**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2050

# Search results for: trigonometric function

##### 2050 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

##### 2049 Adaptive Motion Planning for 6-DOF Robots Based on Trigonometric Functions

**Authors:**
Jincan Li,
Mingyu Gao,
Zhiwei He,
Yuxiang Yang,
Zhongfei Yu,
Yuanyuan Liu

**Abstract:**

Building an appropriate motion model is crucial for trajectory planning of robots and determines the operational quality directly. An adaptive acceleration and deceleration motion planning based on trigonometric functions for the end-effector of 6-DOF robots in Cartesian coordinate system is proposed in this paper. This method not only achieves the smooth translation motion and rotation motion by constructing a continuous jerk model, but also automatically adjusts the parameters of trigonometric functions according to the variable inputs and the kinematic constraints. The results of computer simulation show that this method is correct and effective to achieve the adaptive motion planning for linear trajectories.

**Keywords:**
6-DOF robots,
motion planning,
trigonometric function,
kinematic constraints

##### 2048 Monotone Rational Trigonometric Interpolation

**Authors:**
Uzma Bashir,
Jamaludin Md. Ali

**Abstract:**

This study is concerned with the visualization of monotone data using a piecewise C1 rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and othertwo are leftfree. Figures are used widely to exhibit that the proposed scheme produces graphically smooth monotone curves.

**Keywords:**
Trigonometric splines,
Monotone data,
Shape preserving,
C1 monotone interpolant.

##### 2047 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.

##### 2046 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.

##### 2045 Flexure of Cantilever Thick Beams Using Trigonometric Shear Deformation Theory

**Authors:**
Yuwaraj M. Ghugal,
Ajay G. Dahake

**Abstract:**

A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick cantilever isotropic beams are considered for the numerical studies to demonstrate the efficiency of the. Results obtained are discussed critically with those of other theories.

**Keywords:**
Trigonometric shear deformation,
thick beam,
flexure,
principle of virtual work,
equilibrium equations,
stress.

##### 2044 L1-Convergence of Modified Trigonometric Sums

**Authors:**
Sandeep Kaur Chouhan,
Jatinderdeep Kaur,
S. S. Bhatia

**Abstract:**

**Keywords:**
Conjugate Dirichlet kernel,
Dirichlet kernel,
L1-convergence,
modified sums.

##### 2043 Coefficients of Some Double Trigonometric Cosine and Sine Series

**Authors:**
Jatinderdeep Kaur

**Abstract:**

**Keywords:**
Conjugate Dirichlet kernel,
conjugate Fejer kernel,
Fourier series,
Semi-convexity.

##### 2042 Flexure of Simply Supported Thick Beams Using Refined Shear Deformation Theory

**Authors:**
Yuwaraj M. Ghugal,
Ajay G. Dahake

**Abstract:**

A trigonometric shear deformation theory for flexure of thick beams, taking into account transverse shear deformation effects, is developed. The number of variables in the present theory is same as that in the first order shear deformation theory. The sinusoidal function is used in displacement field in terms of thickness coordinate to represent the shear deformation effects. The noteworthy feature of this theory is that the transverse shear stresses can be obtained directly from the use of constitutive relations with excellent accuracy, satisfying the shear stress free conditions on the top and bottom surfaces of the beam. Hence, the theory obviates the need of shear correction factor. Governing differential equations and boundary conditions are obtained by using the principle of virtual work. The thick simply supported isotropic beams are considered for the numerical studies to demonstrate the efficiency of the results obtained is discussed critically with those of other theories.

**Keywords:**
Trigonometric shear deformation,
thick beam,
flexure,
principle of virtual work,
equilibrium equations,
stress.

##### 2041 A Thought on Exotic Statistical Distributions

**Authors:**
R K Sinha

**Abstract:**

**Keywords:**
Exotic Statistical Distributions,
Kurtosis,
Mixture
Distributions,
Multi-modal

##### 2040 An Extension of the Kratzel Function and Associated Inverse Gaussian Probability Distribution Occurring in Reliability Theory

**Authors:**
R. K. Saxena,
Ravi Saxena

**Abstract:**

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

**Keywords:**
Fox-Wright function,
Inverse Gaussian distribution,
Krtzel function & Bessel function of the third kind.

##### 2039 A New Definition of the Intrinsic Mode Function

**Authors:**
Zhihua Yang,
Lihua Yang

**Abstract:**

This paper makes a detailed analysis regarding the definition of the intrinsic mode function and proves that Condition 1 of the intrinsic mode function can really be deduced from Condition 2. Finally, an improved definition of the intrinsic mode function is given.

