Mathematical and Computational Applications

431 KiB

Open AccessArticle

by İsmail Kocayusufoğlu

Math. Comput. Appl. 2000, 5(3), 201-212; https://doi.org/10.3390/mca5020201 - 01 Dec 2000

Cited by 2 | Viewed by 1144

In this paper, we will define the iso-taxicab trigonmetric functions \(\cos_{I}\theta\), \(\sin_{I}\theta\), \(\tan_{I}\) and \(\cot_{I}\theta\). Then, we will give the subtraction formulas for iso-taxicab trigonometric functions \(\cos_{I}\theta\) and \(\sin_{I}\theta\). Full article

330 KiB

Open AccessArticle

Connections and Minimizing Geodesics of Taxicab Geometry

by İsmail Kocayusufoğlu and Ertuğrul Özdamar

Math. Comput. Appl. 2000, 5(3), 191-200; https://doi.org/10.3390/mca5020191 - 01 Dec 2000

Cited by 2 | Viewed by 1143

Abstract

The aim of this paper is to define the principle fibre bundle and connections and point out the minimizing geodesics of the taxicab geometry. Full article

348 KiB

Open AccessArticle

The Cosine Hyperbolic and Sine Hyperbolic Rules for Dual Hyperbolic Spherical Trigonometry

by H. H. UĞURLU and H. GÜNDOĞAN

Math. Comput. Appl. 2000, 5(3), 185-190; https://doi.org/10.3390/mca5020185 - 01 Dec 2000

Viewed by 1139

Abstract

The dual hyperbolic unit sphere \(H_{0}^{2}\) is the set of all dual time-like units vectors in the dual Lorentzian space \(D_{1}^{3}\) with signature (+,+,-). In this paper, we give the cosine hyperbolic and sine hyperbolic-rules for a dual dual hyperbolic spherical triangle \(\tilde{A}\tilde{B}\tilde{C}\) [...] Read more.

The dual hyperbolic unit sphere \(H_{0}^{2}\) is the set of all dual time-like units vectors in the dual Lorentzian space \(D_{1}^{3}\) with signature (+,+,-). In this paper, we give the cosine hyperbolic and sine hyperbolic-rules for a dual dual hyperbolic spherical triangle \(\tilde{A}\tilde{B}\tilde{C}\) which its sides are great-circle-arcs. Full article

294 KiB

Open AccessArticle

On Approximate Symmetries of a Wave Equation with Quadratic Non-Linearity

by M. Pakdemirli and M. Yürüsoy

Math. Comput. Appl. 2000, 5(3), 179-184; https://doi.org/10.3390/mca5020179 - 01 Dec 2000

Cited by 4 | Viewed by 1029

Abstract

Two different approximate symmetry methods and a proposed new one are contrasted using a wave equation with quadratic non-linearity. For each method, the approximate symmetries are calculated first. Then approximate solutions corresponding to some of the symmetries are calculated. It is found that [...] Read more.

Two different approximate symmetry methods and a proposed new one are contrasted using a wave equation with quadratic non-linearity. For each method, the approximate symmetries are calculated first. Then approximate solutions corresponding to some of the symmetries are calculated. It is found that a given specific approximate solution is attainable only by using the new proposed method. Full article

544 KiB

Open AccessArticle

Uncertainly Analysis of Cryogenic Turbine Efficiency

by Mehmet Kanoglu

Math. Comput. Appl. 2000, 5(3), 169-177; https://doi.org/10.3390/mca5020169 - 01 Dec 2000

Cited by 2 | Viewed by 1184

Abstract

A procedure for estimating uncertainty in the hydraulic efficiency of cryogenic turbines is presented. A case study is performed based on the test data from a cryogenic turbine testing facility. The effects of uncertainties in the measurements of temperature, pressure, and generator power [...] Read more.

