The design of multi-dimensional access methods is difficult as compared to those of one-dimensional case because of no total ordering that preserves spatial locality. One way is to look for the total order that preserves spatial proximity at least to some extent. A space-filling curve is a continuous path which passes through every point in a space once so giving a one-to-one correspondence between the coordinates of the points and the 1D-sequence numbers of points on the curve. The Hilbert curve is a famous space filling curve, since it has been shown to have strong locality preserving properties; that is, it is the best space-filling curve in minimizing the number of clusters. Hence, it has been extensively used to maintain spatial locality of multidimensional data in a wide variety of applications. A window query is an important query operation in spatial (image) databases. Given a Hilbert curve, a window query reports its corresponding orders without the need to decode all the points inside this window into the corresponding Hilbert orders. Chung et al. have proposed an algorithm for decomposing a window into the corresponding Hilbert orders. However, the Hilbert curve requires that the region is of size 2^k x 2^k, where k∈N. The intuitive method such as Chung et al.¡¦s algorithm is to directly use Hilbert curves in the decomposed areas and then connect them. They must generate a sequence of the scanned quadrants additionally before encoding and decoding the Hilbert order of one pixel and scan this sequence one time while encoding and decoding one pixel. In this dissertation, on the design of methods for window queries on a Hilbert curve, we propose an efficient algorithm, named as Quad-Splitting, for decomposing a window into the corresponding Hilbert orders on a Hilbert curve without individual sorting and merging steps. The proposed algorithm does not perform individual sorting and merging steps which are needed in Chung et al.¡¦s algorithm. From our experimental results, we show that the Quad-Splitting algorithm outperforms Chung et al.¡¦s algorithm. On the design of the methods for generating the Hilbert curve of an arbitrary-sized image, we propose approximately even partition approach to generate a pseudo Hilbert curve of an arbitrary-sized image. From our experimental results, we show that our proposed pseudo Hilbert curve preserves the similar strong locality property to the Hilbert curve. On the design of the methods for coding Hilbert curve of an arbitrary-sized image, we propose encoding and decoding algorithms. From our experimental results, we show that our encoding and decoding algorithms outperform the Chung et al.¡¦s algorithms.

¡@¡@Due to wireless communication technologies, positioning technologies, and mobile computing develop quickly, mobile services are becoming practical and important on big spatiotemporal databases management. Mobile service users move only inside a spatial space, e:g: a country. They often issue the K Nearest Neighbor (kNN) query to obtain data objects reachable through the spatial database. The challenge problem of mobile services is how to efficiently answer the data objects which users interest to the corresponding mobile users. One type of kNN query problems is the order-sensitive moving kNN (order-sensitive MkNN) query problem. In the order-sensitive MkNN query problem, the query point is dynamic and unpredictable, the kNN answers should be responded in real time and sorted by the distance in the ascending order. Therefore, how to respond the kNN answers effectively, incrementally and correctly is an important issue. Nutanong et al: have proposed the V*-kNN algorithm to process the order-sensitive MkNN query. The V*-kNN algorithm uses their the V*-diagram algorithm to generate the safe region. It also uses the Incremental Rank Updates algorithm (IRU) to handle the events while the query point passing the bisectors or the boundary of the safe region. However, the V*-kNN algorithm uses the BF-kNN algorithm to retrieve NNs, which is non-incremental. This makes the search time increase while the density of the object increases. Moreover, they do not consider the situation that there are multiple objects at the same order, and the situation that there are multiple events happen in a single step. These situations may cause that the kNN answers are incorrect. Therefore, in this thesis, we propose the Hilbert curve-based kNN algorithm (HC-kNN) algorithm to process the ordersensitive MkNN query. The HC-kNN algorithm can handle the situation that there are multiple events happen in a single step. We also propose new data structure of the kNN answers. Next, we propose the Intersection of Perpendicular Bisectors algorithm (IPB) in order to handle order update events of the kNN answers. The IPB algorithm handles the situation which there are multiple objects at the same order. Finally, based on the Hilbert curve index, we propose the ONHC-kNN algorithm to get NNs incrementally and to generate the safe region. The safe region will not be affected while the density of the object increases. The safe region of our algorithm is larger than that of the V*-kNN algorithm. From our simulation result, we show that the HC-kNN algorithm provides better performance than the V*-kNN algorithm.

