Mathematical and Computational Applications

133 KiB

Open AccessArticle

Perturbative Derivation and Comparisons of Root-Finding Algorithms with Fourth Order Derivatives

by M. Pakdemirli, H. Boyacı and H. A. Yurtsever

Math. Comput. Appl. 2007, 12(2), 117-124; https://doi.org/10.3390/mca12020117 - 1 Aug 2007

Cited by 22 | Viewed by 1423

Perturbation theory is systematically used to generate root finding algorithms with fourth order derivatives. Depending on the number of correction terms in the perturbation expansion and the number of Taylor expansion terms, different root finding formulas can be generated. Expanding Taylor series up [...] Read more.

Perturbation theory is systematically used to generate root finding algorithms with fourth order derivatives. Depending on the number of correction terms in the perturbation expansion and the number of Taylor expansion terms, different root finding formulas can be generated. Expanding Taylor series up to fourth order derivatives and taking two, three and four correction terms in the perturbation expansions, three different root finding algorithms are derived. The algorithms are contrasted numerically with each other as well as with the Newton-Raphson algorithm. It is found that the quadruple-correction-term algorithm performs better than the others. Full article

167 KiB

Open AccessArticle

Recursive Algorithm for Generating Two-Staged Cutting Patterns of Punched Strips

by Yaodong Cui

Math. Comput. Appl. 2007, 12(2), 107-115; https://doi.org/10.3390/mca12020107 - 1 Aug 2007

Cited by 1 | Viewed by 1330

Abstract

The manufacture of parts made of metal sheet often includes two successive processes: the cutting process at which a guillotine shear cuts the sheet into strips, and the punching process at which a stamping press punches out the blanks from the strips. This [...] Read more.

The manufacture of parts made of metal sheet often includes two successive processes: the cutting process at which a guillotine shear cuts the sheet into strips, and the punching process at which a stamping press punches out the blanks from the strips. This paper presents an algorithm for generating optimal two-staged cutting patterns of strips for the cutting process. At the first stage the sheet is divided into segments with parallel cuts. Each segment contains strips with the same length and direction. The segments are cut into strips at the second stage. The algorithm calls a recursion function to determine the optimal strip layouts on segments of various lengths, and calls another recursion function to optimally arrange the segments in the sheet, so that the value of the pattern reaches maximum. The computational results indicate that the algorithm is efficient both in computation time and in material usage. Full article

193 KiB

Open AccessArticle

Multi-Channel Bi-Level Heterogeneous Servers Bulk Arrival Queueing System with Erlangian Service Time

by Ahmed M. M. Sultan

Math. Comput. Appl. 2007, 12(2), 97-105; https://doi.org/10.3390/mca12020097 - 1 Aug 2007

Cited by 9 | Viewed by 1085

Abstract

An easily applicable algorithm to solve problems involving bulk-arrival queues with a breakdown of one of the heterogeneous servers in case of steady state is introduced. A Monte Carlo study for numerically finding the limiting distribution of the number in the system for [...] Read more.

An easily applicable algorithm to solve problems involving bulk-arrival queues with a breakdown of one of the heterogeneous servers in case of steady state is introduced. A Monte Carlo study for numerically finding the limiting distribution of the number in the system for the bulk arrival, multi-server queueing model (M[x]/EK/C; C-1/FCFS) with heterogeneous servers is presented. The system consists of servers of varying efficiency. This paper presents multi-channel queue with Poisson arrivals, Erlangian service time distributions in which all servers have equal breakdown chance. Measures of system performance including mean queue length, mean waiting time, and blocking probability are reported. Numerical results are obtained by simulation of the entire system. Examples of extensive numerical results for certain measures of efficiency are presented in tabular and chart form. In all cases, the proposed method is computationally efficient, accurate and reliable for both high and low values of the model parameters. Full article

251 KiB

Open AccessArticle

The Use of Artificial Neural Networks in Simulation of Mobile Ground Vehicles

by Haldun Göktas, Abdullah Çavusoğlu, Baha Şen and İhsan Toktaş

Math. Comput. Appl. 2007, 12(2), 87-96; https://doi.org/10.3390/mca12020087 - 1 Aug 2007

Viewed by 1113

Abstract

In this study, we have developed a platform which incorporates Artificial Neural Networks (ANNs) in simulating body dynamics of mobile ground vehicles (e.g. cars). This is a part of our research project in which we plan to provide a platform for educating the [...] Read more.

