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1
Content available remote Multiprocessor Scheduling Problem with Release and Delivery Times
Grigoreva Natalia
Annals of Computer Science and Information Systems
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2020
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Vol. 21
263--269
EN
The multiprocessor scheduling problem is defined as follows: tasks have to be executed on several parallel identical processors. For each task we know release time, processing time and delivery time. At most one job can be processed at a time, but all jobs may be simultaneously delivered. Preemption on processors is not allowed. The objective is to minimize the time, by which all tasks are delivered. Scheduling tasks among parallel processors is a NP-hard problem in the strong sense. The best known approximation algorithm is Jackson's algorithm, which generates the list schedule by giving priority to the ready job with the largest delivery time. This algorithm generates no delay schedules. We define an IIT (inserted idle time) schedule as a feasible schedule in which a processor is kept idle at a time when it could begin processing a task. The paper proposes the approximation inserted idle time algorithm for the multiprocessor scheduling. It is proved that deviation of this algorithm from the optimum is smaller then twice the largest processing time. To illustrate the efficiency of our approach we compared two algorithms on randomly generated sets of jobs.
2
Content available remote An Exact Two-Phase Method For Optimal Camera Placement In Art Gallery Problem
Alihodzic Adis, Delalic Sead, Hasic Damir
Annals of Computer Science and Information Systems
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2020
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Vol. 21
215--222
EN
It is well-known that determining the optimal number of guards which can cover the interior of a simple nonconvex polygon presents an NP-hard problem. The optimal guard placement can be described as a problem which seeks for the smallest number of guards required to cover every point in a complex environment. In this paper, we propose an exact twophase method as well as an approximate method for tackling the mentioned issue. The proposed exact approach in the first phase maps camera placement problem to the set covering problem, while in the second phase it uses famous state-of-the-art CPLEX solver to address set covering problem. The performance of our combined exact algorithm was compared to the performance of the approximate one. According to the results presented in the experimental analysis, it can be seen that the exact approach outperforms the approximate method for all instances.
3
Best approximation in quotient probabilistic normed space
Sen M., Nath S., Tripathy B. C.
Journal of Applied Analysis
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2017
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Vol. 23, nr 1
53--57
EN
In this article, we study the best approximation in quotient probabilistic normed space. We define the notion of quotient space of a probabilistic normed space, then prove some theorems of approximation in quotient space are extended to quotient probabilistic normed space.
4
Content available remote A Korovkin type approximation theorem and its application
Büyükyazici Í.
Fasciculi Mathematici
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2010
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Nr 45
13-23
EN
In this paper, we investigate a Korovkin-type approximation theorem for sequences of positive linear operators on the space of all continuous real valued functions defined on [a,b]. We also obtain some approximation properties for sequences of positive linear operators constructed by means of the Bernstein operator.
5
Content available remote Voronovskaja-type theorems and approximation theorems for a class of GBS operators
Pop O. T.
Fasciculi Mathematici
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2009
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Nr 42
91-108
EN
In this paper we will demonstrate a Voronovskajatype theorems and approximation theorems for GBS operators associated to some linear positive operators. Through parti- cular cases, we obtain statements verified by the GBS operators of Bernstein, Schurer, Durrmeyer, Kantorovich, Stancu, Bleimann- Butzer-Hahn, Mirakjan-Favard-Szász, Baskakov, Meyer-König and Zeller, Ismail-May.
6
Content available remote On generalized Mazhar-Totik operators
Wachnicki E.
Demonstratio Mathematica
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2005
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Vol. 38, nr 1
143--151
EN
In this paper we consider the continuous version of the operator investigated by Mazhar and Totik ([2]). Some applications for the limit problem are indicated.
7
Content available remote Global approximation theorems for the generalized modified Szasz-Mirakyan operators in polynomial weight spaces
Świderski T.
Demonstratio Mathematica
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2003
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Vol. 36, nr 2
383--392
EN
In the present paper we study the modified Szasz-Mirakyan operators. This modification generalizes the integral operators proposed by S. M. Mazhar and V. Totik in [3]. Moreover we present bonduary value problems related to these integrals.
8
Some introductory remarks on modeling of the electromagnetic phenomena
Krawczyk A., Kotowski R.