A procedure for estimating uncertainty in the hydraulic efficiency of cryogenic turbines is presented. A case study is performed based on the test data from a cryogenic turbine testing facility. The effects of uncertainties in the measurements of temperature, pressure, and generator power on the turbine hydraulic efficiency are studied and the uncertainty in turbine efficiency is estimated to be ±0.20%. About 79% of the uncertainty is determined to come from the uncertainty in generator power measurement. This uncertainty in turbine efficiency is believed to be reasonable and acceptable for the testing of cryogenic turbines. Full article

588 KiB

Open AccessArticle

On the Nonlinear Transverse Vibrations and Stability of an Axially Accelerating Beam

by H. R. Öz

Math. Comput. Appl. 2000, 5(3), 157-167; https://doi.org/10.3390/mca5020157 - 01 Dec 2000

Viewed by 1061

Abstract

Nonlinear vibrations and stability analysis of an axially moving Euler-Bernoulli type beam are investigated. The beam is on fixed supports and moving with a harmonically varying velocity about a constant mean value. The method of multiple scales is used in the analysis. Nonlinear [...] Read more.

Nonlinear vibrations and stability analysis of an axially moving Euler-Bernoulli type beam are investigated. The beam is on fixed supports and moving with a harmonically varying velocity about a constant mean value. The method of multiple scales is used in the analysis. Nonlinear frequencies depending on vibration amplitudes are obtained. Stability and bifurcations of steady-state solutions are analyzed for frequencies close to two times any natural frequency. It is shown that the amplitudes are bounded in time for frequencies close to zero. The effect of fixed supports is discussed. Full article

271 KiB

Open AccessArticle

On the Ricci Curvature Tensor of (k+1)-Dimensional Semi Ruled Surfaces Evn+1

by Ali Görgülü and Cumali Ekici

Math. Comput. Appl. 2000, 5(3), 149-155; https://doi.org/10.3390/mca5020149 - 01 Dec 2000

Viewed by 1030

Abstract

If we choose a natural companion basis for \((k+1)\)-dimensional semi-ruled surfaces in semi-Euclidean space \(E_{\nu}^{n+1}\), then the metric coefficients are \(g_{ij} = \epsilon_{i}\delta_{ij}\), \(1\leq i\), \(j \leq k\). In this paper we show that the Ricci curvature tensor of a \((k+1)\)-dimensional semi-ruled surfaces [...] Read more.

If we choose a natural companion basis for \((k+1)\)-dimensional semi-ruled surfaces in semi-Euclidean space \(E_{\nu}^{n+1}\), then the metric coefficients are \(g_{ij} = \epsilon_{i}\delta_{ij}\), \(1\leq i\), \(j \leq k\). In this paper we show that the Ricci curvature tensor of a \((k+1)\)-dimensional semi-ruled surfaces in semi-Euclidean space \(E_{\nu}^{n+1}\) is \( S = \sum_{j,h=0}^{k}{\epsilon_{jh}} \left( \epsilon_{0} R_{h-j}^{0} g_{00} + \sum_{i=0}^{k}{R_{hij}^{i}} + \sum_{i=0}^{k}{g_{i0}} \left(\epsilon_{i} R_{hij} + \epsilon_{0} R_{h0j}^{i} \right)\right) \theta_{j} \otimes \theta_{h}. \) Here, \(\{\theta_{0}, \theta_{1}, ... \theta_{k}\}\) is the dual basis of the local coordinate basis \(\{e_{0} , e_{1} , ...e_{k}\}\).
Full article

373 KiB

Open AccessArticle

On the Curvatures of (k+1)-Dimensional Semi-Ruled Surfaces in \({{E}_{v}^{n+1} }\)

by Cumali Ekici and Ali Görgülü

Math. Comput. Appl. 2000, 5(3), 139-148; https://doi.org/10.3390/mca5020139 - 01 Dec 2000

Cited by 1 | Viewed by 1125

Abstract

In this paper, first we will define the generalized (k + 1) -dimensional semi-ruled surface M*, such that the generator space of M* is the semi-subspace of

E_{v}^{n + 1}

where

E_{v}^{n + 1}

is the [...] Read more.

In this paper, first we will define the generalized (k + 1) -dimensional semi-ruled surface M*, such that the generator space of M* is the semi-subspace of

E_{v}^{n + 1}

where

E_{v}^{n + 1}

is the semi-Euclidean space. Then, we will compute the mean curvature, Riemann curvature, Ricci curvature and scalar curvature of M*. Full article

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Math. Comput. Appl., Volume 5, Issue 3 (December 2000) – 8 articles , Pages 139-212

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