Set Systems with No Singleton Intersection

Let $\mathcal{F}$ be a $k$-uniform set system defined on a ground set of size $n$ with no singleton intersection; i.e., no pair $A,B\in\mathcal{F}$ has $|A\cap B|=1$. Frankl showed that $|\mathcal{F}|\leq\binom{n-2}{k-2}$ for $k\geq4$ and $n$ sufficiently large, confirming a conjecture of Erdős and Sós. We determine the maximum size of $\mathcal{F}$ for $k=4$ and all $n$, and also establish a stability result for general $k$, showing that any $\mathcal{F}$ with size asymptotic to that of the best construction must be structurally similar to it

Projections and Dyadic Parseval Frame MRA Wavelets

A classical theorem attributed to Naimark states that, given a Parseval frame $\mathcal{B}$ in a Hilbert space $\mathcal{H}$, one can embed $\mathcal{H}$ in a larger Hilbert space $\mathcal{K}$ so that the image of $\mathcal{B}$ is the projection of an orthonormal basis for $\mathcal{K}$. In the present work, we revisit the notion of Parseval frame MRA wavelets from two papers of Paluszy\'nski, \v{S}iki\'c, Weiss, and Xiao (PSWX) and produce an analog of Naimark's theorem for these wavelets at the level of their scaling functions. We aim to make this discussion as self-contained as possible and provide a different point of view on Parseval frame MRA wavelets than that of PSWX.Comment: 19 page

Damage tolerant composite wing panels for transport aircraft

Commercial aircraft advanced composite wing surface panels were tested for durability and damage tolerance. The wing of a fuel-efficient, 200-passenger airplane for 1990 delivery was sized using grahite-epoxy materials. The damage tolerance program was structured to allow a systematic progression from material evaluations to the optimized large panel verification tests. The program included coupon testing to evaluate toughened material systems, static and fatigue tests of compression coupons with varying amounts of impact damage, element tests of three-stiffener panels to evaluate upper wing panel design concepts, and the wing structure damage environment was studied. A series of technology demonstration tests of large compression panels is performed. A repair investigation is included in the final large panel test

Safe use of symbols in handover documentation for medical teams

Concern has been reported about the safe use of medical abbreviations in documents such as handover sheets and medical notes, especially when information is being communicated between staff of different specialties (BBC 2008, Sheppard et al. 2008). This article describes a study to investigate whether the use of symbols in handover documentation that is shared within and between multidisciplinary teams (MDTs) has similar safety implications. We asked 19 healthcare professionals from a range of specialties to identify 45 different combinations of 38 individual symbols. The symbols and combinations of symbols were extracted from 102 handover sheets taken from 6 different healthcare contexts in 4 London hospitals. Three symbols proposed in Microsoft's Common User Interface guidelines for alert symbols were also included. Results reveal that while some symbols are well understood, many others are either ambiguous or unknown. These results have implications for the safe use of symbols in medical documents, including paper and electronic handover documents and Electronic Patient Records (EPRs), especially where teams comprise individuals from different professional backgrounds, i.e. MDTs. We offer initial suggestions for standardisation and further research

A Volunteer Basketball Clinic for Children with Disabilities: Professional Development Impact on Student-Athletes and Physical Therapy Students

The purpose of this study was to assess the change in perceptions of student-athletes, physical therapy students, and parents of children who helped to facilitate an athletic skills camp for children with disabilities. Participants experienced 3 hours of basketball activity yearly. Data were collected for 3 consecutive years from a total of 51 parents, 15 student-athletes, and 22 physical therapy students. Preand post-survey data were evaluated by two independent researchers. Common themes were developed for all participant groups and cross-group comparisons were evaluated. Findings indicated a synergistic benefit for student-athletes and physical therapy students derived from their impact and children with disabilities. Perceptual changes in students included a decrease in fear in working with disabled children, an appreciation for the value of having fun, and increased growth in civic identity and desire to volunteer

One-pot near-ambient temperature syntheses of aryl(difluoroenol) derivatives from trifluoroethanol

