Projections in a normed linear space and a generalization of the pseudo-inverse

The concept of a "projection function" in a finite-dimensional real or complex normed linear space H (the function P_M which carries every element into the closest element of a given subspace M) is set forth and examined.

If dim M = dim H - 1, then P_M is linear. If P_N is linear for all k-dimensional subspaces N, where 1 ≤ k < dim M, then P_M is linear.

The projective bound Q, defined to be the supremum of the operator norm of P_M for all subspaces, is in the range 1 ≤ Q < 2, and these limits are the best possible. For norms with Q = 1, P_M is always linear, and a characterization of those norms is given.

If H also has an inner product (defined independently of the norm), so that a dual norm can be defined, then when P_M is linear its adjoint P_M^H is the projection on (kernel P_M)^⊥ by the dual norm. The projective bounds of a norm and its dual are equal.

The notion of a pseudo-inverse F⁺ of a linear transformation F is extended to non-Euclidean norms. The distance from F to the set of linear transformations G of lower rank (in the sense of the operator norm ∥F - G∥) is c/∥F⁺∥, where c = 1 if the range of F fills its space, and 1 ≤ c < Q otherwise. The norms on both domain and range spaces have Q = 1 if and only if (F⁺)⁺ = F for every F. This condition is also sufficient to prove that we have (F⁺)^H = (F^H)⁺, where the latter pseudo-inverse is taken using dual norms.

In all results, the real and complex cases are handled in a completely parallel fashion.

Optimal guidance of low-thrust interplanetary space vehicles

The low-thrust guidance problem is defined as the minimum terminal variance (MTV) control of a space vehicle subjected to random perturbations of its trajectory. To accomplish this control task, only bounded thrust level and thrust angle deviations are allowed, and these must be calculated based solely on the information gained from noisy, partial observations of the state. In order to establish the validity of various approximations, the problem is first investigated under the idealized conditions of perfect state information and negligible dynamic errors. To check each approximate model, an algorithm is developed to facilitate the computation of the open loop trajectories for the nonlinear bang-bang system. Using the results of this phase in conjunction with the Ornstein-Uhlenbeck process as a model for the random inputs to the system, the MTV guidance problem is reformulated as a stochastic, bang-bang, optimal control problem. Since a complete analytic solution seems to be unattainable, asymptotic solutions are developed by numerical methods. However, it is shown analytically that a Kalman filter in cascade with an appropriate nonlinear MTV controller is an optimal configuration. The resulting system is simulated using the Monte Carlo technique and is compared to other guidance schemes of current interest.

Hizkuntzaren sustrai biologikoen inguruan

[EUS] Hizkuntzaren sustrai biologikoen ikerketak aurrerapausu handiak egin ditu azken urteotan. Ikerketa hau alorrartekoa da nahitaez, eta hizkuntzalaritza, psikologia, neurozientzia eta genetikaren arteko bilbatura batek osatzen du «biohizkuntzalaritza» eta hizkuntzaren neurokognizioa itxuratzea xede duen eremu berri hau. Artikulu honetan ezagutza eremu honen hastapeneko itxurapen bat eskainzen da, hizkuntzaren genetikan eta neurokognizioan azken urteotan egin diren zenbait urrats aurkeztuaz.

IPCC WGII Fifth Assessment Report (AR5): Expanding the solution space for adaptation

6 p.

Advancing EDL technologies for future space missions : from ground testing facilities to ablative heatshields

Motivated by recent MSL results where the ablation rate of the PICA heatshield was over-predicted, and staying true to the objectives outlined in the NASA Space Technology Roadmaps and Priorities report, this work focuses on advancing EDL technologies for future space missions.

