Journal of Applied Mathematics http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. A Float-Path Theory and Its Application to the Time-Cost Tradeoff Problem Thu, 26 Feb 2015 08:41:19 +0000 http://www.hindawi.com/journals/jam/2015/539374/ Activity floats are vital for project scheduling, such as total floats which determine the maximum permissible delays of activities. Moreover, activity paths in activity networks present essences of many project scheduling problems; for example, the time-cost tradeoff is to shorten long paths at lower costs. We discovered relationships between activity floats and paths and established a float-path theory. The theory helps to compute path lengths using activity floats and analyze activity floats using paths, which helps to transmute a problem into the other simpler one. We discussed applications of the float-path theory and applied it to solve the time-cost tradeoff problem (TCTP), especially the nonlinear and discrete versions. We proposed a simplification from an angle of path as a preprocessing technique for the TCTP. The simplification is a difficult path problem, but we transformed it into a simple float problem using the float-path theory. We designed a polynomial algorithm for the simplification, and then the TCTP may be solved more efficiently. Zhi-xiong Su, Jian-xun Qi, and Han-ying Wei Copyright © 2015 Zhi-xiong Su et al. All rights reserved. Stability Results for an Age-Structured SIS Epidemic Model with Vector Population Tue, 24 Feb 2015 14:52:29 +0000 http://www.hindawi.com/journals/jam/2015/838312/ We formulate an age-structured SIS epidemic model with periodic parameters, which includes host population and vector population. The host population is described by two partial differential equations, and the vector population is described by a single ordinary differential equation. The existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on locally integrable periodic functions. We obtain that if the spectral radius of the Fréchet derivative of the fixed point operator at zero is greater than one, there exists a unique endemic periodic solution, and we investigate the global attractiveness of disease-free steady state of the normalized system. He-Long Liu, Jing-Yuan Yu, and Guang-Tian Zhu Copyright © 2015 He-Long Liu et al. All rights reserved. Generalized Well-Posedness for Symmetric Vector Quasi-Equilibrium Problems Tue, 24 Feb 2015 09:08:34 +0000 http://www.hindawi.com/journals/jam/2015/108357/ We introduce and study well-posedness in connection with the symmetric vector quasi-equilibrium problem, which unifies its Hadamard and Levitin-Polyak well-posedness. Using the nonlinear scalarization function, we give some sufficient conditions to guarantee the existence of well-posedness for the symmetric vector quasi-equilibrium problem. Wei-bing Zhang, Nan-jing Huang, and Donal O’Regan Copyright © 2015 Wei-bing Zhang et al. All rights reserved. Infinitely Many Eigenfunctions for Polynomial Problems: Exact Results Mon, 23 Feb 2015 07:24:38 +0000 http://www.hindawi.com/journals/jam/2015/516159/ Let be a real-valued polynomial function in which the degree of in is greater than or equal to 1. For any polynomial , we assume that is a nonlinear operator with . In this paper, we will find an eigenfunction to satisfy the following equation: for some eigenvalue and we call the problem a fixed point like problem. If the number of all eigenfunctions in is infinitely many, we prove that (i) any coefficients of , are all constants in and (ii) is an eigenfunction in if and only if . Yi-Chou Chen Copyright © 2015 Yi-Chou Chen. All rights reserved. Computing Assortative Mixing by Degree with the -Metric in Networks Using Linear Programming Sun, 22 Feb 2015 15:46:34 +0000 http://www.hindawi.com/journals/jam/2015/580361/ Calculation of assortative mixing by degree in networks indicates whether nodes with similar degree are connected to each other. In networks with scale-free distribution high values of assortative mixing by degree can be an indication of a hub-like core in networks. Degree correlation has generally been used to measure assortative mixing of a network. But it has been shown that degree correlation cannot always distinguish properly between different networks with nodes that have the same degrees. The so-called -metric has been shown to be a better choice to calculate assortative mixing. The -metric is normalized with respect to the class of networks without self-loops, multiple edges, and multiple components, while degree correlation is always normalized with respect to unrestricted networks, where self-loops, multiple edges, and multiple components are allowed. The challenge in computing the normalized -metric is in obtaining the minimum and maximum value within a specific class of networks. We show that this can be solved by using linear programming. We use Lagrangian relaxation and the subgradient algorithm to obtain a solution to the -metric problem. Several examples are given to illustrate the principles and some