Inverse Polynomial Based Explicit Guidance for Lunar Soft Landing During Powered Braking

In this paper an explicit guidance law for the powered descent phase of the soft lunar landing is presented. The descent trajectory, expressed in polynomial form is fixed based on the boundary conditions imposed by the precise soft landing mission. Adapting an inverse model based approach, the guidance command is computed from the known spacecraft trajectory. The guidance formulation ensures the vertical orientation of the spacecraft during touchdown. Also a closed form relation for the final flight time is proposed. The final time is expressed as a function of initial position and velocity of the spacecraft ( at the start of descent) and also depends on the desired landing site. To ensure the fuel minimum descent the proposed explicit method is extended to optimal guidance formulation. The effectiveness of the proposed guidance laws are demonstrated with simulation results.

Explicit and Unique Construction of Tetrablock Unitary Dilation in a Certain Case

Consider the domain E in defined by This is called the tetrablock. This paper constructs explicit boundary normal dilation for a triple (A, B, P) of commuting bounded operators which has as a spectral set. We show that the dilation is minimal and unique under a certain natural condition. As is well-known, uniqueness of minimal dilation usually does not hold good in several variables, e.g., Ando's dilation is known to be not unique, see Li and Timotin (J Funct Anal 154:1-16, 1998). However, in the case of the tetrablock, the third component of the dilation can be chosen in such a way as to ensure uniqueness.

Development of appropriateness explicit criteria for cataract extraction by phacoemulsification

Background: Consensus development techniques were used in the late 1980s to create explicit criteria for the appropriateness of cataract extraction. We developed a new appropriateness of indications tool for cataract following the RAND method. We tested the validity of our panel results. Methods: Criteria were developed using a modified Delphi panel judgment process. A panel of 12 ophthalmologists was assembled. Ratings were analyzed regarding the level of agreement among panelists. We studied the influence of all variables on the final panel score using linear and logistic regression models. The explicit criteria developed were summarized by classification and regression tree analysis. Results: Of the 765 indications evaluated by the main panel in the second round, 32.9% were found appropriate, 30.1% uncertain, and 37% inappropriate. Agreement was found in 53% of the indications and disagreement in 0.9%. Seven variables were considered to create the indications and divided into three groups: simple cataract, with diabetic retinopathy, or with other ocular pathologies. The preoperative visual acuity in the cataractous eye and visual function were the variables that best explained the panel scoring. The panel results were synthesized and presented in three decision trees. Misclassification error in the decision trees, as compared with the panel original criteria, was 5.3%. Conclusion: The parameters tested showed acceptable validity for an evaluation tool. These results support the use of this indication algorithm as a screening tool for assessing the appropriateness of cataract extraction in field studies and for the development of practice guidelines.

Demographics by depth: spatially explicit life-history dynamics of a protogynous reef fish

Distribution and demographics of the hogfish (Lachnolaimus maximus) were investigated by using a combined approach of in situ observations and life history analyses. Presence, density, size, age, and size and age at sex change all varied with depth in the eastern Gulf of Mexico. Hogfish (64–774 mm fork length and 0–19 years old) were observed year-round and were most common over complex, natural hard bottom habitat. As depth increased, the presence and density of hogfish decreased, but mean size and age increased. Size at age was smaller nearshore (<30 m). Length and age at sex change of nearshore hogfish were half those of offshore hogfish and were coincident with the minimum legal size limit. Fishing pressure is presumably greater nearshore and presents a confounding source of increased mortality; however, a strong red tide occurred the year before this study began and likely also affected nearshore demographics. Nevertheless, these data indicate ontogenetic migration and escapement of fast-growing fish to offshore habitat, both of which should reduce the likelihood of fishing-induced evolution. Data regarding the hogfish fishery are limited and regionally dependent, which has confounded previous stock assessments; however, the spatially explicit vital rates reported herein can be applied to future monitoring efforts.