**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**2980

# Search results for: Hamiltonian vector field

##### 2980 Hamiltonian Factors in Hamiltonian Graphs

**Authors:**
Sizhong Zhou,
Bingyuan Pu

**Abstract:**

**Keywords:**
graph,
neighborhood,
factor,
Hamiltonian factor.

##### 2979 An Optimal Control Problem for Rigid Body Motions on Lie Group SO(2, 1)

**Authors:**
Nemat Abazari,
Ilgin Sager

**Abstract:**

In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.

**Keywords:**
Optimal control,
Hamiltonian vector field,
Darboux vector,
maximum principle,
lie group,
Rigid body motion,
Lorentz metric.

##### 2978 Planning Rigid Body Motions and Optimal Control Problem on Lie Group SO(2, 1)

**Authors:**
Nemat Abazari,
Ilgin Sager

**Abstract:**

In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimizes the integral of the Lorentz inner product of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.

**Keywords:**
Optimal control,
Hamiltonian vector field,
Darboux vector,
maximum principle,
lie group,
rigid body motion,
Lorentz metric.

##### 2977 A Sufficient Condition for Graphs to Have Hamiltonian [a, b]-Factors

**Authors:**
Sizhong Zhou

**Abstract:**

Let a and b be nonnegative integers with 2 ≤ a < b, and let G be a Hamiltonian graph of order n with n ≥ (a+b−4)(a+b−2) b−2 . An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F contains a Hamiltonian cycle. In this paper, it is proved that G has a Hamiltonian [a, b]-factor if |NG(X)| > (a−1)n+|X|−1 a+b−3 for every nonempty independent subset X of V (G) and δ(G) > (a−1)n+a+b−4 a+b−3 .

**Keywords:**
graph,
minimum degree,
neighborhood,
[a,
b]-factor,
Hamiltonian [a,
b]-factor.

##### 2976 Mutually Independent Hamiltonian Cycles of Cn x Cn

**Authors:**
Kai-Siou Wu,
Justie Su-Tzu Juan

**Abstract:**

In a graph G, a cycle is Hamiltonian cycle if it contain all vertices of G. Two Hamiltonian cycles C_1 = ⟨u_0, u_1, u_2, ..., u_{n−1}, u_0⟩ and C_2 = ⟨v_0, v_1, v_2, ..., v_{n−1}, v_0⟩ in G are independent if u_0 = v_0, u_i = ̸ v_i for all 1 ≤ i ≤ n−1. In G, a set of Hamiltonian cycles C = {C_1, C_2, ..., C_k} is mutually independent if any two Hamiltonian cycles of C are independent. The mutually independent Hamiltonicity IHC(G), = k means there exist a maximum integer k such that there exists k-mutually independent Hamiltonian cycles start from any vertex of G. In this paper, we prove that IHC(C_n × C_n) = 4, for n ≥ 3.

**Keywords:**
Hamiltonian,
independent,
cycle,
Cartesian product,
mutually independent Hamiltonicity

##### 2975 The Panpositionable Hamiltonicity of k-ary n-cubes

**Authors:**
Chia-Jung Tsai,
Shin-Shin Kao

**Abstract:**

**Keywords:**
Hamiltonian,
panpositionable,
bipanpositionable,
k-ary n-cube.

##### 2974 The Balanced Hamiltonian Cycle on the Toroidal Mesh Graphs

**Authors:**
Wen-Fang Peng,
Justie Su-Tzu Juan

**Abstract:**

The balanced Hamiltonian cycle problemis a quiet new topic of graph theorem. Given a graph G = (V, E), whose edge set can be partitioned into k dimensions, for positive integer k and a Hamiltonian cycle C on G. The set of all i-dimensional edge of C, which is a subset by E(C), is denoted as Ei(C).

