- Zeitschriftendaten
- Format
- Zeitschrift
- eISSN
- 2083-8492
- Erstveröffentlichung
- 05 Apr 2007
- Erscheinungsweise
- 4 Hefte pro Jahr
- Sprachen
- Englisch

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Uneingeschränkter Zugang

#### On an algorithm for the problem of tracking a trajectory of a parabolic equation

Seitenbereich: 457 - 465

#### Zusammenfassung

In this paper, we consider the problem of tracking a solution of a reference parabolic equation by a solution of another equation. A stable algorithm based on the extremal shift method is proposed for this problem. The algorithm is designed to work on a sufficiently large time interval where both equations operate.

#### Schlüsselwörter

- parabolic equation
- tracking problem
- unknown disturbance

Uneingeschränkter Zugang

#### Feedback design of differential equations of reconstruction for second–order distributed parameter systems

Seitenbereich: 467 - 475

#### Zusammenfassung

The paper aims at studying a class of second-order partial differential equations subject to uncertainty involving unknown inputs for which no probabilistic information is available. Developing an approach of feedback control with a model, we derive an efficient reconstruction procedure and thereby design differential equations of reconstruction. A characteristic feature of the obtained equations is that their inputs formed by the feedback control principle constructively approximate unknown inputs of the given second-order distributed parameter system.

#### Schlüsselwörter

- second-order partial differential equation
- equations of reconstruction

Uneingeschränkter Zugang

#### A numerical solution for a class of time fractional diffusion equations with delay

Seitenbereich: 477 - 488

#### Zusammenfassung

This paper describes a numerical scheme for a class of fractional diffusion equations with fixed time delay. The study focuses on the uniqueness, convergence and stability of the resulting numerical solution by means of the discrete energy method. The derivation of a linearized difference scheme with convergence order ^{2−α}+ ^{4}) in L_{∞}-norm is the main purpose of this study. Numerical experiments are carried out to support the obtained theoretical results.

#### Schlüsselwörter

- fractional diffusion equation with delay
- difference scheme
- convergence analysis

Uneingeschränkter Zugang

#### Exact null controllability, complete stabilizability and continuous final observability of neutral type systems

Seitenbereich: 489 - 499

#### Zusammenfassung

For abstract linear systems in Hilbert spaces we revisit the problems of exact controllability and complete stabilizability (stabilizability with an arbitrary decay rate), the latter property being related to exact null controllability. We also consider the case when the feedback is not bounded. We obtain a characterization of complete stabilizability for neutral type systems. Conditions for exact null controllability of neutral type systems are discussed. By duality, we obtain a result about continuous final observability. Illustrative examples are given.

#### Schlüsselwörter

- exact null controllability
- complete stabilizability
- final observability
- neutral type system

Uneingeschränkter Zugang

#### The controllability of nonlinear implicit fractional delay dynamical systems

Seitenbereich: 501 - 513

#### Zusammenfassung

This paper is concerned with the controllability of nonlinear fractional delay dynamical systems with implicit fractional derivatives for multiple delays and distributed delays in control variables. Sufficient conditions are obtained by using the Darbo fixed point theorem. Further, examples are given to illustrate the theory.

#### Schlüsselwörter

- controllability
- fractional delay differential equation
- Mittag-Leffler function
- fixed point theorem

Uneingeschränkter Zugang

#### Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation

Seitenbereich: 515 - 525

#### Zusammenfassung

The aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg–de Vries equation. The method is based on a combination of a discrete variational derivative method in time and finite volume element approximation in space. The resulting scheme is accurate, robust and energy-preserving. In addition, for comparison, we also develop a momentum-preserving finite volume element scheme and an implicit midpoint finite volume element scheme. Finally, a complete numerical study is developed to investigate the accuracy, conservation properties and long time behaviors of the energy-preserving scheme, in comparison with the momentum-preserving scheme and the implicit midpoint scheme, for the complex modified Korteweg–de Vries equation.

#### Schlüsselwörter

- mass
- energy
- momentum
- finite volume element method
- complex modified Korteweg–de Vries equation

Uneingeschränkter Zugang

#### Accurate gradient computations at interfaces using finite element methods

Seitenbereich: 527 - 537

#### Zusammenfassung

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is to get not only an accurate solution, but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea of

#### Schlüsselwörter

- elliptic interface problems
- gradient/flux computation
- IFEM
- mixed FE formulation
- computational tube

Uneingeschränkter Zugang

#### Feedback linearization of an active magnetic bearing system operated with a zero–bias flux

Seitenbereich: 539 - 548

#### Zusammenfassung

Input-output linearization by state feedback is applied to a flux-controlled active magnetic bearing (AMB) system, operated in the zero-bias mode. Two models of the AMB system are employed. The first one is described by the third-order dynamics with a flux-dependent voltage switching scheme, whereas the second one is the fourth-order system, called self-sensing AMB, since it does not require the measurement of the rotor position. In the case of that system we had to find the flat outputs to guarantee its stability. The proposed control schemes are verified by means of numerical simulations performed within the Matlab environment.

