Apollo experience report the command and service module milestone review process

The sequence of the command and service module milestone review process is given, and the Customer Acceptance Readiness Review and Flight Readiness Review plans are presented. Contents of the System Summary Acceptance Documents for the two formal spacecraft reviews are detailed, and supplemental data required for presentation to the review boards are listed. Typical forms, correspondence, supporting documentation, and minutes of a board meeting are included

Evolution equations of curvature tensors along the hyperbolic geometric flow

We consider the hyperbolic geometric flow $\frac{\partial^2}{\partial t^2}g(t)=-2Ric_{g(t)}$ introduced by Kong and Liu [KL]. When the Riemannian metric evolve, then so does its curvature. Using the techniques and ideas of S.Brendle [Br,BS], we derive evolution equations for the Levi-Civita connection and the curvature tensors along the hyperbolic geometric flow. The method and results are computed and written in global tensor form, different from the local normal coordinate method in [DKL1]. In addition, we further show that any solution to the hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.Comment: 15 page

Deformations of the hemisphere that increase scalar curvature

Consider a compact Riemannian manifold M of dimension n whose boundary \partial M is totally geodesic and is isometric to the standard sphere S^{n-1}. A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n-1), then M is isometric to the hemisphere S_+^n equipped with its standard metric. This conjecture is inspired by the positive mass theorem in general relativity, and has been verified in many special cases. In this paper, we construct counterexamples to Min-Oo's conjecture in dimension n \geq 3.Comment: Revised version, to appear in Invent. Mat

Rotational symmetry of self-similar solutions to the Ricci flow

Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and \kappa-noncollapsed. We prove that (M,g) is isometric to the Bryant soliton up to scaling. This solves a problem mentioned in Perelman's first paper.Comment: Final version, to appear in Invent. Mat

A geometric approach to apriori estimates for optimal transport maps

A key inequality which underpins the regularity theory of optimal transport for costs satisfying the Ma--Trudinger--Wang condition is the Pogorelov second derivative bound. This translates to an apriori interior $C^1$ estimate for smooth optimal maps. Here we give a new derivation of this estimate which relies in part on Kim, McCann and Warren's observation that the graph of an optimal map becomes a volume maximizing spacelike submanifold when the product of the source and target domains is endowed with a suitable pseudo-Riemannian geometry that combines both the marginal densities and the cost

A compactness theorem for scalar-flat metrics on manifolds with boundary

Let (M,g) be a compact Riemannian manifold with boundary. This paper is concerned with the set of scalar-flat metrics which are in the conformal class of g and have the boundary as a constant mean curvature hypersurface. We prove that this set is compact for dimensions greater than or equal to 7 under the generic condition that the trace-free 2nd fundamental form of the boundary is nonzero everywhere.Comment: 49 pages. Final version, to appear in Calc. Var. Partial Differential Equation

Rural Vocational and Transition Assessment Practices for Students with Intellectual Disabilities: What Do Educators Really Know?

Transition planning requires quality vocational and transition assessment tailored to the student\u27s needs, strengths, preferences and interests. Limited research is currently available that addresses assessment types and use of results that rural practitioners utilize to aid in transition planning for students with intellectual disabilities (ID). A group of 71 rural educators were surveyed to determine their transition assessment understanding and practices in the rural setting. This descriptive study examined rural educators’ understanding of vocational and transition assessment methods used in their rural settings, the transition assessment instruments they use with students with ID, and the impact that transition assessment has in determining the needs of students with ID. The results indicate the majority of the rural educators in the study reported limited understanding in the use of assessment results for student vocational and transition planning and expressed the need for training in this area to improve outcomes for students with ID

Static flow on complete noncompact manifolds I: short-time existence and asymptotic expansions at conformal infinity

In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum $(M^n,g,V),$ we also compute the asymptotic expansions of $g$ and $V$ at conformal infinity.Comment: 25 page

Co2+ sorption capacity indicators of La Plata region´s soils. Insights and correlations with soil properties

Notwithstanding soil act as a pollutant sink, its Co sorption capacity presents still controversial results. Here, Co2+ sorption on soil samples from La Plata (Argentina) was analyzed. Four sorption indicators were used: Kdis (estimated from the entire sorption isotherm), KF1 (estimated from the lineal part of the sorption isotherm), Kdx, (solid-solution distribution coefficient) and Kr, a dimensionless parameter recently developed. Pearson correlation coefficients between the parameters and soil properties were calculated. Significant and negative correlations with silt were obtained, while significant and positive correlations were established with clay and smectite content. Soil clay fractions were isolated and Co2+ sorption was evaluated, observing relatively high removal. The correlations with kaolinite, magnetite and Mn and Fe oxides showed debatable results: Kdis could be more sensitive than Kr to magnetite variations while Kr seems to be more sensitive to Mn changes. KF1 presented similar behavior to Kr. The studied soils presented a high Co2+ sorption capacity, making them an effective barrier of this pollutant, avoiding its passage to groundwater and crops.Fil: Montes, María Luciana. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Fernandez M. A. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Tecnología de Recursos Minerales y Cerámica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Tecnología de Recursos Minerales y Cerámica; ArgentinaFil: Brendle, J. Université Haute-alsace. Institut de Science Des Matériaux de Mulhouse.; FranciaFil: Michelin, L.. Université Haute-alsace. Institut de Science Des Matériaux de Mulhouse.; FranciaFil: Taylor, Marcela Andrea. Universidad Nacional de La Plata. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Torres Sanchez, Rosa Maria. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas. Centro de Tecnología de Recursos Minerales y Cerámica. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Centro de Tecnología de Recursos Minerales y Cerámica; Argentin

Cichoń’s diagram for uncountable cardinals

We develop a version of Cichoń’s diagram for cardinal invariants on the generalized Cantor space 2 κ or the generalized Baire space κ κ , where κ is an uncountable regular cardinal. For strongly inaccessible κ, many of the ZFC-results about the order relationship of the cardinal invariants which hold for ω generalize; for example, we obtain a natural generalization of the Bartoszyński–Raisonnier–Stern Theorem. We also prove a number of independence results, both with < κ-support iterations and κ-support iterations and products, showing that we consistently have strict inequality between some of the cardinal invariants