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EN
In this paper, we study the behaviors of fixed points sets of non necessarily pseudo-contractive multifunctions. Rather than comparing the images of the involved multifunctions, we make use of some conditions on the fixed points sets to establish general re­sults on their stability and continuous dependence. We illustrate our results by applications to differential inclusions and give stability results of fixed points sets of non necessarily pseudo-contractive multifunctions with respect to the bounded proximal convergence.
EN
A new fire detection system for use on passenger trains, based on a multifunction pointtype sensor, is described. The full development process of the new system is described, and all the choices made in order to make a railway specific product explained. The basic concepts of the system described are: • full compliance to all the standards for safety-related electronics on rolling stocks, • detection performances derived from existing standards for commercial buildings, with adaptation, • multifunction sensors, capable to measure the smoke obscuration and the air temperature, and to control external devices, and also able to drive signal and power outputs, • detection criteria delegated to a central supervisory unit, receiving the real-time information from the multifunction sensors over a safe and robust communication link, redundant CAN bus, • commands to actuate the sensor's output sent selectively over the same communication link. A comparison with other traditional fire detection systems is made, and examples of application and of installation are given, both for fixed and variable composition trains. Reference is made to several existing applications on trains in many countries, like Italy, Switzerland, Finland, Russia, China and Poland. A table is presented with field data from thousands units in operation, demonstrating an MTBF in excess of 20 millions-hour.
PL
Opisano nowy układ wykrywania pożaru do zastosowań kolejowych, który oparty jest na wielofunkcyjnym czujniku typu punktowego. Opisano cały proces opracowania nowego układu oraz omówiono wszystkie dokonane wybory w aspekcie specjalistycznego rozwiązania kolejowego. Zasadnicze założenia przyjęte dla tego układu są następujące: - Pełna zgodność ze wszystkimi normami dla elektroniki układów bezpieczeństwa taboru kolejowego. - Charakterystyki wykrywania pochodzące z istniejących norm bezpieczeństwa budynków i odpowiednio zaadaptowane. - Zdolne do oceny zaciemnienia od dymu oraz pomiaru temperatury powietrza czujniki wielofunkcyjne sterujące urządzeniami zewnętrznymi, a także zdolne do sterowania sygnałami i zasilaniem. - Kryteria wykrywania przekazane do centralnego modułu dozorującego, odbierającego z czujników informacje w czasie rzeczywistym za pośrednictwem bezpiecznych i solidnych łączy komunikacyjnych, zapasowej magistrali CAN. - Polecenia uruchomienia sygnału wyjściowego czujnika są przesyłane selektywnie przez to samo łącze komunikacyjne. Dokonano porównania z innymi tradycyjnymi układami wykrywania pożaru i podano przykłady zastosowań i instalacji. Przywołano szereg zastosowań kolejowych w takich krajach, jak Włochy, Szwajcaria, Finlandia, Rosja, Chiny i Polska. Przedstawiono tabelę z danymi pochodzącymi z eksploatowanych urządzeń, które pokazują, że średni czas bezawaryjnej pracy (MTBF) przekracza 20 milionów godzin
PL
W artykule podjęto temat monofunkcji osiedla przy ulicy Zwoleńskiej w Lipsku i jego planowanej rozbudowy. Jest to typowe prefabrykowane osiedle i artykuł równie dobrze mógłby odnosić się do większości takich osiedli w małych miastach. Pierwszy rozdział jest wstępem do artykułu i wyjaśnieniem podjęcia tematu. Kolejny rozdział przybliża historię miasta i osiedla, ściśle korelując z rozdziałem trzecim, w którym ukazane jest osiedle obecnie, jego funkcje, problemy i plany rozwoju. W rozdziale czwartym autorzy podnoszą przykłady osiedli, których problemem między innymi również była jednolita funkcja, a które zostały dobrze zrewitalizowane, także przez dodanie nowych funkcji, i dzięki temu zmniejszyły się ich problemy. Dzięki temu krótkiemu przeglądowi możliwe było zaproponowanie dla osiedla budynku wielofunkcyjnego, który opisany jest w rozdziale piątym. Ostatni rozdział zawiera podsumowanie referatu.
EN
The article is about the monofunction estate near Zwoleńska street in Lipsko (Poland) and its planned extension. This is a typical prefabricated settlement and article might as well refer to the majority of such housing estates in small towns. The first chapter is an introduction to the article and the explanation of a given topic. The next chapter introduces the history of the town and estate, closely correlating with the third chapter, in which the current settlement is shown, its features, problems and plans for development. In the fourth chapter, the authors gives the examples of settlements, whose issue was also, inter alia, a monofunction and which were well revitalized, also through adding new features, and therefore their problems declined. Thanks to this brief overview it was possible to propose a multi-function building to the estate, which is described in chapter five. The final chapter contains the summary of the article.
PL
W mieście XX/XXI w. wyłaniają się struktury hybrydowe – zespoły współdziałających funkcjonalnie elementów. Stają się próbami utworzenia w tkance miejskiej mikroświata, miasta w mieście, organizmu w dużej mierze samowystarczalnego. Powstające realizacje obiektów hybrydowych stają się urbanistycznym eksperymentem. Istota hybrydowa, mieszcząca w sobie wiele funkcji, zamyka miejskie życie jednostki ludzkiej w jednym architektonicznym organizmie. Czy takie rozwiązania są ważnym głosem w dyskusji nad drogą rozwoju miasta przyszłości?
EN
In the city of the XX/XXI century hybrid structures have been appearing – units of functionally interacting components. They are trying to create a microworld of the urban system, a town in the city, the self- -sufficient unit. The resulting projects of the hybrid objects are an urban experiment. Hybrid creature with a number of functions closes city life of the human individual in one of the architectural unit. Are such solutions an important voice in the discussion about the path of city of the future development?
