378 research outputs found
On number fields with nontrivial subfields
What is the probability for a number field of composite degree to have a
nontrivial subfield? As the reader might expect the answer heavily depends on
the interpretation of probability. We show that if the fields are enumerated by
the smallest height of their generators the probability is zero, at least if
. This is in contrast to what one expects when the fields are enumerated
by the discriminant. The main result of this article is an estimate for the
number of algebraic numbers of degree and bounded height which generate
a field that contains an unspecified subfield of degree . If
we get the correct asymptotics as the height tends to
infinity
The effect of a secondary task on kinematics during turning in Parkinson's disease with mild to moderate impairment
Patients with Parkinson's disease (PD) show typical gait asymmetries. These peculiar motor impairments are exacerbated by added cognitive and/or mechanical loading. However, there is scarce literature that chains these two stimuli. The aim of this study was to investigate the combined effects of a dual task (cognitive task) and turning (mechanical task) on the spatiotemporal parameters in mild to moderate PD. Participants (nine patients with PD and nine controls (CRs)) were evaluated while walking at their self-selected pace without a secondary task (single task), and while repeating the days of the week backwards (dual task) along a straight direction and a 60 degrees and 120 degrees turn. As speculated, in single tasking, PD patients preferred to walk with a shorter stride length (p< 0.05) but similar timing parameters, compared to the CR group; in dual tasking, both groups walked slower with shorter strides. As the turn angle increased, the speed will be reduced (p< 0.001), whereas the ground-foot contact will become greater (p< 0.001) in all the participants. We showed that the combination of a simple cognitive task and a mechanical task (especially at larger angles) could represent an important training stimulus in PD at the early stages of the pathology
Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles
The construction of sections of bundles with prescribed jet values plays a
fundamental role in problems of algebraic and complex geometry. When the jet
values are prescribed on a positive dimensional subvariety, it is handled by
theorems of Ohsawa-Takegoshi type which give extension of line bundle valued
square-integrable top-degree holomorphic forms from the fiber at the origin of
a family of complex manifolds over the open unit 1-disk when the curvature of
the metric of line bundle is semipositive. We prove here an extension result
when the curvature of the line bundle is only semipositive on each fiber with
negativity on the total space assumed bounded from below and the connection of
the metric locally bounded, if a square-integrable extension is known to be
possible over a double point at the origin. It is a Hensel-lemma-type result
analogous to Artin's application of the generalized implicit function theorem
to the theory of obstruction in deformation theory. The motivation is the need
in the abundance conjecture to construct pluricanonical sections from flatly
twisted pluricanonical sections. We also give here a new approach to the
original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the
punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi
to a simple application of the standard method of constructing holomorphic
functions by solving the d-bar equation with cut-off functions and additional
blowup weight functions
On the ratio of consecutive gaps between primes
In the present work we prove a common generalization of Maynard-Tao's recent
result about consecutive bounded gaps between primes and on the
Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work
answers in a strong form a 60 years old problem of Erd\"os, which asked whether
the ratio of two consecutive primegaps can be infinitely often arbitrarily
small, and arbitrarily large, respectively
On certain infinite extensions of the rationals with Northcott property
A set of algebraic numbers has the Northcott property if each of its subsets
of bounded Weil height is finite. Northcott's Theorem, which has many
Diophantine applications, states that sets of bounded degree have the Northcott
property. Bombieri, Dvornicich and Zannier raised the problem of finding fields
of infinite degree with this property. Bombieri and Zannier have shown that
\IQ_{ab}^{(d)}, the maximal abelian subfield of the field generated by all
algebraic numbers of degree at most , is such a field. In this note we give
a simple criterion for the Northcott property and, as an application, we deduce
several new examples, e.g.
\IQ(2^{1/d_1},3^{1/d_2},5^{1/d_3},7^{1/d_4},11^{1/d_5},...) has the Northcott
property if and only if
tends to infinity
A Cross-level Verification Methodology for Digital IPs Augmented with Embedded Timing Monitors
Smart systems implement the leading technology advances in the context of embedded devices. Current design methodologies are not suitable to deal with tightly interacting subsystems of different technological domains, namely analog, digital, discrete and power devices, MEMS and power sources. The interaction effects between the components and between the environment and the system must be modeled and simulated at system level to achieve high performance. Focusing on digital subsystem, additional design constraints have to be considered as a result of the integration of multi-domain subsystems in a single device. The main digital design challenges combined with those emerging from the heterogeneous nature of the whole system directly impact on performance, hence propagation delay, of the digital component. In this paper we propose a design approach to enhance the RTL model of a given digital component for the integration in smart systems, and a methodology to verify the added features at system-level. The design approach consists of ``augmenting'' the RTL model through the automatic insertion of delay sensors, which are capable of detecting and correcting timing failures. The verification methodology consists of an automatic flow of two steps. Firstly the augmented model is abstracted to system-level (i.e., SystemC TLM); secondly mutants, which are code mutations to emulate timing failures, are automatically injected into the abstracted model. Experimental results demonstrate the applicability of the proposed design and verification methodology and the effectiveness of the simulation performance
On some notions of good reduction for endomorphisms of the projective line
Let be an endomorphism of \SR(\bar{\Q}), the projective line over
the algebraic closure of \Q, of degree defined over a number field
. Let be a non-archimedean valuation of . We say that has
critically good reduction at if any pair of distinct ramification points of
do not collide under reduction modulo and the same holds for any
pair of branch points. We say that has simple good reduction at if
the map , the reduction of modulo , has the same degree of
. We prove that if has critically good reduction at and the
reduction map is separable, then has simple good reduction at
.Comment: 15 page
Classification of one-dimensional quasilattices into mutual local-derivability classes
One-dimensional quasilattices are classified into mutual local-derivability
(MLD) classes on the basis of geometrical and number-theoretical
considerations. Most quasilattices are ternary, and there exist an infinite
number of MLD classes. Every MLD class has a finite number of quasilattices
with inflation symmetries. We can choose one of them as the representative of
the MLD class, and other members are given as decorations of the
representative. Several MLD classes of particular importance are listed. The
symmetry-preserving decorations rules are investigated extensively.Comment: 42 pages, latex, 5 eps figures, Published in JPS
Big Line Bundles over Arithmetic Varieties
We prove a Hilbert-Samuel type result of arithmetic big line bundles in
Arakelov geometry, which is an analogue of a classical theorem of Siu. An
application of this result gives equidistribution of small points over
algebraic dynamical systems, following the work of Szpiro-Ullmo-Zhang. We also
generalize Chambert-Loir's non-archimedean equidistribution
Sharpenings of Li's criterion for the Riemann Hypothesis
Exact and asymptotic formulae are displayed for the coefficients
used in Li's criterion for the Riemann Hypothesis. For we obtain
that if (and only if) the Hypothesis is true,
(with and explicitly given, also for the case of more general zeta or
-functions); whereas in the opposite case, has a non-tempered
oscillatory form.Comment: 10 pages, Math. Phys. Anal. Geom (2006, at press). V2: minor text
corrections and updated reference
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