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1
Content available The composition operators between Morrey type spaces
Xu Jiajia
Science, Technology and Innovation
|
2022
|
Vol. 16, no. 3-4
50--56
EN
In this paper, we characterize the boundedness of composition operator Cφ from Morrey space H²K₁ to H²K₂ on the unit complex disk.
2
Content available remote Unconditionally positive NSFD and classical finite difference schemes for biofilm formation on medical implant using Allen-Cahn equation
Tijani Yusuf O., Appadu Appanah Rao
Demonstratio Mathematica
|
2022
|
Vol. 55, nr 1
40--60
EN
The study of biofilm formation is becoming increasingly important. Microbes that produce biofilms have complicated impact on medical implants. In this paper, we construct an unconditionally positive non-standard finite difference scheme for a mathematical model of biofilm formation on a medical implant. The unknowns in many applications reflect values that cannot be negative, such as chemical component concentrations or population numbers. The model employed here uses the bistable Allen-Cahn partial differential equation, which is a generalization of Fisher’s equation. We study consistency and convergence of the scheme constructed. We compare the performance of our scheme with a classical finite difference scheme using four numerical experiments. The technique used in the construction of unconditionally positive method in this study can be applied to other areas of mathematical biology and sciences. The results here elaborate the benefits of the non-standard approximations over the classical approximations in practical applications.
3
Content available remote Existence and uniqueness of the weak solution for Keller-Segel model coupled with Boussinesq equations
Slimani Ali, Bouzettouta Lamine, Guesmia Amar
Demonstratio Mathematica
|
2021
|
Vol. 54, nr 1
558--575
EN
Keller-Segel chemotaxis model is described by a system of nonlinear partial differential equations: a convection diffusion equation for the cell density coupled with a reaction-diffusion equation for chemoattractant concentration. In this work, we study the phenomenon of Keller-Segel model coupled with Boussinesq equations. The main objective of this work is to study the global existence and uniqueness and boundedness of the weak solution for the problem, which is carried out by the Galerkin method.
4
Adjoint of generalized Cesáro operators on analytic function spaces
Naik Sunanda, Nath Pankaj K.
Journal of Applied Analysis
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2020
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Vol. 26, nr 2
185--192
EN
In this article, we define a convolution operator and study its boundedness on mixed-norm spaces. In particular,we obtain awell-known result on the boundedness of composition operators given by Avetisyan and Stević in [K. Avetisyan and S. Stević, The generalized Libera transform is bounded on the Besov mixednorm, BMOA and VMOA spaces on the unit disc, Appl. Math. Comput. 213 (2009), no. 2, 304-311]. Also we consider the adjoint Ab,c for b > 0 of two parameter families of Cesáro averaging operators and prove the boundedness on Besov mixed-norm spaces Bp,qα+(c−1) for c > 1.
5
Content available remote On Deadlockability, Liveness and Reversibility in Subclasses of Weighted Petri Nets
Hujsa T., Devillers R.
Fundamenta Informaticae
|
2018
|
Vol. 161, nr 4
383--421
EN
Liveness, (non-)deadlockability and reversibility are behavioral properties of Petri nets that are fundamental for many real-world systems. Such properties are often required to be monotonic, meaning preserved upon any increase of the marking. However, their checking is intractable in general and their monotonicity is not always satisfied. To simplify the analysis of these features, structural approaches have been fruitfully exploited in particular subclasses of Petri nets, deriving the behavior from the underlying graph and the initial marking only, often in polynomial time. In this paper, we further develop these efficient structural methods to analyze deadlockability, liveness, reversibility and their monotonicity in weighted Petri nets. We focus on the join-free subclass, which forbids synchronizations, and on the homogeneous asymmetric-choice subclass, which allows conflicts and synchronizations in a restricted fashion. For the join-free nets, we provide several structural conditions for checking liveness, (non-)deadlockability, reversibility and their monotonicity. Some of these methods operate in polynomial time. Furthermore, in this class, we show that liveness, non-deadlockability and reversibility, taken together or separately, are not always monotonic, even under the assumptions of structural boundedness and structural liveness. These facts delineate more sharply the frontier between monotonicity and non-monotonicity of the behavior in weighted Petri nets, present already in the join-free subclass. In addition, we use part of this new material to correct a flaw in the proof of a previous characterization of monotonic liveness and boundedness for homogeneous asymmetric-choice nets, published in 2004 and left unnoticed.
