The index of Farey sequence

We define an integer valued function of the Farey fractions which we call the index, and we prove two exact formulae involving this. We give asymptotic formulae for the second moment of the index and for the value distribution. Zagier communicated to us a remarkable formula relating the index to Dedekind sums and this yields further asymptotic formulae

The distribution of totatives

D. H. Lehmer initiated the study of the distribution of totatives, which are numbers coprime with a given integer. This led to various problems considered by P. Erdos, who made a conjecture on such distributions. We clarify results due to Erdos and prove his conjecture by establishing a theorem on the ordering of residues

Model fluid in a porous medium: results for a Bethe lattice

We consider a lattice gas with quenched impurities or `quenched-annealed binary mixture' on the Bethe lattice. The quenched part represents a porous matrix in which the (annealed) lattice gas resides. This model features the 3 main factors of fluids in random porous media: wetting, randomness and confinement. The recursive character of the Bethe lattice enables an exact treatment, whose key ingredient is an integral equation yielding the one-particle effective field distribution. Our analysis shows that this distribution consists of two essentially different parts. The first one is a continuous spectrum and corresponds to the macroscopic volume accessible to the fluid, the second is discrete and comes from finite closed cavities in the porous medium. Those closed cavities are in equilibrium with the bulk fluid within the grand canonical ensemble we use, but are inaccessible in real experimental situations. Fortunately, we are able to isolate their contributions. Separation of the discrete spectrum facilitates also the numerical solution of the main equation. The numerical calculations show that the continuous spectrum becomes more and more rough as the temperature decreases, and this limits the accuracy of the solution at low temperatures.Comment: 13 pages, 12 figure

On the set of divisors of an integer

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46612/1/222_2005_Article_BF01388495.pd

A functionally specialized population of mucosal CD103+ DCs induces Foxp3+ regulatory T cells via a TGF-β– and retinoic acid–dependent mechanism

Foxp3+ regulatory T (T reg) cells play a key role in controlling immune pathological re actions. Many develop their regulatory activity in the thymus, but there is also evidence for development of Foxp3+ T reg cells from naive precursors in the periphery. Recent studies have shown that transforming growth factor (TGF)-β can promote T reg cell development in culture, but little is known about the cellular and molecular mechanisms that mediate this pathway under more physiological conditions. Here, we show that after antigen activation in the intestine, naive T cells acquire expression of Foxp3. Moreover, we identify a population of CD103+ mesenteric lymph node dendritic cells (DCs) that induce the devel opment of Foxp3+ T reg cells. Importantly, promotion of T reg cell responses by CD103+ DCs is dependent on TGF-β and the dietary metabolite, retinoic acid (RA). These results newly identify RA as a cofactor in T reg cell generation, providing a mechanism via which functionally specialized gut-associated lymphoid tissue DCs can extend the repertoire of T reg cells focused on the intestine

Charge dynamics and "ferromagnetism" of A1-xLaxB6 (A=Ca and Sr)

Ferromagnetism has been reported recently in La-doped alkaline-earth hexaborides, A1-xLaxB6 (A=Ca, Sr, and Ba). We have performed the reflectivity, Hall resistivity, and magnetization measurements of A1-xLaxB6. The results indicate that A1-xLaxB6 can be regarded as a simple doped semimetal, with no signature of an excitonic state as suggested by several theories. It is also found that the surface of as-grown samples (10 micrometer in thickness) has a different electronic structure from a bulk one, and a fairly large number of paramagnetic moments are confined in this region. After eliminating these paramagnetic moments at the surface, we could not find any evidence of an intrinsic ferromagnetic moment in our samples, implying the possibility that the ferromagnetism of A1-xLaxB6 reported so far is neither intrinsic.Comment: 7 pages, 8 figure

Relating aviation service difficulty reports to accident data for safety trend prediction

A synthetic model of scheduled-commercial U.S. aviation fatalities was constructed from linear combinations of the time-spectra of critical systems reporting using 5.5 years of Service Difficulty Reports (SDR){sup 2} and Accident Incident Data System (AIDS) records{sup 3}. This model, used to predict near-future trends in aviation accidents, was tested by using the first 36 months of data to construct the synthetic model which was used to predict fatalities during the following eight months. These predictions were tested by comparison with the fatality data. A reliability block diagram (RBD) and third-order extrapolations also were used as predictive models and compared with actuality. The synthetic model was the best predictor because of its use of systems data. Other results of the study are a database of service difficulties for major aviation systems, and a rank ordering of systems according to their contribution to the synthesis. 4 refs., 8 figs., 3 tabs

Composite quarks and leptons in higher space-time dimensions

A new approach towards the composite structure of quarks and leptons in the context of the higher dimensional unified theories is proposed. Owing to the certain strong dynamics, much like an ordinary QCD, every possible vectorlike multiplets of composites appear in higher dimensional bulk space-time, however, through a proper Sherk-Schwarz compactification only chiral set of composite quarks and leptons survive as the massless states in four dimensions. In this scenario restrictions related with the 't Hooft's anomaly matching condition are turned out to be avoided and, as a result, the composite models look rather simple and economic. We demonstrate our approach by an explicit construction of model of preons and their composites unified in the supersymmetric SU(5) GUT in five space-time dimensions. The model predicts exactly three families of the composite quarks and leptons being the triplets of the chiral horizontal symmetry SU(3)_h which automatically appears in the composite spectrum when going to ordinary four dimensions.Comment: 13 pages, tcilatex, no figures, v2 - misprints correcte

Quintessence from Shape Moduli

We show that shape moduli in sub-millimeter extra dimensional scenarios, addressing the gauge hierarchy problem, can dominate the energy density of the universe today. In our scenario, the volume of the extra dimensions is stabilized at a sufficiently high scale to avoid conflicts with nucleosynthesis and solar-system precision gravity experiments, while the shape moduli remain light but couple extremely weakly to brane-localized matter and easily avoid these bounds. Nonlocal effects in the bulk of the extra dimension generate a potential for the shape moduli. The potential has the right form and order of magnitude to account for the present day cosmic acceleration, in a way analogous to models of quintessence as a pseudo Nambu-Goldstone boson.Comment: 8 pages, 1 figur