1,285 research outputs found
Approximation systems for functions in topological and in metric spaces
A notable feature of the TTE approach to computability is the representation
of the argument values and the corresponding function values by means of
infinitistic names. Two ways to eliminate the using of such names in certain
cases are indicated in the paper. The first one is intended for the case of
topological spaces with selected indexed denumerable bases. Suppose a partial
function is given from one such space into another one whose selected base has
a recursively enumerable index set, and suppose that the intersection of base
open sets in the first space is computable in the sense of Weihrauch-Grubba.
Then the ordinary TTE computability of the function is characterized by the
existence of an appropriate recursively enumerable relation between indices of
base sets containing the argument value and indices of base sets containing the
corresponding function value.This result can be regarded as an improvement of a
result of Korovina and Kudinov. The second way is applicable to metric spaces
with selected indexed denumerable dense subsets. If a partial function is given
from one such space into another one, then, under a semi-computability
assumption concerning these spaces, the ordinary TTE computability of the
function is characterized by the existence of an appropriate recursively
enumerable set of quadruples. Any of them consists of an index of element from
the selected dense subset in the first space, a natural number encoding a
rational bound for the distance between this element and the argument value, an
index of element from the selected dense subset in the second space and a
natural number encoding a rational bound for the distance between this element
and the function value. One of the examples in the paper indicates that the
computability of real functions can be characterized in a simple way by using
the first way of elimination of the infinitistic names.Comment: 21 pages, published in Logical Methods in Computer Scienc
Fractional velocity as a tool for the study of non-linear problems
Singular functions and, in general, H\"older functions represent conceptual
models of nonlinear physical phenomena. The purpose of this survey is to
demonstrate the applicability of fractional velocity as a tool to characterize
Holder and in particular singular functions. Fractional velocities are defined
as limit of the difference quotient of a fractional power and they generalize
the local notion of a derivative. On the other hand, their properties contrast
some of the usual properties of derivatives. One of the most peculiar
properties of these operators is that the set of their non trivial values is
disconnected. This can be used for example to model instantaneous interactions,
for example Langevin dynamics. Examples are given by the De Rham and
Neidinger's functions, represented by iterative function systems. Finally the
conditions for equivalence with the Kolwankar-Gangal local fractional
derivative are investigated.Comment: 21 pages; 2 figure
Comparison between the two definitions of AI
Two different definitions of the Artificial Intelligence concept have been
proposed in papers [1] and [2]. The first definition is informal. It says that
any program that is cleverer than a human being, is acknowledged as Artificial
Intelligence. The second definition is formal because it avoids reference to
the concept of human being. The readers of papers [1] and [2] might be left
with the impression that both definitions are equivalent and the definition in
[2] is simply a formal version of that in [1]. This paper will compare both
definitions of Artificial Intelligence and, hopefully, will bring a better
understanding of the concept.Comment: added four new section
Massive dark photons in a Higgs portal model
An extension of the Standard Model with a hidden sector which consists of
gauge singlets (a Dirac fermion and a scalar ) plus a vector boson
(dark massive photon) is studied. The singlet scalar interacts with the
Standard Model sector through the triple and quartic scalar interactions, while
the singlet fermion and vector boson field interact with the Standard Model
only via the singlet scalar. The scalar field generates the vector boson's
mass. Perspectives for future colliders is considered
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