Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterisations of V-sufficiency and C^0-sufficiency of relative jets   We consider the problems of sufficiency of jets relative to a given closed
set. In the non-relative case, criteria for r-jets to be V-sufficient and
C^0-sufficient in C^r mappings or C^{r+1} mappings have been obtained. In
particular, it is shown that V-sufficiency and C^0-sufficiency in C^r functions
or C^{r+1} functions are equivalent. In this paper we discuss characterisations
of V-sufficiency and C^0-sufficiency in the relative case, corresponding to the
above non-relative results. Applying the results obtained in the relative case,
we construct examples of polynomial functions whose relative r-jets are
V-sufficient in C^r functions and C^{r+1} functions but not C^0-sufficient in
C^r functions and C^{r+1} functions, respectively. In addition, we give
characterisations of relative finite V-determinacy and also relative finite C^r
contact determinacy.

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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: stat