Representable Banach Spaces and Uniformly Gateaux-Smooth Norms

It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.

Regular Averaging and Regular Extension Operators in Weakly Compact Subsets of Hilbert Spaces

2000 Mathematics Subject Classification: Primary 46E15, 54C55; Secondary 28B20.

基于模糊集理论的二维线性鉴别分析新方法

二维线性鉴别分析（2DLDA）是一种直接基于矩阵的特征提取方法，跳过传统的基于Fisher鉴别准则的线性鉴别分析方法中必须先将二维矩阵转化成一维矢量的过程，有效地提高了特征提取速度且避免了小样本问题，其识别率优于传统的Fisherface方法。结合模糊集理论，提出了一种新的2DLDA算法——模糊2DLDA（FIDLDA）算法。首先采用FKNN算法得到相应的样本分布信息，并按其对最后得到的特征向量所作的贡献融入到特征抽取过程中，得到有效的样本特征向量集。实验表明，F2DLDA算法的性能优于传统的2DLDA算法和Fisherface方法。

Realisation of a Target Classifier For Noise Sources in the Ocean

This thesis addresses one of the emerging topics in Sonar Signal Processing.,viz.the implementation of a target classifier for the noise sources in the ocean, as the operator assisted classification turns out to be tedious,laborious and time consuming.In the work reported in this thesis,various judiciously chosen components of the feature vector are used for realizing the newly proposed Hierarchical Target Trimming Model.The performance of the proposed classifier has been compared with the Euclidean distance and Fuzzy K-Nearest Neighbour Model classifiers and is found to have better success rates.The procedures for generating the Target Feature Record or the Feature vector from the spectral,cepstral and bispectral features have also been suggested.The Feature vector ,so generated from the noise data waveform is compared with the feature vectors available in the knowledge base and the most matching pattern is identified,for the purpose of target classification.In an attempt to improve the success rate of the Feature Vector based classifier,the proposed system has been augmented with the HMM based Classifier.Institutions where both the classifier decisions disagree,a contention resolving mechanism built around the DUET algorithm has been suggested.

Content Based Video Retrieval using SURF Descriptor

This paper presents a Robust Content Based Video Retrieval (CBVR) system. This system retrieves similar videos based on a local feature descriptor called SURF (Speeded Up Robust Feature). The higher dimensionality of SURF like feature descriptors causes huge storage consumption during indexing of video information. To achieve a dimensionality reduction on the SURF feature descriptor, this system employs a stochastic dimensionality reduction method and thus provides a model data for the videos. On retrieval, the model data of the test clip is classified to its similar videos using a minimum distance classifier. The performance of this system is evaluated using two different minimum distance classifiers during the retrieval stage. The experimental analyses performed on the system shows that the system has a retrieval performance of 78%. This system also analyses the performance efficiency of the low dimensional SURF descriptor.

Automatic Image Annotation Using SURF Descriptors

In recent years there is an apparent shift in research from content based image retrieval (CBIR) to automatic image annotation in order to bridge the gap between low level features and high level semantics of images. Automatic Image Annotation (AIA) techniques facilitate extraction of high level semantic concepts from images by machine learning techniques. Many AIA techniques use feature analysis as the first step to identify the objects in the image. However, the high dimensional image features make the performance of the system worse. This paper describes and evaluates an automatic image annotation framework which uses SURF descriptors to select right number of features and right features for annotation. The proposed framework uses a hybrid approach in which k-means clustering is used in the training phase and fuzzy K-NN classification in the annotation phase. The performance of the system is evaluated using standard metrics.

Aplicação do Sensoriamento Remoto e do Sistema de Informações Geográficas na Detecção de Manchas de Óleo na Região do Pólo de Exploração de Guamaré, R.N.

Objective to establish a methodology for the oil spill monitoring on the sea surface, located at the Submerged Exploration Area of the Polo Region of Guamaré, in the State of Rio Grande do Norte, using orbital images of Synthetic Aperture Radar (SAR integrated with meteoceanographycs products. This methodology was applied in the following stages: (1) the creation of a base map of the Exploration Area; (2) the processing of NOAA/AVHRR and ERS-2 images for generation of meteoceanographycs products; (3) the processing of RADARSAT-1 images for monitoring of oil spills; (4) the integration of RADARSAT-1 images with NOAA/AVHRR and ERS-2 image products; and (5) the structuring of a data base. The Integration of RADARSAT-1 image of the Potiguar Basin of day 21.05.99 with the base map of the Exploration Area of the Polo Region of Guamaré for the identification of the probable sources of the oil spots, was used successfully in the detention of the probable spot of oil detected next to the exit to the submarine emissary in the Exploration Area of the Polo Region of Guamaré. To support the integration of RADARSAT-1 images with NOAA/AVHRR and ERS-2 image products, a methodology was developed for the classification of oil spills identified by RADARSAT-1 images. For this, the following algorithms of classification not supervised were tested: K-means, Fuzzy k-means and Isodata. These algorithms are part of the PCI Geomatics software, which was used for the filtering of RADARSAT-1 images. For validation of the results, the oil spills submitted to the unsupervised classification were compared to the results of the Semivariogram Textural Classifier (STC). The mentioned classifier was developed especially for oil spill classification purposes and requires PCI software for the whole processing of RADARSAT-1 images. After all, the results of the classifications were analyzed through Visual Analysis; Calculation of Proportionality of Largeness and Analysis Statistics. Amongst the three algorithms of classifications tested, it was noted that there were no significant alterations in relation to the spills classified with the STC, in all of the analyses taken into consideration. Therefore, considering all the procedures, it has been shown that the described methodology can be successfully applied using the unsupervised classifiers tested, resulting in a decrease of time in the identification and classification processing of oil spills, if compared with the utilization of the STC classifier

