On the continuity of functors of the type C(X, Y)

We consider the category P, the objects of which are pairs of topological spaces (X, Y). Each such pair (X, Y) is assigned the space of continuous maps Cτ(X, Y) with some topology τ. By imposing some restrictions on objects and morphisms of category P, we define a subcategory K ⊂ P, for which the above map is a functor from K to the category Top of topological spaces and continuous maps. The following question is investigated. What are the additional conditions on K, under which the above functor is continuous? Along the way the problem of finding the limit of the inverse spectrum in the category P is solved. We show, that it reduces to finding the limits of the corresponding direct spectrum and inverse spectrum in the category Top. Point convergence topology, compact-open topology and graph topology are considered as the topology τ.

Hiding information in images using pseudo-random sequences

In this article are discussed techniques of hiding information messages in cover image using direct spectrum spreading technology. This technology is based on the use of poorly correlated pseudorandom (noise) sequences. Modulating the information data with such signals, the message is presented as a noise-like form, which makes it very difficult to detect. Hiding means adding a modulated message to the cover image. If this image is interpreted as noise on the communication channel, then the task of hiding user’s data is equivalent to transmitting a noise-like modulated message on the noise communication channel. At the same it is supposed that noise-like signals are poorly correlated both with each other and with the cover image (or its fragment). However, the latter assumption may not be fulfilled because a realistic image is not an implementation of a random process; its pixels have a strong correlation. Obviously, the selection of pseudo-random spreading signals must take this feature into account. We are investigating various ways of formation spreading sequences while assessing Bit Error Rate (BER) of information data as well as cover image distortion by mean squared error (MSE) and by Peak signal-to-noise ratio (PSNR). The obtained experimental dependencies clearly confirm the advantage of using Walsh sequences. During the research, the lowest BER values were obtained. Even at low values of the signal power of the spreading sequences (P≈5), the BER value, in most cases, did not exceed 0,01. This is the best result of all the sequences under consideration in this work. The values of PSNR when using orthogonal Walsh sequences are, in most cases, comparable to other considered options. However, for a fixed value of PSNR, using the Walsh transform results in significantly lower BER values. It is noted that a promising direction is the use of adaptively generated discrete sequences. So, for example, if the rule for generating expanding signals takes into account the statistical properties of the container, then you can significantly reduce the value of BER. Also, another useful result could be increasing PSNR at a fixed (given) value of BER. The purpose of our work is to justify the choice of extending sequences to reduce BER and MSE (increase PSNR).

Diagnostic Signal Informativeness Increase

Modern requirements for the operation of cars lead to the need to improve the efficiency of their maintenance. Diagnosis as an element of the maintenance process allows you to provide information about the technical condition of a particular element, which allows you to respond in a timely manner to the technical condition change of a diagnostic object with minimal resources. In this paper, we consider the way improving the diagnostic signal quality. It is known that a diagnostic signal must meet several requirements. The most important requirement is informativeness, which shows the decrease of uncertainty about the technical condition of an object, represented by a priori entropy after information application from this diagnostic signal, measured during the diagnosis. There are the methods for a diagnostic signal conversion, which allow to get rid of the noise entering it to a different degree or present it in such a way to facilitate the signal analysis process. Three methods are considered in the work: direct spectrum obtaining, signal envelope spectrum obtaining, and adaptive filtering. The analysis of these methods led to the conclusion that adaptive filtering has the greatest efficiency potential. We have proposed the method that is based on adaptive filtering, but with additional operations. In the course of the diagnostic signal studies and the adaptive filtering algorithm, we found that it is possible to set the function to be detected as a variable, as well as several parameters that affect the result quality. Based on this, a new method for a useful signal extraction was proposed. The results of the work were checked on a signal simulating a car gearbox signal. The results show that the method allows you to obtain the necessary knowledge about a defect, which can be used in the diagnosis. The developed method allows to increase the information content of the diagnostic signal by suppressing its other components. The results of the proposed method correlate with the results of other methods for general cases, i.e., when the ratio of the useful signal to noise is such that high sensitivity of the method is not required to identify the useful signal.