Mathematical and Computational Applications

223 KiB

Open AccessArticle

Fuzzy Decision Support System to Determine Swell/Shrink Factor Affecting Earthwork Optimization of Highways

by A. Burak Göktepe, A. Hilmi Lav, Selim Altun and Gökhan Altıntaş

Math. Comput. Appl. 2008, 13(1), 61-70; https://doi.org/10.3390/mca13010061 - 01 Apr 2008

Cited by 10 | Viewed by 1335

The optimization of cut and fill volumes of a highway infrastructure is crucial for minimizing the total earthwork cost. Borrow material swells after excavation and shrinks when mechanical compaction is applied; in this respect, it may be misleading to calculate cut-fill volumes directly

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The optimization of cut and fill volumes of a highway infrastructure is crucial for minimizing the total earthwork cost. Borrow material swells after excavation and shrinks when mechanical compaction is applied; in this respect, it may be misleading to calculate cut-fill volumes directly without considering the amount of swelling and/or shrinkage. On the other hand, determination of such factors characterizing shrinkage/swelling behavior is highly ambiguous. The aim of this paper is to present the applicability of a fuzzy rule-based system for choosing swelling/shrinkage factors affecting the precision of earthwork optimization. This approach may assist in any highway alignment procedure to handle cut and fill volumes more accurately.

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163 KiB

Open AccessArticle

A Review of Rules Family of Algorithms

by Mehmet Sabih Aksoy

Math. Comput. Appl. 2008, 13(1), 51-60; https://doi.org/10.3390/mca13010051 - 01 Apr 2008

Cited by 14 | Viewed by 1054

Abstract

In recent years, there has been a growing amount of research on inductive learning. Out of this research a number of promising algorithms have surfaced. In the paper after a brief description of knowledge acquisition, induction and inductive learning; RULES family of inductive

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In recent years, there has been a growing amount of research on inductive learning. Out of this research a number of promising algorithms have surfaced. In the paper after a brief description of knowledge acquisition, induction and inductive learning; RULES family of inductive learning algorithms, their strengths as well as weaknesses are explained and discussed. The applications of inductive learning and particularly the applications of RULES family of algorithms are overviewed.

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177 KiB

Open AccessArticle

On the Distributions of a Renewal Reward Process and It’s Additive Functional

by Tahir Khaniyev, Rovshan Aliyev, Zafer Küçük and Nurgul Okur Bekar

Math. Comput. Appl. 2008, 13(1), 41-50; https://doi.org/10.3390/mca13010041 - 01 Apr 2008

Cited by 1 | Viewed by 1391

Abstract

In this study, a renewal reward process with a discrete interference of chance (X(t)) is constructed and distribution of the process X(t) is investigated. One dimensional distribution of the process X(t) is given by means of the probability characteristics of the renewal processes {T [...] Read more.

In this study, a renewal reward process with a discrete interference of chance (X(t)) is constructed and distribution of the process X(t) is investigated. One dimensional distribution of the process X(t) is given by means of the probability characteristics of the renewal processes {T_n } and {S_n }. Moreover, one dimensional distribution function of the additive functional J_f(t) of the process X(t) is expressed by the probability characteristics of the initial sequences of the random variables {ξ_n} and {η_n}. Full article

182 KiB

Open AccessArticle

Two-Stage Group Sequential Designs for Comparative Clinical Trials

by Sevil Bacanlı, Özgür K. Peker and Yaprak Parlak Demirhan

Math. Comput. Appl. 2008, 13(1), 31-40; https://doi.org/10.3390/mca13010031 - 01 Apr 2008

Cited by 1 | Viewed by 1582

Abstract

Group sequential designs are widely used in Phase II clinical trials, which are usually undertaken to evaluate the response probability of specific treatment regimen. In most randomized clinical trials with sequential patient entry, fixed sample size design is unjustified on ethical grounds and

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Group sequential designs are widely used in Phase II clinical trials, which are usually undertaken to evaluate the response probability of specific treatment regimen. In most randomized clinical trials with sequential patient entry, fixed sample size design is unjustified on ethical grounds and sequential designs are often impractical. However group sequential designs are generally more practical and they provide much of the saving possible from sequential designs. Optimal restricted two-stage design is the simplest form of a group sequential design.
In this study, group sequential design obtained by α^*(t) functions characterized using the type-I error probability and optimal restricted two stage design has been compared for the cases that the group sizes are equal. Furthermore, their efficiency regarding fixed sample size design has been calculated and the results have been discussed.

