Uniform G-Convexity for Vector-Valued Lp Spaces

2000 Mathematics Subject Classification: 46B20.

A New Hereditarily l^2 Banach Space

2000 Mathematics Subject Classification: 46B20, 46B26.

Quantization of the Inhomogeneous Bianchi I model:quasi-Heisenberg picture

The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so called quasi-Heisenberg) equations describing explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.

Space division multiple access for wireless sensor networks

This dissertation proposed a self-organizing medium access control protocol (MAC) for wireless sensor networks (WSNs). The proposed MAC protocol, space division multiple access (SDMA), relies on sensor node position information and provides sensor nodes access to the wireless channel based on their spatial locations. SDMA divides a geographical area into space divisions, where there is one-to-one map between the space divisions and the time slots. Therefore, the MAC protocol requirement is the sensor node information of its position and a prior knowledge of the one-to-one mapping function. The scheme is scalable, self-maintaining, and self-starting. It provides collision-free access to the wireless channel for the sensor nodes thereby, guarantees delay-bounded communication in real time for delay sensitive applications. This work was divided into two parts: the first part involved the design of the mapping function to map the space divisions to the time slots. The mapping function is based on a uniform Latin square. A Uniform Latin square of order k = m 2 is an k x k square matrix that consists of k symbols from 0 to k-1 such that no symbol appears more than once in any row, in any column, or in any m x in area of main subsquares. The uniqueness of each symbol in the main subsquares presents very attractive characteristic in applying a uniform Latin square to time slot allocation problem in WSNs. The second part of this research involved designing a GPS free positioning system for position information. The system is called time and power based localization scheme (TPLS). TPLS is based on time difference of arrival (TDoA) and received signal strength (RSS) using radio frequency and ultrasonic signals to measure and detect the range differences from a sensor node to three anchor nodes. TPLS requires low computation overhead and no time synchronization, as the location estimation algorithm involved only a simple algebraic operation.

Space time coding for polynomial phase modulated signals

Polynomial phase modulated (PPM) signals have been shown to provide improved error rate performance with respect to conventional modulation formats under additive white Gaussian noise and fading channels in single-input single-output (SISO) communication systems. In this dissertation, systems with two and four transmit antennas using PPM signals were presented. In both cases we employed full-rate space-time block codes in order to take advantage of the multipath channel. For two transmit antennas, we used the orthogonal space-time block code (OSTBC) proposed by Alamouti and performed symbol-wise decoding by estimating the phase coefficients of the PPM signal using three different methods: maximum-likelihood (ML), sub-optimal ML (S-ML) and the high-order ambiguity function (HAF). In the case of four transmit antennas, we used the full-rate quasi-OSTBC (QOSTBC) proposed by Jafarkhani. However, in order to ensure the best error rate performance, PPM signals were selected such as to maximize the QOSTBC’s minimum coding gain distance (CGD). Since this method does not always provide a unique solution, an additional criterion known as maximum channel interference coefficient (CIC) was proposed. Through Monte Carlo simulations it was shown that by using QOSTBCs along with the properly selected PPM constellations based on the CGD and CIC criteria, full diversity in flat fading channels and thus, low BER at high signal-to-noise ratios (SNR) can be ensured. Lastly, the performance of symbol-wise decoding for QOSTBCs was evaluated. In this case a quasi zero-forcing method was used to decouple the received signal and it was shown that although this technique reduces the decoding complexity of the system, there is a penalty to be paid in terms of error rate performance at high SNRs.

Locally quasi-nilpotent elementary operators

Let A be a unital dense algebra of linear mappings on a complex vector space X. Let φ = Σⁿ _i=1 M_ai,_bi be a locally quasi-nilpotent elementary operator of length n on A. We show that, if {a1, . . . , an} is locally linearly independent, then the local dimension of V (φ) = span{b_ia_j : 1 ≤ i, j ≤ n} is at most n(n−1) 2 . If ldim V (φ) = n(n−1) 2 , then there exists a representation of φ as φ = Σⁿ _i=1 M_ui,_vi with v_iu_j = 0 for i ≥ j. Moreover, we give a complete characterization of locally quasinilpotent elementary operators of length 3.

Expanding the Design Space: Forging the Transition from 3D Printing to Additive Manufacturing

Thesis (Master's)--University of Washington, 2016-08

Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(\Rn)$, $1 \leq p < \infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(\Rn)$, $0spaces.

