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Discrete and Continuous Dynamical Systems - S

December 2015 , Volume 8 , Issue 6

Issue on new trends on nonlinear dynamics and its applications

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New trends on nonlinear dynamics and its applications
Tomás Caraballo and Juan L. G. Guirao
2015, 8(6): i-ii doi: 10.3934/dcdss.2015.8.6i +[Abstract](2336) +[PDF](84.8KB)
Nonlinear Dynamics and Complexity is a wide area of research which is experiencing a big development nowadays. For this reason, we thought that it could be very helpful to publish a theme issue which could provide an overview of the recent developments, discoveries and progresses on this fascinating field of Nonlinear Dynamics and Complexity. Therefore, the main aims of this issue are to present the fundamental and frontier theories and techniques for modern science and technology which can also stimulate more research interest for exploration of nonlinear science and complexity and, to directly pass the new knowledge to the young generation, engineers and technologists in the corresponding fields. Consequently, the contributions which have been accepted for this issue focus on recent developments, findings and progresses on fundamental theories and principles, analytical and symbolic approaches, computational techniques in nonlinear physical science and nonlinear mathemati cs. Amongst others, the main topics of interest in Nonlinear Dynamics and Complexity treated in these papers include, but are not limited to:

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Dynamics of a tethered satellite with variable mass
Elbaz I. Abouelmagd, Juan L. G. Guirao, Aatef Hobiny and Faris Alzahrani
2015, 8(6): 1035-1045 doi: 10.3934/dcdss.2015.8.1035 +[Abstract](2794) +[PDF](425.2KB)
In this paper, we provide an analytical study regarding the dynamics of a tethered satellite system, when the central gravitational field is generated by a variable mass object. We show that, in general, the equations of motion for the tethered satellite in the general case as well as in satellite approximation become different from the classical ones, provided that variable mass is considered. We also prove that these expressions could be reduced to the classical ones under the first Meshcherskii's law for variable mass. Moreover, we show that Meshcherskii's transformation is not valid for the dynamics of a dumbbell satellite system.
Stability of equilibria points for a dumbbell satellite when the central body is oblate spheroid
Elbaz I. Abouelmagd, Juan L. G. Guirao, Aatef Hobiny and Faris Alzahrani
2015, 8(6): 1047-1054 doi: 10.3934/dcdss.2015.8.1047 +[Abstract](2656) +[PDF](276.2KB)
The main aim of the present work is to study the positions of the equilibria points and their stability in the frame work of satellite approximation. The significant implication is that the motion around these points is unstable in the linear sense. The principle of angular momentum conservation is used as a tool to reduce the degree of freedom of the dynamical systems of equations. The positions of the relative equilibria are explicitly found as well as necessary and sufficient conditions for stable motion in the linear sense are stated.
Reproducing kernel functions for difference equations
Ali Akgül, Mustafa Inc and Esra Karatas
2015, 8(6): 1055-1064 doi: 10.3934/dcdss.2015.8.1055 +[Abstract](3580) +[PDF](332.3KB)
In this work, some new reproducing kernel functions for difference equations are found. Reproducing kernel functions have not been obtained for difference equations until now. We need these functions to solve difference equations with the reproducing kernel method. Therefore, these functions are very considerable functions.
A new solution method for nonlinear fractional integro-differential equations
Sertan Alkan
2015, 8(6): 1065-1077 doi: 10.3934/dcdss.2015.8.1065 +[Abstract](4443) +[PDF](445.3KB)
The aim of this paper is to obtain approximate solution of a class of nonlinear fractional Fredholm integro-differential equations by means of sinc-collocation method which is not used for solving them in the literature before. The fractional derivatives are defined in the Caputo sense often used in fractional calculus. The important feature of the present study is that obtained results are stated as two new theorems. The introduced method is tested on some nonlinear problems and it seems that the method is a very efficient and powerful tool to obtain numerical solutions of nonlinear fractional integro-differential equations.
A survey on Navier-Stokes models with delays: Existence, uniqueness and asymptotic behavior of solutions
Tomás Caraballo and Xiaoying Han
2015, 8(6): 1079-1101 doi: 10.3934/dcdss.2015.8.1079 +[Abstract](3438) +[PDF](469.4KB)
In this survey paper we review several aspects related to Navier-Stokes models when some hereditary characteristics (constant, distributed or variable delay, memory, etc) appear in the formulation. First some results concerning existence and/or uniqueness of solutions are established. Next the local stability analysis of steady-state solutions is studied by using the theory of Lyapunov functions, the Razumikhin-Lyapunov technique and also by constructing appropriate Lyapunov functionals. A Gronwall-like lemma for delay equations is also exploited to provide some stability results. In the end we also include some comments concerning the global asymptotic analysis of the model, as well as some open questions and future lines for research.
