Outline of a Theory of non-Rankine-Hugoniot Shock Wave in Weak Mach Reflection

At the previous AFMC, the background for expecting a departure from Rankine-Hugoniot theory at the base of the reflected shock wave in weak Mach reflection was exposed. The results of some pertinent experiments performed in the supersonic wind tunnel were then presented. They confirmed the hypothesised irregular behaviour. In the present contribution, the elaboration of a theory of transgressed shock wave properties is presented. This concept enables to calculate the modified jump process. It fully accounts for the known experimental observations. It is the unyielding boundary conditions that prevail beyond regular reflection which force this remarkable deviation from the classical shock wave theory to take place

Wreath products of cocommutative Hopf algebras

We define wreath products of cocommutative Hopf algebras, and show that they enjoy a universal property of classifying cleft extensions, analogous to the Kaloujnine-Krasner theorem for groups. We show that the group ring of a wreath product of groups is the wreath product of their group rings, and that (with a natural definition of wreath products of Lie algebras) the universal enveloping algebra of a wreath product of Lie algebras is the wreath product of their enveloping algebras. We recover the aforementioned result that group extensions may be classified as certain subgroups of a wreath product, and that Lie algebra extensions may also be classified as certain subalgebras of a wreath product

Spatial distribution patterns and movements of Holothuria arguinensis in the Ria Formosa (Portugal)

Holothurian populations are under pressure worldwide because of increasing demand for beche-de-mer, mainly for Asian consumption. Importations to this area from new temperate fishing grounds provide economic opportunities but also raise concerns regarding future over-exploitation. Studies on the habitat preferences and movements of sea cucumbers are important for the management of sea cucumber stocks and sizing of no-take zones, but information on the ecology and behavior of temperate sea cucumbers is scarce. This study describes the small-scale distribution and movement patterns of Holothuria arguinensis in the intertidal zone of the Ria Formosa national park (Portugal).Mark/recapture studieswere performed to record theirmovements over time on different habitats (sand and seagrass). H. arguinensis preferred seagrass habitats and did not show a size or life stage-related spatial segregation. Its density was 563 ind. ha−1 and mean movement speed was 10 m per day. Movement speed did not differ between habitats and the direction of movement was offshore during the day and shoreward during the night. Median home range size was 35 m2 and overlap among home ranges was 84%. H. arguinensis' high abundance, close association with seagrass and easy catchability in the intertidal zone, indicate the importance of including intertidal lagoons in future studies on temperate sea cucumber ecology since those systems might require different management strategies than fully submerged habitats

Hausdorff dimension of some groups acting on the binary tree

Based on the work of Abercrombie, Barnea and Shalev gave an explicit formula for the Hausdorff dimension of a group acting on a rooted tree. We focus here on the binary tree T. Abert and Virag showed that there exist finitely generated (but not necessarily level-transitive) subgroups of AutT of arbitrary dimension in [0,1]. In this article we explicitly compute the Hausdorff dimension of the level-transitive spinal groups. We then show examples of 3-generated spinal groups which have transcendental Hausdroff dimension, and exhibit a construction of 2-generated groups whose Hausdorff dimension is 1.Comment: 10 pages; full revision; simplified some proof

Hausdorff dimension of some groups acting on the binary tree

Based on the work of Abercrombie [A. G. Abercrombie. Subgroups and subrings of profinite rings. Math. Proc. Cambridge Philos. Soc. 116 (1994), 209-222.], Barnea and Shalev [Y. Barnea and A. Shalev. Hausdorff dimension, pro-p groups, and Kac-Moody algebras. Trans. Amer. Math. Soc. 349 (1997), 5073-5091.] gave an explicit formula for the Hausdorff dimension of a group acting on a rooted tree. We focus here on the binary tree . Abért and Virág [M. Abért and B. Virág. Dimension and randomness in groups acting on rooted trees. J. Amer. Math. Soc. 18 (2005), 157-192.] showed that there exist finitely generated (but not necessarily level-transitive) subgroups of Aut of arbitrary dimension in [0, 1]. In this article we explicitly compute the Hausdorff dimension of the level-transitive spinal groups. We then give examples of 3-generated spinal groups which have transcendental Hausdorff dimension, and construct 2-generated groups whose Hausdorff dimension is

What Price Style? The Fabric-Advisory Function of the Drygoods Commission Merchant, 1850-1880

Using data from nineteenth-century New England, Dr. Siegenthaler isolates a value for the most important function which drygoods marketing agencies performed for the mills they represented. His conclusions cast new light on the key role played by fashion considerations in decision making within the textile industr

First Trace for Irregular Shock Wave Process in Weak Mach Reflection

Referring to von Neumann's words, transition from a two- to a three-shock reflection configuration in the weak domain presents some very considerable theoretical difficulties. It nonetheless remains an observed fact that such a transition does indeed occur in the real world. This paper describes the novel experimental technique and the results which for the first time did yield a "footprint" that something quite out-of-the-ordinary is taking place within the base of the reflected wave where the latter butts the point of shock confluence. The results of the work presented here remained puzzling initially, for they seemed to contradict some preconceived outcome. It was only years later that the specific detail which was first considered to be misleading could be interpreted. It disclosed that the flow through the reflected shock is being forced to deviate from the classic Rankine-Hugoniot shock transformation process. This departure then enables the unyielding boundary conditions to be fulfilled and three-shock reflection to get established. This occurs with some lag past detachment of RR, this interval being required for the properties to adjust to the imposed conditions. The hypothesis of the departure from classic shock theory has been verified in the wind tunnel and was confirmed