Adaptive Filtering for Large Space Structures: A Closed-Form Solution

In a previous paper Schaechter proposes using an extended Kalman filter to estimate adaptively the (slowly varying) frequencies and damping ratios of a large space structure. The time varying gains for estimating the frequencies and damping ratios can be determined in closed form so it is not necessary to integrate the matrix Riccati equations. After certain approximations, the time varying adaptive gain can be written as the product of a constant matrix times a matrix derived from the components of the estimated state vector. This is an important savings of computer resources and allows the adaptive filter to be implemented with approximately the same effort as the nonadaptive filter. The success of this new approach for adaptive filtering was demonstrated using synthetic data from a two mode system

Flow Equations for Uplifting Half-Flat to Spin(7) Manifolds

In this short supplement to [1], we discuss the uplift of half-flat six-folds to Spin(7) eight-folds by fibration of the former over a product of two intervals. We show that the same can be done in two ways - one, such that the required Spin(7) eight-fold is a double G_2 seven-fold fibration over an interval, the G_2 seven-fold itself being the half-flat six-fold fibered over the other interval, and second, by simply considering the fibration of the half-flat six-fold over a product of two intervals. The flow equations one gets are an obvious generalization of the Hitchin's flow equations (to obtain seven-folds of G_2 holonomy from half-flat six-folds [2]). We explicitly show the uplift of the Iwasawa using both methods, thereby proposing the form of the new Spin(7) metrics. We give a plausibility argument ruling out the uplift of the Iwasawa manifold to a Spin(7) eight fold at the "edge", using the second method. For $Spin(7)$ eight-folds of the type $X_7\times S^1$, $X_7$ being a seven-fold of SU(3) structure, we motivate the possibility of including elliptic functions into the "shape deformation" functions of seven-folds of SU(3) structure of [1] via some connections between elliptic functions, the Heisenberg group, theta functions, the already known $D7$-brane metric [3] and hyper-K\"{a}hler metrics obtained in twistor spaces by deformations of Atiyah-Hitchin manifolds by a Legendre transform in [4].Comment: 12 pages, LaTeX; v3: (JMP) journal version which includes clarifying remarks related to connection between Spin(7)-folds and SU(3)structur

Transformation toughened ceramics for the heavy duty diesel engine technology program

The objective of this program is to develop an advanced high temperature oxide structural ceramic for application to the heavy duty diesel engine. The approach is to employ transformation toughening by additions of ZrO.5HfO.5O2 solid solution to the oxide ceramics, mullite (2Al2O3S2SiO2) and alumina (Al2O3). The study is planned for three phases, each 12 months in duration. This report covers Phase 1. During this period, processing techniques were developed to incorporate the ZrO.5HfO.5O2 solid solution in the matrices while retaining the necessary metastable tetragonal phase. Modulus of rupture and of elasticity, coefficient of thermal expansion, fracture toughness by indent technique and thermal diffusivity of representative specimens were measured. In Phase 2, the process will be improved to provide higher mechanical strength and to define the techniques for scale up to component size. In Phase 3, full scale component prototypes will be fabri-]cated

Theory of minimum effort control

Optimum control theory formulations for solving problems in optimum guidance for interplanetary manned space flight mission

Quantum Mechanics in Non-Inertial Frames with a Multi-Temporal Quantization Scheme: II) Non-Relativistic Particles

The non-relativistic version of the multi-temporal quantization scheme of relativistic particles in a family of non-inertial frames (see hep-th/0502194) is defined. At the classical level the description of a family of non-rigid non-inertial frames, containing the standard rigidly linear accelereted and rotating ones, is given in the framework of parametrized Galilei theories. Then the multi-temporal quantization, in which the gauge variables, describing the non-inertial effects, are not quantized but considered as c-number generalized times, is applied to non relativistic particles. It is shown that with a suitable ordering there is unitary evolution in all times and that, after the separation of center of mass, it is still possible to identify the inertial bound states. The few existing results of quantization in rigid non-inertial frames are recovered as special cases

Dynamics of the Tippe Top -- properties of numerical solutions versus the dynamical equations

We study the relationship between numerical solutions for inverting Tippe Top and the structure of the dynamical equations. The numerical solutions confirm oscillatory behaviour of the inclination angle $\theta(t)$ for the symmetry axis of the Tippe Top. They also reveal further fine features of the dynamics of inverting solutions defining the time of inversion. These features are partially understood on the basis of the underlying dynamical equations

Superlattice with hot electron injection: an approach to a Bloch oscillator

A semiconductor superlattice with hot electron injection into the miniband is considered. The injection changes the stationary distribution function and results in a qualitative change of the frequency behaviour of the differential conductivity. In the regime with Bloch oscillating electrons and injection into the upper part of the miniband the region of negative differential conductivity is shifted from low frequencies to higher frequencies. We find that the dc differential conductivity can be made positive and thus the domain instability can be suppressed. At the same time the high-frequency differential conductivity is negative above the Bloch frequency. This opens a new way to make a Bloch oscillator operating at THz frequencies.Comment: RevTeX, 8 pages, 2 figures, to be published in Phys. Rev. B, 15 Januar 200

Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in 2+1 dimensions

Riemann theta functions are used to construct one-periodic and two-periodic wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The basis for the involved solution analysis is the Hirota bilinear formulation, and the particular dependence of the equations on independent variables guarantees the existence of one-periodic and two-periodic wave solutions involving an arbitrary purely imaginary Riemann matrix. The resulting theory is applied to two nonlinear equations possessing Hirota bilinear forms: $u_t+u_{xxy}-3uu_y-3u_xv=0$ and $u_t+u_{xxxxy}-(5u_{xx}v+10u_{xy}u-15u^2v)_x=0$ where $v_x=u_y$, thereby yielding their one-periodic and two-periodic wave solutions describing one dimensional propagation of waves

Ursinus College Bulletin Vol. 5, No. 10

A digitized copy of the July 1889 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1051/thumbnail.jp