Research on operating mechanism for creative products supply chain based on game theory
Tinggui Chen and Yanhui Jiang
2015, 8(6): 1103-1112 doi: 10.3934/dcdss.2015.8.1103 +[Abstract](3160) +[PDF](340.7KB)
In order to solve the problems of insufficient resource utilization, high cost and overstocking of commodities in the creative products supply chain, this paper establishes a supply chain enterprises operating mechanism model from the perspective of game theory, uses repeated game, individual game and group of evolutionary game, verifies the importance of cooperation in creative products supply chain through theoretical proof and examples, puts forward the method to make a win-win game party, and finds the way to coordinate supply chain.
Theoretical properties of fractal dimensions for fractal structures
Manuel Fernández-Martínez
2015, 8(6): 1113-1128 doi: 10.3934/dcdss.2015.8.1113 +[Abstract](2973) +[PDF](370.5KB)
Hausdorff dimension, which is the oldest and also the most accurate model for fractal dimension, constitutes the main reference for any fractal dimension definition that could be provided. In fact, its definition is quite general, and is based on a measure, which makes the Hausdorff model pretty desirable from a theoretical point of view. On the other hand, it turns out that fractal structures provide a perfect context where a new definition of fractal dimension could be proposed. Further, it has been already shown that both Hausdorff and box dimensions can be generalized by some definitions of fractal dimension formulated in terms of fractal structures. Given this, and being mirrored in some of the properties satisfied by Hausdorff dimension, in this paper we explore which ones are satisfied by the fractal dimension definitions for a fractal structure, that are explored along this work.
Generating pre-fractals to approach real IFS-attractors with a fixed Hausdorff dimension
Manuel Fernández-Martínez and Miguel Ángel López Guerrero
2015, 8(6): 1129-1137 doi: 10.3934/dcdss.2015.8.1129 +[Abstract](2795) +[PDF](345.4KB)
In this paper, we explain how to generate adequate pre-fractals in order to properly approximate attractors of iterated function systems on the real line within a priori known Hausdorff dimension. To deal with, we have applied the classical Moran's Theorem, so we have been focused on non-overlapping strict self-similar sets. This involves a quite significant hypothesis: the so-called open set condition. The main theoretical result contributed in this paper becomes quite interesting from a computational point of view, since in such a context, there is always a maximum level (of the natural fractal structure we apply in this work) that may be achieved.
Dynamic systems based on preference graph and distance
Chun-Xiang Guo, Guo Qiang, Jin Mao-Zhu and Zhihan Lv
2015, 8(6): 1139-1154 doi: 10.3934/dcdss.2015.8.1139 +[Abstract](3346) +[PDF](658.9KB)
A group decision-making approach fusing preference conflicts and compatibility measure is proposed , focused on dynamic group decision making with preference information of policymakers at each time describing with dynamic preference Hasse diagram with the identification framework of relation between alternative pairs is H=$\{\succ,\parallel,\succeq,\preceq,\approx,\prec,\phi\}$, and the preference graph may contain incomplete decision making alternatives. First, the relationship between preference sequences is be defined on the basis of concepts about preference, preference sequence and preference graph; and defining the decision function that can reflect dynamic preference, such as conflict ,comply support and preference distance measure. Finally, through the perspective of conflict and compatible aggregating the comprehensive preference of each decision makers in each period, and by establishing the optimization model based on lattice preference distance measure to assemble group preference, gives the specific steps of the decision making. The feasibility and effectiveness of the approach proposed in this paper are illustrated with a numerical example.
Dynamics of shallow water waves with Gardner-Kadomtsev-Petviashvili equation
Anwar Ja'afar Mohamad Jawad, Mohammad Mirzazadeh and Anjan Biswas
2015, 8(6): 1155-1164 doi: 10.3934/dcdss.2015.8.1155 +[Abstract](2967) +[PDF](376.9KB)
This paper obtains soliton and other solutions to the Gardner-Kadomtsev-Petviashvili equation that models shallow water wave equation in (1+2)-dimensions. There are three types of integration architectures that will be employed in order to obtain several forms of solution to this model. These are traveling wave hypothesis, improved $G^{\prime}/G$-expansion method and finally the tanh-coth hypothesis. The constraint conditions that are needed, for these solutions to exist, are also reported.
