**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**114

# Search results for: Cubic Bspline

##### 114 A Comparison of Some Splines-Based Methods for the One-dimensional Heat Equation

**Authors:**
Joan Goh,
Ahmad Abd. Majid,
Ahmad Izani Md. Ismail

**Abstract:**

**Keywords:**
Heat equation,
Collocation based,
Cubic Bspline,
Extended cubic uniform B-spline.

##### 113 Cubic B-spline Collocation Method for Numerical Solution of the Benjamin-Bona-Mahony-Burgers Equation

**Authors:**
M. Zarebnia,
R. Parvaz

**Abstract:**

In this paper, numerical solutions of the nonlinear Benjamin-Bona-Mahony-Burgers (BBMB) equation are obtained by a method based on collocation of cubic B-splines. Applying the Von-Neumann stability analysis, the proposed method is shown to be unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The L∞ and L2 in the solutions show the efficiency of the method computationally.

**Keywords:**
Benjamin-Bona-Mahony-Burgers equation,
Cubic Bspline,
Collocation method,
Finite difference.

##### 112 Characterizations of Γ-Semirings by Their Cubic Ideals

**Authors:**
Debabrata Mandal

**Abstract:**

**Keywords:**
Γ-semiring,
cubic ideal,
normal cubic ideal,
cubic
bi-ideal,
cubic quasi-ideal,
cartesian product,
regular,
intra-regular.

##### 111 Cubic Trigonometric B-Spline Applied to Linear Two-Point Boundary Value Problems of Order Two

**Authors:**
Nur Nadiah Abd Hamid ,
Ahmad Abd. Majid,
Ahmad Izani Md. Ismail

**Abstract:**

**Keywords:**
trigonometric B-spline,
two-point boundary valueproblem,
spline interpolation,
cubic spline

##### 110 Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Binary quadratic form,
elliptic curves,
cubic congruence.

##### 109 Classification of the Bachet Elliptic Curves y2 = x3 + a3 in Fp, where p ≡ 1 (mod 6) is Prime

**Authors:**
Nazli Yildiz İkikardes,
Gokhan Soydan,
Musa Demirci,
Ismail Naci Cangul

**Abstract:**

**Keywords:**
Elliptic curves over finite fields,
quadratic residue,
cubic residue.

##### 108 Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems

**Authors:**
Nur Nadiah Abd Hamid,
Ahmad Abd. Majid,
Ahmad Izani Md. Ismail

**Abstract:**

Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method.

**Keywords:**
two-point boundary value problem,
B-spline,
extendedcubic B-spline.

##### 107 Solution of S3 Problem of Deformation Mechanics for a Definite Condition and Resulting Modifications of Important Failure Theories

**Authors:**
Ranajay Bhowmick

**Abstract:**

Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

**Keywords:**
Cubic equation,
stress invariant,
trigonometric,
explicit solution,
principal stress,
failure criterion.

##### 106 Cubic Trigonometric B-spline Approach to Numerical Solution of Wave Equation

**Authors:**
Shazalina Mat Zin,
Ahmad Abd. Majid,
Ahmad Izani Md. Ismail,
Muhammad Abbas

**Abstract:**

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

**Keywords:**
Collocation method,
Cubic trigonometric B-spline,
Finite difference,
Wave equation.

##### 105 A Comparative Study on Optimized Bias Current Density Performance of Cubic ZnB-GaN with Hexagonal 4H-SiC Based Impatts

**Authors:**
Arnab Majumdar,
Srimani Sen

**Abstract:**

In this paper, a vivid simulated study has been made on 35 GHz Ka-band window frequency in order to judge and compare the DC and high frequency properties of cubic ZnB-GaN with the existing hexagonal 4H-SiC. A flat profile p^{+}pnn^{+} DDR structure of impatt is chosen and is optimized at a particular bias current density with respect to efficiency and output power taking into consideration the effect of mobile space charge also. The simulated results obtained reveals the strong potentiality of impatts based on both cubic ZnB-GaN and hexagonal 4H-SiC. The DC-to-millimeter wave conversion efficiency for cubic ZnB-GaN impatt obtained is 50% with an estimated output power of 2.83 W at an optimized bias current density of 2.5×10^{8} A/m^{2}. The conversion efficiency and estimated output power in case of hexagonal 4H-SiC impatt obtained is 22.34% and 40 W respectively at an optimum bias current density of 0.06×10^{8} A/m^{2}.

**Keywords:**
Cubic ZnB-GaN,
hexagonal 4H-SiC,
Double drift impatt diode,
millimeter wave,
optimized bias current density,
wide band gap semiconductor.