Due to the difficulties in performing flight tests in the hypervelocity regime, a new ground testing facility called the vertical expansion tunnel is proposed. The adverse effects from secondary diaphragm rupture in an expansion tunnel may be reduced or eliminated by orienting the tunnel vertically, matching the test gas pressure and the accelerator gas pressure, and initially separating the test gas from the accelerator gas by density stratification. If some sacrifice of the reservoir conditions can be made, the VET can be utilized in hypervelocity ground testing, without the problems associated with secondary diaphragm rupture.

The performance of different constraints for the Rate-Controlled Constrained-Equilibrium (RCCE) method is investigated in the context of modeling reacting flows characteristic to ground testing facilities, and re-entry conditions. The effectiveness of different constraints are isolated, and new constraints previously unmentioned in the literature are introduced. Three main benefits from the RCCE method were determined: 1) the reduction in number of equations that need to be solved to model a reacting flow; 2) the reduction in stiffness of the system of equations needed to be solved; and 3) the ability to tabulate chemical properties as a function of a constraint once, prior to running a simulation, along with the ability to use the same table for multiple simulations.

Finally, published physical properties of PICA are compiled, and the composition of the pyrolysis gases that form at high temperatures internal to a heatshield is investigated. A necessary link between the composition of the solid resin, and the composition of the pyrolysis gases created is provided. This link, combined with a detailed investigation into a reacting pyrolysis gas mixture, allows a much needed consistent, and thorough description of many of the physical phenomena occurring in a PICA heatshield, and their implications, to be presented.

Through the use of computational fluid mechanics and computational chemistry methods, significant contributions have been made to advancing ground testing facilities, computational methods for reacting flows, and ablation modeling.

Comportamento de bugios (Alouatta clamitans Cabrera, 1940) na Ilha Grande, RJ

Alouatta clamitans é uma espécie endêmica da Mata Atlântica, bioma que vem sendo continuamente reduzido, o que torna de extrema urgência o conhecimento sobre a espécie. No Estado do Rio de Janeiro, sua área de ocorrência abrange a região da Ilha Grande, município de Angra dos Reis. A Ilha Grande possui uma extensa área de preservação, o Parque Estadual da Ilha Grande, que atua na conservação de cerca de 62,5% da sua extensão. O isolamento das espécies em ilhas pode provocar o desenvolvimento de características morfológicas e comportamentais diferentes das espécies do continente. No entanto, não existem trabalhos sistematizados sobre a ecologia e o comportamento da espécie no local. Este estudo objetivou analisar aspectos do comportamento de Alouatta clamitans na Ilha Grande, contribuindo para uma melhor compreensão sobre a biologia da espécie. Durante nove meses foram registrados dados de composição social e comportamento de grupos da espécie através da amostragem por varredura instantânea e todas as ocorrências. Observou-se que o tamanho médio dos grupos foi de cinco indivíduos e a composição social por grupo foi representada por um a dois machos adultos, uma a três fêmeas adultas e imaturos de diferentes classes etárias, com predominância de grupos unimacho. Em média, os grupos eram compostos por 22% de machos adultos, 38% de fêmeas adultas, 4% de machos subadultos, 27% de juvenis e 9% de infantes. O comportamento mais observado foi o repouso (45,2%), seguido da alimentação (28%), movimentação (21,7%) e comportamento social (5,1%), e dentre os comportamentos sociais, o mais exibido foi a vocalização (45,8%), seguido dos comportamentos de catação (33,7%), agonístico (7,9%), brincadeira (5,8%), marcação (4,2%) e comportamento sexual (2,6%). Não foram encontradas diferenças estatisticamente significativas nestas atividades entre os períodos seco e chuvoso. As vocalizações foram predominantemente emitidas por machos e adultos e estiveram relacionadas ao encontro de grupos. O comportamento de catação teve as fêmeas adultas como principais iniciadoras e os machos adultos, principais receptores, sendo realizado durante o comportamento de repouso, após a cópula, após e durante encontro de grupos e após perseguições. Os comportamentos agonísticos tiveram relação com o encontro de grupos em 40% dos registros e em 33,3% destes ocorreu entre fêmeas e pareceu estar associado à disputa por alimento e espaço, mas não houve registros de agressão física. O comportamento de marcação envolveu a utilização da garganta e das costas e esteve relacionado com encontros inter-grupais e com a ocorrência de chuvas. Cinco cópulas foram registradas no período de estudo nos meses de setembro, outubro e fevereiro e tiveram duração menor que um minuto. Nos encontros com primatas de outras espécies, os bugios pareceram neutros em relação aos estímulos. Os dados obtidos sobre a composição dos grupos, padrão de atividades e comportamentos sociais observados na Ilha Grande, de maneira geral, mostraram-se semelhantes aos resultados obtidos em outros trabalhos sobre a espécie e o gênero, de maneira que podemos concluir que os grupos, mesmo residentes em ilha, não demonstraram modificações comportamentais significativas que possam diferenciar-lhes de populações estudadas no continente.

