176 research outputs found
Neutrix Calculus and Finite Quantum Field Theory
In general, quantum field theories (QFT) require regularizations and infinite
renormalizations due to ultraviolet divergences in their loop calculations.
Furthermore, perturbation series in theories like QED are not convergent
series, but are asymptotic series. We apply neutrix calculus, developed in
connection with asymptotic series and divergent integrals, to QFT,obtaining
finite renormalizations. While none of the physically measurable results in
renormalizable QFT is changed, quantum gravity is rendered more manageable in
the neutrix framework.Comment: 10 pages; LaTeX; version to appear in J. Phys. A: Math. Gen. as a
Letter to the Edito
Error term improvements for van der Corput transforms
We improve the error term in the van der Corput transform for exponential
sums
\sum_{a \le n \le b} g(n) exp(2\pi i f(n)).
For many functions g and f, we can extract the next term in the asymptotic,
showing that previous results, such as those of Karatsuba and Korolev, are
sharp. Of particular note, the methods of this paper avoid the use of the
truncated Poisson formula, and thus can be applied to much longer intervals
[a,b] with far better results. We provide a detailed analysis of the error term
in the case g(x)=1 and f(x)=(x/3)^{3/2}.Comment: 72 pages, 10 figure
Multidimensional sampling for simulation and integration: measures, discrepancies, and quasi-random numbers
This is basically a review of the field of Quasi-Monte Carlo intended for
computational physicists and other potential users of quasi-random numbers. As
such, much of the material is not new, but is presented here in a style
hopefully more accessible to physicists than the specialized mathematical
literature. There are also some new results: On the practical side we give
important empirical properties of large quasi-random point sets, especially the
exact quadratic discrepancies; on the theoretical side, there is the exact
distribution of quadratic discrepancy for random point sets.Comment: 51 pages. Full paper, including all figures also available at:
ftp://ftp.nikhef.nl/pub/preprints/96-017.ps.gz Accepted for publication in
Comp.Phys.Comm. Fixed some typos, corrected formula 108,figure 11 and table
Европеизмы как терминологические номинативные единицы в образовании терминосистем татарской юридической терминологии
Цель статьи: выявить особенности адаптации терминоэлементов-европеизмов (слова западно-европейских языков в составе татарского языка)
The paradox of soft singularity crossing and its resolution by distributional cosmological quantitities
A cosmological model of a flat Friedmann universe filled with a mixture of
anti-Chaplygin gas and dust-like matter exhibits a future soft singularity,
where the pressure of the anti-Chaplygin gas diverges (while its energy density
is finite). Despite infinite tidal forces the geodesics pass through the
singularity. Due to the dust component, the Hubble parameter has a non-zero
value at the encounter with the singularity, therefore the dust implies further
expansion. With continued expansion however, the energy density and the
pressure of the anti-Chaplygin gas would become ill-defined, hence from the
point of view of the anti-Chaplygin gas only a contraction is allowed.
Paradoxically, the universe in this cosmological model would have to expand and
contract simultaneously. This obviosly could not happen. We solve the paradox
by redefining the anti-Chaplygin gas in a distributional sense. Then a
contraction could follow the expansion phase at the singularity at the price of
a jump in the Hubble parameter. Although such an abrupt change is not common in
any cosmological evolution, we explicitly show that the set of Friedmann,
Raychaudhuri and continuity equations are all obeyed both at the singularity
and in its vicinity. We also prove that the Israel junction conditions are
obeyed through the singular spatial hypersurface. In particular we enounce and
prove a more general form of the Lanczos equation.Comment: 12 pages; to be published in Phys.Rev.
Continuum Surface Energy from a Lattice Model
We investigate connections between the continuum and atomistic descriptions
of deformable crystals, using certain interesting results from number theory.
The energy of a deformed crystal is calculated in the context of a lattice
model with general binary interactions in two dimensions. A new bond counting
approach is used, which reduces the problem to the lattice point problem of
number theory. The main contribution is an explicit formula for the surface
energy density as a function of the deformation gradient and boundary normal.
The result is valid for a large class of domains, including faceted (polygonal)
shapes and regions with piecewise smooth boundaries.Comment: V. 1: 10 pages, no fig's. V 2: 23 pages, no figures. Misprints
corrected. Section 3 added, (new results). Intro expanded, refs added.V 3: 26
pages. Abstract changed. Section 2 split into 2. Section (4) added material.
V 4, 28 pages, Intro rewritten. Changes in Sec.5 (presentation only). Refs
added.V 5,intro changed V.6 address reviewer's comment
On the asymptotic formula for Goldbach numbers in short intervals
Let
, \Sing(k) = 2
\prod\limits_{p>2}\left(1-\frac{1}{(p-1)^2}\right) \prod\limits_{\substack{
p\mid k\\ p>2 }} \left(\frac{p-1}{p-2}\right) if is even and \Sing(k)
=0 if is odd. It is known that R(k) \sim k\Sing(k) as
for almost all and that \sum_{k\in [n,n+H)}R(k) \sim
\sum_{k\in [n,n+H)} k\Sing(k) \quad\hbox{for} \quad n\to \infty \eqno{(1)}
uniformly for . Here we prove, assuming
and , that (1) holds for
almost all
Chest computed tomography outcomes in a randomized clinical trial in cystic fibrosis: Lessons learned from the first ataluren phase 3 study
A phase 3 randomized double blind controlled, trial in 238 people with cystic fibrosis (CF)
and at least one nonsense mutation (nmCF) investigated the effect of ataluren on FEV1.
The study was of 48 weeks duration and failed to meet its primary endpoint. Unexpectedly
Case Report A Girl with Autoimmune Cytopenias, Nonmalignant Lymphadenopathy, and Recurrent Infections
We describe a girl, now 9 years of age, with chronic idiopathic thrombocytopenic purpura, persistent nonmalignant lymphadenopathy, splenomegaly, recurrent infections, and autoimmune hemolytic anemia. Her symptoms partly fit the definitions of both autoimmune lymphoproliferative syndrome (ALPS) and common variable immunodeficiency disorders (CVIDs). Genetic analysis showed no abnormalities in the ALPS-genes FAS, FASLG, and CASP10. The CVID-associated TACI gene showed a homozygous polymorphism (Pro251Leu), which is found also in healthy controls
- …