simulations indicate that the solutions are generally accurate. Lourens J. Waldorp and Verena D. Schmittmann Copyright © 2015 Lourens J. Waldorp and Verena D. Schmittmann. All rights reserved. Fixed Point Approximation for Asymptotically Nonexpansive Type Mappings in Uniformly Convex Hyperbolic Spaces Sun, 22 Feb 2015 15:32:27 +0000 http://www.hindawi.com/journals/jam/2015/510798/ We use a modified S-iterative process to prove some strong and -convergence results for asymptotically nonexpansive type mappings in uniformly convex hyperbolic spaces, which includes Banach spaces and CAT(0) spaces. Thus, our results can be viewed as extension and generalization of several known results in Banach spaces and CAT(0) spaces (see, e.g., Abbas et al. (2012), Abbas et al. (2013), Bruck et al. (1993), and Xin and Cui (2011)) and improve many results in the literature. Shin Min Kang, Samir Dashputre, Bhuwan Lal Malagar, and Young Chel Kwun Copyright © 2015 Shin Min Kang et al. All rights reserved. On a System of Equations of a Non-Newtonian Micropolar Fluid Thu, 19 Feb 2015 15:28:55 +0000 http://www.hindawi.com/journals/jam/2015/481754/ We investigate a problem for a model of a non-Newtonian micropolar fluid coupled system. The problem has been considered in a bounded, smooth domain of with Dirichlet boundary conditions. The operator stress tensor is given by . To prove the existence of weak solutions we use the method of Faedo-Galerkin and compactness arguments. Uniqueness and periodicity of solutions are also considered. G. M. de Araújo, M. A. F. de Araújo, and E. F. L. Lucena Copyright © 2015 G. M. de Araújo et al. All rights reserved. Offline Model Predictive Control Based on Weighted Projection over Polytopes Wed, 18 Feb 2015 08:42:48 +0000 http://www.hindawi.com/journals/jam/2015/741348/ This work presents a novel offline model predictive control technique for tracking of constrained systems. The quadratic programming problem, commonly found in constrained control methods, is replaced by sequential offline set projections based on priority given to the decision variables. If a preference is established in terms of which decision variables are more desirable, the optimization problem can be solved by sequentially choosing the most important variables and performing a membership test with the projection of the constraint closed set over the related dimensions. Thus, real-time optimization is replaced by offline projection operations and online one-dimensional membership tests. This concept of decision variable prioritization is then applied to a form of model predictive control: feasible target tracking. Three quadratic programming problems are replaced by the proposed method. In the first problem, attainable steady-state demands are computed based on the performance of the plant. The reachable target command is then filtered in terms of dynamic admissibility, creating feasible inputs to the plant. Finally, the control is computed considering the current state and disturbance vectors along with the feasible and attainable command. Simulations of the method executing a path-following task are presented, demonstrating its benefits with negligible online computational burden. Fabio Andrade de Almeida Copyright © 2015 Fabio Andrade de Almeida. All rights reserved. Degeneralization Algorithm for Generation of Büchi Automata Based on Contented Situation Tue, 10 Feb 2015 08:54:45 +0000 http://www.hindawi.com/journals/jam/2015/516104/ We present on-the-fly degeneralization algorithm used to transform generalized Büchi automata (GBA) into Büchi Automata (BA) different from the standard degeneralization algorithm. Contented situation, which is used to record what acceptance conditions are satisfiable during expanding LTL formulae, is attached to the states and transitions in the BA. In order to get the deterministic BA, the Shannon expansion is used recursively when we expand LTL formulae by applying the tableau rules. On-the-fly degeneralization algorithm is carried out in each step of the expansion of LTL formulae. Ordered binary decision diagrams are used to represent the BA and simplify LTL formulae. The temporary automata are stored as syntax directed acyclic graph in order to save storage space. These ideas are implemented in a conversion algorithm used to build a property automaton corresponding to the given LTL formulae. We compare our method to previous work and show that it is more efficient for four sets of random formulae generated by LBTT. Laixiang Shan, Jun Qin, Mingshi Chen, and Zheng Qin Copyright © 2015 Laixiang Shan et al. All rights reserved. Adaptive Time-Stepping Using Control Theory for the Chemical Langevin Equation Mon, 09 Feb 2015 09:51:48 +0000 http://www.hindawi.com/journals/jam/2015/567275/ Stochastic modeling of biochemical systems has been the subject of intense research in recent years due to the large number of important applications of these systems. A critical stochastic model of well-stirred biochemical systems in the regime of relatively large molecular