Some remarks on the simplicial volume of nonpositively curved manifolds

We show that any closed manifold with a metric of nonpositive curvature that admits either a single point rank condition or a single point curvature condition has positive simplicial volume. We use this to provide a differential geometric proof of a conjecture of Gromov in dimension three.Comment: 14 pages, 1 figure. Minor revision

Homological norms on nonpositively curved manifolds

We relate the Gromov norm on homology classes to the harmonic norm on the dual cohomology and obtain double sided bounds in terms of the volume and other geometric quantities of the underlying manifold. Along the way, we provide comparisons to other related norms and quantities as well.Comment: 19 pages, minor change

Congener Host Selection by the Pre-Dispersal Seed Predator, \u3ci\u3eApion Rostrum\u3c/i\u3e (Coleoptera: Apionidae)

Apion rostrum Say (Coleoptera: Apionidae) is the major seed predator of the wild indigo congeners, Baptisia alba and B. bracteata in the Russell Kirt Tallgrass Prairie, a reconstructed prairie located at College of DuPage, Illinois. This study, conducted during 2006, investigated factors attracting A. rostrum to each congener. The two Baptisia differ in developmental period, stature, and patterns of dispersion. B. bracteata flowers and initiates pods usually along a single raceme during late spring, and is a shorter plant that grows in clusters. In contrast, B. alba flowers and initiates pods beginning a month after B. bracteata, produces a tall central raceme with often several satellite racemes, and does not grow in dense clusters. Mating and ovipositing A. rostrum were observed on B. bracteata during the first half of June, and with greater abundance on B. alba from early June through mid July. Results of stepwise multiple regression showed a positive relationship of weevil counts per plant to raceme counts per cluster for B. bracteata and to inflated pod counts per plant for B. alba. The developmental synchrony between A. rostrum and pods of B. alba is evidence of a closer evolutionary relationship than the seed predator has with B. bracteata. This can explain the greater number of reproductive weevils seen on B. alba as well as the higher levels of pod infestations

Tourism curriculum in the University Sector: Does it meet future requirements? Evidence from Australia

In the contemporary competitive and globally connected marketplace, factors that guaranteed business success in the past may be of limited relevance in the future. Within the paradigms of today’s business, many successful operators continually introduce new products and services to maintain their market leadership position. Whilst firms in the tourism industry seek to maintain competitive position through policy planning, strategic marketing, budgeting and R&D, tourism education providers occupy a key position by seeking to enhance the skill levels of management and employees, both present and future. This paper reviews some Australian tourism and hospitality education programmes and course curriculum and briefly compares them with some trends in other English-speaking countries. The research explores tourism industry demand, trainees’ expectations and additionally identifies gaps and opportunities for the future curriculum content. The findings may, therefore, assist tourism programme providers with a broader perspective with which to shape future tourism courses

Star formation and the interstellar medium in z>6 UV-luminous Lyman-break galaxies

We present Atacama Large Millimeter Array (ALMA) detections of atomic carbon line and dust continuum emission in two UV-luminous galaxies at redshift 6. The far-infrared (FIR) luminosities of these galaxies are substantially lower than similar starbursts at later cosmic epochs, indicating an evolution in the dust properties with redshift, in agreement with the evolution seen in ultraviolet (UV) attenuation by dust. The [CII] to FIR ratios are found to be higher than at low redshift showing that [CII] should be readily detectable by ALMA within the reionization epoch. One of the two galaxies shows a complex merger nature with the less massive component dominating the UV emission and the more massive component dominating the FIR line and continuum. Using the interstellar atomic carbon line to derive the systemic redshifts we investigate the velocity of Lyman alpha emission emerging from high-z galaxies. In contrast to previous work, we find no evidence for decreasing Lyman alpha velocity shifts at high-redshift. We observe an increase in velocity shifts from z$\sim$2 to z$\sim$6, consistent with the effects of increased IGM absorption.Comment: 10 pages, 9 figures, submitted to ApJ, revised after referees comment

Perfect state transfer in cubelike graphs

Suppose $C$ is a subset of non-zero vectors from the vector space $\mathbb{Z}_2^d$. The cubelike graph $X(C)$ has $\mathbb{Z}_2^d$ as its vertex set, and two elements of $\mathbb{Z}_2^d$ are adjacent if their difference is in $C$. If $M$ is the $d\times |C|$ matrix with the elements of $C$ as its columns, we call the row space of $M$ the code of $X$. We use this code to study perfect state transfer on cubelike graphs. Bernasconi et al have shown that perfect state transfer occurs on $X(C)$ at time $\pi/2$ if and only if the sum of the elements of $C$ is not zero. Here we consider what happens when this sum is zero. We prove that if perfect state transfer occurs on a cubelike graph, then it must take place at time $\tau=\pi/2D$, where $D$ is the greatest common divisor of the weights of the code words. We show that perfect state transfer occurs at time $\pi/4$ if and only if D=2 and the code is self-orthogonal.Comment: 10 pages, minor revision