A Discontinuity in the Distribution of Fixed Point Sums

The quantity $f(n,r)$, defined as the number of permutations of the set $[n]=\{1,2,... n\}$ whose fixed points sum to $r$, shows a sharp discontinuity in the neighborhood of $r=n$. We explain this discontinuity and study the possible existence of other discontinuities in $f(n,r)$ for permutations. We generalize our results to other families of structures that exhibit the same kind of discontinuities, by studying $f(n,r)$ when ``fixed points'' is replaced by ``components of size 1'' in a suitable graph of the structure. Among the objects considered are permutations, all functions and set partitions.Comment: 1 figur

The Asymptotic Number of Irreducible Partitions

A partition of [1, n] = {1,..., n} is called irreducible if no proper subinterval of [1, n] is a union of blocks. We determine the asymptotic relationship between the numbers of irreducible partitions, partitions without singleton blocks, and all partitions when the block sizes must lie in some specified set

Report on water quality data evaluation and program design services for the James and York rivers in conjunction with the 208 planning program for the Tidewater region of Virginia

The study area considered in this report includes the following: The James River from Fort Monroe to the mouth of the Chickahominy River (statute mile 45) including the small tributaries on the north shore but not the Chickahominy; the York River from its mouth to the confluence of the Mattaponi and Pamunkey at West Point (statute mile 33.5) including the small tributaries along the south shore; and the small drainage area adjacent to Chesapeake Bay lying between the York and James basins. The two rivers included in this basin are Poquoson River and Back River

From non-Hermitian effective operators to large-scale no-core shell model calculations for light nuclei

No-core shell model (NCSM) calculations using ab initio effective interactions are very successful in reproducing experimental nuclear spectra. The main theoretical approach is the use of effective operators, which include correlations left out by the truncation of the model space to a numerically tractable size. We review recent applications of the effective operator approach, within a NCSM framework, to the renormalization of the nucleon-nucleon interaction, as well as scalar and tensor operators.Comment: To be submited to J. Phys. A, special issue on "The Physics of Non-Hermitian Operators

HST STIS spectroscopy of the triple nucleus of M31: two nested disks in Keplerian rotation around a Supermassive Black Hole

We present HST spectroscopy of the nucleus of M31 obtained with STIS. Spectra taken around the CaT lines at 8500 see only the red giants in the double bright- ness peaks P1 and P2. In contrast, spectra taken at 3600-5100 A are sensitive to the tiny blue nucleus embedded in P2, the lower surface brightness red nucleus. P2 has a K-type spectrum, but the embedded blue nucleus has an A-type spectrum with strong Balmer absorption lines. Given the small likelihood for stellar collisions, a 200 Myr old starburst appears to be the most plausible origin of the blue nucleus. In stellar population, size, and velocity dispersion, the blue nucleus is so different from P1 and P2 that we call it P3. The line-of-sight velocity distributions of the red stars in P1+P2 strengthen the support for Tremaine s eccentric disk model. The kinematics of P3 is consistent with a circular stellar disk in Keplerian rotation around a super-massive black hole with M_bh = 1.4 x 10^8 M_sun. The P3 and the P1+P2 disks rotate in the same sense and are almost coplanar. The observed velocity dispersion of P3 is due to blurred rotation and has a maximum value of sigma = 1183+-201 km/s. The observed peak rotation velocity of P3 is V = 618+-81 km/s at radius 0.05" = 0.19 pc corresponding to a circular rotation velocity at this radius of ~1700 km/s. Any dark star cluster alternative to a black hole must have a half-mass radius <= 0.03" = 0.11 pc. We show that this excludes clusters of brown dwarfs or dead stars on astrophysical grounds.Comment: Astrophysical Journal, Sep 20, 2005, 21 pages including 20 figure

Correction: A Feasible and Efficacious Mobile-Phone Based Lifestyle Intervention for Filipino Americans with Type 2 Diabetes: Randomized Controlled Trial.

[This corrects the article DOI: 10.2196/diabetes.8156.]

Recognizing and Tackling Inhaler Technique Decay in Asthma and Chronic Obstructive Pulmonary Disesase (COPD) Clinical Practice

A poor inhaler technique continues to represent a substantial barrier to effective asthma and chronic obstructive pulmonary disease management. It can result in perceived lack of treatment effectiveness even with apparent adherence to a prescribed regimen of inhaled maintenance therapies, potentially resulting in an unnecessary change or escalation of treatment. Many patients are not trained to inhaler mastery in real-world practice; furthermore, even where mastery is initially achieved, an ongoing assessment and education are seldom maintained. In this review, we present an overview of the evidence for deterioration of the inhaler technique over time after training, investigate the factors that contribute to this deterioration, and explore innovative approaches to addressing the problem. We also propose steps forward drawn from the literature and our clinical insights.</p