"basis problem" is a correct and usable phrase in written English.
It refers to a problem or issue that forms the foundation or essential basis of a larger issue or situation. Example: The basis problem of the education system is the lack of equal opportunities for students from different socioeconomic backgrounds.
Such a solution to the preferred basis problem might be only partial in the sense that there are many inequivalent ways of selecting sets of decoherent histories (see e.g. Dowker and Kent 1995, 1996).
Saunders and David Wallace have deployed structuralism to solve the problem of how macroscopic objects with more or less determinate properties can be recovered from the Everett interpretation of quantum states (the so-called preferred basis problem) (Saunders 1993b , 1995 and Wallace 2003).
Singling out position as a preferred variable for solving the preferred basis problem might be considered as a weakness, but on the other hand, it is implausible that out of a mathematical theory of vectors in Hilbert space one can derive what our world should be.
One of the main goals of invariant theory was to solve the "finite basis problem".
Techniques such as Hilbert's original non-constructive solution to the finite basis problem could not be used to get quantitative information about the invariants of a group action, and furthermore, they did not apply to all group actions.
In her 1915 paper, Noether found a solution to the finite basis problem for a finite group of transformations G acting on a finite-dimensional vector space over a field of characteristic zero.
Thus, the linearly constrained basis pursuit problem has a sole solution and its dual problem is smooth.
On this basis, the problem of harmonic retrieval is treated as a problem of finding the extremum values for which the niche GA is resorted.
Through the establishment of a nonuniform grid, on the basis of problem (Q), the solving process of the original problem (P) is then transformed into checking the feasibility of a series of linear programming problems.
On this basis, the problem of multicopter's health evaluation is transformed to a hybrid state estimation problem.
A practical challenge for the regularized basis pursuit problem is to offer an efficient method to solve the non-smooth optimization problems.
