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1
Content available Difference equations with impulses
EN
Difference equations with impulses are studied focussing on the existence of periodic or bounded orbits, asymptotic behavior and chaos. So impulses are used to control the dynamics of the autonomous difference equations. A model of supply and demand is also considered when Li-Yorke chaos is shown among others.
PL
Lokalne przemieszczenia wzdłużne szyn, mogą zaburzyć stabilności temperatury neutralnej w szynach toru bezstykowego. Pomiar przemieszczeń oznaczonych na szynie punktów bazowych w stosunku do punktów stałych, jest obecnie jedyną metodą stosowaną na sieci PKP, która pozwala na okresową kontrolę temperatury neutralnej. W artykule przedstawione zostanie nowe urządzenie i metoda pomiaru przemieszczeń punktów bazowych w stosunku do punktów stałych w aspekcie współczesnych technologii prowadzenia pomiarów przemieszczeń.
EN
Local longitudinal displacement of the rails may disturb the stability of the neutral temperature in the contactless rails. The measurement of displacements of the base points marked on rail in relation to fixed points is currently the only one method used on the PKP network, which allows for periodic control of the neutral temperature. A new device and a method for measuring displacements of base points in relation to fixed points in the aspect of modern technologies for conducting displacement measurements have been presented in the paper.
EN
The Burrows-Wheeler Transform is a well known transformation widely used in Data Compression: important competitive compression software, such as Bzip (cf. [1]) and Szip (cf. [2]) and some indexing software, like the FM-index (cf. [3]), are deeply based on the Burrows Wheeler Transform. The main advantage of using BWT for data compression consists in its feature of “clustering” together equal characters. In this paper we show the existence of fixed points of BWT, i.e., words on which BWT has no effect. We show a characterization of the permutations associated to BWT of fixed points and we give the explicit form of fixed points on a binary ordered alphabet {a, b} having at most four b’s and those having at most four a’s.
PL
Stabilności temperatury neutralnej w szynach toru bezstykowego na sieci PKP do chwili obecnej kontroluje się na podstawie pomiarów przemieszczeń oznaczonych na szynie punktów bazowych, względem ustalonego przekroju kontrolnego. W artykule przedstawiony zostanie nowy sposób i urządzenie do pomiaru przemieszczeń punktów bazowych w stosunku do punktów stałych.
EN
Stability of neutral temperature at contactless rail track of PKP network, up to now, is monitored based on the measurement of displacements of basis points marked on a rail relative to the fixed control section. A new method and an apparatus for measuring the displacement of basis points relative to the fixed points has been presented in the paper.
EN
This is the continuation of four earlier studies of a scalar fractional differential equation of Riemann-Liouville type [formula] in which we first invert it as a Volterra integral equation [formula] and then transform it into [formula] where R is completely monotone with [formula] and J is an arbitrary positive constant. Notice that when x is restricted to a bounded set, then by choosing J large enough, we can frequently change the sign of the integrand in going from (b) to (c). Moreover, the same kind of transformation will produce a similar effect in a wide variety of integral equations from applied mathematics. Because of that change in sign, we can obtain an a priori upper bound on solutions of (b) with a parameter λ ∈ (0, 1] and then obtain an a priori lower bound on solutions of (c). Using this property and Schaefer’s fixed point theorem, we obtain positive solutions of an array of fractional differential equations of both Caputo and Riemann-Liouville type as well as problems from turbulence, heat transfer, and equations of logistic growth. Very simple results establishing global existence and uniqueness of solutions are also obtained in the same way.
6
Content available remote Probabilistic generalized metric spaces and nonlinear contractions
EN
We give a probabilistic generalization of the theory of generalized metric spaces [2]. Then, we prove a fixed point theorem for a self-mapping of a probabilistic generalized metric space, satisfying the very general nonlinear contraction condition without the assumption that the space is Hausdorff.
7
Content available remote L*-operators of convexity
EN
A notion of L^*-spaces is investigated as a generalization of convex subspaces. This gives some topological extensions for celebrated theorems due to Maynard Smith, Brouwer and Nash.
PL
W pracy jest badane pojęcie uogólnionej wypukłości, które umożliwia otrzymanie bardzo prostych dowodów twierdzenia Maynarda Smitha o istnieniu strategii ewolucyjnych w modelach biologicznych oraz twierdzenia o sygnaturach dających znaczne rozszerzenia twierdzenia Nasha o równowadze.