#### Schlüsselwörter

- active magnetic bearing
- flux control
- zero-bias
- feedback linearization
- flat outputs

Uneingeschränkter Zugang

#### The interval Shapley value of an M/M/1 service system

Seitenbereich: 549 - 562

#### Zusammenfassung

Service systems and their cooperation are one of the most important and hot topics in management and information sciences. To design a reasonable allocation mechanism of service systems is the key issue in the cooperation of service systems. In this paper, we systematically introduce the interval Shapley value as cost allocation of cooperative interval games 〈

#### Schlüsselwörter

- M/M/1 service system
- cooperative interval game
- cost allocation
- Shapley value

Uneingeschränkter Zugang

#### A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

Seitenbereich: 563 - 573

#### Zusammenfassung

In a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming different

#### Schlüsselwörter

- pentagonal intuitionistic fuzzy number
- interval valued intuitionistic fuzzy number
- interval valued intuitionistic fuzzy arithmetic
- modified interval valued intuitionistic fuzzy arithmetic
- interval valued intuitionistic fuzzy multi-objective linear programming problem

Uneingeschränkter Zugang

#### Is an interval the right result of arithmetic operations on intervals?

Seitenbereich: 575 - 590

#### Zusammenfassung

For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, this is not true. Interval arithmetic is complicated. This is confirmed by the fact that, for years, new, alternative versions of this arithmetic have been created and published. These new versions tried to remove shortcomings and weaknesses of previously proposed options of the arithmetic, which decreased the prestige not only of interval arithmetic itself, but also of fuzzy arithmetic, which, to a great extent, is based on it. In our opinion, the main reason for the observed shortcomings of the present IA is the assumption that the direct result of arithmetic operations on intervals is also an interval. However, the interval is not a direct result but only a simplified representative (indicator) of the result. This hypothesis seems surprising, but investigations prove that it is true. The paper shows what conditions should be satisfied by the result of interval arithmetic operations to call it a “result”, how great its dimensionality is, how to perform arithmetic operations and solve equations. Examples illustrate the proposed method of interval computations.

#### Schlüsselwörter

- interval arithmetic
- one-dimensional interval arithmetic
- multi-dimensional interval arithmetic
- RDM interval arithmetic

Uneingeschränkter Zugang

#### A column generation technique for routing and spectrum allocation in cloud–ready survivable elastic optical networks

Seitenbereich: 591 - 603

#### Zusammenfassung

Driven by increasing user requirements and expectations, the fast development of telecommunications networks brings new challenging optimization problems. One of them is routing and spectrum allocation (RSA) of three types of network flows (unicast, anycast, multicast) in elastic optical networks (EONs) implementing dedicated path protection (DPP). In the paper, we model this problem as integer linear programming (ILP) and we introduce two new optimization approaches—a dedicated heuristic algorithm and a column generation (CG)-based method. Then, relying on extensive simulations, we compare algorithm performance with reference methods and evaluate CG efficiency in detail. The results show that the proposed CG method significantly outperforms reference algorithms and achieves results very close to optimal ones (the average distance to optimal results was at most 2.1%).

#### Schlüsselwörter

- elastic optical network
- anycast traffic
- multicast traffic
- network survivability
- column generation technique

Uneingeschränkter Zugang

#### Heuristic algorithms for joint optimization of unicast and anycast traffic in elastic optical network–based large–scale computing systems

Seitenbereich: 605 - 622

#### Zusammenfassung

In recent years elastic optical networks have been perceived as a prospective choice for future optical networks due to better adjustment and utilization of optical resources than is the case with traditional wavelength division multiplexing networks. In the paper we investigate the elastic architecture as the communication network for distributed data centers. We address the problems of optimization of routing and spectrum assignment for large-scale computing systems based on an elastic optical architecture; particularly, we concentrate on anycast user to data center traffic optimization. We assume that computational resources of data centers are limited. For this offline problems we formulate the integer linear programming model and propose a few heuristics, including a meta-heuristic algorithm based on a tabu search method. We report computational results, presenting the quality of approximate solutions and efficiency of the proposed heuristics, and we also analyze and compare some data center allocation scenarios.

#### Schlüsselwörter

- elastic optical networks
- optimization
- distributed data center
- algorithm
- tabu search

Uneingeschränkter Zugang

#### On the existence of a nontrivial equilibrium in relation to the basic reproductive number

Seitenbereich: 623 - 636

#### Zusammenfassung

Equilibrium analysis in autonomous evolutionary models is of central importance for developing long term treatments. This task typically includes checks on the existence and stability of some equilibria. Prior to touching on the stability, one often attempts to determine the existence where the basic reproductive number _{0} plays a critical role as a threshold parameter. When analyzing a nontrivial equilibrium (e.g., an endemic, boundary, or coexistence equilibrium) where _{0} is explicit, we usually come across a typical result: if _{0} >1, then a nontrivial equilibrium exists in the biological sense. However, for more sophisticated models, _{0} can be too complicated to be revealed in terms of the involving parameters; the task of relating the formulation of a nontrivial equilibrium to _{0} thus becomes intractable. This paper shows how to mitigate such a problem with the aid of functional analysis, adopting the framework of a nonlinear eigenvalue problem. An equilibrium equation is first to be transformed into a canonical equation in a lower dimension, and then the existence is confirmed under several conditions. Three models are tested showing the applicability of this approach.

#### Schlüsselwörter

- autonomous model
- nontrivial equilibrium
- basic reproductive number
- nonlinear eigenvalue problem

Uneingeschränkter Zugang

#### On the Farey sequence and its augmentation for applications to image analysis

Seitenbereich: 637 - 658

#### Zusammenfassung

We introduce a novel concept of the

#### Schlüsselwörter

- Farey sequence
- Farey table
- fraction rank
- theory of fractions
- image analysis