Periodic orbits for a generalized Friedmann-Robertson-Walker Hamiltonian system in dimension $6$
Fatima Ezzahra Lembarki and Jaume Llibre
2015, 8(6): 1165-1211 doi: 10.3934/dcdss.2015.8.1165 +[Abstract](2552) +[PDF](580.4KB)
A generalized Friedmann-Robertson-Walker Hamiltonian system is studied in dimension $6$. The averaging theory is the tool used to provide sufficient conditions on the six parameters of the system which guarantee the existence of continuous families of period orbits parameterized by the energy.
Prediction method based on optimization theory and its application
Chen Li, Fajie Wei and Shenghan Zhou
2015, 8(6): 1213-1221 doi: 10.3934/dcdss.2015.8.1213 +[Abstract](2787) +[PDF](358.3KB)
BP neural network is a kind of prediction method, but it has some disadvantages. So an improved particle swarm optimization scheme is used to optimize neural network parameters and structure. Both training convergence speed and classification accuracy is improved. Interest rate is always the focus in the economic research. The proposed scheme is used for seven days interbank offered rate prediction in China and the result shows that the BP neural network based on improved PSO has higher accuracy than the BP algorithm, which can provide important reference for central bank to work out monetary policy.
Intelligent control model and its simulation of flue temperature in coke oven
Gongfa Li, Wei Miao, Guozhang Jiang, Yinfeng Fang, Zhaojie Ju and Honghai Liu
2015, 8(6): 1223-1237 doi: 10.3934/dcdss.2015.8.1223 +[Abstract](2765) +[PDF](1182.5KB)
In this paper, one-variable linear regression mathematical model of top of regenerator temperature and flue temperature in machine side is built using the linear regress theory. The parameters of ARX model is determined by identification method of least square method and the mathematical model of flue temperature control is established. Applying the basis cascade control theory, system adopts flue temperature and coal flue gas flow as controlled parameters of host circuit and subsidiary circuit respectively. The compound Fuzzy-PID control strategy is presented combined with the characteristics of temperature system after analyzing the conventional PID control algorithm and fuzzy control algorithm. Using step signal and periodic signal to simulate the conventional PID and compound Fuzzy-PID algorithm, the result has indicated: Compound Fuzzy PID control algorithm combines with the advantages of fuzzy control and PID control algorithm, including fast response speed and strong anti-interference ability. When external conditions change, the fuzzy PID compound control can show the strong adaptability and robustness which effectively improve the stability of the control system.
Research on the optimal initial shunt strategy of Jiuzhaigou based on the optimization model
Yuxue Li, Maozhu Jin, Peiyu Ren and Zhixue Liao
2015, 8(6): 1239-1249 doi: 10.3934/dcdss.2015.8.1239 +[Abstract](2903) +[PDF](375.8KB)
Tourism load imbalance is a serious problem in Jiuzhaigou, which may destroy the environment and reduce the feeling of tourists. A reasonable initial shunt strategy is the key factor in making the scenic become balance. So, this paper considers this problem by finding an optimal initial shunt strategy. An optimization model containing two flow models is built, which takes the total overload balance as objective. In order to solve this model and find the optimal initial shunt strategy, a hGA is proposed as solution method. Finally, a comparison analysis is conducted to show the efficiency of this model in remitting the local overload problem.
Implementation of Mamdami fuzzy control on a multi-DOF two-wheel inverted pendulum robot
Yubai Liu, Xueshan Gao and Fuquan Dai
2015, 8(6): 1251-1266 doi: 10.3934/dcdss.2015.8.1251 +[Abstract](2653) +[PDF](816.1KB)
These days a Two-wheel inverted pendulum (TWIP) robot attracts public attention as it is an efficient ergonomics and easy to operate by nuance personals. Furthermore it has attractive design features like compact in size and zero turning radius. However, the traditional TWIP robots have to change its posture to reach the desired speedup and deceleration by changing the robot posture forward and backward make it difficult to control its motion process. Thus, this paper presents here the Mamdami fuzzy control logic to overcome the motion control of Multi-DOF TWIP robot and make its motion smooth and steady control. By introducing two additional DOFs the slider and the swinging configuration, the robot can maintain its vertical posture even climbing and descending on slopes. To validate the robustness of the proposed method, classic PID controller is introduced for comparison in simulations and experiments. The simulation results demonstrate the effectiveness of the system design and the better performance in robustness over classic PID control strategy. Finally, the control scheme is implemented on the practical self-designed hardware.
