Carleman estimates with sharp weights and boundary observability for wave operators with critically singular potentials

We establish a new family of Carleman inequalities for wave operators on cylindrical spacetime domains containing a potential that is critically singular, diverging as an inverse square on all the boundary of the domain. These estimates are sharp in the sense that they capture both the natural boundary conditions and the natural $H^1$-energy. The proof is based around three key ingredients: the choice of a novel Carleman weight with rather singular derivatives on the boundary, a generalization of the classical Morawetz inequality that allows for inverse-square singularities, and the systematic use of derivative operations adapted to the potential. As an application of these estimates, we prove a boundary observability property for the associated wave equations.Comment: 31 pages; accepted versio

Bulk-boundary correspondences and unique continuation in asymptotically Anti-de Sitter spacetimes

This article surveys the research presented by the author at the MATRIX Institute workshop "Hyperbolic Differential Equations in Geometry and Physics" in April 2022. The work is centered about establishing rigorous mathematical statements toward the AdS/CFT correspondence in theoretical physics, in particular in dynamical settings. The contents are mainly based on the recent paper with G. Holzegel that proved a unique continuation result for the Einstein-vacuum equations from asymptotically Anti-de Sitter (aAdS) conformal boundaries. We also discuss some preceding results, in particular novel Carleman estimates for wave equations on aAdS spacetimes, which laid the foundations toward the main correspondence theorems.Comment: To be published in "MATRIX Annals

Qualitative Outcomes for Youth Who Participate in Inclusive Programs: A Multi-Case Analysis Across 14 Camps and Outdoor Schools

As the number of inclusive programs grows, an important question arises: What are the out­comes of participation in an inclusive camp or outdoor school where children live, learn, and play with peers of varying abilities. Residential camps and outdoor schools and their research partners are striving to develop effective meth­ods to examine the outcomes for program par­ticipants (Dworken. 2001). Both quantitative and qualitative methods have been used to examine outcomes such as changes in skill levels, self-perceptions, attitudes, social interaction, and infonnant or self-reported growth in various ar­eas of development. Qualitative research may help us describe the scope, depth, and context surrounding those outcomes as well as how par­ticipants\u27 experiences during a program carry over into their functioning in other environments or situations. In the present study, qualitative outcomes of inclusive residential camps and outdoor schools for children with and without disabilities are described

Global stability of traveling waves for (1+1)(1+1)-dimensional systems of quasilinear wave equations

A key feature of $(1+1)$-dimensional nonlinear wave equations is that they admit left or right traveling waves, under appropriate algebraic conditions on the nonlinearities. In this paper, we prove global stability of such traveling wave solutions for $(1+1)$-dimensional systems of nonlinear wave equations, given a certain asymptotic null condition and sufficient decay for the traveling wave. We first consider semilinear systems as a simpler model problem; we then proceed to treat more general quasilinear systems.Comment: Comments are welcome

The Eagle Ford Formation

Geological Science

Effective Practices and Participant Outcomes for Youth: Inclusive Camps and Outdoor Schools

This research project investigated resident camp and outdoor school programs and em­ployed validated instrumentation to help deter­mine the effects of inclusive practices on the growth and development of youth with and without disabilities (Brannan, Fullerton, Arick, Robb, and Bender, in press)

Pengaruh Orientasi Serat Terhadap Kekuatan Tarik Nata De Coco Dengan Perlakuan TEMPO

Pengembangan biomaterial terus dilakukan pada dunia industri karena sifatnya yang biodegradable. Biomaterial yang menarik digunakan saat ini adalah nano selulosa dengan sifatnya yang biodegradable, fleksibel, dan kekuatan tarik yang tinggi. Nano selulosa yang dibuat menggunakan metode fermentasi dengan bantuan bakteri, yang disebut selulosa bakteri. Proses fermentasi yang dilakukan tanpa reaksi kimia menjadikan selulosa bakteri lebih ramah lingkungan dan biaya lebih murah. Oleh karena itu, selulosa bakteri akan digunakan pada penelitian ini. Nata de coco digunakan sebagai selulosa bakteri pada penelitian ini. Nata de coco merupakan fermentasi dari air kelapa dengan menggunakan bakteri Acetobacter Xylinum. Nata de coco memiliki orientasi serat yang acak pada ukuran nano. Oleh karena itu, Nata de coco akan diberikan variasi waktu penggantungan 0, 15, 30, dan 60 menit untuk mendapatkan orientasi serat yang sama. Dengan orientasi serat yang sama dan perlakuan TEMPO akan meningkatkan kekuatan tarik nata de coco. Pengujian tarik digunakan untuk mendapatkan sifat mekanik film biopolimer nata de coco. Kekuatan tarik semakin meningkat seiring dengan semakin lama waktu penggantungan. Sementara nilai elongasi semakin menurun seiring dengan semakin lama waktu penggantungan. Hasil ini didapatkan karena serat memiliki orientasi yang sama setelah dilakukan penggantungan. Nata de coco yang sudah diberikan perlakuan TEMPO memiliki gugus hidroksil bebas yang lebih banyak dibandingkan tanpa perlakuan TEMPO sehingga meningkatkan kekuatan tarik

Uma investigação sobre a natureza e as causas do investimento transnacional em telecomunicações : o estudo de caso da decisão da Bellsouth em participar do leilão da banda-b no Brasil

Orientador: Marcio Wohlers de AlmeidaDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de EconomiaMestrad