numbers, far from the thermodynamic limit, is the chemical Langevin equation. This model is represented as a system of stochastic differential equations, with multiplicative and noncommutative noise. Often biochemical systems in applications evolve on multiple time-scales; examples include slow transcription and fast dimerization reactions. The existence of multiple time-scales leads to mathematical stiffness, which is a major challenge for the numerical simulation. Consequently, there is a demand for efficient and accurate numerical methods to approximate the solution of these models. In this paper, we design an adaptive time-stepping method, based on control theory, for the numerical solution of the chemical Langevin equation. The underlying approximation method is the Milstein scheme. The adaptive strategy is tested on several models of interest and is shown to have improved efficiency and accuracy compared with the existing variable and constant-step methods. Silvana Ilie and Monjur Morshed Copyright © 2015 Silvana Ilie and Monjur Morshed. All rights reserved. An Introduction to Fuzzy Testing of Multialternative Hypotheses for Group of Samples with the Single Parameter: Through the Fuzzy Confidence Interval of Region of Acceptance Sun, 08 Feb 2015 11:12:53 +0000 http://www.hindawi.com/journals/jam/2015/365304/ Classical statistics and many data mining methods rely on “statistical significance” as a sole criterion for evaluating alternative hypotheses. It is very useful to find out the significant difference existing between the samples as well as the population or between two samples. But in this paper, the researchers try to apply the concepts of fuzzy group testing of hypothesis problem between multi group of samples of same size or different, through comparing the parameters like mean, standard deviation, and so forth. Hence we can compare multigroups such that they have the significant difference in their mean or standard deviation or other parameters through the fuzzy group testing of multihypotheses. The authors introduced and investigated the concepts very first time through fuzzy analysis that can decide which group(s) or samples can be taken for further investigation and either is rejected or accepted and hence the next discussion provides the properties of group of samples which may result in the optimized solution for the problem. Manikandan Harikrishnan, Jeyabharathi Sundarrajan, and Muthuraj Rengasamy Copyright © 2015 Manikandan Harikrishnan et al. All rights reserved. Multiobjective Optimization Method Based on Adaptive Parameter Harmony Search Algorithm Thu, 05 Feb 2015 09:13:46 +0000 http://www.hindawi.com/journals/jam/2015/165601/ The present trend in industries is to improve the techniques currently used in design and manufacture of products in order to meet the challenges of the competitive market. The crucial task nowadays is to find the optimal design and machining parameters so as to minimize the production costs. Design optimization involves more numbers of design variables with multiple and conflicting objectives, subjected to complex nonlinear constraints. The complexity of optimal design of machine elements creates the requirement for increasingly effective algorithms. Solving a nonlinear multiobjective optimization problem requires significant computing effort. From the literature it is evident that metaheuristic algorithms are performing better in dealing with multiobjective optimization. In this paper, we extend the recently developed parameter adaptive harmony search algorithm to solve multiobjective design optimization problems using the weighted sum approach. To determine the best weightage set for this analysis, a performance index based on least average error is used to determine the index of each weightage set. The proposed approach is applied to solve a biobjective design optimization of disc brake problem and a newly formulated biobjective design optimization of helical spring problem. The results reveal that the proposed approach is performing better than other algorithms. P. Sabarinath, M. R. Thansekhar, and R. Saravanan Copyright © 2015 P. Sabarinath et al. All rights reserved. Epidemic Models with Immunization and Mutations on a Finite Population Thu, 05 Feb 2015 07:56:30 +0000 http://www.hindawi.com/journals/jam/2015/239767/ We propose two variants of a stochastic epidemic model in which the disease is spread by mobile particles performing random walks on the complete graph. For the first model, we study the effect on the epidemic size of an immunization mechanism that depends on the activity of the disease. In the second model, the transmission agents can gain lives at random during their existences. We prove limit theorems for the final outcome of these processes. The epidemic model with mutations exhibits phase transition, meaning that if the mutation parameter is sufficiently large, then asymptotically all the individuals in the population are infected. Elcio Lebensztayn Copyright © 2015 Elcio Lebensztayn. All rights reserved. Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems Wed, 04 Feb 2015 13:45:08 +0000 http://www.hindawi.com/journals/jam/2015/960728/ This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stable process known as CGMY model. A double discretization finite difference scheme is used for the treatment of the unbounded nonlocal integral term. We also introduce in the scheme the Patankar-trick to guarantee unconditional nonnegative numerical solutions. Integration formula of open type is used in order to improve the accuracy of the approximation of the integral part. Stability and consistency are also studied. Illustrative examples are included. M. Fakharany, R. Company, and L. Jódar Copyright © 2015 M. Fakharany et al. All rights reserved. On Fuzzy Solutions for Diffusion Equation Sat, 31 Jan 2015 16:59:00 +0000 http://www.hindawi.com/journals/jam/2015/874931/ Our main goal is to define a fuzzy solution for problems involving diffusion. To this end, the solution of fuzzy diffusion-reaction-advection equation will be defined as Zadeh’s extension of deterministic solution of the associated problem. Important aspects such as unity and stability of these solutions will also be studied. Graphical representations of these solutions will be presented. Jefferson Leite, Moiseis Cecconello, Jackellyne Leite, and R. C. Bassanezi Copyright © 2015 Jefferson Leite et al. All rights reserved. Almost Periodic Time Scales and Almost Periodic Functions on Time Scales Thu, 29 Jan 2015 14:23:47 +0000 http://www.hindawi.com/journals/jam/2015/730672/ We propose some new concepts of almost periodic time scales and almost periodic functions on time scales and give some basic properties of these new types of almost periodic time scales and almost periodic functions on time scales. We also give some comments on a recent paper by Wang and Agarwal (2014) concerning a new almost periodic time scale. Yongkun Li and Bing Li Copyright © 2015 Yongkun Li and Bing Li. All rights reserved. Shear Current Effects on Monochromatic Water Waves Crossing Trenches Thu, 29 Jan 2015 13:32:21 +0000 http://www.hindawi.com/journals/jam/2015/256084/ The reflection coefficients of monochromatic water waves over trenches with shear current are estimated analytically. The diffraction of waves by an abrupt depth change and shear current is formulated by the matched eigenfunction expansion method. The proper number of steps and evanescent modes are proposed by a series of convergence tests. The accuracy of the predicted reflection coefficients is checked by estimating the wave energy. Reflection and transmission characteristics are studied for various shear current conditions. The different combinations of strength, width of shear current, and incident wave angle with constant water depth topography are examined. The optimal figure of the trench with shear current is obtained by estimating the reflection coefficients for various sloped transitions. The resonant reflection of the water waves is found by multiarrayed optimal trenches and the interaction of sinusoidally varying topography with shear current. Jun-Whan Lee, Koo-Yong Park, and Yong-Sik Cho Copyright © 2015 Jun-Whan Lee et al. All rights reserved. A Filled Function Method Dominated by Filter for Nonlinearly Global Optimization Wed, 28 Jan 2015 16:47:11 +0000 http://www.hindawi.com/journals/jam/2015/245427/ This work presents a filled function method based on the filter technique for global optimization. Filled function method is one of the effective methods for nonlinear global optimization, since it can effectively find a better minimizer. Filter technique is applied to local optimization methods for its excellent numerical results. In order to optimize the filled function method, the filter method is employed for global optimizations in this method. A new filled function is proposed first, and then the algorithm and its properties are proved. The numerical results are listed at the end. Wei Wang, Xiaoshan Zhang, and Min Li Copyright © 2015 Wei Wang et al. All rights reserved. An Empirical Study of Hybrid DEA and Grey System Theory on Analyzing Performance: A Case from Indian Mining Industry Tue, 27 Jan 2015 12:36:50 +0000 http://www.hindawi.com/journals/jam/2015/395360/ India, which has long been recognized as a well-endowed nation in natural mineral resources, is a major minerals producer. According to the report of Indian Ministry of Mines 2013, Indian mining and metals sector ranked the fourth among the mineral producer countries, behind China, United States, and Russia and had in fact led the economy into recovery from the global financial crisis. Since this industry has turned into a significant issue, this paper attempts to rank the performance of 23 Indian mining and metal companies and to evaluate and measure the productivity change of these sectors during different time periods (2010–2014). Besides, the authors would like to choose one advanced model of MPI to see the performance of these companies in the past-present period and the 4-year