Application of support vector machine model in wind power prediction based on particle swarm optimization
Ning Lu and Ying Liu
2015, 8(6): 1267-1276 doi: 10.3934/dcdss.2015.8.1267 +[Abstract](3156) +[PDF](318.8KB)
Wind energy is a kind of renewable and clean energy, and wind power is a non-hydropower renewable energy which has the best technical and economic conditions for large-scale development. It is characterized by fluctuation, intermittency, low energy density, etc., so wind power is also fluctuating. When a large-scale wind farm is connected to a power grid, great fluctuation in wind power will cause adverse effect to the power balance and frequency adjustment of the power grid. If the generation power of the wind farm can be prediction, the electricity dispatch department can arrange dispatch plans in advance according to the change in wind power and better protect the power balance and operation safety of the power grid. In this article, a SVM model is used to predict wind power and modified PSO is used to optimize SVM parameters, realizing the optimized selection of the SVM model parameters, which makes such prediction more close to actual law. Actual calculation examples shows that the prediction method used in the article has good convergence, high prediction precision and actual application value.
Higher order uniformly close-to-convex functions
Khalida Inayat Noor and Muhammad Aslam Noor
2015, 8(6): 1277-1290 doi: 10.3934/dcdss.2015.8.1277 +[Abstract](2663) +[PDF](372.0KB)
In this paper, we define and study some subclasses of analytic functions related with $k$-uniformly close-to-convex functions of higher order in the unit disc. These classes unify a number of classes previously studied. The results obtained include rate of growth of coefficients, inclusion relations, radius problems and necessary conditions for univalency. We derive many known results as special cases.
Characteristic analysis of carrier based on the filtering and a multi-wavelet method for the information hiding
Shuai Ren, Tao Zhang and Fangxia Shi
2015, 8(6): 1291-1299 doi: 10.3934/dcdss.2015.8.1291 +[Abstract](2496) +[PDF](2956.6KB)
The characteristic consistency between the original and the stego carriers is an important indicator to evaluate an information hiding algorithm. Different from the traditional carrier pre-processing methods which are based on the operation domains, we propose a characteristics analysis-based preprocessing scheme. We use the Gaussian pyramid filtering and CARDBAL2 multi-wavelet transform to analyze the energy characteristics of the carrier, so the original carrier can be decomposed into several sub-regions with different energy level. And at the same time, the processed carrier shows us the redundancy space structurally through the combination bit plane method, which can provide some invisible hiding positions. Obviously, the energy and structure characteristics are at least related with the robustness and invisibility of the hiding result respectively. So we can improve these performances compared with the traditional methods. At the same time, some optimization theories like the Chebyshev map are used to improve other performances. At last, the experimental shows the achievements of this scheme in the form of data.
The application of improved-DAA for the vehicle network node security in single- and multi-trusted domain
Shuai Ren, Tao Zhang, Fangxia Shi and Zongzong Lou
2015, 8(6): 1301-1309 doi: 10.3934/dcdss.2015.8.1301 +[Abstract](2690) +[PDF](699.9KB)
Similar to network, vehicle-mounted system has its own vulnerability, which can be used by the attackers. Different from the traditional network security technologies, node security is one of the most important technologies of the vehicle network and it is difficult to achieve because of the mobility and flexibility. In this paper, trusted computing and direct anonymous attestation theories are adopted to establish protocol system of trusted vehicle information authentication, thus the security of authentication process for nodes in vehicle network can be improved. First, we use DAA to achieve the identity authentication for the accessor in single-trusted domain. Second, the improved-DAA will be used to try to promote the security situation in multi-trusted domain. It is illustrated that the efficiency of verification can be increased and the possibility of being attacked can be decreased in single-trusted domain. And the execution efficiency in multi-trusted domain can be improved theoretically.
Designing dynamical systems for security and defence network knowledge management. A case of study: Airport bird control falconers organizations
Jose-Luis Roca-Gonzalez
2015, 8(6): 1311-1329 doi: 10.3934/dcdss.2015.8.1311 +[Abstract](3159) +[PDF](1688.8KB)
The main purpose of this paper is to show and highlight through an example, the relevance of designing a properly strategic communication model (SCM) in order to improve organizations efficiency standards when a sharing knowledge network is used. This example shows as well that even if this configuration upgrades the competitor s standards it will give as an answer the ontological foundations for the knowledge to be shared that guarantee the best practice involved in the framework of the Knowledge Management (KM process).
