND GENERALIZED ENTROPY [PDF]
Journal of the Institute of Mathematics of Jussieu, 2021 AbstractWe construct the complete set of orders of growth and define on it the generalized entropy of a dynamical system. With this object, we provide a framework wherein we can study the separation of orbits of a map beyond the scope of exponential growth. We show that this construction is particularly useful for studying families of dynamical systems
Javier Correa, Enrique R. Pujals
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Nucleation and growth of orbital ordering [PDF]
Nature Communications, 2020 AbstractThe dynamics of the first-order phase transitions involving a large displacement of atoms, for example, a liquid-solid transition, is generally dominated by the nucleation of the ordered phase and the growth of the nuclei, where the interfacial energy between the two phases plays an important role.
Takuro Katsufuji +4 more
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On the Growth of Solutions of Nonhomogeneous Higher order Complex Linear Differential Equations
Ibn Al-Haitham Journal for Pure and Applied Sciences, 2022 The nonhomogeneous higher order linear complex differential equation (HOLCDE) with meromorphic (or entire) functions is considered in this paper. The results are obtained by putting some conditions on the coefficients to prove that the hyper order of ...
Ayad Alkhalidy
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Growth laws for phase ordering [PDF]
Physical Review E, 1994 12 pages, LaTeX, second ...
Bray, A. J., Rutenberg, A. D.
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On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equations [PDF]
Opuscula Mathematica, 2017 In this paper, we investigate the growth of meromorphic solutions of the linear differential equation \[f^{(k)}+h_{k-1}(z)e^{P_{k-1}(z)}f^{(k-1)}+\ldots +h_{0}(z)e^{P_{0}(z)}f=0,\] where \(k\geq 2\) is an integer, \(P_{j}(z)\) (\(j=0,1,\ldots ,k-1\)) are
Karima Hamani, Benharrat Belaïdi
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Applied Mathematics in Science and Engineering, 2023 The authors address the complex oscillation problems of all solutions of homogenous linear differential equations with meromorphic coefficients. Sufficient conditions for estimating the growth of meromorphic solution with infinite order have been ...
Zhongwei He, Lingyun Gao
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The monetary growth order [PDF]
, 2012 Growth of monetary assets and debts is commonly described by the formula of compound interest which for the case of continuous compounding is the exponential growth law. Its differential form is dc/dt = i c where dc/dt describes the rate of monetary growth, i the compounded interest rate and c the actual principal.
G\\\"unter von Kiedrowski +1 more
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Microscopic modeling of the growth of order in an alloy: Nucleated and continuous ordering [PDF]
Physical Review B, 1996 We study the early-stages of ordering in $Cu_3 Au$ using a model Hamiltonian derived from the effective medium theory of cohesion in metals: an approach providing a microscopic description of interatomic interactions in alloys. Our simulations show a crossover from a nucleated growth regime to a region where the ordering does not follow any simple ...
Chakraborty, Bulbul, Xi, Zhigang
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Electronic Journal of Qualitative Theory of Differential Equations, 2011 In this paper, we investigate the order and the hyper-order of entire solutions of the linear differential equation \begin{equation*} f^{\left( k\right) }+\left( D_{k-1}+B_{k-1}e^{b_{k-1}z}\right) f^{\left(k-1\right) }+ ...
H. Habib, B. Belaidi
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