The Experts below are selected from a list of 93 Experts worldwide ranked by ideXlab platform

V. M. Luchko - One of the best experts on this subject based on the ideXlab platform.

  • Cauchy problem for a parabolic pseudodifferential Higher-Order Equation with pulse action
    Journal of Mathematical Sciences, 2012
    Co-Authors: V. M. Luchko
    Abstract:

    We consider the Cauchy problem and the problem with pulse action for a pseudodifferential higherorder Equation with respect to t . We construct solutions of these problems, study their properties, and prove a theorem on correctness.

  • Cauchy problem for a parabolic pseudodifferential Higher-Order Equation with pulse action
    Journal of Mathematical Sciences, 2012
    Co-Authors: V. M. Luchko
    Abstract:

    UDC 517.956 We consider the Cauchy problem and the problem with pulse action for a pseudodifferential higherorder Equation with respect to t . We construct solutions of these problems, study their properties, and prove a theorem on correctness. The theory of pseudodifferential operators and pseudodifferential Equations, whose modern form was formed in the middle of the 1960s, is studied in many works [2–8, 11, 12]. After determination that pseudodifferential operators are closely connected with problems of analysis and contemporary mathematical physics, especially in the theory of elliptic boundary-value problems [10], the number of such works has considerably increased. Linear parabolic pseudodifferential Equations with nonsmooth symbols were defined by Eidel’man, Drin’, and Iwasaki at the beginning of the 1970s in [2, 3, 8, 9, 11, 12]. The symbols of these pseudodifferential operators are nonsmooth at the point σ= 0 , σ∈ R n . For this reason, standard methods, which are used for pseudodifferential operators with smooth symbols, cannot be applied to the investigation of problems for these pseudodifferential Equations. Investigation of these Equations with constant (independent of the space coordinates x ∈R n and the time coordinate t ∈(0,T ]) homogeneous symbol was originated in [8]. The fundamental solution of the Cauchy problem for these Equations was determined with the use of the Fourier transformation. In [7], Fedoryuk establishes that the exact asymptotics of the fundamental solution of the Cauchy problem as x →∞ is power rather than exponential as for differential Equations. In [3], Schauder estimates are obtained and the correct solvability of the Cauchy problem in classes of Holder functions is established. For the subsequent development of this theory, Kochubei’s works [4, 11] were very important. In these works, for the first time, it is noted that pseudodifferential operators with nonsmooth symbols can be interpreted as hypersingular integral operations. This enabled one to use the well-developed theory of hypersingular integral operations for the investigation of the Cauchy problem. Kochubei constructed and studied fundamental solutions of the Cauchy problem, proved theorems on solvability of the Cauchy problem in classes of functions with power increase as x →∞ , and indicated connections of the obtained results with theory of random processes.

  • Cauchy problem for a parabolic Higher-Order Equation with pulse action
    Journal of Mathematical Sciences, 2009
    Co-Authors: V. M. Luchko
    Abstract:

    We prove the existence and establish some estimates of a solution of the Cauchy problem for a parabolic pulse-action Equation of higher order in t .

So Hirata - One of the best experts on this subject based on the ideXlab platform.

  • Higher-Order Equation-of-motion coupled-cluster methods for electron attachment
    Journal of Chemical Physics, 2007
    Co-Authors: Muneaki Kamiya, So Hirata
    Abstract:

    High-order Equation-of-motion coupled-cluster methods for electron attachment (EA-EOM-CC) have been implemented with the aid of the symbolic algebra program TCE into parallel computer programs. Two types of size-extensive truncation have been applied to the electron-attachment and cluster excitation operators: (1) the electron-attachment operator truncated after the 2p-1h, 3p-2h, or 4p-3h level in combination with the cluster excitation operator after doubles, triples, or quadruples, respectively, defining EA-EOM-CCSD, EA-EOM-CCSDT, or EA-EOM-CCSDTQ; (2) the combination of up to the 3p-2h electron-attachment operator and up to the double cluster excitation operator [EA-EOM-CCSD(3p-2h)] or up to 4p-3h and triples [EA-EOM-CCSDT(4p-3h)]. These methods, capable of handling electron attachment to open-shell molecules, have been applied to the electron affinities of NH and C2, the excitation energies of CH, and the spectroscopic constants of all these molecules with the errors due to basis sets of finite sizes ...

  • Higher-Order Equation-of-motion coupled-cluster methods for ionization processes
    Journal of Chemical Physics, 2006
    Co-Authors: Muneaki Kamiya, So Hirata
    Abstract:

    Compact algebraic Equations defining the Equation-of-motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both α and β ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N2 and C...