Difluoroalkenylzinc reagents prepared from 1-(2’-methoxy-ethoxymethoxy)-2,2,2-trifluoroethane and 1-(N,N-diethylcarbamoyloxy)-2,2,2-trifluoroethane at ice bath temperatures, underwent Negishi coupling with a range of aryl halides in a convenient one pot procedure. While significant differences between the enol acetal and carbamate reagents were revealed, the Negishi protocol compared very favourably with alternative coupling procedures in terms of overall yields from trifluoroethanol

A coherent middle Pliocene magnetostratigraphy, Wanganui Basin, New Zealand

We document magnetostratigraphies for three river sections (Turakina, Rangitikei, Wanganui) in Wanganui Basin and interpret them as corresponding to the Upper Gilbert, the Gauss and lower Matuyama Chrons of the Geomagnetic Polarity Timescale, in agreement with foraminiferal biostratigraphic datums. The Gauss-Gilbert transition (3.58 Ma) is located in both the Turakina and Wanganui River sections, while the Gauss-Matuyama transition (2.58 Ma) is located in all three sections, as are the lower and upper boundaries of the Mammoth (3.33–3.22 Ma) and Kaena (3.11–3.04 Ma) Subchrons. Our interpretations are based in part on the re-analysis of existing datasets and in part on the acquisition and analysis of new data, particularly for the Wanganui River section. The palaeomagnetic dates of these six horizons provide the only numerical age control for a thick (up to 2000 m) mudstone succession (Tangahoe Mudstone) that accumulated chiefly in upper bathyal and outer neritic palaeoenvironments. In the Wanganui River section the mean sediment accumulation rate is estimated to have been about 1.8 m/k.y., in the Turakina section it was about 1.5 m/k.y., and in the Rangitikei section, the mean rate from the beginning of the Mammoth Subchron to the Hautawa Shellbed was about 1.1 m/k.y. The high rates may be associated with the progradation of slope clinoforms northward through the basin. This new palaeomagnetic timescale allows revised correlations to be made between cyclothems in the Rangitikei River section and the global Oxygen Isotope Stages (OIS) as represented in Ocean Drilling Program (ODP) Site 846. The 16 depositional sequences between the end of the Mammoth Subchron and the Gauss-Matuyama Boundary are correlated with OIS MG2 to 100. The cyclothems average 39 k.y. in duration in our age model, which is close to the 41 k.y. duration of the orbital obliquity cycles. We support the arguments advanced recently in defence of the need for local New Zealand stages as a means of classifying New Zealand sedimentary successions, and strongly oppose the proposal to move stage boundaries to selected geomagnetic polarity transitions. The primary magnetisation of New Zealand mudstone is frequently overprinted with secondary components of diagenetic origin, and hence it is often difficult to obtain reliable magnetostratigraphic records. We suggest specific approaches, analytical methods, and criteria to help ensure robustness and coherency in the palaeomagnetic identification of chron boundaries in typical New Zealand Cenozoic mudstone successions

The cone condition and t-designs

AbstractThe existence of a t-(v,k,λ) design implies that certain ‘almost constant’ vectors belong to the convex cone generated by the columns of the incidence matrix of t-subsets versus k-subsets of a v-set. We prove that some vectors are not in, or in a few cases are in, this cone—whether a design exists or not. When certain vectors are shown not to be in this cone, the implication is an inequality on the parameters or a condition on the structure of a t-design. We unify a number of known inequalities for t-designs, and derive some new ones concerning t-wise balanced designs, with this approach

Chandra localization of XTE J1906+090 and discovery of its optical and infrared counterparts

We present the Chandra identification and localization of the transient X-ray source XTE J1906+090 and the discovery of its optical and infrared counterparts. Our analysis of archival Chandra ACIS-I observations of the field found the source approximately 8 away from the position determined earlier with the RXTE PCA. We have confirmed the source identification with timing analysis of the X-ray data, which detected the source spin period of 89.6 s. The best Chandra position for the source is R.A. = 19h04m47491, decl. = +09024140. Subsequently, we performed optical observations of the field around the new location and discovered a coincident optical source with R-band magnitude of 18.7. A search in the Two Micron All Sky Survey catalog revealed an infrared point source with J = 15.2, H = 14.2, and K = 13.5, whose location is also coincident with our Chandra and optical positions. Our results add fresh evidence for a Be/X-ray transient nature for XTE J1906+090