Journal of Technical Physics
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2002
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Vol. 43, no 4
417-418
9
Motional finite element simulation of magnetic brakes and solid rotor induction machines
De Gersem H., Hameyer K.
Journal of Technical Physics
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2002
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Vol. 43, no 4
389-397
EN
The torques of a magnetic brake and a solid rotor induction machine, fed by sinusoidal voltage sources, are simulated by a motional finite element method. Oscillatory solutions occurring for motional models with elevated velocities, are prevented by adaptive mesh refinement relying upon intermediate solutions stabilised by upwinded finite element test functions. A relaxed successive approximation deals with the non-linear material properties. The connections of the conductors and windings within the finite element model to external loads, impedances and supplies are represented by an electric circuit and added to the system of equations. The technical examples indicate the advantages of the motional formulation.
10
Using improved impedance boundary conditions to derive distributions of electromagnetic fields
Apanasewicz S., Pawłowski S.
Journal of Technical Physics
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2000
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Vol. 41, no 2
159-171
EN
In this paper the improved boundary condition of impedance type the harmonic low-frequency electromagnetic field calculation is presented. It is based on the application of successive approximations in two-dimensional case. As an illustration of the presented method the calculation of electromagnetic field in the neighbourhood of metallic wall is given. A comparison of approximate solutions with the exact one is done (Figs. 3-8).
11
Aproksymacja i stabilizacja odporna wielowymiarowych układów liniowych stacjonarnych ze skupionymi, współmiernymi opóźnieniami
Kozera W.
Studia / Wyższa Szkoła Morska w Szczecinie
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1999
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nr 31
1-179
PL
Istnienie opóźnień w procesach transportu, mieszania, spalania, ewolucji, fluktuacji ekonomicznych, biurokracji sprawia, że aby efektywnie sterować tymi procesami należy uwzględnić opóźnienia w ich modelach matematycznych. W niniejszej pracy przedstawiono oryginalne metody skończenie wymiarowej aproksymacji równań różniczkowo-różnicowych, opisujących wielowymiarowe układy liniowe stacjonarne ze skupionymi opóźnieniami, za pomocą zwyczajnych równań różniczkowych lub różnicowych. Ułatwia to znacznie analizę oraz syntezę tych układów. Ponadto zaproponowano sposoby wyznaczania łatwych do realizacji technicznej stabilizujących sprzężeń zwrotnych ciągłych i dyskretno-ciągłych (hybrydowych), odpornych na niedokładności modelowania. Można je łatwo uogólnić na przypadek syntezy kompensatorów odpornych takżena niepewności strukturalne wynikające np. ze zmian parametrów, bądź nieliniowości układu oraz spełniające szereg dodatkowych wymagań jakościowych (kompensatory wielozadaniowe). Prezentowane metody zostały zweryfikowane na licznych, odpowiednio dobranych przykładach, a uzyskane wyniki świadczą o ich dużej efektywności. Praca zawiera jedynie własne rozwiązania autora rozpatrywanych zagadnień, które porównano z ważniejszymi, praktycznymi rozwiązaniami znanymi z literatury.
EN
Due to time delays in processes of transport, mixing, burning, evolution, economic fluctuation, bureaucracy etc., the effective control of these processes requires accounting for these delays in mathematical models of the processes. This work presents original methods of finite-dimensional approximations of differential-difference equations describing multivariable linear time-invariant systems with commensurate delays. These approximations are performed bymeans of ordinary differential of difference equations. This substantially facilitates the analysis and synthesis of the systems. Moreover, presented are ways of determining stabilizing continuous and discrete-continnuous (hybrid) robust control laws attenuating the unstructured uncertainties of modelling, easy for technical realization. They can be readily generalized to cover the synthesis of robust compensators attenuating also structured uncertainties resulting e.g. either from parameter variations or nonlinear disortion of the system and satisfying a number of additional performance specifications (multipurpose compensators). The described methods have been verified by many relevant examples. The results prove high effectiveness of the methods. The work contains only the author's solutions of the problems and compares them with major practical solutions found in the literature on the subject.
12
Content available remote On approximation of (1.A) semigroups by discrete semigroups
Bobrowski A.
Bulletin of the Polish Academy of Sciences. Mathematics
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1998
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Vol. 46, no 2
141-154
EN
A generalization of a recent result of N. Tanaka concerning approximation by "integrated" discrete semigroups is presented.
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