##### 104 Evaluating Sinusoidal Functions by a Low Complexity Cubic Spline Interpolator with Error Optimization

**Authors:**
Abhijit Mitra,
Harpreet Singh Dhillon

**Abstract:**

We present a novel scheme to evaluate sinusoidal functions with low complexity and high precision using cubic spline interpolation. To this end, two different approaches are proposed to find the interpolating polynomial of sin(x) within the range [- π , π]. The first one deals with only a single data point while the other with two to keep the realization cost as low as possible. An approximation error optimization technique for cubic spline interpolation is introduced next and is shown to increase the interpolator accuracy without increasing complexity of the associated hardware. The architectures for the proposed approaches are also developed, which exhibit flexibility of implementation with low power requirement.

**Keywords:**
Arithmetic,
spline interpolator,
hardware design,
erroranalysis,
optimization methods.

##### 103 The Growth of the Watermelons with Geometric Shapes and Comparing Retention between Cubic and Hexagonal Forms

**Authors:**
M. Malekyarand,
M. Shariati Ghalehno,
A. Mokhber Dezfuli,
H. Saebi Monfared,
S. R. Ghoraishi K.

**Abstract:**

Shape and form of the watermelon fruits are important factors to save spaces and reducing damage during storing of the fruits. In order to save spaces and prevent fruit damage in watermelon the following experiment was carried out in the farm. The fruits were boxed when they were approximately one cm less than the box diameter. The cubic, hexagonal forms were compared in this research. To do this, different boxes were designed with different holes on the sides to holes the watermelons fruits for shaping. The shapes of the boxes were hexagonal and cubic. The boxes holes sizes were the same with 10mm diameter each. Each side of the boxes had different holes including: without holes to 75 holes. The result showed that the best shape for watermelon storing to save space and prevent fruit damage was hexagonal form. The percentages of the fruit damage were 33 to 80 respectively.

**Keywords:**
Cubic form,
fruit damage,
hexagonal,
watermelon shape.

##### 102 Solving One-dimensional Hyperbolic Telegraph Equation Using Cubic B-spline Quasi-interpolation

**Authors:**
Marzieh Dosti,
Alireza Nazemi

**Abstract:**

In this paper, the telegraph equation is solved numerically by cubic B-spline quasi-interpolation .We obtain the numerical scheme, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the temporal derivative of the dependent variable. The advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement. The results of numerical experiments are presented, and are compared with analytical solutions by calculating errors L2 and L∞ norms to confirm the good accuracy of the presented scheme.

**Keywords:**
Cubic B-spline,
quasi-interpolation,
collocation method,
second-order hyperbolic telegraph equation.

##### 101 Numerical Treatment of Matrix Differential Models Using Matrix Splines

**Authors:**
Kholod M. Abualnaja

**Abstract:**

This paper consider the solution of the matrix differential models using quadratic, cubic, quartic, and quintic splines. Also using the Taylor’s and Picard’s matrix methods, one illustrative example is included.

**Keywords:**
Matrix Splines,
Cubic Splines,
Quartic Splines.

##### 100 A Review on Higher Order Spline Techniques for Solving Burgers Equation Using B-Spline Methods and Variation of B-Spline Techniques

**Authors:**
Maryam Khazaei Pool,
Lori Lewis

**Abstract:**

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

**Keywords:**
Burgers’ Equation,
Septic B-spline,
Modified Cubic
B-Spline Differential Quadrature Method,
Exponential Cubic
B-Spline Technique,
B-Spline Galerkin Method,
and Quintic B-Spline
Galerkin Method.

##### 99 Cryptography over Sextic Extension with Cubic Subfield

**Authors:**
A. Chillali,
M. Sahmoudi

**Abstract:**

In this paper, we will give a cryptographic application over the integral closure O_Lof sextic extension L, namely L is an extension of Q of degree 6 in the form Q(a,b), which is a rational quadratic and monogenic extension over a pure monogenic cubic subfield K generated by a who is a root of monic irreducible polynomial of degree 2 andb is a root of irreducible polynomial of degree 3.