5
Content available remote Upper and lower almost cl-supercontinuous multifunctions
EN
The notion of almost cl-supercontinuity (≡ almost clopen continuity) of functions (Acta Math. Hungar. 107 (2005), 193–206; Applied Gen. Topology 10 (1) (2009), 1–12) is extended to the realm of multifunctions. Basic properties of upper (lower) almost cl-supercontinuous multifunctions are studied and their place in the hierarchy of strong variants of continuity of multifunctions is discussed. Examples are included to reflect upon the distinctiveness of upper (lower) almost cl-supercontinuity of multifunctions from that of other strong variants of continuity of multifunctions which already exist in the literature.
6
Content available remote On continuous convergence of nets of multifunctions
EN
This paper expands the classical concept of the continuous convergence of nets of multifunctions introduced by Cao, Reilly and Vamanamurthy in [7]. We introduce some new types of properties of convergence of such nets which guarantee the upper or lower semicontinuity of the limit multifunction. Furthermore, we obtain some analogous results concerning generalized continuity properties of multifunctions.
EN
By using m-open multifunctions from a topological space into an m-space, we establish the unified theory for several weak forms of open multifunctions in the sense of Kuratowski between bitopological spaces.
8
Content available remote On Lipschitz selections of multifunctions with decomposable values
EN
Some conditions for existence of Lipschitz selections of multifunctions with decomposable values are given.
9
Content available remote A common fixed point theorem for two multifunctions defined on closed ball
EN
We prove a common fixed point theorem for two mul-tifunctions defined on a closed ball of a complete metric space with values in the set of all nonempty and closed subsets of this space, multifunctions which satisfy an implicit contractive relation of Latif-Beg type.
10
Content available remote On Frigon-Granas type multifunctions satisfying an implicit relation
EN
The purpose of this paper is to prove two general fixed point theorems for two multifunctions T1,T2 : B(xo,r) - > Pcl(X) satisfying an implicit relation, which generalize Theorem 3.1 [2], Theorem 3.1 [3], Theorem 3.1 [1] and Theorem 3.1 [6]. In the last part we extend the results for a sequence of multifunctions.
EN
The problem of existence of adjoint functions to boundary solutions is considered – it depends on the geometry of the attained set at the end point. This is applied to prove the smoothness of boundary solutions in the case of strictly convex right-hand side of di.erential inclusion which in turn permitts to show the smoothness of barrier solutions on semipermeable surfaces.
EN
We study optimal control of systems governed by a coupled system of hemivariational inequalities, modeling a dynamic thermoviscoelastic problem, which describes frictional contact between a body and a foundation. We employ the Kelvin-Voigt vis-coelastic law, include the thermal effects and consider the general nonmonotone and multivalued subdifferential boundary conditions. We consider optimal control problem for boundary and distributed parameter control systems, time optimal control problem and maximum stay control problem. We deliver conditions that guarantee the existence of optimal solutions.
13
Content available remote Stability of generalized functional-differential equations
EN
The basic idea of this paper is to use Lyapunov functions to show that the trivial solution functional-differential equations of the form x(t] ∈ F(t,Xt] is stable and is asymptotically stable, and that of perturbed functional-differential equations of the form x(t) ∈ F(t,xt) + G(t,xt) is asymptotically stable.
EN
In this paper the sensitivity of optimal solutions to control problems for the systems described by stationary and evolution heinivariational inequalities (HVIs) under perturbations of state relations and of cost functionals is investigated. First, basing on the theory of sequential [Gamma]-convergence we recall the abstract scheme concerning convergence of minimal values and minimizers. The abstract scheme works provided we can establish two properties: the Kuratowski convergence of solution sets for HVIs (state relations) and some complementary [Gamma]-convergence of the cost functionals. Then these two properties are implemented in each considered case.
15
Content available remote Continuous selections in [alpha]-convex metric spaces
EN
The existence of continuous selections is proved for a class of lower semicontinuous multifunctions whose values are closed convex subsets of a complete metric space equipped with an appropriate notion of convexity. The approach is based on the notion of pseudo-barycenter of an ordered n-tuple of points.
16
EN
The aim of this paper is to study uniform and topological structures on spaces of multifunctions. Uniform structures on hyperspaces compatible with the Fell, the Wijsman and the Hausdorff metric topology respectively are studied and the links between them are explored. Topologies induced by the above uniformities on spaces of multifunctions are considered and compared. Also connections between uniform convergence of multifunctions and their equi-semicontinuity are investigated.
EN
The paper studies, in the context of Banach spaces, the problem of three boundary conditions for both second order differential inclusions and second order ordinary differential equations. The results are obtained in several new settings of Sobolev-type spaces involving Bochner and Pettis integrals. Some classes of second order multivalued evolution equations associated with m-accretive operators are also considered. Applications to some control problems are provided with the help of narrow convergence for Young measures.
18
Content available remote On a characterization of Pettis integrable multifunctions
EN
We present a rectification of the proof of the implication i) -> ii) in Theorem 3.2 of [4]. This result gives a charactrization of Pettis integrable multifunctions with convex weakly compact values.
19
Content available remote (Psi ,p)-integral equivalence of multivalued differential systems with delay
EN
In our paper we deal with (If/ , p) -integral equivalence of systems: (a) x'(t) EA(t)x(t) +F(t,x,), (b) y'(t) = A(t) y(t). To reach this aim we use Ky Fan fixed point theorem. To proofuniforrnly boundedness we use Iemrnas 6 and 7 which deal with g-compactness.
20
Content available remote Set-valued iterative square roots of bijections
EN
There are different ideas how to generalize the notion of an iterative root, especially when a function does not have a "real" root. We consider a multifunction as a substitute for this notion.
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