**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**300

# Search results for: Stokes’ Theorem

##### 300 On the Maximum Theorem: A Constructive Analysis

**Authors:**
Yasuhito Tanaka

**Abstract:**

**Keywords:**
Maximum theorem,
Constructive mathematics,
Sequentially
locally at most one maximum.

##### 299 Toward a New Simple Analytical Formulation of Navier-Stokes Equations

**Authors:**
Gunawan Nugroho,
Ahmed M. S. Ali,
Zainal A. Abdul Karim

**Abstract:**

**Keywords:**
Navier-Stokes Equations,
potential function,
turbulent flows.

##### 298 One Some Effective Solutions of Stokes Axisymmetric Equation for a Viscous Fluid

**Authors:**
N. Khatiashvili,
K. Pirumova,
D. Janjgava

**Abstract:**

The Stokes equation connected with the fluid flow over the axisymmetric bodies in a cylindrical area is considered. The equation is studied in a moving coordinate system with the appropriate boundary conditions. Effective formulas for the velocity components are obtained. The graphs of the velocity components and velocity profile are plotted.

**Keywords:**
Stokes system,
viscous fluid.

##### 297 Fermat’s Last Theorem a Simple Demonstration

**Authors:**
Jose William Porras Ferreira

**Abstract:**

This paper presents two solutions to the Fermat’s Last Theorem (FLT). The first one using some algebraic basis related to the Pythagorean theorem, expression of equations, an analysis of their behavior, when compared with power and power and using " the “Well Ordering Principle” of natural numbers it is demonstrated that in Fermat equation . The second one solution is using the connection between and power through the Pascal’s triangle or Newton’s binomial coefficients, where de Fermat equation do not fulfill the first coefficient, then it is impossible that:

z^{n}=x^{n}+y^{n} for n>2 and (x, y, z) E Z^{+} - {0}

**Keywords:**
Fermat’s Last Theorem,
Pythagorean Theorem,
Newton Binomial Coefficients,
Pascal’s Triangle,
Well Ordering Principle.

##### 296 Generalized Stokes’ Problems for an Incompressible Couple Stress Fluid

**Authors:**
M.Devakar,
T.K.V.Iyengar

**Abstract:**

In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest.

**Keywords:**
Couple stress fluid,
Generalized Stokes’ problems,
Laplace transform,
Numerical inversion

##### 295 Significance of Splitting Method in Non-linear Grid system for the Solution of Navier-Stokes Equation

**Abstract:**

Solution to unsteady Navier-Stokes equation by Splitting method in physical orthogonal algebraic curvilinear coordinate system, also termed 'Non-linear grid system' is presented. The linear terms in Navier-Stokes equation are solved by Crank- Nicholson method while the non-linear term is solved by the second order Adams-Bashforth method. This work is meant to bring together the advantage of Splitting method as pressure-velocity solver of higher efficiency with the advantage of consuming Non-linear grid system which produce more accurate results in relatively equal number of grid points as compared to Cartesian grid. The validation of Splitting method as a solution of Navier-Stokes equation in Nonlinear grid system is done by comparison with the benchmark results for lid driven cavity flow by Ghia and some case studies including Backward Facing Step Flow Problem.

**Keywords:**
Navier-Stokes,
'Non-linear grid system',
Splitting method.

##### 294 Comparison of Two Types of Preconditioners for Stokes and Linearized Navier-Stokes Equations

**Authors:**
Ze-Jun Hu,
Ting-Zhu Huang,
Ning-Bo Tan

**Abstract:**

To solve saddle point systems efficiently, several preconditioners have been published. There are many methods for constructing preconditioners for linear systems from saddle point problems, for instance, the relaxed dimensional factorization (RDF) preconditioner and the augmented Lagrangian (AL) preconditioner are used for both steady and unsteady Navier-Stokes equations. In this paper we compare the RDF preconditioner with the modified AL (MAL) preconditioner to show which is more effective to solve Navier-Stokes equations. Numerical experiments indicate that the MAL preconditioner is more efficient and robust, especially, for moderate viscosities and stretched grids in steady problems. For unsteady cases, the convergence rate of the RDF preconditioner is slightly faster than the MAL perconditioner in some circumstances, but the parameter of the RDF preconditioner is more sensitive than the MAL preconditioner. Moreover the convergence rate of the MAL preconditioner is still quite acceptable. Therefore we conclude that the MAL preconditioner is more competitive than the RDF preconditioner. These experiments are implemented with IFISS package.

**Keywords:**
Navier-Stokes equations,
Krylov subspace method,
preconditioner,
dimensional splitting,
augmented Lagrangian preconditioner.

##### 293 Discovering Liouville-Type Problems for p-Energy Minimizing Maps in Closed Half-Ellipsoids by Calculus Variation Method

**Authors:**
Lina Wu,
Jia Liu,
Ye Li

**Abstract:**

**Keywords:**
Bochner Formula,
Stokes’ Theorem,
Cauchy-Schwarz
Inequality,
first and second variation formulas,
Hardy-Sobolev type
inequalities,
Liouville-type problem,
p-harmonic map.

