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em Bulgarian Digital Mathematics Library at IMI-BAS


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In this article, we examine a realization of an open addressing hash table in the chained allocated memory, giving us the opportunity to decrease the number of linear probing when a given element has not been inserted in the table.

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As is well known, the Convergence Theorem for the Recurrent Neural Networks, is based in Lyapunov ́s second method, which states that associated to any one given net state, there always exist a real number, in other words an element of the one dimensional Euclidean Space R, in such a way that when the state of the net changes then its associated real number decreases. In this paper we will introduce the two dimensional Euclidean space R2, as the space associated to the net, and we will define a pair of real numbers ( x, y ) , associated to any one given state of the net. We will prove that when the net change its state, then the product x ⋅ y will decrease. All the states whose projection over the energy field are placed on the same hyperbolic surface, will be considered as points with the same energy level. On the other hand we will prove that if the states are classified attended to their distances to the zero vector, only one pattern in each one of the different classes may be at the same energy level. The retrieving procedure is analyzed trough the projection of the states on that plane. The geometrical properties of the synaptic matrix W may be used for classifying the n-dimensional state- vector space in n classes. A pattern to be recognized is seen as a point belonging to one of these classes, and depending on the class the pattern to be retrieved belongs, different weight parameters are used. The capacity of the net is improved and the spurious states are reduced. In order to clarify and corroborate the theoretical results, together with the formal theory, an application is presented.

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Due to the rapid growth of the number of digital media elements like image, video, audio, graphics on Internet, there is an increasing demand for effective search and retrieval techniques. Recently, many search engines have made image search as an option like Google, AlltheWeb, AltaVista, Freenet. In addition to this, Ditto, Picsearch, can search only the images on Internet. There are also other domain specific search engines available for graphics and clip art, audio, video, educational images, artwork, stock photos, science and nature [www.faganfinder.com/img]. These entire search engines are directory based. They crawls the entire Internet and index all the images in certain categories. They do not display the images in any particular order with respect to the time and context. With the availability of MPEG-7, a standard for describing multimedia content, it is now possible to store the images with its metadata in a structured format. This helps in searching and retrieving the images. The MPEG-7 standard uses XML to describe the content of multimedia information objects. These objects will have metadata information in the form of MPEG-7 or any other similar format associated with them. It can be used in different ways to search the objects. In this paper we propose a system, which can do content based image retrieval on the World Wide Web. It displays the result in user-defined order.

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The paper has been presented at the International Conference Pioneers of Bulgarian Mathematics, Dedicated to Nikola Obreshko and Lubomir Tschakalo , So a, July, 2006.

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2000 Mathematics Subject Classification: 91A46, 91A35.