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

On Lyapunov and Upper Bohl Exponents of Diagonal Discrete Linear Time-Varying Systems

In this paper the necessary and sufficient conditions for two given functions to be the Lyapunov and the upper Bohl exponents of a certain discrete linear system with diagonal coefficients are presented. The obtained conditions are described in terms of easily verifiable properties

Serologic and immunohistochemical prognostic biomarkers of cutaneous malignancies

Biomarkers are important tools in clinical diagnosis and prognostic classification of various cutaneous malignancies. Besides clinical and histopathological aspects (e.g. anatomic site and type of the primary tumour, tumour size and invasion depth, ulceration, vascular invasion), an increasing variety of molecular markers have been identified, providing the possibility of a more detailed diagnostic and prognostic subgrouping of tumour entities, up to even changing existing classification systems. Recently published gene expression or proteomic profiling data relate to new marker molecules involved in skin cancer pathogenesis, which may, after validation by suitable studies, represent future prognostic or predictive biomarkers in cutaneous malignancies. We, here, give an overview on currently known serologic and newer immunohistochemical biomarker molecules in the most common cutaneous malignancies, malignant melanoma, squamous cell carcinoma and cutaneous lymphoma, particularly emphasizing their prognostic and predictive significance

Architectural narration – interpretations, speculations or empirical facts?

Znaczenie w architekturze, a w szczególności zagadnienia związane ze strukturami symbolicznymi, należą niewątpliwie do najtrudniejszych tematów w teorii architektury. Problematyka ta wychodzi znacznie poza zakres zagadnień techniczno-użytkowych, stąd wymaga zastosowania specyficznych podejść badawczych, zbliżonych do tych, jakie stosowane są w naukach humanistycznych i społecznych. W ostatnich dekadach daje się zaobserwować wyraźne przesunięcie punktu ciężkości zainteresowań projektantów architektury z zagadnień techniczno-użytkowych ku problemom związanym z ekspresją artystyczną, a w związku z tym także ku symbolizmowi. Być może jest to rodzaj ucieczki od sfery nie dającej już projektantom tak rozległych możliwości samorealizacji, jaką oferuje sfera ekspresji symbolicznej. Zjawisko takie jest znamienne dla schyłkowych okresów w historii architektury i sztuki takich, jak np. manieryzm czy secesja, a wiele przesłanek wskazuje na to, że w podobnym okresie żyjemy.Meaning in architecture, particularly in terms of symbolic structures, is undoubtedly one of the most challenging themes in the theory of architecture. The discussion of meaning goes far beyond purely technical and utilitarian concepts, and therefore needs to employ unique research methods, more in line with those used in humanities and social studies. The past decades saw architects make a definite shift from a technical and utilitarian perspective towards artistic expression, and consequently – symbolism. Such a change of focus might be a form of flight from an over-exploited and restricting approach towards one that, like symbolism, still offers room for creative self-expression. The phenomenon is by no means a new one – we have seen it emerge throughout history towards the end of architectural or artistic periods; it was reflected in Mannerism or Art Nouveau, and there are reasons to believe we are witnessing a similar process now

Stability and controllability of switched systems

The study of properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. This paper aims to briefly survey recent results on stability and controllability of switched linear systems. First, the stability analysis for switched systems is reviewed. We focus on the stability analysis for switched linear systems under arbitrary switching, and we highlight necessary and sufficient conditions for asymptotic stability. After that, we review the controllability results

Banach fixed-point theorem in semilinear controllability problems – a survey

The main aim of this article is to review the existing state of art concerning the complete controllability of semilinear dynamical systems. The study focus on obtaining the sufficient conditions for the complete controllability for various systems using the Banach fixedpoint theorem. We describe the results for stochastic semilinear functional integro-differential system, stochastic partial differential equations with finite delays, semilinear functional equations, a stochastic semilinear system, a impulsive stochastic integro-differential system, semilinear stochastic impulsive systems, an impulsive neutral functional evolution integro-differential system and a nonlinear stochastic neutral impulsive system. Finally, two examples are presented

On a continuity of characteristic exponents of linear discrete time-varying systems

In this paper we present a sufficient condition for continuity of Lyapunov exponents of discrete time-varying linear system. Basing on this result we show that Lyapunov exponents of time-invariant systems depend continuously on the time-varying perturbations

The selected problems of controllability of discrete-time switched linear systems with constrained switching rule

In this paper the controllability problem for discrete-time linear switched systems is considered. The main goal is to find a control signal that steers any initial state to a given final state independently of the switching signal. In the paper, it is assumed that there are some constraints posed on the switching signal. Moreover, we present a necessary and sufficient conditions of some kinds of controllability. Three types of controllability, namely: from zero initial state to any final state, from any initial state to zero final state and from any initial state to any final state are considered. Finally, three illustrative examples are shown