**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**155

# Search results for: Noether theorem

##### 155 Multisymplectic Geometry and Noether Symmetries for the Field Theories and the Relativistic Mechanics

**Authors:**
H. Loumi-Fergane,
A. Belaidi

**Abstract:**

The problem of symmetries in field theory has been analyzed using geometric frameworks, such as the multisymplectic models by using in particular the multivector field formalism. In this paper, we expand the vector fields associated to infinitesimal symmetries which give rise to invariant quantities as Noether currents for classical field theories and relativistic mechanic using the multisymplectic geometry where the Poincaré-Cartan form has thus been greatly simplified using the Second Order Partial Differential Equation (SOPDE) for multi-vector fields verifying Euler equations. These symmetries have been classified naturally according to the construction of the fiber bundle used. In this work, unlike other works using the analytical method, our geometric model has allowed us firstly to distinguish the angular moments of the gauge field obtained during different transformations while these moments are gathered in a single expression and are obtained during a rotation in the Minkowsky space. Secondly, no conditions are imposed on the Lagrangian of the mechanics with respect to its dependence in time and in q^{i}, the currents obtained naturally from the transformations are respectively the energy and the momentum of the system.

**Keywords:**
Field theories,
relativistic mechanics,
Lagrangian formalism,
multisymplectic geometry,
symmetries,
Noether theorem,
conservation laws.

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

**Authors:**
Yasuhito Tanaka

**Abstract:**

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

##### 153 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.

##### 152 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.

##### 151 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

##### 150 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.

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

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

**Abstract:**

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

##### 148 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

##### 147 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

##### 146 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.

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

**Authors:**
Yilun Shang

**Abstract:**

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

##### 144 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.

##### 143 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.

##### 142 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.

##### 141 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.

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

**Authors:**
Maharavo Randrianarivony

**Abstract:**

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

##### 139 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.

##### 138 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.

##### 137 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

##### 136 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.

##### 135 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

##### 134 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.

##### 133 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator

**Authors:**
Lv Yuhua

**Abstract:**

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Cone,
fixed point index,
eigenvalue problem,
p-Laplace operator,
positive solutions.

##### 132 Simplified Equations for Rigidity and Lateral Deflection for Reinforced Concrete Cantilever Shear Walls

**Authors:**
Anas M. Fares

**Abstract:**

**Keywords:**
Cantilever shear walls,
flexural deformation,
lateral deflection,
lateral loads,
reinforced concrete shear walls,
rigidity,
shear deformation,
virtual work theorem.

##### 131 The Boundary Theory between Laminar and Turbulent Flows

**Authors:**
Tomasz M. Jankowski

**Abstract:**

**Keywords:**
Freed gravitons,
free gravitons.

##### 130 Analysis of Permanence and Extinction of Enterprise Cluster Based On Ecology Theory

**Authors:**
Ping Liu,
Yongkun Li

**Abstract:**

This paper is concerned with the permanence and extinction problem of enterprises cluster constituted by m satellite enterprises and a dominant enterprise. We present the model involving impulsive effect based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environment. Applying comparison theorem of impulsive differential equation, we establish sufficient conditions which ultimately affect the fate of enterprises: permanence, extinction, and co-existence. Finally, we present numerical examples to explain the economical significance of mathematical results.

**Keywords:**
Enterprise cluster,
permanence,
extinction,
impulsive,
comparison theorem.

##### 129 A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation

**Authors:**
Fengxia Zheng,
Chuanyun Gu

**Abstract:**

**Keywords:**
Fractional differential equation,
Boundary value
problem,
Positive solution,
Existence and uniqueness,
Fixed point
theorem of a sum operator.

##### 128 Existence of Solutions for a Nonlinear Fractional Differential Equation with Integral Boundary Condition

**Abstract:**

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: Dαt x(t) = f(t, x(t),Dβ t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle.

**Keywords:**
Fractional differential equation,
Integral boundary condition,
Schauder fixed point theorem,
Banach contraction principle.

##### 127 Positive Periodic Solutions for a Predator-prey Model with Modified Leslie-Gower Holling-type II Schemes and a Deviating Argument

**Authors:**
Yanling Zhu,
Kai Wang

**Abstract:**

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.

**Keywords:**
Predator-prey model,
Holling II type functional response,
positive periodic solution,
coincidence degree theorem.

##### 126 The Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation Boundary Value Problem

**Authors:**
Chuanyun Gu,
Shouming Zhong

**Abstract:**

In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.

**Keywords:**
Fractional differential equation,
Boundary value problem,
Positive solution,
Existence and uniqueness,
Fixed point theorem of a sum operator