future period (2015–2018) by using forecasting results of Grey system theory. The results revealed that from the past to future period the National Mineral Development Corporation, Hindalco Industries Limited, and Coal India always keep their highest best rankings among 23 DMUs regarding performance scores. This study contributes better insights of Indian mining industry as it is the core of the economy. Lai-Wang Wang, Thanh-Tuyen Tran, and Nhu-Ty Nguyen Copyright © 2015 Lai-Wang Wang et al. All rights reserved. Simulation and Modeling of Flow in a Gas Compressor Wed, 21 Jan 2015 06:32:50 +0000 http://www.hindawi.com/journals/jam/2015/682469/ The presented research demonstrates the results of a series of numerical simulations of gas flow through a single-stage centrifugal compressor with a vaneless diffuser. Numerical results were validated with experiments consisting of eight regimes with different mass flow rates. The steady-state and unsteady simulations were done in ANSYS FLUENT 13.0 and NUMECA FINE/TURBO 8.9.1 for one-period geometry due to periodicity of the problem. First-order discretization is insufficient due to strong dissipation effects. Results obtained with second-order discretization agree with the experiments for the steady-state case in the region of high mass flow rates. In the area of low mass flow rates, nonstationary effects significantly influence the flow leading stationary model to poor prediction. Therefore, the unsteady simulations were performed in the region of low mass flow rates. Results of calculation were compared with experimental data. The numerical simulation method in this paper can be used to predict compressor performance. Anna Avramenko, Alexey Frolov, and Jari Hämäläinen Copyright © 2015 Anna Avramenko et al. All rights reserved. Nonlinearities Distribution Homotopy Perturbation Method Applied to Solve Nonlinear Problems: Thomas-Fermi Equation as a Case Study Tue, 20 Jan 2015 14:26:16 +0000 http://www.hindawi.com/journals/jam/2015/405108/ We propose an approximate solution of T-F equation, obtained by using the nonlinearities distribution homotopy perturbation method (NDHPM). Besides, we show a table of comparison, between this proposed approximate solution and a numerical of T-F, by establishing the accuracy of the results. U. Filobello-Nino, H. Vazquez-Leal, K. Boubaker, A. Sarmiento-Reyes, A. Perez-Sesma, A. Diaz-Sanchez, V. M. Jimenez-Fernandez, J. Cervantes-Perez, J. Sanchez-Orea, J. Huerta-Chua, L. J. Morales-Mendoza, M. Gonzalez-Lee, C. Hernandez-Mejia, and F. J. Gonzalez-Martinez Copyright © 2015 U. Filobello-Nino et al. All rights reserved. Data Transformation Technique to Improve the Outlier Detection Power of Grubbs’ Test for Data Expected to Follow Linear Relation Wed, 14 Jan 2015 11:17:44 +0000 http://www.hindawi.com/journals/jam/2015/708948/ Grubbs test (extreme studentized deviate test, maximum normed residual test) is used in various fields to identify outliers in a data set, which are ranked in the order of . However, ranking of data eliminates the actual sequence of a data series, which is an important factor for determining outliers in some cases (e.g., time series). Thus in such a data set, Grubbs test will not identify outliers correctly. This paper introduces a technique for transforming data from sequence bound linear form to sequence unbound form . Applying Grubbs test to the new transformed data set detects outliers more accurately. In addition, the new technique improves the outlier detection capability of Grubbs test. Results show that, Grubbs test was capable of identifing outliers at significance level 0.01 after transformation, while it was unable to identify those prior to transforming at significance level 0.05. K. K. L. B. Adikaram, M. A. Hussein, M. Effenberger, and T. Becker Copyright © 2015 K. K. L. B. Adikaram et al. All rights reserved. Palmprint Authentication System Based on Local and Global Feature Fusion Using DOST Wed, 31 Dec 2014 14:17:43 +0000 http://www.hindawi.com/journals/jam/2014/918376/ Palmprint is the region between wrist and fingers. In this paper, a palmprint personal identification system is proposed based on the local and global information fusion. The local and global information is critical for the image observation based on the results of the relationship between physical stimuli and perceptions. The local features of the enhanced palmprint are extracted using discrete orthonormal Stockwell transform. The global feature is obtained by reducing the scale of discrete orthonormal Stockwell transform to infinity. The local and global matching distances of the two palmprint images are fused to get the final matching distance of the proposed scheme. The results show that the fusion of local and global features outperforms the existing works on the available three datasets. N. B. Mahesh Kumar and K. Premalatha Copyright © 2014 N. B. Mahesh Kumar and K. Premalatha. All rights reserved. Completely Monotonic and Related Functions: Their Applications Wed, 31 Dec 2014 12:51:56 +0000 