**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**717

# Search results for: Hamiltonian cycle

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

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

**Abstract:**

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

##### 716 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.

##### 715 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

##### 714 Hamiltonian Factors in Hamiltonian Graphs

**Authors:**
Sizhong Zhou,
Bingyuan Pu

**Abstract:**

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

##### 713 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.

##### 712 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.

##### 711 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.

##### 710 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.

##### 709 An Improved Construction Method for MIHCs on Cycle Composition Networks

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

**Abstract:**

Many well-known interconnection networks, such as kary n-cubes, recursive circulant graphs, generalized recursive circulant graphs, circulant graphs and so on, are shown to belong to the family of cycle composition networks. Recently, various studies about mutually independent hamiltonian cycles, abbreviated as MIHC-s, on interconnection networks are published. In this paper, using an improved construction method, we obtain MIHC-s on cycle composition networks with a much weaker condition than the known result. In fact, we established the existence of MIHC-s in the cycle composition networks and the result is optimal in the sense that the number of MIHC-s we constructed is maximal.

**Keywords:**
Hamiltonian cycle,
k-ary n-cube,
cycle composition networks,
mutually independent.

##### 708 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.

##### 707 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.

##### 706 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.

##### 705 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.

##### 704 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

##### 703 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.

##### 702 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.

##### 701 On Minimum Cycle Bases of the Wreath Product of Wheels with Stars

**Authors:**
M. M. M. Jaradat,
M. K. Al-Qeyyam

**Abstract:**

The length of a cycle basis of a graph is the sum of the lengths of its elements. A minimum cycle basis is a cycle basis with minimum length. In this work, a construction of a minimum cycle basis for the wreath product of wheels with stars is presented. Moreover, the length of minimum cycle basis and the length of its longest cycle are calculated.

**Keywords:**
Cycle space,
minimum cycle basis,
wreath product.

##### 700 A Lagrangian Hamiltonian Computational Method for Hyper-Elastic Structural Dynamics

**Authors:**
Hosein Falahaty,
Hitoshi Gotoh,
Abbas Khayyer

**Abstract:**

Performance of a Hamiltonian based particle method in simulation of nonlinear structural dynamics is subjected to investigation in terms of stability and accuracy. The governing equation of motion is derived based on Hamilton's principle of least action, while the deformation gradient is obtained according to Weighted Least Square method. The hyper-elasticity models of Saint Venant-Kirchhoff and a compressible version similar to Mooney- Rivlin are engaged for the calculation of second Piola-Kirchhoff stress tensor, respectively. Stability along with accuracy of numerical model is verified by reproducing critical stress fields in static and dynamic responses. As the results, although performance of Hamiltonian based model is evaluated as being acceptable in dealing with intense extensional stress fields, however kinds of instabilities reveal in the case of violent collision which can be most likely attributed to zero energy singular modes.

**Keywords:**
Hamilton's principle of least action,
particle based method,
hyper-elasticity,
analysis of stability.

##### 699 Exterior Calculus: Economic Profit Dynamics

**Authors:**
Troy L. Story

**Abstract:**

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

##### 698 Reliability-Based Life-Cycle Cost Model for Engineering Systems

**Authors:**
Reza Lotfalian,
Sudarshan Martins,
Peter Radziszewski

**Abstract:**

The effect of reliability on life-cycle cost, including initial and maintenance cost of a system is studied. The failure probability of a component is used to calculate the average maintenance cost during the operation cycle of the component. The standard deviation of the life-cycle cost is also calculated as an error measure for the average life-cycle cost. As a numerical example, the model is used to study the average life-cycle cost of an electric motor.

**Keywords:**
Initial Cost,
Life-cycle cost,
Maintenance Cost,
Reliability.

##### 697 Applying Different Working Fluids in a Combined Power and Ejector Refrigeration Cycle with Low Temperature Heat Sources

**Authors:**
Samad Jafarmadar,
Amin Habibzadeh

**Abstract:**

A power and cooling cycle, which combines the organic Rankine cycle and the ejector refrigeration cycle supplied by waste heat energy sources, is discussed in this paper. 13 working fluids including wet, dry, and isentropic fluids are studied in order to find their performances on the combined cycle. Various operating conditions’ effects on the proposed cycle are examined by fixing power/refrigeration ratio. According to the results, dry and isentropic fluids have better performance compared with wet fluids.

**Keywords:**
Combined power and refrigeration cycle,
low temperature heat sources,
organic rankine cycle,
working fluids.

##### 696 Hamiltonian Related Properties with and without Faults of the Dual-Cube Interconnection Network and Their Variations

**Authors:**
Shih-Yan Chen,
Shin-Shin Kao

**Abstract:**

**Keywords:**
Hypercubes,
dual-cubes,
fault-tolerant
hamiltonian property,
dual-cube extensive networks,
dual-cube-like
networks.

##### 695 Analysis of the Result for the Accelerated Life Cycle Test of the Motor for Washing Machine by Using Acceleration Factor

**Authors:**
Youn-Sung Kim,
Jin-Ho Jo,
Mi-Sung Kim,
Jae-Kun Lee

**Abstract:**

**Keywords:**
Accelerated life cycle test,
reliability test,
motor for washing machine,
brushless dc motor test.

##### 694 Information System Life Cycle: Applications in Construction and Manufacturing

**Authors:**
Carlos J. Costa,
Manuela Aparício

**Abstract:**

In this paper, we present the information life cycle, and analyze the importance of managing the corporate application portfolio across this life cycle. The approach presented here does not correspond just to the extension of the traditional information system development life cycle. This approach is based in the generic life cycle employed in other contexts like manufacturing or marketing. In this paper it is proposed a model of an information system life cycle, supported in the assumption that a system has a limited life. But, this limited life may be extended. This model is also applied in several cases; being reported here two examples of the framework application in a construction enterprise, and in a manufacturing enterprise.

