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Tytuł:
The modal mu-calculus: a survey
Autorzy:
Lenzi, G.
Powiązania:
https://bibliotekanauki.pl/articles/1964197.pdf
Data publikacji:
2005
Wydawca:
Politechnika Gdańska
Tematy:
mu-calculus
fixed points
model checking
Opis:
The modal mu-calculus is an extension of modal logic with two operators mu and ni, which give the least and greatest fixpoints of monotone operators on powersets. This powerful logic is widely used in computer science, in the area of verification of correctness of concurrent systems. In this survey we review both the theoretical aspects of the modal mu-calculus and its applications to computer science.
Źródło:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk; 2005, 9, 3; 293-316
1428-6394
Pojawia się w:
TASK Quarterly. Scientific Bulletin of Academic Computer Centre in Gdansk
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the computation of the Nielsen numbers and the converse of the Lefschetz coincidence theorem
Autorzy:
Wong, Peter
Powiązania:
https://bibliotekanauki.pl/articles/1215078.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
fixed points
coincidences
roots
Lefschetz number
Nielsen number
Opis:
Let $f,g:M_1 → M_2$ be maps where $M_1$ and $M_2$ are connected triangulable oriented n-manifolds so that the set of coincidences $C_{f,g}= {x ∈ M_1 | f(x)=g(x)}$ is compact in $M_1$. We define a Nielsen equivalence relation on $C_{f,g}$ and assign the coincidence index to each Nielsen coincidence class. In this note, we show that, for n ≥ 3, if $M_2= \widetilde M_2/K$ where $\widetilde M_2$ is a connected simply connected topological group and K is a discrete subgroup then all the Nielsen coincidence classes of f and g have the same coincidence index. In particular, when $M_1$ and $M_2$ are compact, f and g are deformable to be coincidence free if the Lefschetz coincidence number L(f,g) vanishes.
Źródło:
Fundamenta Mathematicae; 1991-1992, 140, 2; 191-196
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Borel partitions of unity and lower Carathéodory multifunctions
Autorzy:
Srivastava, S.
Powiązania:
https://bibliotekanauki.pl/articles/1208394.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Carathéodory functions and multifunctions
Carathéodory selections
fixed points
Opis:
We prove the existence of Carathéodory selections and representations of a closed convex valued, lower Carathéodory multifunction from a set A in $A(ℰ ⊗ ℬ(X))$ into a separable Banach space Y, where ℰ is a sub-σ-field of the Borel σ-field ℬ(E) of a Polish space E, X is a Polish space and A is the Suslin operation. As applications we obtain random versions of results on extensions of continuous functions and fixed points of multifunctions. Such results are useful in the study of random differential equations and inclusions and in mathematical economics.
  As a key tool we prove that if A is an analytic subset of E × X and if ${U_n : n ∈ w}$ is a sequence of Borel sets in A such that $A=∪_n U_n$ and the section $U_n(e)$ is open in A(e), e ∈ E, n ∈ w, then there exist Borel functions $p_n : A → [0,1]$, n ∈ w, such that for every e ∈ E, ${p_n(e,·) : n ∈ w}$ is a locally Lipschitz partition of unity subordinate to ${U_n(e) : n ∈ w}$.
Źródło:
Fundamenta Mathematicae; 1994-1995, 146, 3; 239-249
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Difference equations with impulses
Autorzy:
Danca, Marius
Feckan, Michal
Pospisil, Michal
Powiązania:
https://bibliotekanauki.pl/articles/255372.pdf
Data publikacji:
2019
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
difference equations
impulses
stability
fixed points
Li-Yorke chaos
Opis:
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.
Źródło:
Opuscula Mathematica; 2019, 39, 1; 5-22
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Integral and fractional equations, positive solutions, and Schaefer’s fixed point theorem
Autorzy:
Becker, L. C.
Burton, T. A.
Purnaras, I. K.
Powiązania:
https://bibliotekanauki.pl/articles/255409.pdf
Data publikacji:
2016
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fixed points
fractional differential equations
integral equations
Riemann-Liouville operators
Opis:
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.
Źródło:
Opuscula Mathematica; 2016, 36, 4; 431-458
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solving equations by topological methods
Autorzy:
Górniewicz, L.
Powiązania:
https://bibliotekanauki.pl/articles/255235.pdf
Data publikacji:
2005
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
Lefschetz number
fixed points
CAC-maps
condensing maps
ANR-spaces
fixed point index
Opis:
In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in diffrential equations.
Źródło:
Opuscula Mathematica; 2005, 25, 2; 195-225
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fixed points and stability in neutral nonlinear differential equations with variable delays
Autorzy:
Ardjouni, A.
Djoudi, A.
Powiązania:
https://bibliotekanauki.pl/articles/255378.pdf
Data publikacji:
2012
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
fixed points
stability
nonlinear neutral differential equation
integral equation
variable delays
Opis:
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.
Źródło:
Opuscula Mathematica; 2012, 32, 1; 5-19
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fixed points of mappings in Klee admissible spaces
Autorzy:
Górniewicz, L.