http://www.hindawi.com/journals/jam/2014/768516/ Senlin Guo, Andrea Laforgia, Necdet Batir, and Qiu-Ming Luo Copyright © 2014 Senlin Guo et al. All rights reserved. A Comparison of Evolutionary Computation Techniques for IIR Model Identification Thu, 25 Dec 2014 06:49:51 +0000 http://www.hindawi.com/journals/jam/2014/827206/ System identification is a complex optimization problem which has recently attracted the attention in the field of science and engineering. In particular, the use of infinite impulse response (IIR) models for identification is preferred over their equivalent FIR (finite impulse response) models since the former yield more accurate models of physical plants for real world applications. However, IIR structures tend to produce multimodal error surfaces whose cost functions are significantly difficult to minimize. Evolutionary computation techniques (ECT) are used to estimate the solution to complex optimization problems. They are often designed to meet the requirements of particular problems because no single optimization algorithm can solve all problems competitively. Therefore, when new algorithms are proposed, their relative efficacies must be appropriately evaluated. Several comparisons among ECT have been reported in the literature. Nevertheless, they suffer from one limitation: their conclusions are based on the performance of popular evolutionary approaches over a set of synthetic functions with exact solutions and well-known behaviors, without considering the application context or including recent developments. This study presents the comparison of various evolutionary computation optimization techniques applied to IIR model identification. Results over several models are presented and statistically validated. Erik Cuevas, Jorge Gálvez, Salvador Hinojosa, Omar Avalos, Daniel Zaldívar, and Marco Pérez-Cisneros Copyright © 2014 Erik Cuevas et al. All rights reserved. Analysis of Repairable Geo/G/1 Queues with Negative Customers Wed, 24 Dec 2014 13:32:15 +0000 http://www.hindawi.com/journals/jam/2014/350621/ We consider discrete-time Geo/G/1 queues with negative customers and a repairable server. The server is subject to failure due to a negative customer arrival. As soon as a negative customer arrives at a system, the server fails and one positive (ordinary) customer is forced to leave. At a failure instant, the server is turned off and the repair process immediately begins. We construct the mathematical model and present the probability generating functions of the system size distribution and the FCFS sojourn time distribution. Finally, some numerical examples are given to show the influence of negative customer arrival on the performance measures of the system. Doo Ho Lee and Kilhwan Kim Copyright © 2014 Doo Ho Lee and Kilhwan Kim. All rights reserved. Applied Mathematics in Biomedical Sciences and Engineering 2014 Wed, 24 Dec 2014 08:44:25 +0000 http://www.hindawi.com/journals/jam/2014/470483/ Chang-Hwan Im, Kiwoon Kwon, Hang Joon Jo, and Pedro Serranho Copyright © 2014 Chang-Hwan Im et al. All rights reserved. Radial Basis Point Interpolation Method with Reordering Gauss Domains for 2D Plane Problems Tue, 23 Dec 2014 06:27:10 +0000 http://www.hindawi.com/journals/jam/2014/219538/ We present novel Gauss integration schemes with radial basis point interpolation method (RPIM). These techniques define new Gauss integration scheme, researching Gauss points (RGD), and reconstructing Gauss domain (RGD), respectively. The developments lead to a curtailment of the elapsed CPU time without loss of the accuracy. Numerical results show that the schemes reduce the computational time to 25% or less in general. Shi-Chao Yi, Fu-jun Chen, and Lin-Quan Yao Copyright © 2014 Shi-Chao Yi et al. All rights reserved. Intelligent Modeling and Verification 2014 Mon, 22 Dec 2014 09:38:10 +0000 http://www.hindawi.com/journals/jam/2014/632027/ Guiming Luo, Xiaoyu Song, Xiaojing Yang, and Krishnaiyan Thulasiraman Copyright © 2014 Guiming Luo et al. All rights reserved. Initial Time Difference Stability of Causal Differential Systems in terms of Lyapunov Functions and Lyapunov Functionals Mon, 22 Dec 2014 00:10:31 +0000 http://www.hindawi.com/journals/jam/2014/832015/ We investigate the qualitative behavior of a perturbed causal differential equation that differs in initial position and initial time with respect to the unperturbed causal differential equations. We compare the classical notion of stability of the causal differential systems to the notion of initial time difference stability of causal differential systems and present a comparison result in terms of Lyapunov functions. We have utilized Lyapunov functions and Lyapunov functional in the study of stability theory of causal differential systems when establishing initial time difference stability of the perturbed causal differential system with respect to the unperturbed causal differential system. Coşkun Yakar and Mustafa Bayram Gücen Copyright © 2014 Coşkun Yakar and Mustafa Bayram Gücen. All rights reserved.