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In this paper, we focus our attention on deriving and analyzing an efficient energy-preserving formula for the system of nonlinear oscillatory or highly oscillatory second-order differential equations q″(t)+Mq(t)="fq(t), where M is a symmetric positive semi-definite matrix with ∥M∥≫1 and f q)= -∇qU q) is the negative gradient of a real-valued function U(q).
And this is the time-honoured formula for the system to survive, leaner and meaner to fight another day.
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We derive the system stability condition, and obtain formulas for the system state probabilities, blocking probabilities, starvation probability, stockout probability, system availability in the steady state.
On basis of the stripping-like determinations, we propose a stoichiometric formula, K2−zTlIzNiII[FeII CN ]6 (z≤1), for the system in which interstitial K+ was substituted with Tl(I); and a more general KxTlIzNiIIy[FeII CN ]6 formula that also reflects the possibility of codeposition of separate nickel hexacyanoferrate and thallium hexacyanoferrate microstructures during the film growth.
In this regard, the present paper proposes an exact formula for computing the system stationary availability of a k-out-of-n system.
Green's function formula for the coupled system is derived by two methods: modal analysis and Laplace transform.
This study presents an expression for the optimal number of simultaneous data transmissions under the distributed coordinate function mechanism derived using the Markov chain model, as well as an analytical formula for the optimal system throughput given the length of the contention window and the number of nodes in the network.
The atomic stress formula for the atomic system is calculated by [15] (30).
The unified formula for the PCT floor system was then developed for the first time based on the orthotropic plate theory to calculate the natural frequencies.
In the semiclassical limit, the method of nonlinear steepest descent ([4,5]), supplemented by the g-function mechanism, is applied to this RHP to produce explicit asymptotic solution formulae for the integrable system.
For a start, any law that involves government departments spending extra money in England, or which reduces the amount of money spent in England, will have a knock-on impact on how much money other parts of the United Kingdom receive under the Barnett formula - the system for allocating Treasury funds to devolved administrations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com