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  • Mathematics  (8)
  • 1
    Online Resource
    Online Resource
    2-Local isometries on vector-valued differentiable functions
    Springer Science and Business Media LLC ; 2023
    In:  Annals of Functional Analysis Vol. 14, No. 4 ( 2023-10)
    Details
    In: Annals of Functional Analysis, Springer Science and Business Media LLC, Vol. 14, No. 4 ( 2023-10)
    Type of Medium: Online Resource
    ISSN: 2639-7390 , 2008-8752
    URL: Article
    DOI: 10.1007/s43034-023-00295-9
    Language: English
    Publisher: Springer Science and Business Media LLC
    Publication Date: 2023
    detail.hit.zdb_id: 2606458-3
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  • 2
    Online Resource
    Online Resource
    Regularization Method for the Approximate Split Equality Problem in Infinite-Dimensional Hilbert Spaces
    Hindawi Limited ; 2013
    In:  Abstract and Applied Analysis Vol. 2013 ( 2013), p. 1-5
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2013 ( 2013), p. 1-5
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2013/813635
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 3
    Online Resource
    Online Resource
    Optimal Tracking for a Divergent-Type Parabolic PDE System in Current Profile Control
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-8
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-8
    Abstract: We consider the optimal tracking problem for a divergent-type parabolic PDE system, which can be used to model the spatial-temporal evolution of the magnetic diffusion process in a tokamak plasma. With the feedforward trajectories generated by numerical optimization, we derive a linear system to describe the error evolution. The weak variation approach is then extended to cylindrical coordinates to obtain a Riccati-type PDE for feedback kernel synthesis. Then, a finite difference method is used to give numerical solutions for the Riccati-type PDE. The obtained feedback kernel is finally used to simulate the closed-loop system. The simulation results demonstrate that the proposed tracking method can attenuate the tracking error effectively.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/940965
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
    SSG: 17,1
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  • 4
    Online Resource
    Online Resource
    New Scheme of Finite Difference Heterogeneous Multiscale Method to Solve Saturated Flow in Porous Media
    Hindawi Limited ; 2014
    In:  Abstract and Applied Analysis Vol. 2014 ( 2014), p. 1-19
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2014 ( 2014), p. 1-19
    Abstract: A new finite difference scheme, the development of the finite difference heterogeneous multiscale method (FDHMM), is constructed for simulating saturated water flow in random porous media. In the discretization framework of FDHMM, we follow some ideas from the multiscale finite element method and construct basic microscopic elliptic models. Tests on a variety of numerical experiments show that, in the case that only about a half of the information of the whole microstructure is used, the constructed scheme gives better accuracy at a much lower computational time than FDHMM for the problem of aquifer response to sudden change in reservoir level and gives comparable accuracy at a much lower computational time than FDHMM for the weak drawdown problem.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2014/575298
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2064801-7
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  • 5
    Online Resource
    Online Resource
    Computation of Gram Matrix and Its Partial Derivative Using Precise Integration Method for Linear Time-Invariant Systems
    Hindawi Limited ; 2014
    In:  Journal of Applied Mathematics Vol. 2014 ( 2014), p. 1-10
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2014 ( 2014), p. 1-10
    Abstract: Gram matrix is an important tool in system analysis and design as it provides a description of the input-output behavior for system; its partial derivative matrix is often required in some numerical algorithms. It is essential to study computation of these matrices. Analytical methods only work in some special circumstances; for example, the system matrix is diagonal matrix or Jordan matrix. In most cases, numerical integration method is needed, but there are two problems when compute using traditional numerical integration method. One is low accuracy: as high accuracy requires extremely small integration step, it will result in large amount of computation; and another is stability and stiffness issues caused by the dependence on the property of system matrix. In order to overcome these problems, this paper proposes an efficient numerical method based on the key idea of precise integration method (PIM) for the Gram matrix and its partial derivative of linear time-invariant systems. Since matrix inverse operation is not required in this method, it can be used with high precision no matter the system is normal or singular. The specific calculation algorithm and block diagram are also given. Finally, numerical examples are given to demonstrate the correctness and validity of this method.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2014/134604
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2014
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 6
    Online Resource
    Online Resource
    Common Fixed Point Theorems for Nonlinear Contractive Mappings in Dislocated Metric Spaces
    Hindawi Limited ; 2013
    In:  Abstract and Applied Analysis Vol. 2013 ( 2013), p. 1-5
    Details
    In: Abstract and Applied Analysis, Hindawi Limited, Vol. 2013 ( 2013), p. 1-5
    Abstract: In 1986, Matthews generalized Banach contraction mapping theorem in dislocated metric space that is a wider space than metric space. In this paper, we established common fixed point theorems for a class of contractive mappings. Our results extend the corresponding ones of other authors in dislocated metric spaces.
    Type of Medium: Online Resource
    ISSN: 1085-3375 , 1687-0409
    URL: Article
    DOI: 10.1155/2013/483059
    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
    Doubly Constrained Robust Blind Beamforming Algorithm
    Hindawi Limited ; 2013
    In:  Journal of Applied Mathematics Vol. 2013 ( 2013), p. 1-8
    Details
    In: Journal of Applied Mathematics, Hindawi Limited, Vol. 2013 ( 2013), p. 1-8
    Abstract: We propose doubly constrained robust least-squares constant modulus algorithm (LSCMA) to solve the problem of signal steering vector mismatches via the Bayesian method and worst-case performance optimization, which is based on the mismatches between the actual and presumed steering vectors. The weight vector is iteratively updated with penalty for the worst-case signal steering vector by the partial Taylor-series expansion and Lagrange multiplier method, in which the Lagrange multipliers can be optimally derived and incorporated at each step. A theoretical analysis for our proposed algorithm in terms of complexity cost, convergence performance, and SINR performance is presented in this paper. In contrast to the linearly constrained LSCMA, the proposed algorithm provides better robustness against the signal steering vector mismatches, yields higher signal captive performance, improves greater array output SINR, and has a lower computational cost. The simulation results confirm the superiority of the proposed algorithm on beampattern control and output SINR enhancement.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2013/245609
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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  • 8
    Online Resource
    Online Resource
    Convergence Analysis of an Iterative Method for Nonlinear Partial Differential Equations
    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: We will combine linear successive overrelaxation method with nonlinear monotone iterative scheme to obtain a new iterative method for solving nonlinear equations. The basic idea of this method joining traditional monotone iterative method (known as the method of lower and upper solutions) which depends essentially on the monotone parameter is that by introducing an acceleration parameter one can construct a sequence to accelerate the convergence. The resulting increase in the speed of convergence is very dramatic. Moreover, the sequence can accomplish monotonic convergence behavior in the iterative process when some suitable acceleration parameters are chosen. Under some suitable assumptions in aspect of the nonlinear function and the matrix norm generated from this method, we can prove the boundedness and convergence of the resulting sequences. Application of the iterative scheme is given to a logistic model problem in ecology, and numerical results for a test problem with known analytical solution are given to demonstrate the accuracy and efficiency of the present method.
    Type of Medium: Online Resource
    ISSN: 1110-757X , 1687-0042
    URL: Article
    DOI: 10.1155/2013/487273
    Language: English
    Publisher: Hindawi Limited
    Publication Date: 2013
    detail.hit.zdb_id: 2578385-3
    SSG: 17,1
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