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Based on the test results, the paper presents empirical formulae for both strength and Young's modulus.
The asymptotic power functions and the corresponding sample size formulae for both the one- and two-sided tests based on the large-sample normal approximation are derived.
The possible natural answers to this question lead to three reasonable alternatives, respectively giving rise to point-based logics discussed above, interval-based logics, and mixed, two-sorted logics, where points and intervals are considered as separate sorts on a par and formulae for both sorts are constructed.
Based on this model and considering that unencumbered service time (UST) and cell dwell time (CDT) of SUs are independent generally distributed random variables, analytical formulae for both the probability distributions of channel holding times and inter-cell handoff attempts rate are derived.
Key formulae for both approaches are in Table 1.
Examining the update formulae for both weakly penalized and PL approaches (see Appendix C), we observe that deteriorated convergence stems from: (1) initial residual amplification, and (2) the amplification of the residual.
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"It's a winning formula for both generations".
Other options include less generous formulas for both initial benefits and annual cost-of-living increases for retirees in future decades.
The crucial step came in a book by a physician called Girolamo Cardano which presented formulas for both cubic and quartic equations.At this point, the future of algebra looked rosy.
Because it is colleges' job to administer federal aid, officers at B.U. apply two different analyses to the data, one that reflects eligibility for federal aid and one that reflects eligibility for B.U. aid (some colleges use only the federal formula for both jobs).
Formulas for both inflationary and non-inflationary conditions are derived.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com