**Keywords:**
Empirical Mode Decomposition (EMD),
Hilbert-Huang transform(HHT),
Intrinsic Mode Function(IMF).

##### 2038 Analytical Modeling of Globular Protein-Ferritin in α-Helical Conformation: A White Noise Functional Approach

**Authors:**
Vernie C. Convicto,
Henry P. Aringa,
Wilson I. Barredo

**Abstract:**

**Keywords:**
Globular protein,
modulating function,
white noise,
winding probability.

##### 2037 Studying Mistaken Theory of Calendar Function of Iran-s Cross-Vaults

**Authors:**
Ali Salehipour

**Abstract:**

**Keywords:**
cross-vault,
fire temple,
Calendar function,
Sassanid period

##### 2036 On the Exact Solution of Non-Uniform Torsion for Beams with Axial Symmetric Cross-Section

**Authors:**
A.Campanile,
M. Mandarino,
V. Piscopo,
A. Pranzitelli

**Abstract:**

**Keywords:**
Non-uniform torsion,
Axial symmetric cross-section,
Fourier series,
Helmholtz equation,
FE method.

##### 2035 Traveling Wave Solutions for Shallow Water Wave Equation by (G'/G)-Expansion Method

**Authors:**
Anjali Verma,
Ram Jiwari,
Jitender Kumar

**Abstract:**

This paper presents a new function expansion method for finding traveling wave solution of a non-linear equation and calls it the (G'/G)-expansion method. The shallow water wave equation is reduced to a non linear ordinary differential equation by using a simple transformation. As a result the traveling wave solutions of shallow water wave equation are expressed in three forms: hyperbolic solutions, trigonometric solutions and rational solutions.

**Keywords:**
Shallow water wave equation,
Exact solutions,
(G'/G) expansion method.

##### 2034 Comparison between Beta Wavelets Neural Networks, RBF Neural Networks and Polynomial Approximation for 1D, 2DFunctions Approximation

**Authors:**
Wajdi Bellil,
Chokri Ben Amar,
Adel M. Alimi

**Abstract:**

This paper proposes a comparison between wavelet neural networks (WNN), RBF neural network and polynomial approximation in term of 1-D and 2-D functions approximation. We present a novel wavelet neural network, based on Beta wavelets, for 1-D and 2-D functions approximation. Our purpose is to approximate an unknown function f: Rn - R from scattered samples (xi; y = f(xi)) i=1....n, where first, we have little a priori knowledge on the unknown function f: it lives in some infinite dimensional smooth function space and second the function approximation process is performed iteratively: each new measure on the function (xi; f(xi)) is used to compute a new estimate Ôêºf as an approximation of the function f. Simulation results are demonstrated to validate the generalization ability and efficiency of the proposed Beta wavelet network.

**Keywords:**
Beta wavelets networks,
RBF neural network,
training algorithms,
MSE,
1-D,
2D function approximation.

##### 2033 Evaluation on Recent Committed Crypt Analysis Hash Function

**Authors:**
A. Arul Lawrence Selvakumar,
C. Suresh Ganandhas

**Abstract:**

This paper describes the study of cryptographic hash functions, one of the most important classes of primitives used in recent techniques in cryptography. The main aim is the development of recent crypt analysis hash function. We present different approaches to defining security properties more formally and present basic attack on hash function. We recall Merkle-Damgard security properties of iterated hash function. The Main aim of this paper is the development of recent techniques applicable to crypt Analysis hash function, mainly from SHA family. Recent proposed attacks an MD5 & SHA motivate a new hash function design. It is designed not only to have higher security but also to be faster than SHA-256. The performance of the new hash function is at least 30% better than that of SHA-256 in software. And it is secure against any known cryptographic attacks on hash functions.

**Keywords:**
Crypt Analysis,
cryptographic.

##### 2032 The Core and Shapley Function for Games on Augmenting Systems with a Coalition Structure

**Authors:**
Fan-Yong Meng

**Abstract:**

In this paper, we first introduce the model of games on augmenting systems with a coalition structure, which can be seen as an extension of games on augmenting systems. The core of games on augmenting systems with a coalition structure is defined, and an equivalent form is discussed. Meantime, the Shapley function for this type of games is given, and two axiomatic systems of the given Shapley function are researched. When the given games are quasi convex, the relationship between the core and the Shapley function is discussed, which does coincide as in classical case. Finally, a numerical example is given.