  • Higher-Order Equation-of-motion coupled-cluster methods
    Journal of Chemical Physics, 2004
    Co-Authors: So Hirata
    Abstract:

    The Equation-of-motion coupled-cluster (EOM-CC) methods truncated after double, triple, or quadruple cluster and linear excitation operators (EOM-CCSD, EOM-CCSDT, and EOM-CCSDTQ) have been derived and implemented into parallel execution programs. They compute excitation energies, excited-state dipole moments, and transition moments of closed- and open-shell systems, taking advantage of spin, spatial (real Abelian), and permutation symmetries simultaneously and fully (within the spin–orbital formalisms). The related Λ Equation solvers for coupled-cluster (CC) methods through and up to connected quadruple excitation (CCSD, CCSDT, and CCSDTQ) have also been developed. These developments have been achieved, by virtue of the algebraic and symbolic manipulation program that automated the formula derivation and implementation altogether. The EOM-CC methods and CC Λ Equations introduce a class of second quantized ansatz with a de-excitation operator (Ŷ), a number of excitation operators (X), and a physical (e.g....

Muneaki Kamiya - One of the best experts on this subject based on the ideXlab platform.

  • Higher-Order Equation-of-motion coupled-cluster methods for electron attachment
    Journal of Chemical Physics, 2007
    Co-Authors: Muneaki Kamiya, So Hirata
    Abstract:

    High-order Equation-of-motion coupled-cluster methods for electron attachment (EA-EOM-CC) have been implemented with the aid of the symbolic algebra program TCE into parallel computer programs. Two types of size-extensive truncation have been applied to the electron-attachment and cluster excitation operators: (1) the electron-attachment operator truncated after the 2p-1h, 3p-2h, or 4p-3h level in combination with the cluster excitation operator after doubles, triples, or quadruples, respectively, defining EA-EOM-CCSD, EA-EOM-CCSDT, or EA-EOM-CCSDTQ; (2) the combination of up to the 3p-2h electron-attachment operator and up to the double cluster excitation operator [EA-EOM-CCSD(3p-2h)] or up to 4p-3h and triples [EA-EOM-CCSDT(4p-3h)]. These methods, capable of handling electron attachment to open-shell molecules, have been applied to the electron affinities of NH and C2, the excitation energies of CH, and the spectroscopic constants of all these molecules with the errors due to basis sets of finite sizes ...

  • Higher-Order Equation-of-motion coupled-cluster methods for ionization processes
    Journal of Chemical Physics, 2006
    Co-Authors: Muneaki Kamiya, So Hirata
    Abstract:

    Compact algebraic Equations defining the Equation-of-motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both α and β ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N2 and C...

Lai-sheng Wang - One of the best experts on this subject based on the ideXlab platform.

  • A fourth order partial differential Equation model from the Weber's total variation for image restoration
    2011 3rd International Conference on Advanced Computer Control, 2011
    Co-Authors: Dong-hong Zhao, Lai-sheng Wang
    Abstract:

    Here we examine the partial regularity of minimums of a Laplace functional with the Weber TV image restoration in Bounded Variation space. Most conventional image processors consider little the influence of human vision psychology. This paper proposed a new functional. Furthermore, this functional is not only to use Laplace operator but also to add the human psychology system. Of course, because we add the influence of human vision psychology for the regularity item, this adds the difficult extent of the proposed problem of this text. Due to the singular nature of the Laplace, we study a regularized Laplace. With the proof of the experiment, it was to be found that this functional thus smoothes the image, and preserves edges via total variation because this functional lead into a higher order Equation-a fourth order partial differential Equation.

Li-ya Dong - One of the best experts on this subject based on the ideXlab platform.

  • SAR Image Denoising Method Based on Improved Wiener Filtering and P-M&LLT Partial Differential Equation
    2015 International Conference on Computer Science and Applications (CSA), 2015
    Co-Authors: Xing-tong Chen, Li-ya Dong
    Abstract:

    In order to remove the speckle noise produced by SAR system in the process of imaging, an improved SAR image denoising algorithm based on Wiener filtering and P-M&LLT partial differential Equation is proposed. In the algorithm, the image edge is preserved by P-M Equation of the low order partial differential Equations, and the higher order Equation LLT method can recover the image smooth region and avoid the block effect. Experimental results show that the integrated model combining the three methods is the better solution to filter the speckle noise and keep the contradiction between the image details, and the noise effect of the SAR image will be better.