Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type

We establish the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as a second-order, nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the location of the transonic shock which divides the two regions of smooth flow, and the equation is hyperbolic in the upstream region where the smooth perturbed flow is supersonic. We develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem. Our results indicate that there exists a unique solution of the free boundary problem such that the equation is always elliptic in the downstream region and the free boundary is smooth, provided that the hyperbolic phase is close to a uniform flow. We prove that the free boundary is stable under the steady perturbation of the hyperbolic phase. We also establish the existence and stability of multidimensional transonic shocks near spherical or circular transonic shocks.

     

A Pilot Survey of Vocal Health in Young Singers

The objective of this study was to determine the incidence of vocal problems in young choir singers and to correlate vocal problems with demographic and behavioral information. A questionnaire addressing vocal habits and hygiene was offered to 571 young choir singers, up to 25 years of age, who sing at least weekly; 129 (22.6%) responded. More than one-half of the respondents had experienced vocal difficulty, particularly older adolescents. Detrimental behaviors and circumstances surveyed were not reflective of the incidence of vocal difficulty, except for morning hoarseness, chronic fatigue, insomnia, and female gender after puberty. Voice care professionals should be aware that self-reported voice difficulties are common among young choral singers, especially postpubescent girls, and children with symptoms consistent with reflux (morning hoarseness) and emotional stress (insomnia). Laryngologists should communicate with choral conductors and singing teachers to enhance early identification and treatment of children with voice complaints, and to develop choral educational strategies that help decrease their incidence.     

Evolution of multiprotocol label switching

Multiprotocol label switching (MPLS) is rapidly emerging as an Internet Engineering Task Force (IETF) standard intended to enhance the speed, scalability, and service provisioning capabilities in the Internet. MPLS uses the technique of packet forwarding based on labels, to enable the implementation of a simpler high-performance packet forwarding engine. This also decouples packet forwarding from routing, facilitating the provision of varied routing services independent of the packet forwarding paradigm. The authors track the evolution of this technology in relation to other existing technologies. Then an overview of the MPLS architecture and design is provided. In addition, some of the work that was a precursor to MPLS is discussed, as well as related issues and debates     

Hidden-Action in Network Routing

In communication networks, such as the Internet or mobile ad-hoc networks, the actions taken by intermediate nodes or links are typically hidden from the communicating endpoints; all the endpoints can observe is whether or not the end-to-end transmission was successful. Therefore, in the absence of incentives to the contrary, rational (i.e., selfish) intermediaries may choose to forward messages at a low priority or simply not forward messages at all. Using a principal-agent model, we show how the hidden-action problem can be overcome through appropriate design of contracts in both the direct (the endpoints contract with each individual router directly) and the recursive (each router contracts with the next downstream router) cases. We further show that, depending on the network topology, per-hop or per-path monitoring may not necessarily improve the utility of the principal or the social welfare of the system.     

On the spectral picture of an irreducible subnormal operator II

In this paper we show that the spectral picture of an irreducible subnormal operator may be arbitrarily prescribed subject only to certain natural necessary conditions. This completes work begun by the second author.