8
Content available remote Ergodicity of the Martyna-Klein-Tuckerman Thermostat and the 2014 Ian Snook Prize
EN
Nosé and Hoover’s 1984 work showed that although Nosé and Nosé-Hoover dynamics were both consistent with Gibbs’ canonical distribution neither dynamics, when applied to the harmonic oscillator, provided Gibbs’ Gaussian distribution. Further investigations indicated that two independent thermostat variables are necessary, and often sufficient, to generate Gibbs’ canonical distribution for an oscillator. Three successful time-reversible and deterministic sets of twothermostat motion equations were developed in the 1990s. We analyze one of them here. It was developed by Martyna, Klein, and Tuckerman in 1992. Its ergodicity was called into question by Patra and Bhattacharya in 2014. This question became the subject of the 2014 Snook Prize. Here we summarize the previous work on this problem and elucidate new details of the chaotic dynamics in the neighborhood of the two fixed points. We apply six separate tests for ergodicity and conclude that the MKT equations are fully compatible with all of them, in consonance with our recent work with Clint Sprott and Puneet Patra.
EN
In this paper, we introduce a new explicit iterative scheme for approximation of fixed points of demicontinuous pseudocontractive mappings in uniformly smooth Banach spaces and prove strong convergence of our proposed iterative scheme. Furthermore, we modify our explicit iterative scheme for approximation of zeroes of bounded demicontinuous accretive mappings in uniformly smooth Banach spaces. Our result improves, extends and unifies most of the results that have been proved for this class of mappings.
10
Content available remote The Brouwer Fixed Point Theorem for Some Set Mappings
EN
For some classes X⊂2Bn of closed subsets of the disc Bn⊂Rn we prove that every Hausdorff-continuous mapping f:X→X has a fixed point A∈X in the sense that the intersection A∩f(A) is nonempty.
11
Content available remote Fixed Points of Maps of Sets of Polyhedra into the Disc
EN
We prove that Platonic and some Archimedean polyhedra have the fixed point property in a non-classical sense.
EN
By means of Krasnoselskii's fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307-3315], and also those of T.A. Burton [Fixed Point Theory 4 (2003), 15-32; Dynam. Systems Appl. 11 (2002), 499-519] and B. Zhang [Nonlinear Anal. 63 (2005), e233-e242]. In the end we provide an example to illustrate our claim.
13
Content available remote A new class of multivalent analytic functions defined by the hadamard product
EN
The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for classes of functions with two fixed points. Some remarks depicting consequences of the main results are also mentioned.
14
Content available remote Well-posedness of the fixed point problem for ø-max-contractions
EN
We study the well-posedness of the fixed point problem for self-mappings of a metric space which are ø-max-contractions (see [6]).
15
Content available remote Well-posedness of fixed point problem for mappings satisfying an implicit relation
EN
The notion of well-posedness of a fixed point problem has generated much interest to a several mathematicians, for example, F. S. De Blassi and J. Myjak (1989), S. Reich and A. J. Zaslavski (2001), B. K. Lahiri and P. Das (2005) and V. Popa (2006 and 2008). The aim of this paper is to prove for mappings satisfying some implicit relations in orbitally complete metric spaces, that fixed point problem is well-posed.
EN
In this paper, we prove two fixed point theorems for mappings satisfying contractive condition of integral type on d-complete Hausdorff topological spaces.
17
Content available remote More maps for which F(T)=F(Tn)
EN
We continue our investigation of situations in which the fixed point sets for maps and their iterates are the same.
18
Content available remote Fixed point theorems for multivalued mappings in symmetric spaces
EN
In this paper we prove some fixed point theorems for multivalued mappings using rational inequality in a symmetric space. These results are generalizations of some well known results in metric spaces and also in the setting of symmetric spaces.
19
Content available remote Fixed points of mappings in Klee admissible spaces
EN
In this paper we generalize the Lefschetz fixed point theorem from the case of metric ANR-s to the case of acceptable subsets of Klee admissible spaces. The results presented in this paper were announced in an earlier publication of the authors.
20
Content available remote A generalization of the Opial's theorem
EN
Opial presented in 1967 a theorem, which can be applied in order to prove the weak convergence of sequences (xk) in a Hilbert space, generated by iterative schemes of the form xk+1= Uxk for a nonexpansive and asymptotically regular operator U with nonempty Fix U. Several iterative schemes have, however, the form xk+i1 = UkXk, where (Uk) is a sequence of operators with a common fixed point. We show that under some conditions on the sequence (Uk) the sequence (xk) converges weakly to a common fixed point of operators Uk- We show also that the Opial's theorem and the Krasnoselskii-Mann theorem are the corollaries descending from the obtained results. Finally, we present some applications of the results to the convex feasibility problems.
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