Tsien's method for generating non-Keplerian trajectories. Part 2: The question of thrust to orbit a sphere and the restricted three-body problem

Tsien's method is extended to treat the orbital motion of a body undergoing accelerations and decelerations. A generalized solution is discussed for the generalized case where a body undergoes azimuthal and radial thrust and the problem is further simplified for azimuthal thrust alone. Judicious selection of thrust could generate either an elliptic or hyperbolic trajectory. This is unexpected especially when the body has only enough energy for a lower state trajectory. The methodology is extended treating the problem of vehicle thrust for orbiting a sphere and vehicle thrust within the classical restricted three-body problem. Results for the latter situation can produce hyperbolic trajectories through eigen value decomposition. Since eigen values for no-thrust can be imaginary, thrust can generate real eigen values to describe hyperbolic trajectories. Keplerian dynamics appears to represent but a small subset of a much larger non-Keplerian domain especially when thrust effects are considered. The need for high thrust long duration space-based propulsion systems for changing a trajectory's canonical form is clearly demonstrated

Max-stable sketches: estimation of Lp-norms, dominance norms and point queries for non-negative signals

Max-stable random sketches can be computed efficiently on fast streaming positive data sets by using only sequential access to the data. They can be used to answer point and Lp-norm queries for the signal. There is an intriguing connection between the so-called p-stable (or sum-stable) and the max-stable sketches. Rigorous performance guarantees through error-probability estimates are derived and the algorithmic implementation is discussed

Experimental investigations of low-energy (4 to 40 eV) collisions of O(-)(P2) ions and O(P3) atoms with surfaces

Using a newly-developed, magnetically confined source, low-energy, ground state oxygen negative ions and neutral atoms are generated. The energy range is variable, and atom and neutrals have been generated at energies varying from 2 eV to 40 eV and higher. It was found that the interaction of these low-energy species with a solid magnesium fluoride target leads to optical emissions in the (at least) visible and infrared regions of the spectrum. Researchers describe y details of the photodetachment source, and present spectra of the neutral and ion glows in the wavelength range 250 to 850 nm (for O(-)) and 600 to 850 nm (for O), and discuss the variability of the emissions for incident energies between 4 and 40 eV

Karakteristik Pengeringan Bawang Merah (Alium Ascalonicum. L) Menggunakan Alat Pengering ERK (Greenhouse)

Aim of this research was to determine drying rate and moisture content changes on Greenhouse (ERK) Dryer. Result was showed using graphic by analyzing drying rate characteristics of Greenhouse Dryer. Data analysis was performed using mathematical approach that solved using Microsoft Excel. Method used in this research was experimental method. Based on the results, onion drying using ERK showed decreasing rate of weight changes. Sample shrinkage was 25.7% with average moisture content 60.06% for sample weight 0.187 kg. Average humidity (RH) was lower than ambient humidity on the range of 63.4% to 83.0%. Characteristics of onion drying was the decreasing rate of moisture content of 0.17% with equation MR: y = -0,017 + 1,061, R2 is 0,985. Value of Ln MR at first day was y = -0,019x and decreasing rate of moisture content 0,19%. Whereas decreasing rate at second, third and fourth day were 0,008%, 0,11% and 0,002% respectively for 1 hour interval period. Keywords: red onion, Greenhouse effect, drying rate, dryer &nbsp

Asymptotic behavior of the quadratic variation of the sum of two Hermite processes of consecutive orders

Hermite processes are self--similar processes with stationary increments which appear as limits of normalized sums of random variables with long range dependence. The Hermite process of order $1$ is fractional Brownian motion and the Hermite process of order $2$ is the Rosenblatt process. We consider here the sum of two Hermite processes of order $q\geq 1$ and $q+1$ and of different Hurst parameters. We then study its quadratic variations at different scales. This is akin to a wavelet decomposition. We study both the cases where the Hermite processes are dependent and where they are independent. In the dependent case, we show that the quadratic variation, suitably normalized, converges either to a normal or to a Rosenblatt distribution, whatever the order of the original Hermite processes

The Trace Problem for Toeplitz Matrices and Operators and its Impact in Probability

The trace approximation problem for Toeplitz matrices and its applications to stationary processes dates back to the classic book by Grenander and Szeg\"o, "Toeplitz forms and their applications". It has then been extensively studied in the literature. In this paper we provide a survey and unified treatment of the trace approximation problem both for Toeplitz matrices and for operators and describe applications to discrete- and continuous-time stationary processes. The trace approximation problem serves indeed as a tool to study many probabilistic and statistical topics for stationary models. These include central and non-central limit theorems and large deviations of Toeplitz type random quadratic functionals, parametric and nonparametric estimation, prediction of the future value based on the observed past of the process, etc. We review and summarize the known results concerning the trace approximation problem, prove some new results, and provide a number of applications to discrete- and continuous-time stationary time series models with various types of memory structures, such as long memory, anti-persistent and short memory