    The case of study takes advantage of some lesson from Network Centric Warfare (NCW) and the Network Enable Capability (NEC) systems to developed a Strategic Communication Model that looks for increasing the falcon breeding efficiency which it is a direct function of the falcons flight efficiency which creates a free wild-life area in the most sensitive airport locations and which is a priority concern of nowadays falconer's organizations.
Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term
María Rosa, María de los Santos Bruzón and María de la Luz Gandarias
2015, 8(6): 1331-1339 doi: 10.3934/dcdss.2015.8.1331 +[Abstract](3262) +[PDF](372.8KB)
Memory effect in diffusion-reaction equation with finite memory transport plays an important role in physical, biological and chemical sciences. In this work we consider a Fisher equation, which has a nonlinear convection term with finite memory transport, from the point of view of Lie classical reductions. By using a direct method we obtain some travelling waves solutions. Furthermore, by using the multipliers method, we derive some nontrivial conservation laws for this equation.
Statistical query-based rule derivation system by backward elimination algorithm
Ayla Sayli and Ayse Oncu Sarihan
2015, 8(6): 1341-1356 doi: 10.3934/dcdss.2015.8.1341 +[Abstract](2498) +[PDF](599.5KB)
Computers play a serious role in human life, especially web-based applications running twenty four hours per day. These applications are based on relational database management system and they receive many queries from the users. These queries are executed in the commercial systems one by one without any consideration of past experiences and data analysis. The execution of queries can be faster if some rules were derived from the past queries. In this paper, we propose a statistical query-based rule derivation system by the backward elimination algorithm, which analysis the data based on the past queries in order to derive new rules, and then it uses these rules for the execution of new queries. The computational results are presented and analysed that the system is very efficient and promising.
Nondeterministic semantics of compound diagrams
Fairouz Tchier
2015, 8(6): 1357-1371 doi: 10.3934/dcdss.2015.8.1357 +[Abstract](2311) +[PDF](411.6KB)
We presented a unified description of flow control and single steps of a program is given to obtain flexible definitions of algebraic manipulations. This is achieved by using the notion of relational diagram. We show how the notion of relational diagram, introduced by Schmidt, can be used to give a demonic definition for a wide range of programming constructs. It is shown that the input-output relation of a compound diagram is equal to that of the diagram in which each sub-diagram has been replaced by its input-output relation. This process is repeated until elementary diagrams is obtained.
A geometric inversion algorithm for parameters calculation in Francis turbine
Liying Wang, Weiguo Zhao, Dan Zhang and Linming Zhao
2015, 8(6): 1373-1384 doi: 10.3934/dcdss.2015.8.1373 +[Abstract](2310) +[PDF](641.4KB)
In terms of the structure and working~principle~of Francis turbine, a geometric inversion algorithm for parameters calculation in Francis turbine is proposed in this paper. Firstly through defining unit parameters the linear characteristics of turbine are derived in a certain opening, then the geometric parameters can be reversely calculated. The HL160-LJ--25 model turbine is used to verify the linear relation between the characteristic flow and the characteristic efficiency and reversely perform parameters calculation, and then the relation curves are established between the geometric parameters of turbine and the opening of guide blade, which can make us accurately acquire the energy characteristics of the prototype turbine. It is useful for us to acquire the proper parameters of turbine for purposes of reducing pressure fluctuation of turbine and improving its operating efficiency.
Weighted two-phase supervised sparse representation based on Gaussian for face recognition
Shuhua Xu and Fei Gao
2015, 8(6): 1385-1400 doi: 10.3934/dcdss.2015.8.1385 +[Abstract](2490) +[PDF](429.9KB)
As recently newly techniques, two-phase sparse representation algorithms have been presented, which achieve an excellent performance in face recognition via different phase sparse representation, capturing more local structural information of samples. However, there are some defects in these algorithms:1) The Euclidean distance metric applied in these algorithms fails to capture nonlinear structural information, leading to that the performance of these algorithms is sensitive to the geometric structure of facial images. 2) To select the m nearest neighbors of the test sample is achieved directly by applying sparse representation in training samples, which ignores prior information to construct the sparse representation model. In order to solve these problems, a Weighted Two-Phase Supervised Sparse Representation based on Gaussian (GWTPSSR) algorithm is proposed on basic of existing two-phase sparse representation algorithm, in which the nonlinear local information of samples is captured by exploiting effectively the Gaussian distance metric instead of the Euclidean distance metric. Besides, GWTPSSR recreates reconstruction set from training samples in the sparse representation model for each test sample, making full use of prior information to eliminate some training samples far from the test sample. Compared with existing two-phase sparse representation algorithms, experimental results on standard face datasets show that GWTPSSR has better robustness and classification performance.
Big data dynamic compressive sensing system architecture and optimization algorithm for internet of things
Jian-Wu Xue, Xiao-Kun Xu and Feng Zhang
2015, 8(6): 1401-1414 doi: 10.3934/dcdss.2015.8.1401 +[Abstract](3312) +[PDF](1410.7KB)
In order to reduce the amount of data collected in the Internet of things, to improve the processing speed of big data. To reduce the collected data from Internet of Things by compressed sensing sampling method is proposed. To overcome high computational complexity of compressed sensing algorithms, the search terms of the gradient projection sparse reconstruction algorithm (GPSR-BB) are improved by using multi-objective optimization particle swarm optimization algorithm; it can effectively improve the reconstruction accuracy of the algorithm. Application results show that the proposed multi-objective particle swarm optimization-Genetic algorithm (MOPSOGA) is than traditional GPSR-BB algorithm iterations decreased 51.6%. The success rate of reconstruction is higher than that of the traditional algorithm of 0.15; it's with a better reconstruction performance.
Research on the method of step feature extraction for EOD robot based on 2D laser radar
Qiang Yin, Gongfa Li and Jianguo Zhu
2015, 8(6): 1415-1421 doi: 10.3934/dcdss.2015.8.1415 +[Abstract](3340) +[PDF](649.6KB)
Considering the requirements of climbing obstacle and stairs for Explosive Ordnance Disposal (EOD) robot, a method about step feature extraction based on two-dimensional (2D) laser radar is in great demand. In this paper, we research the three-dimensional (3D) environment feature extraction (EFE) method including the 3D point clouds map construction, the line feature extraction and the plane feature extraction. The EFE method can be applied to feature extraction of the step vertical plane. Based on the method, we construct a 3D feature recognition system (FRS) using 2D laser radar. FRS can help us extract quickly the step vertical planes from 3D laser radar line map, thus can provide necessary environment information for the decision and action of EOD robot. We demonstrate the ability of FRS by applying it to some typical step environment.
Visualization analysis of traffic congestion based on floating car data
Jingmei Zhou, Xiangmo Zhao, Xin Cheng and Zhigang Xu
2015, 8(6): 1423-1433 doi: 10.3934/dcdss.2015.8.1423 +[Abstract](3680) +[PDF](549.3KB)
Traffic congestion visualization is an important part in traffic information service. However, the real-time data is difficult to obtain and its analysis method is not accurate, so the reliability of congestion state visualization is low. This paper proposes a visualization analysis algorithm of traffic congestion based on Floating Car Data (FCD), which utilizes the FCD to estimate and display dynamic traffic state on the electronic map. Firstly, an improved map matching method is put forward to match rapidly the FCD with road sections, which includes two steps of coarse and precise matching. Then, the traffic speed is estimated and classified to display different traffic states. Eventually, multi-group experiments have been conducted based on more than 8000 taxies in Xi’an. The experimental results show that FCD can be matched accurately with the selected road sections which accuracy can reach up to \({\rm{96\% }}\), and the estimated traffic real-time state can achieve \({\rm{94\% }}\) in terms of reliability. So this visualization analysis algorithm can display accurately road traffic state in real time.
A q-analogue of the multiplicative calculus: Q-multiplicative calculus
Gokhan Yener and Ibrahim Emiroglu
2015, 8(6): 1435-1450 doi: 10.3934/dcdss.2015.8.1435 +[Abstract](3497) +[PDF](365.3KB)
In this paper, we propose q-analog of some basic concepts of multiplicative calculus and we called it as q-multiplicative calculus. We successfully introduced q-multiplicative calculus and some basic theorems about derivatives, integrals and infinite products are proved within this calculus.

2021 Impact Factor: 1.865
5 Year Impact Factor: 1.622
2021 CiteScore: 3.6

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