This yields the asserted result.
Combining (4.3), (4.4), (4.5) with (4.2) and making some elementary simplifications, the asserted result (4.1) follows.
To obtain the asserted result, we split the error to be estimated in the following way: biglVert q^{ast}-q^{ast}_{L}bigrVert _{0,Omega} leq biglVert q^{ast}-p_{L}bigrVert _{0,Omega} +biglVert p_{L}-q^{ast}_{L} bigrVert _{0,Omega}, quad forall p_{L}in P_{M}( Lambda) otimes P_{N}(I).
In the course of this transaction, a variety of fraud claims were eventually asserted, resulting in litigation.
In Nashville, 117 school-business partnerships and six partnership councils, the report asserts, resulted in an increased graduation rate, a decreasing suspension rate, and better standing under No Child Left Behind.
Public Works Board President Kevin James acknowledged the inequities but asserted they result from greater demand for sanitation workers in some areas.
The key evidence in the case rested not only on the claims of two very young girls, but on scientific testimony from a dubious pediatrician, Dr. Nancy Kellogg, who examined the girls and purported to find abrasions on one of their hymens that were, she asserted, a result of the assault.
Two years later, an inquiry by an outside financial examiner asserted that results had been affected by the practice of moving as much as $50 billion in debts off of the books and into what was known as a Repo 105 transaction.
asserts the result given in Proposition 1. □. Below are the links to the authors' original submitted files for images.
Following the same process, we can obtain the cases Γ j ( J k G 2 ( J T ) k + j ) = q k ( 1 : N − j, 1 ) for k = 2, 3, …, L, through some straightforward manipulation, and assert the result given in Proposition 3.1.
In 2003, in a civil suit brought by a firm dissatisfied with the ranking of Google's search results, Google asserted that its search results were constitutionally protected speech.