**Keywords:**
Hamiltonian cycle,
balanced,
Cartesian product.

##### 2973 A Hamiltonian Decomposition of 5-star

**Authors:**
Walter Hussak,
Heiko Schröder

**Abstract:**

Star graphs are Cayley graphs of symmetric groups of permutations, with transpositions as the generating sets. A star graph is a preferred interconnection network topology to a hypercube for its ability to connect a greater number of nodes with lower degree. However, an attractive property of the hypercube is that it has a Hamiltonian decomposition, i.e. its edges can be partitioned into disjoint Hamiltonian cycles, and therefore a simple routing can be found in the case of an edge failure. The existence of Hamiltonian cycles in Cayley graphs has been known for some time. So far, there are no published results on the much stronger condition of the existence of Hamiltonian decompositions. In this paper, we give a construction of a Hamiltonian decomposition of the star graph 5-star of degree 4, by defining an automorphism for 5-star and a Hamiltonian cycle which is edge-disjoint with its image under the automorphism.

**Keywords:**
interconnection networks,
paths and cycles,
graphs andgroups.

##### 2972 Exterior Calculus: Economic Growth Dynamics

**Authors:**
Troy L. Story

**Abstract:**

Mathematical models of dynamics employing exterior calculus are mathematical representations of the same unifying principle; namely, the description of a dynamic system with a characteristic differential one-form on an odd-dimensional differentiable manifold leads, by analysis with exterior calculus, to a set of differential equations and a characteristic tangent vector (vortex vector) which define transformations of the system. Using this principle, a mathematical model for economic growth is constructed by proposing a characteristic differential one-form for economic growth dynamics (analogous to the action in Hamiltonian dynamics), then generating a pair of characteristic differential equations and solving these equations for the rate of economic growth as a function of labor and capital. By contracting the characteristic differential one-form with the vortex vector, the Lagrangian for economic growth dynamics is obtained.

**Keywords:**
Differential geometry,
exterior calculus,
Hamiltonian geometry,
mathematical economics.

##### 2971 A Further Study on the 4-Ordered Property of Some Chordal Ring Networks

**Authors:**
Shin-Shin Kao,
Hsiu-Chunj Pan

**Abstract:**

Given a graph G. A cycle of G is a sequence of vertices of G such that the first and the last vertices are the same. A hamiltonian cycle of G is a cycle containing all vertices of G. The graph G is k-ordered (resp. k-ordered hamiltonian) if for any sequence of k distinct vertices of G, there exists a cycle (resp. hamiltonian cycle) in G containing these k vertices in the specified order. Obviously, any cycle in a graph is 1-ordered, 2-ordered and 3- ordered. Thus the study of any graph being k-ordered (resp. k-ordered hamiltonian) always starts with k = 4. Most studies about this topic work on graphs with no real applications. To our knowledge, the chordal ring families were the first one utilized as the underlying topology in interconnection networks and shown to be 4-ordered. Furthermore, based on our computer experimental results, it was conjectured that some of them are 4-ordered hamiltonian. In this paper, we intend to give some possible directions in proving the conjecture.

**Keywords:**
Hamiltonian cycle,
4-ordered,
Chordal rings,
3-regular.

##### 2970 A Systematic Approach for Finding Hamiltonian Cycles with a Prescribed Edge in Crossed Cubes

**Authors:**
Jheng-Cheng Chen,
Chia-Jui Lai,
Chang-Hsiung Tsai,

**Abstract:**

The crossed cube is one of the most notable variations of hypercube, but some properties of the former are superior to those of the latter. For example, the diameter of the crossed cube is almost the half of that of the hypercube. In this paper, we focus on the problem embedding a Hamiltonian cycle through an arbitrary given edge in the crossed cube. We give necessary and sufficient condition for determining whether a given permutation with n elements over Zn generates a Hamiltonian cycle pattern of the crossed cube. Moreover, we obtain a lower bound for the number of different Hamiltonian cycles passing through a given edge in an n-dimensional crossed cube. Our work extends some recently obtained results.

**Keywords:**
Interconnection network,
Hamiltonian,
crossed cubes,
prescribed edge.

##### 2969 The Frequency Graph for the Traveling Salesman Problem

**Authors:**
Y. Wang

**Abstract:**

**Keywords:**
Traveling salesman problem,
frequency graph,
local
optimal Hamiltonian path,
four vertices and three lines inequality.

##### 2968 Exterior Calculus: Economic Profit Dynamics

**Authors:**
Troy L. Story

**Abstract:**

**Keywords:**
Differential geometry,
exterior calculus,
Hamiltonian
geometry,
mathematical economics,
economic functions,
and
dynamics

##### 2967 Lyapunov Type Inequalities for Fractional Impulsive Hamiltonian Systems

**Authors:**
Kazem Ghanbari,
Yousef Gholami

**Abstract:**

**Keywords:**
Fractional derivatives and integrals,
Hamiltonian
system,
Lyapunov type inequalities,
stability,
disconjugacy.