**Keywords:**
Information systems/technology,
informatio nsystems life cycle,
organization engineering,
information economics.

##### 693 Managing the Information System Life Cycle in Construction and Manufacturing

**Authors:**
Carlos J. Costa,
Manuela Aparício

**Abstract:**

In this paper we present the information life cycle and analyze the importance of managing the corporate application portfolio across this life cycle. The approach presented here corresponds not just to the extension of the traditional information system development life cycle. This approach is based in the generic life cycle. In this paper it is proposed a model of an information system life cycle, supported in the assumption that a system has a limited life. But, this limited life may be extended. This model is also applied in several cases; being reported here two examples of the framework application in a construction enterprise and in a manufacturing enterprise.

**Keywords:**
Information systems/technology,
information systems life cycle,
organization engineering,
information economics.

##### 692 The Effect of Catastrophic Losses on Insurance Cycle: Case of Croatia

**Authors:**
D. Jakovčević,
M. Mihelja Žaja

**Abstract:**

This paper provides an analysis of the insurance cycle in the Republic of Croatia and whether they are affected by catastrophic losses on a global level. In general, it is considered that insurance cycles are particularly pronounced in periods of financial crisis, but are also affected by the growing number of catastrophic losses. They cause the change of insurance cycle and premium growth and intensification and narrowing of the coverage conditions, so these variables move in the same direction and these phenomena point to a new cycle. The main goal of this paper is to determine the existence of insurance cycle in the Republic of Croatia and investigate whether catastrophic losses have an influence on insurance cycles.

**Keywords:**
Catastrophic loss,
insurance cycle,
premium,
Republic of Croatia.

##### 691 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.

##### 690 Cascaded Transcritical/Supercritical CO2 Cycles and Organic Rankine Cycles to Recover Low-Temperature Waste Heat and LNG Cold Energy Simultaneously

**Authors:**
Haoshui Yu,
Donghoi Kim,
Truls Gundersen

**Abstract:**

Low-temperature waste heat is abundant in the process industries, and large amounts of Liquefied Natural Gas (LNG) cold energy are discarded without being recovered properly in LNG terminals. Power generation is an effective way to utilize low-temperature waste heat and LNG cold energy simultaneously. Organic Rankine Cycles (ORCs) and CO_{2} power cycles are promising technologies to convert low-temperature waste heat and LNG cold energy into electricity. If waste heat and LNG cold energy are utilized simultaneously in one system, the performance may outperform separate systems utilizing low-temperature waste heat and LNG cold energy, respectively. Low-temperature waste heat acts as the heat source and LNG regasification acts as the heat sink in the combined system. Due to the large temperature difference between the heat source and the heat sink, cascaded power cycle configurations are proposed in this paper. Cascaded power cycles can improve the energy efficiency of the system considerably. The cycle operating at a higher temperature to recover waste heat is called top cycle and the cycle operating at a lower temperature to utilize LNG cold energy is called bottom cycle in this study. The top cycle condensation heat is used as the heat source in the bottom cycle. The top cycle can be an ORC, transcritical CO_{2} (tCO_{2}) cycle or supercritical CO_{2} (sCO_{2}) cycle, while the bottom cycle only can be an ORC due to the low-temperature range of the bottom cycle. However, the thermodynamic path of the tCO_{2} cycle and sCO_{2} cycle are different from that of an ORC. The tCO_{2} cycle and the sCO_{2} cycle perform better than an ORC for sensible waste heat recovery due to a better temperature match with the waste heat source. Different combinations of the tCO_{2} cycle, sCO_{2} cycle and ORC are compared to screen the best configurations of the cascaded power cycles. The influence of the working fluid and the operating conditions are also investigated in this study. Each configuration is modeled and optimized in Aspen HYSYS. The results show that cascaded tCO_{2}/ORC performs better compared with cascaded ORC/ORC and cascaded sCO_{2}/ORC for the case study.

**Keywords:**
LNG cold energy,
low-temperature waste heat,
organic Rankine cycle,
supercritical CO2 cycle,
transcritical CO2 cycle.

##### 689 A Study on the Accelerated Life Cycle Test Method of the Motor for Home Appliances by Using Acceleration Factor

**Authors:**
Youn-Sung Kim,
Mi-Sung Kim,
Jae-Kun Lee

**Abstract:**

This paper deals with the accelerated life cycle test method of the motor for home appliances that demand high reliability. Life Cycle of parts in home appliances also should be 10 years because life cycle of the home appliances such as washing machine, refrigerator, TV is at least 10 years. In case of washing machine, the life cycle test method of motor is advanced for 3000 cycle test (1cycle = 2hours). However, 3000 cycle test incurs loss for the time and cost. Objectives of this study are to reduce the life cycle test time and the number of test samples, which could be realized by using acceleration factor for the test time and reduction factor for the number of sample.

**Keywords:**
Accelerated life cycle test,
motor reliability test,
motor for washing machine,
BLDC motor.

##### 688 Comparative Exergy Analysis of Ammonia-Water Rankine Cycles and Kalina Cycle

**Authors:**
Kyoung Hoon Kim

**Abstract:**

**Keywords:**
Ammonia-water,
Rankine cycle,
Kalina cycle,
exergy,
exergy destruction,
low-temperature heat source.