**Keywords:**
Integral bases,
Cryptography,
Discrete logarithm
problem.

##### 98 Large Strain Compression-Tension Behavior of AZ31B Rolled Sheet in the Rolling Direction

**Authors:**
A. Yazdanmehr,
H. Jahed

**Abstract:**

Being made with the lightest commercially available industrial metal, Magnesium (Mg) alloys are of interest for light-weighting. Expanding their application to different material processing methods requires Mg properties at large strains. Several room-temperature processes such as shot and laser peening and hole cold expansion need compressive large strain data. Two methods have been proposed in the literature to obtain the stress-strain curve at high strains: 1) anti-buckling guides and 2) small cubic samples. In this paper, an anti-buckling fixture is used with the help of digital image correlation (DIC) to obtain the compression-tension (C-T) of AZ31B-H24 rolled sheet at large strain values of up to 10.5%. The effect of the anti-bucking fixture on stress-strain curves is evaluated experimentally by comparing the results with those of the compression tests of cubic samples. For testing cubic samples, a new fixture has been designed to increase the accuracy of testing cubic samples with DIC strain measurements. Results show a negligible effect of anti-buckling on stress-strain curves, specifically at high strain values.

**Keywords:**
Large strain,
compression-tension,
loading-unloading,
Mg alloys.

##### 97 Tuning Cubic Equations of State for Supercritical Water Applications

**Authors:**
Shyh-Ming Chern

**Abstract:**

Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and reasonable accuracy, are normally fitted to vapor-liquid equilibrium *P*-*v*-*T* data. As a result, they often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the* P*-*v*-*T* data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating *P*-*v*-*T* data of the supercritical region into the retuning of a cubic EoS can improve its performance at and above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new *F* of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

**Keywords:**
Equation of state,
EoS,
supercritical water,
SCW.

##### 96 Generating Arabic Fonts Using Rational Cubic Ball Functions

**Authors:**
Fakharuddin Ibrahim,
Jamaludin Md. Ali,
Ahmad Ramli

**Abstract:**

^{1}continuity. The conditions considered are known as the G

^{1}Hermite condition. A simple application of the proposed method is to generate an Arabic font satisfying the required continuity.

**Keywords:**
Continuity,
data interpolation,
Hermite condition,
rational Ball curve.

##### 95 New Newton's Method with Third-order Convergence for Solving Nonlinear Equations

**Authors:**
Osama Yusuf Ababneh

**Abstract:**

For the last years, the variants of the Newton-s method with cubic convergence have become popular iterative methods to find approximate solutions to the roots of non-linear equations. These methods both enjoy cubic convergence at simple roots and do not require the evaluation of second order derivatives. In this paper, we present a new Newton-s method based on contra harmonic mean with cubically convergent. Numerical examples show that the new method can compete with the classical Newton's method.

**Keywords:**
Third-order convergence,
non-linear equations,
root finding,
iterative method.

##### 94 DQ Analysis of 3D Natural Convection in an Inclined Cavity Using an Velocity-Vorticity Formulation

**Abstract:**

In this paper, the differential quadrature method is applied to simulate natural convection in an inclined cubic cavity using velocity-vorticity formulation. The numerical capability of the present algorithm is demonstrated by application to natural convection in an inclined cubic cavity. The velocity Poisson equations, the vorticity transport equations and the energy equation are all solved as a coupled system of equations for the seven field variables consisting of three velocities, three vorticities and temperature. The coupled equations are simultaneously solved by imposing the vorticity definition at boundary without requiring the explicit specification of the vorticity boundary conditions. Test results obtained for an inclined cubic cavity with different angle of inclinations for Rayleigh number equal to 103, 104, 105 and 106 indicate that the present coupled solution algorithm could predict the benchmark results for temperature and flow fields. Thus, it is convinced that the present formulation is capable of solving coupled Navier-Stokes equations effectively and accurately.

**Keywords:**
Natural convection,
velocity-vorticity formulation,
differential quadrature (DQ).

##### 93 Numerical Calculation of the Ionization Energy of Donors in a Cubic Quantum well and Wire

**Authors:**
Sara Sedaghat,
Mahmood Barati,
Iraj Kazeminezhad

**Abstract:**

**Keywords:**
quantum well,
quantum wire,
quantum dot,
impuritystate

##### 92 Constructing Approximate and Exact Solutions for Boussinesq Equations using Homotopy Perturbation Padé Technique