##### 2966 Near-Field Robust Adaptive Beamforming Based on Worst-Case Performance Optimization

**Authors:**
Jing-ran Lin,
Qi-cong Peng,
Huai-zong Shao

**Abstract:**

**Keywords:**
Robust adaptive beamforming (RABF),
near-field,
steering vector mismatches,
diagonal loading,
worst-case performanceoptimization.

##### 2965 Vector Control Using Series Iron Loss Model of Induction, Motors and Power Loss Minimization

**Authors:**
Kheldoun Aissa,
Khodja Djalal Eddine

**Abstract:**

**Keywords:**
Field Oriented Controller,
Induction Motor,
Loss ModelController,
Series Iron Loss.

##### 2964 An Augmented Automatic Choosing Control Designed by Extremizing a Combination of Hamiltonian and Lyapunov Functions for Nonlinear Systems with Constrained Input

**Authors:**
Toshinori Nawata,
Hitoshi Takata

**Abstract:**

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

**Keywords:**
Augmented Automatic Choosing Control,
NonlinearControl,
Genetic Algorithm,
Hamiltonian,
Lyapunovfunction

##### 2963 Vector Control of Multimotor Drive

**Authors:**
Archana S. Nanoty,
A. R. Chudasama

**Abstract:**

**Keywords:**
Field oriented control,
multiphase induction motor,
power electronics converter.

##### 2962 Image Modeling Using Gibbs-Markov Random Field and Support Vector Machines Algorithm

**Authors:**
Refaat M Mohamed,
Ayman El-Baz,
Aly A. Farag

**Abstract:**

**Keywords:**
Image Modeling,
MRF,
Parameters Estimation,
SVM Learning.

##### 2961 An Efficient Hamiltonian for Discrete Fractional Fourier Transform

**Authors:**
Sukrit Shankar,
Pardha Saradhi K.,
Chetana Shanta Patsa,
Jaydev Sharma

**Abstract:**

**Keywords:**
Fractional Fourier Transform,
Hamiltonian,
Eigen
Vectors,
Discrete Hermite Gaussians.

##### 2960 Quantum Localization of Vibrational Mirror in Cavity Optomechanics

**Authors:**
Madiha Tariq,
Hena Rabbani

**Abstract:**

Recently, cavity-optomechanics becomes an extensive research field that has manipulated the mechanical effects of light for coupling of the optical field with other physical objects specifically with regards to dynamical localization. We investigate the dynamical localization (both in momentum and position space) for a vibrational mirror in a Fabry-Pérot cavity driven by a single mode optical field and a transverse probe field. The weak probe field phenomenon results in classical chaos in phase space and spatio temporal dynamics in position |ψ(x)²| and momentum space |ψ(p)²| versus time show quantum localization in both momentum and position space. Also, we discuss the parametric dependencies of dynamical localization for a designated set of parameters to be experimentally feasible. Our work opens an avenue to manipulate the other optical phenomena and applicability of proposed work can be prolonged to turn-able laser sources in the future.

**Keywords:**
Dynamical localization,
cavity optomechanics,
hamiltonian chaos,
probe field.

##### 2959 Numerical Simulation of Plasma Actuator Using OpenFOAM

**Authors:**
H. Yazdani,
K. Ghorbanian

**Abstract:**

This paper deals with modeling and simulation of the plasma actuator with OpenFOAM. Plasma actuator is one of the newest devices in flow control techniques which can delay separation by inducing external momentum to the boundary layer of the flow. The effects of the plasma actuators on the external flow are incorporated into Navier-Stokes computations as a body force vector which is obtained as a product of the net charge density and the electric field. In order to compute this body force vector, the model solves two equations: One for the electric field due to the applied AC voltage at the electrodes and the other for the charge density representing the ionized air. The simulation result is compared to the experimental and typical values which confirms the validity of the modeling.