##### 292 Power Series Form for Solving Linear Fredholm Integral Equations of Second Order via Banach Fixed Point Theorem

**Authors:**
Adil AL-Rammahi

**Abstract:**

In this paper, a new method for solution of second order linear Fredholm integral equation in power series form was studied. The result is obtained by using Banach fixed point theorem.

**Keywords:**
Fredholm integral equation,
power series,
Banach fixed point theorem,
Linear Systems.

##### 291 Positive Solutions for Semipositone Discrete Eigenvalue Problems via Three Critical Points Theorem

**Authors:**
Benshi Zhu

**Abstract:**

**Keywords:**
Discrete eigenvalue problems,
positive solutions,
semipositone,
three critical points theorem

##### 290 Constructive Proof of Tychonoff’s Fixed Point Theorem for Sequentially Locally Non-Constant Functions

**Authors:**
Yasuhito Tanaka

**Abstract:**

We present a constructive proof of Tychonoff’s fixed point theorem in a locally convex space for uniformly continuous and sequentially locally non-constant functions.

**Keywords:**
sequentially locally non-constant functions,
Tychonoff’s
fixed point theorem,
constructive mathematics.

##### 289 Mechanical Quadrature Methods for Solving First Kind Boundary Integral Equations of Stationary Stokes Problem

**Authors:**
Xin Luo,
Jin Huang,
Pan Cheng

**Abstract:**

By means of Sidi-Israeli’s quadrature rules, mechanical quadrature methods (MQMs) for solving the first kind boundary integral equations (BIEs) of steady state Stokes problem are presented. The convergence of numerical solutions by MQMs is proved based on Anselone’s collective compact and asymptotical compact theory, and the asymptotic expansions with the odd powers of the errors are provided, which implies that the accuracy of the approximations by MQMs possesses high accuracy order O (h3). Finally, the numerical examples show the efficiency of our methods.

**Keywords:**
Stokes problem,
boundary integral equation,
mechanical
quadrature methods,
asymptotic expansions.

##### 288 Weyl Type Theorem and the Fuglede Property

**Authors:**
M. H. M. Rashid

**Abstract:**

**Keywords:**
Fuglede Property,
Weyl’s theorem,
generalized
derivation,
Aluthge Transformation.

##### 287 Extremal Properties of Generalized Class of Close-to-convex Functions

**Authors:**
Norlyda Mohamed,
Daud Mohamad,
Shaharuddin Cik Soh

**Abstract:**

**Keywords:**
Argument of f ′(z) ,
Carathéodory Function,
Closeto-
convex Function,
Distortion Theorem,
Extremal Properties

##### 286 A Constructive Proof of the General Brouwer Fixed Point Theorem and Related Computational Results in General Non-Convex sets

**Authors:**
Menglong Su,
Shaoyun Shi,
Qing Xu

**Abstract:**

In this paper, by introducing twice continuously differentiable mappings, we develop an interior path following following method, which enables us to give a constructive proof of the general Brouwer fixed point theorem and thus to solve fixed point problems in a class of non-convex sets. Under suitable conditions, a smooth path can be proven to exist. This can lead to an implementable globally convergent algorithm. Several numerical examples are given to illustrate the results of this paper.

**Keywords:**
interior path following method,
general Brouwer fixed
point theorem,
non-convex sets,
globally convergent algorithm

##### 285 A Sandwich-type Theorem with Applications to Univalent Functions

**Authors:**
Sukhwinder Singh Billing,
Sushma Gupta,
Sukhjit Singh Dhaliwal

**Abstract:**

**Keywords:**
Univalent function,
Starlike function,
Differential subordination,
Differential superordination.

##### 284 On the Central Limit Theorems for Forward and Backward Martingales

**Authors:**
Yilun Shang

**Abstract:**

**Keywords:**
central limit theorem,
martingale difference sequence,
backward martingale.

##### 283 Cryptographic Attack on Lucas Based Cryptosystems Using Chinese Remainder Theorem

**Authors:**
Tze Jin Wong,
Lee Feng Koo,
Pang Hung Yiu

**Abstract:**

_{4,6}) cryptosystem under the Lenstra’s attack as compared to the other two Lucas based cryptosystems such as LUC and LUC

_{3}cryptosystems. All the Lucas based cryptosystems were exposed mathematically to the Lenstra’s attack using Chinese Remainder Theorem and Dickson polynomial. Result shows that the possibility for successful Lenstra’s attack is less against LUC

_{4,6}cryptosystem than LUC

_{3}and LUC cryptosystems. Current study concludes that LUC

_{4,6}cryptosystem is more secure than LUC and LUC

_{3}cryptosystems in sustaining against Lenstra’s attack.