6
Content available remote Completeness Results for Generalized Communication-free Petri Nets with Arbitrary Arc Multiplicities
Mayr E. W., Weihmann J.
Fundamenta Informaticae
|
2016
|
Vol. 143, nr 3/4
355--391
EN
We investigate gcf-Petri nets, a generalization of communication-free Petri nets allowing arbitrary arc multiplicities, and characterized by the sole restriction that each transition has at most one incoming arc. We use canonical firing sequences with nice properties for gcf-PNs to show that the RecLFS, (zero-)reachability, covering, and boundedness problems of gcf-PNs are in PSPACE. By simulating PSPACE-Turing machines by gss-PNs, a subclass of gcf-PNs where additionally all transitions have at most one outgoing arc, we ultimately obtain PSPACE-completess for these problems in case of gss-PNs or gcf-PNs. Additionally, we prove PSPACE-completeness for the liveness problem of gcf-PNs. Last, we show PSPACE-hardness as well as a doubly exponential space upper bound for the containment and equivalence problems of gss-PNs or gcf-PNs.
7
Content available remote A Survey of Decidability Results for Elementary Object Systems
Köhler-Bußmeier M.
Fundamenta Informaticae
|
2014
|
Vol. 130, nr 1
99--123
EN
This contribution presents recent results on Elementary Object Systems (EOS). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. In this work we study the relationship of EOS to existing Petri net formalisms. It turns out that EOS are equivalent to counter programs. But even for the restricted subclass of conservative EOS reachability and liveness are undecidable problems. On the other hand for other properties like boundedness are still decidable for conservative EOS. We also study the sub-class of generalised state machines, which is worth mentioning since it combines decidability of many theoretically interesting properties with a quite rich practical modelling expressiveness.
8
Content available remote Qualitative properties for a higher order rational difference equation
Elabbasy E.M., Eleissawy S M
Fasciculi Mathematici
|
2013
|
Nr 50
33--50
EN
The main objective of this paper is to study the behavior of solutions of the difference equation ...[wzór] where the initial conditions x-r, x-r+1,...,x0 are arbitrary positive real numbers, r = max{q, l,p} is nonnegative integer and a, b, c, d are positive constants. Also, we give the solution of some special cases of this equation.
9
Content available remote Weighted composition operators from weighted hardy spaces to weighted-type spaces
Zhu X.
Demonstratio Mathematica
|
2013
|
Vol. 46, nr 2
335--344
EN
The boundedness and compactness of the weighted composition operator from weighted Hardy spaces to weighted-type spaces are studied in this paper.
10
Content available Stability criteria for a class of stochastic distributed delay systems
Ficak B., Klamka J.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2013
|
Vol. 61, nr 1
221-228
EN
In the paper linear distributed delay stochastic systems are considered. Using theory of stochastic differential equations sufficient conditions for different kinds of stability are formulated and proved. The article attempts to generalise results presented in the paper [1] and thus theorems proved in [1] become a special case of a generalised approach. The considered class is wider - the function that influence dynamics of a problem can be a real solution of N-degree linear deterministic differential equation. Therefore the generalised reduction technique of distributed delay to lumped delay has to be applied. Criteria for numerous properties of the aforementioned class followed Mao theory designed for point delay systems [2, 3].
11
Content available remote Conservative Elementary Object Systems
Köhler-Bußmeier M., Heitmann F.
Fundamenta Informaticae
|
2012
|
Vol. 120, nr 3/4
325-339
EN
This contribution presents decidability results for the formalism of Elementary Object Systems (EOS). Object nets are Petri nets which have Petri nets as tokens – an approach known as the nets-within-nets paradigm. In this paper we study the relationship of the reachability and the liveness problem. We prove that both problems are undecidable for EOS (even for the subclass of conservative EOS) while it is well known that both are decidable for classical p/t nets. Despite these undecidability results, boundedness can be decided for conservative EOS using a monotonicity argument similar to that for p/t nets.
