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1

Advanced Morphological Distances Based on Dilation and Erosion

Dražić Slobodan

Fundamenta Informaticae

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2019

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Vol. 164, nr 1

17--39

EN

Distances based on morphological operations have shown good performance in a number of applications. Still, the existing erosion and dilation distance for gray scale images can not be computed in all situations. Furthermore, it is possible that dissimilarity between objects which are compared grows strongly, but the value of a mentioned distance does not change. We present a proposition with the necessary and sufficient conditions for computing these morphological distances and discuss drawbacks that they possess. In addition, we propose novel morphological distances, which can be computed in all situations and provide results with desirable properties. The applicability of novel morphological distances is presented in illustrative examples, including their applicability to real data.

2

Rough Sets Based LEM2 Rules Generation Supported by FPGA

Kopczyński M., Grześ T., Stepaniuk J.

Fundamenta Informaticae

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2016

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Vol. 148, nr 1/2

107--122

EN

In this paper we propose a combination of capabilities of the FPGA based device and PC computer for rough sets based data processing resulting in generating decision rules. Presented architecture has been tested on the exemplary datasets. Obtained results confirm the significant acceleration of the computation time using hardware supporting rough set operations in comparison to software implementation.

3

Universal Query Language for Unified State Model

Wiśniewski P., Stencel K.

Fundamenta Informaticae

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2014

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Vol. 129, nr 1/2

177--192

EN

Unified State Model (USM) is a single data model that allows conveying objects of major programming languages and databases. USM exploits and emphasizes common properties of their data models. USM is equipped with mappings from these data models onto it. With USM at hand, we have faced the next natural research question whether numerous query languages for the data subsumed by USM can be clearly mapped onto a common language. We have designed and proposed such a language called the Unified Query Language (UQL). UQL is intended to be a minimalistic and elegant query language that allows expressing queries of languages of data models covered by USM. In this paper we define UQL and its concise set of operators. Next we conduct a mild introduction into UQL features by showing examples of SQL and ODMG OQL queries and their mapping onto UQL. We conclude by presenting the mapping of the theoretical foundations of these two major query languages onto UQL. They are the multiset relational algebra and the object query algebra. This is an important step towards the establishment of a fully-fledged common query language for USM and its subsumed data models.

4

On summing and related operators acting from a Hilbert space

Tien N., Tarieladze V., Vidal R.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 4

365-375

EN

We study the situation when the behaviour of an operator from a Hilbert space to a Banach space on all orthonormal bases determines whether it belongs to a prescribed class of operators. The cases of (q, 2)-summing, almost summing and [gamma]-summing operators are treated in a unified way.

5

Generalized vector quasi-variational inequalities

Song W.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 4

401-417

EN

First we establish a general existence theorem for a generalized vector qusi-variational inequality in a topological vector space by using a set-valued and vector generalization of Ky Fan minimax principle. As applications, several existence theorems for generalized vector quasi-variational inequalities are derived under assumptions of order-lower (order-upper) semicontinuity or monotonicity of set-valued mappings.

6

A nonstandard difference Sturm-Liouville operator

Javorskij J., Ljance V.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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Vol. 46, no 3

285-290

EN

After Nelson's Radically Elementary Probability Theory [1] a natural question arises: whether a hyperfinite-dimensional space is sufficiently rich to be used for the same goal as an infinite-dimensional one. Here a hyperfinite 3-diagonal matrix is investigated, which spectral properties are simular to the Naimarks's singular nonselfadjoint Sturm-Liouville differential operator on semi-axis [2, 3].