Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $n$-dimensional Observables on $k$-Perfect MV-Algebras and $k$-Perfect
  Effect Algebras. II. One-to-one Correspondence   The paper is a continuation of the research on a one-to-one correspondence
between $n$-dimensional spectral resolutions and $n$-dimensional observables on
lexicographic types of quantum structures which started in \cite{DvLa4}. In
Part I, we presented the main properties of $n$-dimensional spectral
resolutions and observables, and we deeply studied characteristic points which
are crucial for our study. In present Part II, there is a main body of our
research. We investigate a one-to-one correspondence between $n$-dimensional
observables and $n$-dimensional spectral resolutions with values in a kind of a
lexicographic form of quantum structures like perfect MV-algebras or perfect
effect algebras. The multidimensional version of this problem is more
complicated than a one-dimensional one because if our algebraic structure is
$k$-perfect for $k>1$, then even for the two-dimensional case of spectral
resolutions we have more characteristic points. The obtained results are
applied to existence of an $n$-dimensional meet joint observable of $n$
one-dimensional observables on a perfect MV-algebra and a sum of
$n$-dimensional observables.

12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg