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 $R(k)=\sum\limits_{l+m=k}\Lambda(l)\Lambda(m)$, \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 $k$ is even and \Sing(k) =0 if $k$ is odd. It is known that R(k) \sim k\Sing(k) as $N\to \infty$ for almost all $k\in [N,2N]$ 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 $H\geq n^{1/6+\epsilon}$. Here we prove, assuming $N^\epsilon\leq H\leq N^{1/6+\epsilon}$ and $N\to\infty$, that (1) holds for almost all $n\in [N,2N]$

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