649 research outputs found
A precise description of the p-adic valuation of the number of alternating sign matrices
Following Sun and Moll, we study v_p(T(N)), the p-adic valuation of the
counting function of the alternating sign matrices. We find an exact analytic
expression for it that exhibits the fluctuating behaviour, by means of Fourier
coefficients. The method is the Mellin-Perron technique, which is familiar in
the analysis of the sum-of-digits function and related quantities
Comparison of measured and predicted performance of a SIS waveguide mixer at 345 GHz
The measured gain and noise of a SIS waveguide mixer at 345 GHz have been compared with theoretical values, calculated from the quantum mixer theory using a three port model. As a mixing element, we use a series array of two Nb-Al2O3-Nb SIS junctions. The area of each junction is 0.8 sq microns and the normal state resistance is 52 omega. The embedding impedance of the mixer has been determined from the pumped DC-IV curves of the junction and is compared to results from scale model measurements (105 x). Good agreement was obtained. The measured mixer gain, however, is a factor of 0.45 plus or minus 0.5 lower than the theoretical predicted gain. The measured mixer noise temperature is a factor of 4-5 higher than the calculated one. These discrepancies are independent on pump power and are valid for a broad range of tuning conditions
A low noise 410-495 heterodyne two tuner mixer, using submicron Nb/Al2O3/Nb tunneljunctions
A 410-495 GHz heterodyne receiver, with an array of two Nb/Al2O3/Nb tunneljunctions as mixing element is described. The noise temperature of this receiver is below 230 K (DSB) over the whole frequency range, and has lowest values of 160 K in the 435-460 GHz range. The calculated DSB mixergain over the whole frequency range varies from -11.9 plus or minus 0.6 dB to -12.6 plus or minus 0.6 dB and the mixer noise is 90 plus or minus 30 K
Recommended from our members
The good, the bad and the ugly: pandemic priority decisions and triage.
In this analysis we discuss the change in criteria for triage of patients during three different phases of a pandemic like COVID-19, seen from the critical care point of view. Availability of critical care beds has become a hot topic, and in many countries, we have seen a huge increase in the provision of temporary intensive care bed capacity. However, there is a limit where the hospitals may run out of resources to provide critical care, which is heavily dependent on trained staff, just-in-time supply chains for clinical consumables and drugs and advanced equipment. In the first (good) phase, we can still do clinical prioritisation and decision-making as usual, based on the need for intensive care and prognostication: what are the odds for a good result with regard to survival and quality of life. In the next (bad phase), the resources are mostly available, but the system is stressed by many patients arriving over a short time period and auxiliary beds in different places in the hospital being used. We may have to abandon admittance of patients with doubtful prognosis. In the last (ugly) phase, usual medical triage and priority setting may not be sufficient to decrease inflow and there may not be enough intensive care unit beds available. In this phase different criteria must be applied using a utilitarian approach for triage. We argue that this is an important transition where society, and not physicians, must provide guidance to support triage that is no longer based on medical priorities alone
How large are the level sets of the Takagi function?
Let T be Takagi's continuous but nowhere-differentiable function. This paper
considers the size of the level sets of T both from a probabilistic point of
view and from the perspective of Baire category. We first give more elementary
proofs of three recently published results. The first, due to Z. Buczolich,
states that almost all level sets (with respect to Lebesgue measure on the
range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states
that the average number of points in a level set is infinite. The third result,
also due to Lagarias and Maddock, states that the average number of local level
sets contained in a level set is 3/2. In the second part of the paper it is
shown that, in contrast to the above results, the set of ordinates y with
uncountably infinite level sets is residual, and a fairly explicit description
of this set is given. The paper also gives a negative answer to a question of
Lagarias and Maddock by showing that most level sets (in the sense of Baire
category) contain infinitely many local level sets, and that a continuum of
level sets even contain uncountably many local level sets. Finally, several of
the main results are extended to a version of T with arbitrary signs in the
summands.Comment: Added a new Section 5 with generalization of the main results; some
new and corrected proofs of the old material; 29 pages, 3 figure
Counting and effective rigidity in algebra and geometry
The purpose of this article is to produce effective versions of some rigidity
results in algebra and geometry. On the geometric side, we focus on the
spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic
hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum
determines the commensurability class of the 2-manifold (resp., 3-manifold). We
establish effective versions of these rigidity results by ensuring that, for
two incommensurable arithmetic manifolds of bounded volume, the length sets
(resp., the complex length sets) must disagree for a length that can be
explicitly bounded as a function of volume. We also prove an effective version
of a similar rigidity result established by the second author with Reid on a
surface analog of the length spectrum for hyperbolic 3-manifolds. These
effective results have corresponding algebraic analogs involving maximal
subfields and quaternion subalgebras of quaternion algebras. To prove these
effective rigidity results, we establish results on the asymptotic behavior of
certain algebraic and geometric counting functions which are of independent
interest.Comment: v.2, 39 pages. To appear in Invent. Mat
Patterns in rational base number systems
Number systems with a rational number as base have gained interest
in recent years. In particular, relations to Mahler's 3/2-problem as well as
the Josephus problem have been established. In the present paper we show that
the patterns of digits in the representations of positive integers in such a
number system are uniformly distributed. We study the sum-of-digits function of
number systems with rational base and use representations w.r.t. this
base to construct normal numbers in base in the spirit of Champernowne. The
main challenge in our proofs comes from the fact that the language of the
representations of integers in these number systems is not context-free. The
intricacy of this language makes it impossible to prove our results along
classical lines. In particular, we use self-affine tiles that are defined in
certain subrings of the ad\'ele ring and Fourier
analysis in . With help of these tools we are able to
reformulate our results as estimation problems for character sums
- …