On the Sequences Realizing Perron and Lyapunov Exponents of Discrete Linear Time-Varying Systems

We investigate properties of partial exponents (in particular, the Lyapunov and Perron exponents) of discrete time-varying linear systems. In the set of all increasing sequences of natural numbers, we define an equivalence relation with the property that sequences in the same equivalence class have the same partial exponent. We also define certain subclass of all increasing sequences of natural numbers, including all arithmetic sequences, such that all partial exponents are achievable on a sequence from this class. Finally, we show that the Perron and Lyapunov exponents may be approximated by partial exponents achievable on sequences in certain sense similar to geometric sequences

THE BIULETYN INFORMACYJNY ZARZĄDUMUZEÓW I OCHRONY ZABYTKÓW BULLETIN,1955–1987

In 1955–1987, the Directorate of Museums andMonument Preservation (until 1959: Central Directorateof Museums and Monument Preservation), a structuralunit of the Ministry of Culture and Art, published BiuletynInformacyjny, a bulletin dedicated to documenting theactivity of museums in Poland. In 1955-1959, it was calledBiuletyn Informacyjny Centralnego Zarządu Muzeówi Ochrony Zabytków, while in 1959–1987, it was publishedunder the name Biuletyn Informacyjny Zarządu Muzeówi Ochrony Zabytków. It was published as a bimonthly ora quarterly with a limited circulation (400–600 copies),and was delivered to museums. The following served as itssubsequent Editors-in-Chief: Mieczysław Ptaśnik (until 1972),Stanisław Brzostowski (until 1976), and Franciszek Midura(until 1987). The core content of the publication coveredshort factual information reporting on definite achievementsof particular museums or Minister’s initiatives, as well aslonger papers authored in their majority by the EditorialStaff and museum curators who submitted their materials.Informative texts were included in the sections whosenames altered. The most important of them were as follows:I. ‘Research and Academic Discoveries’, II. ‘Publications’,III. ‘Exhibitions’, IV. ‘New Acquisitions’, V. ‘EducationalActions’, VI. ‘Conservation Works’, VII. ’Foreign Cooperation’,VIII. ‘Foreign Museums’, IX. ‘Conferences’, X. ‘Communiqués’,XI. ‘Papers’. Despite bearing features of a journal publishedunder the ideological and political control of the Communistregime, the Biuletyn Informacyjny Zarządu Muzeów i OchronyZabytków bulletin essentially constitutes a reliable source forthe history of Polish museology in 1955-1987

On the assignability of regularity coefficients and central exponents of discrete linear time-varying systems

In this paper we investigate the problem of assignability of the so-called regularity coefficients and central exponents of discrete linear time-varying systems. The main result presents a possibility of assignability of Lyapunov, Perron, Grobman regularity coefficients and central exponents by a linear time-varying feedback under the assumptions of uniform complete controllability

Controllability Problem of Fractional Neutral Systems: A Survey

The following article presents recent results of controllability problem of dynamical systems in infinite-dimensional space. Generally speaking, we describe selected controllability problems of fractional order systems, including approximate controllability of fractional impulsive partial neutral integrodifferential inclusions with infinite delay in Hilbert spaces, controllability of nonlinear neutral fractional impulsive differential inclusions in Banach space, controllability for a class of fractional neutral integrodifferential equations with unbounded delay, controllability of neutral fractional functional equations with impulses and infinite delay, and controllability for a class of fractional order neutral evolution control systems

Bariery przy opracowywaniu i wdrażaniu strategii oraz jej wpływ na zarządzanie Muzeum Historycznym Miasta Krakowa

Barriers to development and implementation of strategy and its effects on management at the Historical Museum of the City of KrakówThe article discusses the effects of development strategy on management at the Historical Museum of the City of Kraków. The authors have concentrated on discussing the organizational innovations resulting from the assumed strategic objectives. The strategy implementation process and the corresponding barriers have been presented in the article as wel

Asymptotic properties of discrete linear fractional equations

In this paper we study the dynamical behavior of linear discrete-time fractional systems. The first main result is that the norm of the difference of two different solutions of a time-varying discrete-time Caputo equation tends to zero not faster than polynomially. The second main result is a complete description of the decay to zero of the trajectories of one-dimensional time-invariant stable Caputo and Riemann-Liouville equations. Moreover, we present Volterra convolution equations, that are equivalent to Caputo equations

Variation of constant formulas for fractional difference equations

In this paper, we establish variation of constant formulas for both Caputo and Riemann- Liouville fractional difference equations. The main technique is the Z -transform. As an application, we prove a lower bound on the separation between two different solutions of a class of nonlinear scalar fractional difference equations

Controlling Wolbachia transmission and invasion dynamics among aedes aegypti population via impulsive control strategy

This work is devoted to analyzing an impulsive control synthesis to maintain the self-sustainability of Wolbachia among Aedes Aegypti mosquitoes. The present paper provides a fractional order Wolbachia invasive model. Through fixed point theory, this work derives the existence and uniqueness results for the proposed model. Also, we performed a global Mittag-Leffler stability analysis via Linear Matrix Inequality theory and Lyapunov theory. As a result of this controller synthesis, the sustainability of Wolbachia is preserved and non-Wolbachia mosquitoes are eradicated. Finally, a numerical simulation is established for the published data to analyze the nature of the proposed Wolbachia invasive model.Prince Sultan Universit