**Keywords:**
Cooperative game,
augmenting system,
Shapley function,
core.

##### 2031 Calculation of Wave Function at the Origin (WFO) for the Ground State of Doubly Heavy Mesons Based On the Variational Method

**Authors:**
Maryam Momeni Feili,
Mahvash Zandy Navgaran

**Abstract:**

The wave function at the origin is an important quantity in studying many physical problems concerning heavy quarkonia. This is because that it is using for calculating spin state hyperfine splitting and also crucial to evaluating the production and decay amplitude of the heavy quarkonium. In this paper, we present the variational method by using the single-parameter wave function to estimate the WFO for the ground state of heavy mesons.

**Keywords:**
Wave function at the origin,
heavy mesons,
bound states,
variational method,
non-relativistic quark model,
potential model,
trial wave function.

##### 2030 A Transfer Function Representation of Thermo-Acoustic Dynamics for Combustors

**Authors:**
Myunggon Yoon,
Jung-Ho Moon

**Abstract:**

**Keywords:**
Thermoacoustics,
dynamics,
combustor,
transfer
function.

##### 2029 Predicting Protein Function using Decision Tree

**Authors:**
Manpreet Singh,
Parminder Kaur Wadhwa,
Surinder Kaur

**Abstract:**

**Keywords:**
Sequence Derived Features,
decision tree.

##### 2028 Assessing the Function of Light and Colorin Architectural View

**Authors:**
Gholam Hossein Naseri,
Manucher Tamizi

**Abstract:**

**Keywords:**
Architectural View ,
Color ,
Light

##### 2027 Particle Swarm Optimization and Quantum Particle Swarm Optimization to Multidimensional Function Approximation

**Authors:**
Diogo Silva,
Fadul Rodor,
Carlos Moraes

**Abstract:**

**Keywords:**
PSO,
QPSO,
function approximation,
AI,
optimization,
multidimensional functions.

##### 2026 Statistical Approach to Basis Function Truncation in Digital Interpolation Filters

**Authors:**
F. Castillo,
J. Arellano,
S. Sánchez

**Abstract:**

**Keywords:**
Interpolation,
basis function,
over-sampling.

##### 2025 A Case Study to Assess the Validity of Function Points

**Authors:**
Neelam Bawane nee' Singhal,
C. V. Srikrishna

**Abstract:**

**Keywords:**
Function Points,
Data Flow Diagram,
Lines ofCodes.

##### 2024 Characteristic Function in Estimation of Probability Distribution Moments

**Authors:**
Vladimir S. Timofeev

**Abstract:**

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

**Keywords:**
Characteristic function,
distributional moments,
robustness,
outlier,
statistical estimation problem,
statistical simulation.

##### 2023 Subclasses of Bi-Univalent Functions Associated with Hohlov Operator

**Authors:**
Rashidah Omar,
Suzeini Abdul Halim,
Aini Janteng

**Abstract:**

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function *f *ϵ* A *is said to be bi-univalent in the open unit disk *D* if both *f *and *f ^{-1}* are univalent in

*D*. The symbol

*A*denotes the class of all analytic functions

*f*in

*D*and it is normalized by the conditions

*f*(0) =

*f’*(0) – 1=0. The class of bi-univalent is denoted by The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function

*f*is subordinate to an analytic function

*g*if there is an analytic function

*w*defined on

*D*with

*w*(0) = 0 and |

*w*(z)| < 1 satisfying

*f*(

*z*) =

*g*[

*w*(

*z*)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

**Keywords:**
Analytic functions,
bi-univalent functions,
Hohlov operator,
subordination.

##### 2022 Explicit Chain Homotopic Function to Compute Hochschild Homology of the Polynomial Algebra

**Authors:**
Z. Altawallbeh

**Abstract:**

In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra, by providing certain homotopic function.

**Keywords:**
Exterior algebra,
free resolution,
free and projective
modules,
Hochschild homology,
homotopic function,
symmetric
algebra.

##### 2021 Some Solitary Wave Solutions of Generalized Pochhammer-Chree Equation via Exp-function Method

**Authors:**
Kourosh Parand,
Jamal Amani Rad

**Abstract:**

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

**Keywords:**
Exp-function method,
generalized Pochhammer- Chree equation,
solitary wave solution,
ODE's.