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We extend to larger classes of norms some inequalities concerning sums of positive operators and sums of operators having orthogonal ranges.
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Differences between the two age groups concerning these sums of risk alleles were initially examined using the Mann-Whitney U test.
Likewise, diabetic patients with neuropathia and those without did not differ concerning the sum of GERD symptoms (median 3, IQR 2 4, vs. median 3, IQR 2 5, respectively; p = 0.411).
The present paper is concerned with the sums of the products of an arbitrary number of the above-mentioned polynomials and numbers.
Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for (mathbb{F}_{n}), which is concerned with finite sums of reciprocals of Fibonacci numbers.
Concerning these sums, many authors had studied their properties and obtained a series of interesting results, see [1, 2].
We get extensions of some results given by Labbas and de Malafosse concerning applications of the sum of operators in the nondifferential case.
At a time when the cuts are biting, the cost of living spiralling and government insisting "we're all in this together", it should be of particular concern that vast sums of money are being spent on incorrect decisions.
It has become a target for Mr. Putin, who, in a briefing for foreign journalists this month, voiced concern that "enormous sums" of money had disappeared from the gas company.
Theorem 3.1 concerns the weighted sums of random vectors in Hilbert space.
The remaining allegation concerns the sum of €400 ($527), part of a hotel bill from 2008, and €370 for food.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com