In this study, we have developed a platform which incorporates Artificial Neural Networks (ANNs) in simulating body dynamics of mobile ground vehicles (e.g. cars). This is a part of our research project in which we plan to provide a platform for educating the driver candidates in virtual environments: where the drivers can be educated fully in “Artificial Cities”. To start with, 6 different makes of cars with different engine properties has been simulated with the appropriate data provided by the manufacturers and rules of physics. A joystick steering wheel has been used to produce the necessary inputs for the ANN based physics engine. To train the network, Scaled Conjugate Gradient (SCG) and Levenberg-Marquardt (LM) learning algorithms and a logistic sigmoid transfer function have been used. The statistical error levels are negligible. The Absolute Fraction of Variance (R²) values for both the training and test data are about 99.999% and the mean error value for both data group is lesser than 0.5%. Full article

165 KiB

Open AccessArticle

Optimal Retailer’s Inventory Policy Under Supplier Credits Linked to Retailer Payment Time

by Yung-Fu Huang and Kuang-Hua Hsu

Math. Comput. Appl. 2007, 12(2), 77-86; https://doi.org/10.3390/mca12020077 - 1 Aug 2007

Cited by 4 | Viewed by 1250

Abstract

This paper wants to investigate the retailer’s optimal cycle time and optimal payment time under supplier credits including conditionally permissible delay in payments and cash discount depending on retailer payment time. That is, the retailer can obtain fully permissible delay in payments and [...] Read more.

This paper wants to investigate the retailer’s optimal cycle time and optimal payment time under supplier credits including conditionally permissible delay in payments and cash discount depending on retailer payment time. That is, the retailer can obtain fully permissible delay in payments and cash discount if the payment is paid before the period of full delay payments permitted by the supplier. Otherwise, the retailer will just obtain partially permissible delay in payments within the period of partial delay payments permitted by the supplier. The supplier uses this policy to attract retailer to pay the payment as soon as possible to shorten the collection period. One theorem is developed to efficiently determine the optimal replenishment and payment policy for the retailer. Full article

166 KiB

Open AccessArticle

A Correspondence Between IBA-I and IBA-II Model and Electromagnetic Transitions of Some Erbium Isotopes

by Harun Resit Yazar and İhsan Uluer

Math. Comput. Appl. 2007, 12(2), 69-76; https://doi.org/10.3390/mca12020069 - 1 Aug 2007

Cited by 1 | Viewed by 1085

Abstract

Since the lowest levels are symmetric under the interchange of neutrons and protons from calculations in the interacting boson approximation IBA-2 model, IBA-1 model space, in which neutron and proton degrees of freedom are not distinguished can be considered as a subspace of [...] Read more.

Since the lowest levels are symmetric under the interchange of neutrons and protons from calculations in the interacting boson approximation IBA-2 model, IBA-1 model space, in which neutron and proton degrees of freedom are not distinguished can be considered as a subspace of the IBA-2 model space. Using the microscopic background of the IBA-2 model, a correspondence can be established between IBA-1 and IBA-2 model space. Since the space of the IBA-1 model can be regarded as a subspace of the IBA-2 model there is a unique way to “Project” the operators of the IBA-2 model onto those of IBA-1. This projection can be carried out by using the Fspin formalism. In the IBA-2, the lowest states are indeed fully symmetric, the calculations with the help of this projection, we explore the energy levels and the electric quadrupole transition probabilities B(E2;I_i I_f) and -ray E2/M1 mixing ratios for selected transitions of ^166-168Er .Owing to admixtures of non-fully-symmetric states in IBA-2, we renormalized the parameters (ε) and (κ).This is the first time we show that this projection can be applied to some heavier isotopes and the results obtained for ^166-168Er isotopes are reasonably in good agreement with the previous experimental values. Full article

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Math. Comput. Appl., Volume 12, Issue 2 (August 2007) – 6 articles , Pages 69-124

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