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The analysis of the distribution of roots to Eq. (2.3) is based on the conclusion given in [7]: the sum of the order of zeros of Eq. (2.4) can change only if a zero appears or accesses the unit circle as the parameter β is varied.
In the following, the analysis on the distribution of the roots to equation (2.2) is based on the conclusion: the sum of the order of the zeros of equation (2.2) in an open right-plane can change only if a zero appears or crosses the imaginary axis as parameter is varied.
H_{j_{text{VMI}} } = Hs + Hb_j (6 The sum of the order cost and average inventory holding cost of the vendor for buyer 'j' namely 'OSM j ', thus can be stated as in (7): {text{OSM}}_j = ({Ss + Sb_{_j } } y_j /Q_j + Q_j ({Hs + Hb_{_j } })({1 - y_j /P_j }) /2 (7).
As ((tau_{1},tau _{2},ldots,tau_{m})) vary, the sum of the order of the zeros of (p lambda,e^{-lambdatau _{1}},ldots,e^{-lambdatau_{m}})) on the open right half plane can change only if a zero appears on the imaginary axis.
As ((tau_{1}, tau_{2},ldots,tau_{m})) vary, the sum of the order of the zeros of (P lambda,e^{ - lambdatau_{1} },ldots,e^{ - lambdatau_{m} } )) on the open right half plane can change if and only if there are zeros crossing the imaginary axis.
Two scores are calculated from the adjective list: the number of adjectives chosen (McGill Pain Questionnaire, Number of Words Chosen (MPQ-NWC)), and the intensity of these adjectives (sum of the order of the words chosen; MPQ Pain Rating Index (MPQ-PRI)).
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The outer product of two tensors is another tensor, the order of which is given by the sum of the orders of the two former tensors.
From the consequence of the distribution of zeros of a transcendental function given by Ruan and Wei [20], we know that as τ varies, the sum of the orders of the roots of (3.13) in the open right half plane can change only if a zero appears on or crosses the imaginary axis.
As ((tau_{1},ldots2},tau_{m}au_{m})) vary, the sum of the orders of the zeros of (P lambda,e^{ - lambdatau_{1} },ldots,e^{ - lambdatau_{m} } )) in the open right half plane can change only if a zero appears on or crosses the imaginary axis.
Government and industry must decide whether to invest vast sums, of the order of hundreds, perhaps even thousands of billions of dollars in production of synthetic liquid fuels from coal or oil shale.
In order-theoretical terms, ≤ is the direct sum of the linear order relations defined on the individual sequences.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com