Results of bulk sediment X-ray diffraction analysis and quantification of mineral phases based on the RockJock and on the QUAX quantitative analysis

We have performed quantitative X-ray diffraction (qXRD) analysis of 157 grab or core-top samples from the western Nordic Seas between (WNS) ~57°-75°N and 5° to 45° W. The RockJock Vs6 analysis includes non-clay (20) and clay (10) mineral species in the <2 mm size fraction that sum to 100 weight %. The data matrix was reduced to 9 and 6 variables respectively by excluding minerals with low weight% and by grouping into larger groups, such as the alkali and plagioclase feldspars. Because of its potential dual origins calcite was placed outside of the sum. We initially hypothesized that a combination of regional bedrock outcrops and transport associated with drift-ice, meltwater plumes, and bottom currents would result in 6 clusters defined by "similar" mineral compositions. The hypothesis was tested by use of a fuzzy k-mean clustering algorithm and key minerals were identified by step-wise Discriminant Function Analysis. Key minerals in defining the clusters include quartz, pyroxene, muscovite, and amphibole. With 5 clusters, 87.5% of the observations are correctly classified. The geographic distributions of the five k-mean clusters compares reasonably well with the original hypothesis. The close spatial relationship between bedrock geology and discrete cluster membership stresses the importance of this variable at both the WNS-scale and at a more local scale in NE Greenland.

On Uniformly Convex and Uniformly Kadec-Klee Renomings

We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for Lp(X) spaces and C(K) spaces for K scattered compact space.

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. Even mathematicians like H. Poincare worried about this. He observed that mathematical models are over idealizations, for instance, he said that only in Mathematics, equality is a transitive relation. A first attempt to save this situation was perhaps given by K. Menger in 1951 by introducing the concept of statistical metric space in which the distance between points is a probability distribution on the set of nonnegative real numbers rather than a mere nonnegative real number. Other attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A. Sklar and others. An aspect in common to all these approaches is that they model impreciseness in a probabilistic manner. They are not able to deal with situations in which impreciseness is not apparently of a probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.

FUZZY CONIFOLD Y-F(6) AND MONOPOLES ON S-F(2) x S-F(2)

In this paper, we construct the fuzzy (finite-dimensional) analogs of the conifold Y-6 and its base X-5. We show that fuzzy X-5 is (the analog of) a principal U(1) bundle over fuzzy spheres S-F(2) x S-F(2) and explicitly construct the associated monopole bundles. In particular, our construction provides an explicit discretization of the spaces T-k,T-k and T-k,T-0.

On contractive cyclic fuzzy maps in metric spaces and some related results on fuzzy best proximity points and fuzzy fixed points

This paper investigates some properties of cyclic fuzzy maps in metric spaces. The convergence of distances as well as that of sequences being generated as iterates defined by a class of contractive cyclic fuzzy mapping to fuzzy best proximity points of (non-necessarily intersecting adjacent subsets) of the cyclic disposal is studied. An extension is given for the case when the images of the points of a class of contractive cyclic fuzzy mappings restricted to a particular subset of the cyclic disposal are allowed to lie either in the same subset or in its next adjacent one.

Evaluation of Speaker Normalization Methods for Vowel Recognition Using Fuzzy ARTMAP and K-NN

A procedure that uses fuzzy ARTMAP and K-Nearest Neighbor (K-NN) categorizers to evaluate intrinsic and extrinsic speaker normalization methods is described. Each classifier is trained on preprocessed, or normalized, vowel tokens from about 30% of the speakers of the Peterson-Barney database, then tested on data from the remaining speakers. Intrinsic normalization methods included one nonscaled, four psychophysical scales (bark, bark with end-correction, mel, ERB), and three log scales, each tested on four different combinations of the fundamental (Fo) and the formants (F1 , F2, F3). For each scale and frequency combination, four extrinsic speaker adaptation schemes were tested: centroid subtraction across all frequencies (CS), centroid subtraction for each frequency (CSi), linear scale (LS), and linear transformation (LT). A total of 32 intrinsic and 128 extrinsic methods were thus compared. Fuzzy ARTMAP and K-NN showed similar trends, with K-NN performing somewhat better and fuzzy ARTMAP requiring about 1/10 as much memory. The optimal intrinsic normalization method was bark scale, or bark with end-correction, using the differences between all frequencies (Diff All). The order of performance for the extrinsic methods was LT, CSi, LS, and CS, with fuzzy AHTMAP performing best using bark scale with Diff All; and K-NN choosing psychophysical measures for all except CSi.