Ślosarski, M.
Powiązania:
https://bibliotekanauki.pl/articles/970263.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
punkt stały
Lefschetz number
fixed points
topological vector spaces
Klee admissible spaces
Opis:
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.
Źródło:
Control and Cybernetics; 2007, 36, 3; 825-832
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Classes of meromorphic multivalent functions with Montel’s normalization
Autorzy:
Dziok, Jacek
Powiązania:
https://bibliotekanauki.pl/articles/747206.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Meromorphic functions
varying arguments
fixed points
Montel’s normalization
subordination
Hadamard product
Opis:
In the paper we define classes of meromorphic multivalent functions with Montel’s normalization. We investigate the coefficients estimates, distortion properties, the radius of starlikeness, subordination theorems and partial sums for the defined classes of functions. Some remarks depicting consequences of the main results are also mentioned.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2012, 66, 2
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Fuzzy fixed point results with rational type contractions in partially ordered complex-valued metric spaces
Autorzy:
Sarwar, Muhammad
Humaira, Humaira
Huang, Huaping
Powiązania:
https://bibliotekanauki.pl/articles/962851.pdf
Data publikacji:
2018
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Complex-valued metric spaces
fixed points
common fixed point
fuzzy mappings
Cauchy sequence
contractive condition
Opis:
In this manuscript, some fixed point results for fuzzy mappings with rational type contraction in the context of a complete partially ordered complex-valued metric space are established. The derived results generalize some fixed point theorems in the existing literature. An appropriate example is given.
Źródło:
Commentationes Mathematicae; 2018, 58, 1-2; 57-78
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A generalization of the Opials theorem
Autorzy:
Cegielski, A.
Powiązania:
https://bibliotekanauki.pl/articles/970267.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
punkt stały
słaba zbieżność
nonexpansive operators
asymptotically regular operators
fixed points
weak convergence
Opis:
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.
Źródło:
Control and Cybernetics; 2007, 36, 3; 601-610
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Semi-compatibility in non-archimedean Menger PM-space
Autorzy:
Singh, Bijendra
Jain, Arihant
Agarwal, Pallavi
Powiązania:
https://bibliotekanauki.pl/articles/746307.pdf
Data publikacji:
2009
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
Non-Archimedean Menger probabilistic metric space
Common fixed points
Compatible maps
Semi-compatible maps
Opis:
The object of this paper is to establish fixed point theorem for six self maps and an example using the concept of semi-compatible self maps in a non-Archimedean Menger PM-space. Our result generalizes the result of Cho et. al. [2].
Źródło:
Commentationes Mathematicae; 2009, 49, 1
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The automorphism groups of Zariski open affine subsets of the affine plane
Autorzy:
Jelonek, Zbigniew
Powiązania:
https://bibliotekanauki.pl/articles/1311651.pdf
Data publikacji:
1994
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
polynomial automorphisms
the set of fixed points of a polynomial automorphism
the affine plane
Opis:
We study some properties of the affine plane. First we describe the set of fixed points of a polynomial automorphism of ℂ². Next we classify completely so-called identity sets for polynomial automorphisms of ℂ². Finally, we show that a sufficiently general Zariski open affine subset of the affine plane has a finite group of automorphisms.
Źródło:
Annales Polonici Mathematici; 1994-1995, 60, 2; 163-171
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximating fixed points of a countable family of strict pseudocontractions in Banach spaces
Autorzy:
Cholamjiak, P.
Powiązania:
https://bibliotekanauki.pl/articles/254873.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
common fixed points
convergence theorem
modified Mann iteration
strict pseudocontractions
q-uniformly smooth Banach spaces
Opis:
We prove the strong convergence of the modified Mann-type iterative scheme for a countable family of strict pseudocontractions in q-uniformly smooth Banach spaces. Our results mainly improve and extend the results announced in [Y. Yao, H. Zhou, Y.-C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J. Appl. Math. Comput. 29 (2009), 383–389].
Źródło:
Opuscula Mathematica; 2014, 34, 1; 67-79
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Time to the convergence of evolution in the space of population states
Autorzy:
Karcz-Dulęba, I.
Powiązania:
https://bibliotekanauki.pl/articles/907643.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
ewolucja fenotypowa
układ dynamiczny
punkt stały
phenotypic evolution
dynamical system
time to convergence
fixed points
Opis:
Phenotypic evolution of two-element populations with proportional selection and normally distributed mutation is considered. Trajectories of the expected location of the population in the space of population states are investigated. The expected location of the population generates a discrete dynamical system. The study of its fixed points, their stability and time to convergence is presented. Fixed points are located in the vicinity of optima and saddles. For large values of the standard deviation of mutation, fixed points become unstable and periodical orbits arise. In this case, fixed points are also moved away from optima. The time to convergence to fixed points depends not only on the mutation rate, but also on the distance of the points from unstability. Results show that a population spends most time wandering slowly towards the optimum with mutation as the main evolution factor.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2004, 14, 3; 279-287
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 26

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