332 research outputs found
Orthogonality of p-adic characters
AbstractFor an abelian topological group G and a non-archimedean complete valued field K necessary and sufficient conditions are derived in order that the K-valued characters on G form an orthogonal set with respect to the supremum norm (Theorems 2.1, 2.2, 3.1, 4.3). Examples of groups satisfying these conditions (for example Qp) are considered in § 5
The metric approximation property in non-archimedean normed spaces
A normed space E over a rank 1 non-archimedean valued field K has the metric approximation property (MAP) if the identity on E can be approximated pointwise by finite rank operators of norm 1. Characterizations and hereditary properties of the MAP are obtained. For Banach spaces E of countable type the following main result is derived: E has the MAP if and only if E is the orthogonal direct sum of finite-dimensional spaces (Theorem 4.9). Examples of the MAP are also given. Among them, Example 3.3 provides a solution to the following problem, posed by the first author in [8, 4.5]. Does every Banach space of countable type over K have the MAP
Comparing recent reviews about touch screen for Dementia with lessons learnt from the field
Conclusions were synthesised from recent reviews on (touchscreen)technologies and people with dementia and lessons learnt, using these devices in projects in the UK, the Netherlands and Canada. The combined findings provide a strong basis for defining new strategies for exploiting touchscreen technology for people with dementia
Comparing recent reviews about touchscreens for dementia with lessons from the field
Conclusions were synthesised from recent reviews on (touchscreen)technologies and people with dementia and lessons learnt using these devices in projects in the UK, the Netherlands and Canada. The combined findings provide a strong basis for defining new strategies for exploiting touchscreen technology for people with dementia
The structures of Hausdorff metric in non-Archimedean spaces
For non-Archimedean spaces and let and be the
ballean of (the family of the balls in ), the space of mappings from
to and the space of mappings from the ballen of to
respectively. By studying explicitly the Hausdorff metric structures related to
these spaces, we construct several families of new metric structures (e.g., ) on the corresponding spaces, and study their convergence,
structural relation, law of variation in the variable including
some normed algebra structure. To some extent, the class is a counterpart of the usual Levy-Prohorov metric in the
probability measure spaces, but it behaves very differently, and is interesting
in itself. Moreover, when is compact and is a complete
non-Archimedean field, we construct and study a Dudly type metric of the space
of valued measures on Comment: 43 pages; this is the final version. Thanks to the anonymous
referee's helpful comments, the original Theorem 2.10 is removed, Proposition
2.10 is stated now in a stronger form, the abstact is rewritten, the
Monna-Springer is used in Section 5, and Theorem 5.2 is written in a more
general for
p-Adic and Adelic Generalization of Quantum Cosmology
p-Adic and adelic generalization of ordinary quantum cosmology is considered.
In [1], we have calculated p-adic wave functions for some minisuperspace
cosmological models according to the "no-boundary" Hartle-Hawking proposal. In
this article, applying p-adic and adelic quantum mechanics, we show existence
of the corresponding vacuum eigenstates. Adelic wave function contains some
information on discrete structure of space-time at the Planck scale.Comment: 12 page
Linear Fractional p-Adic and Adelic Dynamical Systems
Using an adelic approach we simultaneously consider real and p-adic aspects
of dynamical systems whose states are mapped by linear fractional
transformations isomorphic to some subgroups of GL (2, Q), SL (2, Q) and SL (2,
Z) groups. In particular, we investigate behavior of these adelic systems when
fixed points are rational. It is shown that any of these rational fixed points
is p-adic indifferent for all but a finite set of primes. Thus only for finite
number of p-adic cases a rational fixed point may be attractive or repelling.
It is also shown that real and p-adic norms of any nonzero rational fixed point
are connected by adelic product formula.Comment: 17 page
Invariance in adelic quantum mechanics
Adelic quantum mechanics is form invariant under an interchange of real and
p-adic number fields as well as rings of p-adic integers. We also show that in
adelic quantum mechanics Feynman's path integrals for quadratic actions with
rational coefficients are invariant under changes of their entries within
nonzero rational numbers.Comment: 6 page
Orthogonal sequences in non-archmedean locally convex spaces
AbstractThe problem of the existence of (orthogonal) bases and basic sequences in non-archimedean locally convex spaces is studied. To this end we derive a characterization of compactoidity in terms of orthogonal sequences (Theorem 2.2)
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