"the basis given" is a grammatically correct phrase and can be used in written English.
It is commonly used to refer to the foundational information or reasoning that is provided or assumed in a sentence or discussion. Example: "The decision to move forward with the project was based on the budget and timeline, which were the basis given by the stakeholders."
Its reflexivity is directly expressed in the axiom x = x, and theorems expressing its symmetry and transitivity can easily be derived from the basis given.
When the final state of the composite system (measured system plus measuring device) is very nearly degenerate when written in the basis given by the measured observable and the apparatus's pointer (that is, when the probabilities for the various results are nearly equal), the spectral decomposition does not, in general, select as definite-valued properties close to those ideally expected.
Considering the maps (f_{i,j}) written in the basis given by the Fundamental Theorem of Persistent Homology, we say that (xin H_{p}(K_{i})) (with (x neq0)) is born in (H_{p}(K_{i})) if it is not in the image of (f_{i-1,i}) (i.e., (f^{-1}_{i-1,i}(x)=emptyset)).
The basis gives us a reason to respect the object; it may also indicate more precisely how to respect it.
The primary basis given for this restriction was to achieve better fitting models and statistically significant E-R trends.
Thus, the risks and benefits of SGLT2 inhibitors should be assessed in older patients on a case-by-case basis given the newness of the drug class.
The modal truncation augmentation method (MTAM) is also presented to handle the modal truncation problem by making the equilibrium equations into a subspace equation spanned in terms of the columns of a projection basis given in the GMAM.
This would at least keep the couples together and remove the financial hardships they face until the necessary checks can be completed, hopefully on a more expedited basis given the increased funding.
Given a simplicial complex K, let (C_{p}(K)) denote the (mathbb {F}_{2} -vector space with basis given by the p-simplices oF}_{2} -vector
"This is a very, very shaky basis, given the differences that can occur," Mr. Avery said.
Anticancer treatment for APC would be preferable on an outpatient rather than an inpatient basis, given the short life expectancy and quality of life considerations.
