Integral Difference Ratio Functions on Integers

number theoryInternational audienceTo Jozef, on his 80th birthday, with our gratitude for sharing with us his prophetic vision of Informatique Abstract. Various problems lead to the same class of functions from integers to integers: functions having integral difference ratio, i.e. verifying f (a) − f (b) ≡ 0 (mod (a − b)) for all a > b. In this paper we characterize this class of functions from Z to Z via their a la Newton series expansions on a suitably chosen basis of polynomials (with rational coefficients). We also exhibit an example of such a function which is not polynomial but Bessel like

Quantitative study of molecular N_2 trapped in disordered GaN:O films

The structure of disordered GaN:O films grown by ion-assisted deposition is investigated using x-ray absorption near-edge spectroscopy and Raman spectroscopy. It is found that between 4 and 21 % of the nitrogen in the films is in the form of molecular N_2 that interacts only weakly with the surrounding matrix. The anion to cation ratio in the GaN:O host remains close to unity, and there is a close correlation between the N_2 fraction, the level of oxygen impurities, and the absence of short-range order in the GaN:O matrix.Comment: 5 pages, 3 figure

Scale invariant correlations and the distribution of prime numbers

Negative correlations in the distribution of prime numbers are found to display a scale invariance. This occurs in conjunction with a nonstationary behavior. We compare the prime number series to a type of fractional Brownian motion which incorporates both the scale invariance and the nonstationary behavior. Interesting discrepancies remain. The scale invariance also appears to imply the Riemann hypothesis and we study the use of the former as a test of the latter.Comment: 13 pages, 8 figures, version to appear in J. Phys.

Tuberculosis in Dr Granville's mummy: a molecular re-examination of the earliest known Egyptian mummy to be scientifically examined and given a medical diagnosis

‘Dr Granville's mummy’ was described to the Royal Society of London in 1825 and was the first ancient Egyptian mummy to be subjected to a scientific autopsy. The remains are those of a woman, Irtyersenu, aged about 50, from the necropolis of Thebes and dated to about 600 BC. Augustus Bozzi Granville (1783–1872), an eminent physician and obstetrician, described many organs still in situ and attributed the cause of death to a tumour of the ovary. However, subsequent histological investigations indicate that the tumour is a benign cystadenoma. Histology of the lungs demonstrated a potentially fatal pulmonary exudate and earlier studies attempted to associate this with particular disease conditions. Palaeopathology and ancient DNA analyses show that tuberculosis was widespread in ancient Egypt, so a systematic search for tuberculosis was made, using specific DNA and lipid biomarker analyses. Clear evidence for Mycobacterium tuberculosis complex DNA was obtained in lung tissue and gall bladder samples, based on nested PCR of the IS6110 locus. Lung and femurs were positive for specific M. tuberculosis complex cell-wall mycolic acids, demonstrated by high-performance liquid chromatography of pyrenebutyric acid–pentafluorobenzyl mycolates. Therefore, tuberculosis is likely to have been the major cause of death of Irtyersenu

Electronic properties of (Ga,Mn)N thin films with high Mn content

Optical and dc resistivity measurements as well as x-ray spectroscopies have been performed on (Ga,Mn)N films containing Mn at up to 11 at. %. The results indicate that at higher Mn contents, the Fermi level is situated within extended states, while GaN host interband optical transitions are unaffected. The Mn state is confirmed to be 3d⁵, as in the case of lower Mn content films; however, the high Mn content merges the 3d levels into a band located just below the host conduction band. The Fermi level is located within these Mn states just below the conduction band, in sharp contrast to its midgap position in fully crystalline, low Mn concentration materials. The difference in the position of the Fermi level at high Mn dopant levels has important implications for the promotion of ferromagnetism in this material.The authors gratefully acknowledge financial support from the New Zealand Foundation for Research Science and Technology through its New Economy Research Fund and through a postdoctoral fellowship of one of the authors B.J.R.. The work of the MacDiarmid Institute is supported by a New Zealand Centre of Research Excellence award. Another author S.G. wishes to thank Education New Zealand for financial support of the XANES measurements

Single phase nanocrystalline GaMnN thin films with high Mn content

Ga₁ˍₓ Mnₓ Nthin films with a Mn content as high as x=0.18 have been grown using ion-assisted deposition and a combination of Rutherford backscattering spectroscopy and nuclear reaction analysis was used to determine their composition. The structure of the films was determined from x-ray diffraction,transmission electron microscopy, and extended x-ray absorption fine structure(EXAFS). The films are comprised of nanocrystals of random stacked GaMnN and there is no evidence of Mn-rich secondary phases or clusters. EXAFS measurements at the Mn and Ga edge are almost identical to those at the Ga edge from Mn-free nanocrystallineGaNfilms, showing that the Mn occupies the Ga lattice sites, and simulated radial distribution functions of possible Mn-rich impurity phases bear no resemblance to the experimental data. The results indicate that these are the most heavily Mn-doped single phase GaNfilms studied to date.The authors gratefully acknowledge financial support from the New Zealand Foundation for Research Science and Technology through its New Economy Research Fund, and through a postdoctoral fellowship of one of the authors B.J.R.. The work of the MacDiarmid Institute is supported by a New Zealand Centre of Research Excellence award. Another author S.G. wishes to thank Education New Zealand for financial support of the EXAFS measurements

Autonomous Coordination of Science Observations Using Multiple Spacecraft

This software provides capabilities for autonomous cross-cueing and coordinated observations between multiple orbital and landed assets. Previous work has been done in re-tasking a single Earth orbiter or a Mars rover in response to that craft detecting a science event. This work enables multiple spacecraft to communicate (over a network designed for deep-space communications) and autonomously coordinate the characterization of such a science event. This work investigates a new paradigm of space science campaigns where opportunistic science observations are autonomously coordinated among multiple spacecraft. In this paradigm, opportunistic science detections can be cued by multiple assets where a second asset is requested to take additional observations characterizing the identified surface feature or event. To support this new paradigm, an autonomous science system for multiple spacecraft assets was integrated with the Interplanetary Network DTN (Delay Tolerant Network) to provide communication between spacecraft assets. This technology enables new mission concepts that are not feasible with current technology. The ability to rapidly coordinate activities across spacecraft without requiring ground in the loop enables rapid reaction to dynamic events across platforms, such as a survey instrument followed by a targeted high resolution instrument, as well as regular simultaneous observations

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

Regular graphs of large girth and arbitrary degree

For every integer d > 9, we construct infinite families {G_n}_n of d+1-regular graphs which have a large girth > log_d |G_n|, and for d large enough > 1,33 log_d |G_n|. These are Cayley graphs on PGL_2(q) for a special set of d+1 generators whose choice is related to the arithmetic of integral quaternions. These graphs are inspired by the Ramanujan graphs of Lubotzky-Philips-Sarnak and Margulis, with which they coincide when d is prime. When d is not equal to the power of an odd prime, this improves the previous construction of Imrich in 1984 where he obtained infinite families {I_n}_n of d+1-regular graphs, realized as Cayley graphs on SL_2(q), and which are displaying a girth > 0,48 log_d |I_n|. And when d is equal to a power of 2, this improves a construction by Morgenstern in 1994 where certain families {M_n}_n of 2^k+1-regular graphs were shown to have a girth > 2/3 log_d |M_n|.Comment: (15 pages) Accepted at Combinatorica. Title changed following referee's suggestion. Revised version after reviewing proces