Variable Recruitment in Bundles of Miniature Pneumatic Artificial Muscles and Space Qualified Pneumatic Artificial Muscles

The natural compliance and force generation properties of pneumatic artificial muscles (PAMs) allow them to operate like human muscles in anthropomorphic robotic manipulators. Traditionally, manipulators use a single PAM or multiple PAMs actuated in unison in place of a human muscle. However, these manipulators experience efficiency losses when operated outside their target performance ranges. The unidirectional actuation behavior of a miniature PAM bundle and bidirectional actuation behavior of an antagonistic pair of miniature PAM bundles are characterized and modeled. The results are used to motivate the application of a variable recruitment control strategy to a parallel bundle of miniature PAMs as an attempt to mimic the selective recruitment of motor units in a human muscle to improve the operating efficiency of the actuator. Additionally, the fabrication and quasi-static testing results for PAMs assembled from candidate space qualified bladder and braided sleeve materials for use in space robotics are assessed.

Mackey topology on locally convex spaces and on locally quasi-convex groups. Similarities and historical remarks

A counterpart of the Mackey–Arens Theorem for the class of locally quasi-convex topological Abelian groups (LQC-groups) was initiated in Chasco et al. (Stud Math 132(3):257–284, 1999). Several authors have been interested in the problems posed there and have done clarifying contributions, although the main question of that source remains open. Some differences between the Mackey Theory for locally convex spaces and for locally quasi-convex groups, stem from the following fact: The supremum of all compatible locally quasi-convex topologies for a topological abelian group G may not coincide with the topology of uniform convergence on the weak quasi-convex compact subsets of the dual groupG∧. Thus, a substantial part of the classical Mackey–Arens Theorem cannot be generalized to LQC-groups. Furthermore, the mentioned fact gives rise to a grading in the property of “being a Mackey group”, as defined and thoroughly studied in Díaz Nieto and Martín-Peinador (Proceedings in Mathematics and Statistics 80:119–144, 2014). At present it is not known—and this is the main open question—if the supremum of all the compatible locally quasi-convex topologies on a topological group is in fact a compatible topology. In the present paper we do a sort of historical review on the Mackey Theory, and we compare it in the two settings of locally convex spaces and of locally quasi-convex groups. We point out some general questions which are still open, under the name of Problems.

Two near-optimal layouts for trusslike bridge structures bearing uniform weight between supports

Although the primary objective on designing a structure is to support the external loads, the achievement of an optimal layout that reduces all costs associated with the structure is an aspect of increasing interest. The problem of finding the optimal layout for bridgelike structures subjected to a uniform load is considered. The problem is formulated following a theory on economy of frame structures, using the stress volume as the objective function and including the selection of appropriate values for statically indeterminate reactions. It is solved in a function space of finite dimension instead of using a general variational approach, obtaining near-optimal solutions. The results obtained with this profitable strategy are very close to the best layouts known to date, with differences of less than 2% for the stress volume, but with a simpler layout that can be recognized in some real bridges. This strategy could be a guide to preliminary design of bridges subject to a wide class of costs.

Hilbert Space Valued Signal Plus Noise Models: Analysis of Structural Breaks under High Dimensionality and Temporal Dependence

This thesis is concerned with change point analysis for time series, i.e. with detection of structural breaks in time-ordered, random data. This long-standing research field regained popularity over the last few years and is still undergoing, as statistical analysis in general, a transformation to high-dimensional problems. We focus on the fundamental »change in the mean« problem and provide extensions of the classical non-parametric Darling-Erdős-type cumulative sum (CUSUM) testing and estimation theory within highdimensional Hilbert space settings. In the first part we contribute to (long run) principal component based testing methods for Hilbert space valued time series under a rather broad (abrupt, epidemic, gradual, multiple) change setting and under dependence. For the dependence structure we consider either traditional m-dependence assumptions or more recently developed m-approximability conditions which cover, e.g., MA, AR and ARCH models. We derive Gumbel and Brownian bridge type approximations of the distribution of the test statistic under the null hypothesis of no change and consistency conditions under the alternative. A new formulation of the test statistic using projections on subspaces allows us to simplify the standard proof techniques and to weaken common assumptions on the covariance structure. Furthermore, we propose to adjust the principal components by an implicit estimation of a (possible) change direction. This approach adds flexibility to projection based methods, weakens typical technical conditions and provides better consistency properties under the alternative. In the second part we contribute to estimation methods for common changes in the means of panels of Hilbert space valued time series. We analyze weighted CUSUM estimates within a recently proposed »high-dimensional low sample size (HDLSS)« framework, where the sample size is fixed but the number of panels increases. We derive sharp conditions on »pointwise asymptotic accuracy« or »uniform asymptotic accuracy« of those estimates in terms of the weighting function. Particularly, we prove that a covariance-based correction of Darling-Erdős-type CUSUM estimates is required to guarantee uniform asymptotic accuracy under moderate dependence conditions within panels and that these conditions are fulfilled, e.g., by any MA(1) time series. As a counterexample we show that for AR(1) time series, close to the non-stationary case, the dependence is too strong and uniform asymptotic accuracy cannot be ensured. Finally, we conduct simulations to demonstrate that our results are practically applicable and that our methodological suggestions are advantageous.