12
Content available On the global attractivity and the periodic character of a recursive sequence
Elsayed E. M.
Opuscula Mathematica
|
2010
|
Vol. 30, no. 4
431-446
EN
In this paper we investigate the global convergence result, boundedness, and periodicity of solutions of the recursive sequence [formula], where the parameters a, b, c, d and e are positive real numbers and the initial conditions x-2, x-1 and x0 are positive real numbers.
13
Content available remote Patterns of boundedness of the rational system xn+1 = ...[wzór] and yn+1 = ...[wzór]
Camouzis E., Drymonis E., Ladas G.
Fasciculi Mathematici
|
2010
|
Nr 44
9-18
EN
We establish the boundedness character of solutions of the rational system in the title, with the parameters α1, β1 positive and the remaining eight parameters nonnegative and with arbitrary nonnegative initial conditions such that the denominators are always positive. We present easily verifiable necessary and sufficient conditions, explicitly stated in terms of the parameters, which determine the boundedness character of the system.
14
Content available remote On the solutions of a rational system of difference equations
Elsayed E. M.
Fasciculi Mathematici
|
2010
|
Nr 45
25-36
EN
In this paper we deal with the solutions of the system of the difference equations xn+1 = ...[wzór], yn+1 = ...[wzór], with a nonzero real numbers initial conditions.
15
Content available remote On the difference equation xn+1 = α + ...[wzór]
Yalçinkaya ĺ.
Fasciculi Mathematici
|
2009
|
Nr 42
133-139
EN
In this paper, we investigate the global behavior of the difference equation of order three xn+1 = α + ...[wzór], n = 0, 1,… where the parameters α, k ∈ (0, ∞) and the initial values x-2, x-1 and x0 are arbitrary positive real numbers.
16
Content available remote On some fundamental aspects of certain sum-difference equations
Pachpatte B. G.
Fasciculi Mathematici
|
2009
|
Nr 41
119-134
17
Content available remote Sequences which satisfy a logarithmic linear inequality
Stević S.
Fasciculi Mathematici
|
2004
|
Nr 34
85-95
EN
In this note we discuss the boundedness and convergence of a sequence which satisfies the following logarithmic linear inequality where k(1) + k(2) +... + km = 1. We focus our attention especially to the case n = 2. Also we describe a situation where this inequality occurs naturally.
18
Content available remote Boundedness and persistence of solutions of a nonlinear difference equation
Stević S.
Demonstratio Mathematica
|
2003
|
Vol. 36, nr 1
99--104
EN
In this paper we obtain sufficient conditions for the boundedness as well ;is for the unboundedness of the positive solutions of the difference equation xn+1=f(xn,...,xn-k+1), n=0,1,2,...,where k is a positive integer and the initial conditions x-k+1, X-k+2,...x0 are arbitrary positive numbers.
19
Content available remote Abundance, biomass and density boundaries in the Hymenoptera : analysis of the abundance - weight relationship and differences between forest and open landscape habitats
Ulrich W.
Polish Journal of Ecology
|
1999
|
Vol. 47, no 1
73-86
EN
The density - weight distributions of the hymenopteran species in a beech forest on limestone and a dry meadow on limestone near Gottingen (FRG) were studied. Species and density distributions (logarithmic size classes) turned out to follow normal and log-normal distributions with the meadow having the more narrow shape. Upper weight classes accumulated more total biomass m^-2 than lower ones, resulting in a rejection of the equal biomass hypothesis in the case of the Hymenoptera. An analysis of the density - weight relationship revealed an upper density boundary for the hymenopteran species which can be defined by second order polynomial functions. Mean and upper densities of small hymenopteran species ranged well below their boundaries, with an asymptotic relationship between distance from the boundary and species weight. The area defined by the boundaries may mark the area of stability: exceeding the species specific boundary was always followed by a marked decline oreven a collapse of population density.
20
Content available remote Stability for certain fourth order nonlinear differential equations
Lin S., Liu Z., Yu Y.
Demonstratio Mathematica
|
1998
|
Vol. 31, nr 1
87-96
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