**Keywords:**
Active flow control,
flow field,
OpenFOAM,
plasma actuator.

##### 2958 Multi Switched Split Vector Quantizer

**Authors:**
M. Satya Sai Ram,
P. Siddaiah,
M. Madhavi Latha

**Abstract:**

**Keywords:**
Unconstrained vector quantization,
Linear predictiveCoding,
Split vector quantization,
Multi stage vector quantization,
Switched Split vector quantization,
Line Spectral Frequencies.

##### 2957 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.

##### 2956 On Chvátal’s Conjecture for the Hamiltonicity of 1-Tough Graphs and Their Complements

**Authors:**
Shin-Shin Kao,
Yuan-Kang Shih,
Hsun Su

**Abstract:**

In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

**Keywords:**
Complement,
degree sum,
Hamiltonian,
tough.

##### 2955 Distribution Sampling of Vector Variance without Duplications

**Authors:**
Erna T. Herdiani,
Maman A. Djauhari

**Abstract:**

**Keywords:**
Asymptotic distribution,
covariance matrix,
likelihood ratio test,
vector variance.

##### 2954 Octonionic Reformulation of Vector Analysis

**Authors:**
Bhupendra C. S. Chauhan,
P. S. Bisht,
O. P. S. Negi

**Abstract:**

**Keywords:**
Octonions,
Vector Space and seven dimensions

##### 2953 Position Vector of a Partially Null Curve Derived from a Vector Differential Equation

**Authors:**
Süha Yılmaz,
Emin Özyılmaz,
Melih Turgut,
Şuur Nizamoğlu

**Abstract:**

In this paper, position vector of a partially null unit speed curve with respect to standard frame of Minkowski space-time is studied. First, it is proven that position vector of every partially null unit speed curve satisfies a vector differential equation of fourth order. In terms of solution of the differential equation, position vector of a partially null unit speed curve is expressed.

**Keywords:**
Frenet Equations,
Partially Null Curves,
Minkowski Space-time,
Vector Differential Equation.

##### 2952 Comparative Analysis of Geographical Routing Protocol in Wireless Sensor Networks

**Authors:**
Rahul Malhotra

**Abstract:**

The field of wireless sensor networks (WSN) engages a lot of associates in the research community as an interdisciplinary field of interest. This type of network is inexpensive, multifunctionally attributable to advances in micro-electromechanical systems and conjointly the explosion and expansion of wireless communications. A mobile ad hoc network is a wireless network without fastened infrastructure or federal management. Due to the infrastructure-less mode of operation, mobile ad-hoc networks are gaining quality. During this work, we have performed an efficient performance study of the two major routing protocols: Ad hoc On-Demand Distance Vector Routing (AODV) and Dynamic Source Routing (DSR) protocols. We have used an accurate simulation model supported NS2 for this purpose. Our simulation results showed that AODV mitigates the drawbacks of the DSDV and provides better performance as compared to DSDV.

**Keywords:**
Routing protocols,
mobility,
Mobile Ad-hoc Networks,
Ad-hoc On-demand Distance Vector,
Dynamic Source Routing,
Destination Sequence Distance Vector,
Quality of Service.

##### 2951 Vector Space of the Extended Base-triplets over the Galois Field of five DNA Bases Alphabet

**Authors:**
Robersy Sánchez,
Ricardo Grau

**Abstract:**

A plausible architecture of an ancient genetic code is derived from an extended base triplet vector space over the Galois field of the extended base alphabet {D, G, A, U, C}, where the letter D represent one or more hypothetical bases with unspecific pairing. We hypothesized that the high degeneration of a primeval genetic code with five bases and the gradual origin and improvements of a primitive DNA repair system could make possible the transition from the ancient to the modern genetic code. Our results suggest that the Watson-Crick base pairing and the non-specific base pairing of the hypothetical ancestral base D used to define the sum and product operations are enough features to determine the coding constraints of the primeval and the modern genetic code, as well as the transition from the former to the later. Geometrical and algebraic properties of this vector space reveal that the present codon assignment of the standard genetic code could be induced from a primeval codon assignment. Besides, the Fourier spectrum of the extended DNA genome sequences derived from the multiple sequence alignment suggests that the called period-3 property of the present coding DNA sequences could also exist in the ancient coding DNA sequences.

**Keywords:**
Genetic code vector space,
primeval genetic code,
power spectrum.