**Authors:**
Mohamed M. Mousa,
Aidarkhan Kaltayev

**Abstract:**

**Keywords:**
Homotopy perturbation method,
Padé approximants,
cubic Boussinesq equation,
modified Boussinesq equation.

##### 91 Tensile Properties of Aluminum Silicon Nickel Iron Vanadium High Entropy Alloys

**Authors:**
Sefiu A. Bello,
Nasirudeen K. Raji,
Jeleel A. Adebisi,
Sadiq A. Raji

**Abstract:**

Pure metals are not used in most cases for structural applications because of their limited properties. Presently, high entropy alloys (HEAs) are emerging by mixing comparative proportions of metals with the aim of maximizing the entropy leading to enhancement in structural and mechanical properties. Aluminum Silicon Nickel Iron Vanadium (AlSiNiFeV) alloy was developed using stir cast technique and analysed. Results obtained show that the alloy grade G0 contains 44 percentage by weight (wt%) Al, 32 wt% Si, 9 wt% Ni, 4 wt% Fe, 3 wt% V and 8 wt% for minor elements with tensile strength and elongation of 106 Nmm^{-2} and 2.68%, respectively. X-ray diffraction confirmed intermetallic compounds having hexagonal closed packed (HCP), orthorhombic and cubic structures in cubic dendritic matrix. This affirmed transformation from the cubic structures of elemental constituents of the HEAs to the precipitated structures of the intermetallic compounds. A maximum tensile strength of 188 Nmm^{-2} with 4% elongation was noticed at 10wt% of silica addition to the G0. An increase in tensile strength with an increment in silica content could be attributed to different phases and crystal geometries characterizing each HEA.

**Keywords:**
High entropy alloys,
phases,
model,
tensile strength.

##### 90 Compressive Strength Development of Normal Concrete and Self-Consolidating Concrete Incorporated with GGBS

**Authors:**
M. Nili,
S. Tavasoli,
A. R. Yazdandoost

**Abstract:**

In this paper, an experimental investigation on the effect of Isfahan Ground Granulate Blast Furnace Slag (GGBS) on the compressive strength development of self-consolidating concrete (SCC) and normal concrete (NC) was performed. For this purpose, Portland cement type I was replaced with GGBS in various Portions. For NC and SCC Mixes, 10*10*10 cubic cm specimens were tested in 7, 28 and 91 days. It must be stated that in this research water to cement ratio was 0.44, cement used in cubic meter was 418 Kg/m³ and Superplasticizer (SP) Type III used in SCC based on Poly-Carboxylic acid. The results of experiments have shown that increasing GGBS Percentages in both types of concrete reduce Compressive strength in early ages.

**Keywords:**
Compressive strength,
GGBS,
normal concrete,
self-consolidating concrete.

##### 89 Circular Approximation by Trigonometric Bézier Curves

**Authors:**
Maria Hussin,
Malik Zawwar Hussain,
Mubashrah Saddiqa

**Abstract:**

We present a trigonometric scheme to approximate a circular arc with its two end points and two end tangents/unit tangents. A rational cubic trigonometric Bézier curve is constructed whose end control points are defined by the end points of the circular arc. Weight functions and the remaining control points of the cubic trigonometric Bézier curve are estimated by variational approach to reproduce a circular arc. The radius error is calculated and found less than the existing techniques.

**Keywords:**
Control points,
rational trigonometric Bézier curves,
radius error,
shape measure,
weight functions.

##### 88 Design of Stilling Basins using Artificial Roughness

**Authors:**
N. AboulAtta,
G. Ezizah,
N. Yousif ,
S. Fathy

**Abstract:**

**Keywords:**
hydraulic jump,
energy dissipater,
roughened bed,
stilling basin.

##### 87 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations

**Authors:**
N. Ebrahimi,
J. Rashidinia

**Abstract:**

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

**Keywords:**
Convergence analysis,
Cubic B-spline,
Newton-
Cotes formula,
System of Fredholm and Volterra integral equations.

##### 86 Parametric Study on Grindability of GFRP Laminates Using Different Abrasives

**Authors:**
P. Chockalingam,
C. K. Kok,
T. R. Vijayaram

**Abstract:**

A study on grindability of chopped strand mat glass fiber reinforced polymer laminates (CSM GFRP) have been carried out to evaluate the significant parameters on wheel performance. Performance of Aluminum oxide and c-BN wheels during grinding of CSM GFRP laminate was evaluated in terms of grinding force and surface roughness during grinding. The cubic Boron Nitride wheel experiences higher tangential grinding forces components and lower normal force component than Aluminum oxide grinding wheels. In case of surface finish, Aluminum oxide grinding wheels outdo the cubic Boron Nitride grinding wheels.

**Keywords:**
Grinding,
glass fiber reinforced polymer laminates,
grinding force,
surface finish.

##### 85 Parametric Transition as a Spiral Curve and Its Application in Spur Gear Tooth with FEA

**Authors:**
S. H. Yahaya,
J. M. Ali,
T.A. Abdullah

**Abstract:**

**Keywords:**
Bézier-like cubic function,
Curvature continuity,
Cshapedtransition curve,
Spur gear tooth.