Space-charge-limited current in fast neutron irradiated silicon

DC and transient measurements of space-charge-limited currents through alloyed and symmetrical n^+ν n^+ structures made of nominally 75 kΩcm ν-type silicon are studied before and after the introduction of defects by 14 MeV neutron radiation. In the transient measurements, the current response to a large turn-on voltage step is analyzed. Right after the voltage step is applied, the current transient reaches a value which we shall call "initial current" value. At longer times, the transient current decays from the initial current value if traps are present.

Before the irradiation, the initial current density-voltage characteristics J(V) agree quantitatively with the theory of trap-free space-charge-limited current in solids. We obtain for the electron mobility a temperature dependence which indicates that scattering due to impurities is weak. This is expected for the high purity silicon used. The drift velocity-field relationships for electrons at room temperature and 77°K, derived from the initial current density-voltage characteristics, are shown to fit the relationships obtained with other methods by other workers. The transient current response for t > 0 remains practically constant at the initial value, thus indicating negligible trapping.

Measurement of the initial (trap-free) current density-voltage characteristics after the irradiation indicates that the drift velocity-field relationship of electrons in silicon is affected by the radiation only at low temperature in the low field range. The effect is not sufficiently pronounced to be readily analyzed and no formal description of it is offered. In the transient response after irradiation for t > 0, the current decays from its initial value, thus revealing the presence of traps. To study these traps, in addition to transient measurements, the DC current characteristics were measured and shown to follow the theory of trap-dominated space-charge-limited current in solids. This theory was applied to a model consisting of two discrete levels in the forbidden band gap. Calculations and experiments agreed and the capture cross-sections of the trapping levels were obtained. This is the first experimental case known to us through which the flow of space-charge-limited current is so simply representable.

These results demonstrate the sensitivity of space-charge-limited current flow as a tool to detect traps and changes in the drift velocity-field relationship of carriers caused by radiation. They also establish that devices based on the mode of space-charge-limited current flow will be affected considerably by any type of radiation capable of introducing traps. This point has generally been overlooked so far, but is obviously quite significant.

A movable-cavity cold atom space clock

We present an experimental scheme of a cold atom space clock with a movable cavity. By using a single microwave cavity, we find that the clock has a significant advantage, i.e. the longitudinal cavity phase shift is eliminated. A theoretical analysis has been carried out in terms of the relation between the atomic transition probability and the velocity of the moving cavity by taking into account the velocity distribution of cold atoms. The requirements for the microwave power and its stability for atomic pi/2 excitation at different moving velocities of the cavity lead to the determination of the proper working parameters of the rubidium clock in frequency accuracy 10(-17). Finally, the mechanical stability for the scheme is analysed and the ways of solving the possible mechanical instability of the device are proposed.