Nan Wan is a half-closed embayment in the most southern part of Taiwan. While facing the Luzon Strait, it also connects to the Pacific Ocean in its southeast, and is adjacent the Taiwan Strait and the South China Sea . In view of general oceanic circulation, Nan Wan Bay happens to lie to the rim of South China Sea circumfluence and Kuroshio where a variety of water mass exchange has taken place, causing saline intrusion and mixed of water. Seasonal variation and tidal fluctuations also contribute to the exchange of water masses. The Third Nuclear Power Station of Taiwan Power Company is located in Nan Wan with its thermal discharge outlet adjacent to Maobitou to the west of the bay in order to minimize the effect of warm water discharge on the local marine ecology and coral . A long-term monitoring program on water temperature and other environmental factors has been set up implemented .this research report will first describe the archives regarding the hydrology in Nan Wan in support of monitoring the process in temperature variation . Previous research efforts are found somehow unable reveal precisely the physical mechanism leading to water temperature variations in the bay, due to limited facilities, short of information or poor analytical tools. This report adopts 14 records of water temperature at the thermal outlet of the Third Nuclear Power Station for signal analysis. As to non-linear and unstable data analysis, it is based on the Hilbert-Huang Transform. HHT includes Empirical Mode Decomposition, EMD which could decompose the raw data into numerous Intrinsic Mode Function, IMF. It is allowed to comprehend the main causes for the rising and dropping of water temperature based on the variation of spectroscopy by transferring through Hilbert and analyzing via IMF. Furthermore, the characteristic of each quantity could be developed according to the quantities acquired from the former method of HHT. The analytical report of water temperature covers 14 records dating from 1999 to 2003. In light of the analytical report, tide and wind account for the main cause of the temperature variation in waters while demanding information to ensure whether it is influenced by other factors like internal waves, water masses or landforms, etc. In addition, the report compares the difference in the same of data between FFT and HHT and moreover concludes the advantages and disadvantages as reference for researches.

In general we know that the fixed point locus of a 1-dimensional additive linear algebraic group,G_{a}, action over a complete nonsingular variety is connected. In thesis, we explicitly identify a subset of the G_{a}-fixed locus of the punctual Hilbert scheme of the d points,Hilb^{d}(P^{2} / 0),in P^{2}. In particular we give an other proof of the fact that Hilb^{d}(P^{2} / 0) is connected.

Modern data collection methods are now frequently returning observations that should be viewed as the result of digitized recording or sampling from stochastic processes rather than vectors of finite length. In spite of great demands, only a few classification methodologies for such data have been suggested and supporting theory is quite limited. The focus of this dissertation is on discrimination and classification in this infinite dimensional setting. The methodology and theory we develop are based on the abstract canonical correlation concept of Eubank and Hsing (2005), and motivated by the fact that Fisher's discriminant analysis method is intimately tied to canonical correlation analysis. Specifically, we have developed a theoretical framework for discrimination and classification of sample paths from stochastic processes through use of the Loeve-Parzen isomorphism that connects a second order process to the reproducing kernel Hilbert space generated by its covariance kernel. This approach provides a seamless transition between the finite and infinite dimensional settings and lends itself well to computation via smoothing and regularization. In addition, we have developed a new computational procedure and illustrated it with simulated data and Canadian weather data.

In this paper, we establish several strong convergence results of general approximate proximal algorithm and general Bregman-function-based approximate proximal algorithm for solving the generalized variational inequality problem with pseudomonotone multifunction.

No description available.

La réalisation de Hodge du polylogarithme d'un schéma abélien complexe de dimension g est une (2g-1)-extension de modules de Hodge. Lorsque le schéma abélien est principalement polarisé, on en donne une description au niveau topologique. Pour cela, on utilise des courants de type "courants de Green" introduits par Levin. On applique alors ce résultat aux familles modulaires de Hilbert-Blumenthal pour montrer que certaines classes d'Eisenstein (construites à partir du polylogarithme et d'une section de torsion) dégénèrent, en l'infini, en une valeur spéciale de fonction L du corps de nombres totalement réel sous-jacent. On en déduit deux autres résultats : une version partielle du théorème de Klingen-Siegel et un résultat de non nullité pour certaines de ces classes d'Eisenstein. Ainsi, on montre que pour tout entier g plus grand que 2, il existe un schéma abélien complexe de dimension g tel que certaines de ses classes d'Eisenstein soient non nulles.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 136-138). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 136-138). Also available on the Internet.