Laser probing of the atmosphere Semiannual status report

Light backscattering experiment in laser probing studies of atmospheric layer above 100 k

Comments on Ringwood's paper 'Petrogenesis of Apollo 11 basalts and implications for lunar origin'

Apollo 11 basalt petrogenesis and theories of lunar evolution comparing lunar and earth environment

Phobos and Deimos: A base for sampling the Martian past

Future exploration of Mars is summed up by the proposal that the Martian satellites provide an ideal base for exploring the surface of Mars. For example, a manned base on Deimos could direct a series of unmanned rovers and sample recovery operations, providing an immediate feedback to the operation. Samples analyzed in such an environment would be fresh, and most importantly, would not require quarantine

“Some Teachers Just Simply Care”: Respect in Urban Student-Teacher Relationships

Teachers are ethically obligated to care for their students. One overlooked means of demonstrating care is through respect. However, because respectful behaviors are culturally dependent, exploring experiences of respect from students of color is needed to provide insight into student-teacher relationships. To understand students’ experiences of respect from teachers in the school setting, we interviewed 12 adolescents and emerging adults of color (M age = 17, SD age = 1.81) who attended Urban schools, about their experiences of respect from their teachers. We deductively and inductively coded the interviews separately for definitions of respect and experiences of respect from teachers using six themes of respect. Ultimately, youth often defined respect as the golden rule and politeness. However, when discussing instances of respect with teachers, youth described teachers demonstrating care for students’ personal lives and academic success. Our findings suggest that students identify behaviors associated with care as respectful, which diverge from decontextualized definitions of respect. Policy changes should focus on promoting student-teacher relationships, focusing on culturally sensitive teaching and caring for students. Specifically, policy should support classroom level changes, such as the co-construction of respect expectations between students and teachers

Differential Galois Theory of Linear Difference Equations

We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hoelder's Theorem that the Gamma function satisfies no polynomial differential equation and are able to give general results that imply, for example, that no differential relationship holds among solutions of certain classes of q-hypergeometric functions.Comment: 50 page

Loop algebras, gauge invariants and a new completely integrable system

One fruitful motivating principle of much research on the family of integrable systems known as ``Toda lattices'' has been the heuristic assumption that the periodic Toda lattice in an affine Lie algebra is directly analogous to the nonperiodic Toda lattice in a finite-dimensional Lie algebra. This paper shows that the analogy is not perfect. A discrepancy arises because the natural generalization of the structure theory of finite-dimensional simple Lie algebras is not the structure theory of loop algebras but the structure theory of affine Kac-Moody algebras. In this paper we use this natural generalization to construct the natural analog of the nonperiodic Toda lattice. Surprisingly, the result is not the periodic Toda lattice but a new completely integrable system on the periodic Toda lattice phase space. This integrable system is prescribed purely in terms of Lie-theoretic data. The commuting functions are precisely the gauge-invariant functions one obtains by viewing elements of the loop algebra as connections on a bundle over $S^1$