(Report of the) Institute of Marine Biology and Oceanography, Fourah Bay College, University of Sierra Leone

Details are given of the Institute and its activities, in particular the research projects being undertaken. These include studies on the marine molluscs of Sierra Leone, the cockle fishery, a preliminary investigation on the fouling organisms affecting the raft-cultured oyster populations, larval oyster ecology in relation to oyster culture, preliminary studies on the reproductive cycle of the mangrove oyster (Crassostrea tulipa), and catch composition of fishes taken by beach-seines at Lumley (Freetown). Records of the west African manatee (Trichechus senegalensis) are noted.

Part I - The radiation of elastic waves from a spherical cavity in a half space. Part II - Precision determination of focal depths and epicenters of earthquakes.

Part I: The dynamic response of an elastic half space to an explosion in a buried spherical cavity is investigated by two methods. The first is implicit, and the final expressions for the displacements at the free surface are given as a series of spherical wave functions whose coefficients are solutions of an infinite set of linear equations. The second method is based on Schwarz's technique to solve boundary value problems, and leads to an iterative solution, starting with the known expression for the point source in a half space as first term. The iterative series is transformed into a system of two integral equations, and into an equivalent set of linear equations. In this way, a dual interpretation of the physical phenomena is achieved. The systems are treated numerically and the Rayleigh wave part of the displacements is given in the frequency domain. Several comparisons with simpler cases are analyzed to show the effect of the cavity radius-depth ratio on the spectra of the displacements.

Part II: A high speed, large capacity, hypocenter location program has been written for an IBM 7094 computer. Important modifications to the standard method of least squares have been incorporated in it. Among them are a new way to obtain the depth of shocks from the normal equations, and the computation of variable travel times for the local shocks in order to account automatically for crustal variations. The multiregional travel times, largely based upon the investigations of the United States Geological Survey, are confronted with actual traverses to test their validity.

It is shown that several crustal phases provide control enough to obtain good solutions in depth for nuclear explosions, though not all the recording stations are in the region where crustal corrections are considered. The use of the European travel times, to locate the French nuclear explosion of May 1962 in the Sahara, proved to be more adequate than previous work.

A simpler program, with manual crustal corrections, is used to process the Kern County series of aftershocks, and a clearer picture of tectonic mechanism of the White Wolf fault is obtained.

Shocks in the California region are processed automatically and statistical frequency-depth and energy depth curves are discussed in relation to the tectonics of the area.

General-domain compressible Navier-Stokes solvers exhibiting quasi-unconditional stability and high-order accuracy in space and time

This thesis presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional spatial domains. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of higher-order backward differentiation formulae (BDF) and the alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. In fact this thesis presents, for the first time in the literature, high-order time-convergence curves for Navier-Stokes solvers based on the ADI strategy---previous ADI solvers for the Navier-Stokes equations have not demonstrated orders of temporal accuracy higher than one. An extended discussion is presented in this thesis which places on a solid theoretical basis the observed quasi-unconditional stability of the methods of orders two through six. The performance of the proposed solvers is favorable. For example, a two-dimensional rough-surface configuration including boundary layer effects at Reynolds number equal to one million and Mach number 0.85 (with a well-resolved boundary layer, run up to a sufficiently long time that single vortices travel the entire spatial extent of the domain, and with spatial mesh sizes near the wall of the order of one hundred-thousandth the length of the domain) was successfully tackled in a relatively short (approximately thirty-hour) single-core run; for such discretizations an explicit solver would require truly prohibitive computing times. As demonstrated via a variety of numerical experiments in two- and three-dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, useful stability properties, limited dispersion, and high parallel efficiency.

Contribution to the biology and geographical distribution of Aegagropila sauteri (Nees) Kutz. [Translation of: Gidrobiologicheskie Zhurnal, Kiev 4(3), 68-69, 1967]

Aegagropila sauteri is a peculiar green algae, the branched thalli of which, according to the amount of growth, forms velvety spheres of a diameter of 3-4, sometimes to 5-6 cm. and bigger. Investigators attribute it to a special genus of green algae. The authors examine Aegagropila sauteri in Lake Markakol (Kazakhstan).