**Keywords:**
Lucas sequence,
Dickson Polynomial,
faulty signature,
corresponding signature,
congruence.

##### 282 Reduction of Search Space by Applying Controlled Genetic Operators for Weight Constrained Shortest Path Problem

**Authors:**
A.K.M. Khaled Ahsan Talukder,
Taibun Nessa,
Kaushik Roy

**Abstract:**

**Keywords:**
Genetic Algorithm,
Evolutionary Optimization,
Multi Objective Optimization,
Non-linear Schema Theorem,
WCSPP.

##### 281 Recursive Wiener-Khintchine Theorem

**Authors:**
Khalid M. Aamir,
Mohammad A. Maud

**Abstract:**

Power Spectral Density (PSD) computed by taking the Fourier transform of auto-correlation functions (Wiener-Khintchine Theorem) gives better result, in case of noisy data, as compared to the Periodogram approach. However, the computational complexity of Wiener-Khintchine approach is more than that of the Periodogram approach. For the computation of short time Fourier transform (STFT), this problem becomes even more prominent where computation of PSD is required after every shift in the window under analysis. In this paper, recursive version of the Wiener-Khintchine theorem has been derived by using the sliding DFT approach meant for computation of STFT. The computational complexity of the proposed recursive Wiener-Khintchine algorithm, for a window size of N, is O(N).

**Keywords:**
Power Spectral Density (PSD),
Wiener-KhintchineTheorem,
Periodogram,
Short Time Fourier Transform (STFT),
TheSliding DFT.

##### 280 Some Applications of Gröbner bases

**Authors:**
Hassan Noori,
Abdolali Basiri,
Sajjad Rahmany

**Abstract:**

**Keywords:**
Gr¨obner bases,
Application of Gr¨obner bases,
Automatic
Geometric Theorem Proving,
Graph Coloring,
Cryptography.

##### 279 Quadrilateral Decomposition by Two-Ear Property Resulting in CAD Segmentation

**Authors:**
Maharavo Randrianarivony

**Abstract:**

**Keywords:**
Quadrangulation,
simply connected,
two-ear theorem.

##### 278 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem

**Authors:**
Thanin Sitthiwirattham,
Jiraporn Reunsumrit

**Abstract:**

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

**Keywords:**
Positive solution,
Boundary value problem,
Fixed
point theorem,
Cone.

##### 277 Periodic Solutions for a Third-order p-Laplacian Functional Differential Equation

**Authors:**
Yanling Zhu,
Kai Wang

**Abstract:**

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g t, 0 −τ x(t + s) dα(s) + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

**Keywords:**
p–Laplacian,
distributed delay,
periodic solution,
Mawhin's continuation theorem.

##### 276 On the Strong Solutions of the Nonlinear Viscous Rotating Stratified Fluid

**Authors:**
A. Giniatoulline

**Abstract:**

**Keywords:**
Galerkin method,
Navier-Stokes equations,
nonlinear partial differential equations,
Sobolev spaces,
stratified fluid.

##### 275 Lagrange-s Inversion Theorem and Infiltration

**Authors:**
Pushpa N. Rathie,
Prabhata K. Swamee,
André L. B. Cavalcante,
Luan Carlos de S. M. Ozelim

**Abstract:**

**Keywords:**
Green-Ampt Equation,
Lagrange's Inversion
Theorem,
Talsma-Parlange Equation,
Three-Parameter Infiltration
Equation

##### 274 Fourth Order Accurate Free Convective Heat Transfer Solutions from a Circular Cylinder

**Authors:**
T. V. S. Sekhar,
B. Hema Sundar Raju

**Abstract:**

**Keywords:**
Higher order compact scheme,
Navier-Stokes
equations,
Energy equation,
Natural convection,
Boussinesq's
approximation and Mean Nusselt number.

##### 273 Multiple Positive Periodic Solutions to a Predator-prey system with Harvesting Terms and Holling II Type Functional Response

**Authors:**
Pan Wang,
Yongkun Li

**Abstract:**

In this paper, a periodic predator-prey system with harvesting terms and Holling II type functional response is considered. Sufficient criteria for the existence of at least sixteen periodic solutions are established by using the well known continuation theorem due to Mawhin. An example is given to illustrate the main result.

**Keywords:**
Periodic solution,
predator-prey system,
harvesting terms,
continuation theorem.

##### 272 A new Configurable Decimation Filter using Pascal-s Triangle Theorem

**Authors:**
A. Chahardah Cherik,
E. Farshidi

**Abstract:**

**Keywords:**
Decimation filter,
sigma delta,
Pascal's triangle'stheorem,
memory

##### 271 PI Control for Second Order Delay System with Tuning Parameter Optimization

**Authors:**
R. Farkh,
K. Laabidi,
M. Ksouri

**Abstract:**

**Keywords:**
Genetic algorithm,
Hermit-Biehler theorem,
optimization,
PI controller,
second order delay system,
stability region.