Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Debye relaxations: two types of memories and their Stieltjes
  character   We show that spectral functions relevant for commonly used models of the
non-Debye relaxation are related to the Stieltjes functions supported on the
positive semiaxis. Using only this property it can be shown that the response
and relaxation functions are nonnegative. They are connected to each other and
obey the time evolution provided by integral equations involving the memory
function $M(t)$ which is the Stieltjes function as well. This fact is also due
to the Stieltjes character of the spectral function. Stochastic processes based
approach to the relaxation phenomena gives possibility to identify the memory
function $M(t)$ with the Laplace (L\'evy) exponent of some infinitely divisible
stochastic process and to introduce its partner memory $k(t)$. Both memories
are related by the Sonine equation and lead to equivalent evolution equations
which may be freely interchanged in dependence of our knowledge on memories
governing the process.

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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph