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  • Mathematics  (13)
  • 1
    Online Resource
    Online Resource
    An Iterative Algorithm for the Split Equality and Multiple-Sets Split Equality Problem
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-5
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-5
    Abstract: The multiple-sets split equality problem (MSSEP) requires finding a point x ∈ ∩ i = 1 N C i , y ∈ ∩ j = 1 M Q j such that A x = B y , where N and M are positive integers, { C 1 , C 2 , … , C N } and { Q 1 , Q 2 , … , Q M } are closed convex subsets of Hilbert spaces H 1 , H 2 , respectively, and A : H 1 → H 3 , B : H 2 → H 3 are two bounded linear operators. When N = M = 1 , the MSSEP is called the split equality problem (SEP). If   B = I , then the MSSEP and SEP reduce to the well-known multiple-sets split feasibility problem (MSSFP) and split feasibility problem (SFP), respectively. One of the purposes of this paper is to introduce an iterative algorithm to solve the SEP and MSSEP in the framework of infinite-dimensional Hilbert spaces under some more mild conditions for the iterative coefficient.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/620813
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 2
    Online Resource
    Online Resource
    Intelligent Optimized Combined Model Based on GARCH and SVM for Forecasting Electricity Price of New South Wales, Australia
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-9
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-9
    Abstract: Daily electricity price forecasting plays an essential role in electrical power system operation and planning. The accuracy of forecasting electricity price can ensure that consumers minimize their electricity costs and make producers maximize their profits and avoid volatility. However, the fluctuation of electricity price depends on other commodities and there is a very complicated randomization in its evolution process. Therefore, in recent years, although large number of forecasting methods have been proposed and researched in this domain, it is very difficult to forecast electricity price with only one traditional model for different behaviors of electricity price. In this paper, we propose an optimized combined forecasting model by ant colony optimization algorithm (ACO) based on the generalized autoregressive conditional heteroskedasticity (GARCH) model and support vector machine (SVM) to improve the forecasting accuracy. First, both GARCH model and SVM are developed to forecast short-term electricity price of New South Wales in Australia. Then, ACO algorithm is applied to determine the weight coefficients. Finally, the forecasting errors by three models are analyzed and compared. The experiment results demonstrate that the combined model makes accuracy higher than the single models.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/504064
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 3
    Online Resource
    Online Resource
    On Convergence of Fixed Points in Fuzzy Metric Spaces
    Hindawi Limited ; 2013
    In:  Abstract and Applied Analysis Vol. 2013 ( 2013), p. 1-6
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2013 ( 2013), p. 1-6
    Abstract: We mainly focus on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in fuzzy metric spaces. Our results provide a novel research direction for fixed point theory in fuzzy metric spaces as well as a substantial extension of several important results from classical metric spaces.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2013/135202
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 4
    Online Resource
    Online Resource
    Nonsmooth Recursive Identification of Sandwich Systems with Backlash-Like Hysteresis
    Hindawi Limited ; 2012
    In:  Journal of Applied Mathematics Vol. 2012 ( 2012), p. 1-16
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2012 ( 2012), p. 1-16
    Abstract: A recursive gradient identification algorithm based on the bundle method for sandwich systems with backlash-like hysteresis is presented in this paper. In this method, a dynamic parameter estimation scheme based on a subgradient is developed to handle the nonsmooth problem caused by the backlash embedded in the system. The search direction of the algorithm is estimated based on the so-called bundle method. Then, the convergence of the algorithm is discussed. After that, simulation results on a nonsmooth sandwich system are presented to validate the proposed estimation algorithm. Finally, the application of the proposed method to an X-Y moving positioning stage is illustrated.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2012/457603
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2012
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 5
    Online Resource
    Online Resource
    Simplified Boundary Element Method for Kinematic Response of Single Piles in Two-Layer Soil
    Hindawi Limited ; 2013
    In:  Journal of Applied Mathematics Vol. 2013 ( 2013), p. 1-12
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2013 ( 2013), p. 1-12
    Abstract: A simple approach is formulated to predict the elastic, kinematic pile bending during harmonic or transient excitation for a circular pile (rather than a simplified thin strip). The kinematic response of a pile embedded in two-layer soil is resolved in the frequency domain caused by the upward propagation of shear waves from the underlying bedrock. The simplified approach is generally valid to nonhomogeneous soil profiles, in light of the good comparison with the dynamic FE method and BDWF solution. It employs the soil-displacement-influence coefficients I s to consider the pile-soil interaction (resembling the spring constant k x in the BDWF) and provides conservative estimations of maximum kinematic bending moments at the soil-layer interface (with a sharper stiffness contrast). The accuracy of the approach may be improved by incorporating the interaction of soil into the soil-displacement-influence coefficients I s for such cases with V b / V a 〈 3 .
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2013/241482
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 6
    Online Resource
    Online Resource
    On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems
    Hindawi Limited ; 2013
    In:  Abstract and Applied Analysis Vol. 2013 ( 2013), p. 1-11
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2013 ( 2013), p. 1-11
    Abstract: The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2013/681523
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 7
    Online Resource
    Online Resource
    Identification of Hysteresis in Human Meridian Systems Based on NARMAX Model
    Hindawi Limited ; 2012
    In:  Journal of Applied Mathematics Vol. 2012 ( 2012), p. 1-16
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2012 ( 2012), p. 1-16
    Abstract: It has been found that the response of acupuncture point on the human meridian line exhibits nonlinear dynamic behavior when excitation of electroacupuncture is implemented on another meridian point. This nonlinear phenomenon is in fact a hysteretic phenomenon. In order to explore the characteristic of human meridian and finally find a way to improve the treatment of diseases via electro-acupuncture method, it is necessary to identify the model to describe the corresponding dynamic hysteretic phenomenon of human meridian systems stimulated by electric-acupuncture. In this paper, an identification method using nonlinear autoregressive and moving average model with exogenous input (NARMAX) is proposed to model the dynamic hysteresis in human meridian. As the hysteresis is a nonlinear system with multivalued mapping, the traditional NARMAX model is unavailable to it directly. Thus, an expanded input space is constructed to transform the multi-valued mapping of the hysteresis to a one-to-one mapping. Then, the identification method using NARMAX model on the constructed expanded input space is developed. Finally, the proposed method is applied to hysteresis modeling for human meridian systems.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2012/451927
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2012
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 8
    Online Resource
    Online Resource
    -Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces
    Hindawi Limited ; 2013
    In:  Abstract and Applied Analysis Vol. 2013 ( 2013), p. 1-6
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2013 ( 2013), p. 1-6
    Abstract: New △-convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained. Consider an asymptotically nonexpansive self-mapping of a closed convex subset of a CAT(0) space . Consider the iteration process , where is arbitrary and or for , where . It is shown that under certain appropriate conditions on   △-converges to a fixed point of .
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2013/251705
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 9
    Online Resource
    Online Resource
    An Interior Point Method for L 1 / 2 -SVM and Application to Feature Selection in Classification
    Hindawi Limited ; 2014
    In:  Journal of Applied Mathematics Vol. 2014 ( 2014), p. 1-16
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2014 ( 2014), p. 1-16
    Abstract: This paper studies feature selection for support vector machine (SVM). By the use of the L 1 / 2 regularization technique, we propose a new model L 1 / 2 -SVM. To solve this nonconvex and non-Lipschitz optimization problem, we first transform it into an equivalent quadratic constrained optimization model with linear objective function and then develop an interior point algorithm. We establish the convergence of the proposed algorithm. Our experiments with artificial data and real data demonstrate that the L 1 / 2 -SVM model works well and the proposed algorithm is more effective than some popular methods in selecting relevant features and improving classification performance.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2014/942520
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 10
    Online Resource
    Online Resource
    Strong Convergence of Viscosity Approximation Methods for Nonexpansive Mappings in CAT(0) Spaces
    Hindawi Limited ; 2012
    In:  Journal of Applied Mathematics Vol. 2012 ( 2012), p. 1-11
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2012 ( 2012), p. 1-11
    Abstract: Viscosity approximation methods for nonexpansive mappings in CAT(0) spaces are studied. Consider a nonexpansive self-mapping T of a closed convex subset C of a CAT(0) space X . Suppose that the set Fix ( T ) of fixed points of T is nonempty. For a contraction f on C and t ∈ ( 0,1 ) , let x t ∈ C be the unique fixed point of the contraction x ↦ t f ( x ) ⊕ ( 1 - t ) T x . We will show that if X is a CAT(0) space satisfying some property, then { x t } converge strongly to a fixed point of T which solves some variational inequality. Consider also the iteration process { x n } , where x 0 ∈ C is arbitrary and x n + 1 = α n f ( x n ) ⊕ ( 1 - α n ) T x n for n ≥ 1 , where { α n } ⊂ ( 0,1 ) . It is shown that under certain appropriate conditions on α n , { x n } converge strongly to a fixed point of T which solves some variational inequality.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2012/421050
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2012
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
    Location Call Number Limitation Availability
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