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168 KiB

Open AccessArticle

Numerical Verification and Comparison of Error of Asymptotic Expansion Solution of the Duffing Equation

by Jianping Cai, Shuhui Chen and Cuihong Yang

Math. Comput. Appl. 2008, 13(1), 23-29; https://doi.org/10.3390/mca13010023 - 01 Apr 2008

Cited by 3 | Viewed by 1096

Abstract

A numerical order verification technique is applied to demonstrate that the asymptotic expansions of solutions of the Duffing equation obtained respectively by the Lindstedt-Poincaré(LP) method and the modified Lindstedt-Poincaré(MLP) method are uniformly valid for small parameter values. A numerical comparison of error shows

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A numerical order verification technique is applied to demonstrate that the asymptotic expansions of solutions of the Duffing equation obtained respectively by the Lindstedt-Poincaré(LP) method and the modified Lindstedt-Poincaré(MLP) method are uniformly valid for small parameter values. A numerical comparison of error shows that the MLP method is valid whereas the LP method is invalid for large parameter values.

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202 KiB

Open AccessArticle

Hopf Point Analysis for Ratio-Dependent Food Chain Models

by Rukiye Kara and Mehmet Can

Math. Comput. Appl. 2008, 13(1), 9-22; https://doi.org/10.3390/mca13010009 - 01 Apr 2008

Viewed by 1051

Abstract

In this paper periodic and quasi-periodic behavior of a food chain model with three trophic levels are studied. Michaelis-Menten type ratio-dependent functional response is considered. There are two equilibrium points of the system. It is found out that at most one of these [...] Read more.

In this paper periodic and quasi-periodic behavior of a food chain model with three trophic levels are studied. Michaelis-Menten type ratio-dependent functional response is considered. There are two equilibrium points of the system. It is found out that at most one of these equilibrium points is stable at a time. In the parameter space, there are passages from instability to stability, which are called Hopf bifurcation points. For the first equilibrium point, it is possible to find bifurcation points analytically and to prove that the system has periodic solutions around these points. However for the second equilibrium point the computation is more tedious and bifurcation points can only be found by numerical experiments. It has been found that around these points there are periodic solutions and when this point is unstable, the solution is an enlarging spiral from inside and approaches to a limit cycle. Full article

153 KiB

Open AccessArticle

The Study of Dependence of the Radial Parts of 0-→0+ First Forbidden β-Decay Matrix Elements on the Parameters in Woods-Saxon Potential

by İsmail Kenar, Serdar Ünlü and Ismail Maraş

Math. Comput. Appl. 2008, 13(1), 1-8; https://doi.org/10.3390/mca13010001 - 01 Apr 2008

Cited by 1 | Viewed by 1021

Abstract

In this paper, 0^-→0⁺ first forbidden β-decay matrix elements have been calculated. For ^206-214Pb→^206-214Bi transitions relativistic M^±(ρ_A,λ=0) and nonrelativistic M^±(j_A,κ =1,λ=0) matrix elements have been calculated. In this calculations, [...] Read more.

In this paper, 0^-→0⁺ first forbidden β-decay matrix elements have been calculated. For ^206-214Pb→^206-214Bi transitions relativistic M^±(ρ_A,λ=0) and nonrelativistic M^±(j_A,κ =1,λ=0) matrix elements have been calculated. In this calculations, the eigenfunctions and eigenvalues of Schrodinger equation solved by the more realistic Woods-Saxon potential have been used. The dependence of the radial parts in the matrix elements on the parameters (r₀: the radii of nucleus, η: isovector parameter, r_c: Coulomb radius and χ diffusion parameter) of Woods-Saxon potential has been investigated.
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Math. Comput. Appl., Volume 13, Issue 1 (April 2008) – 7 articles , Pages 1-70

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