The Experts below are selected from a list of 249 Experts worldwide ranked by ideXlab platform

Paul S Pedersen - One of the best experts on this subject based on the ideXlab platform.

  • cauchy s Integral Theorem on a finitely generated real commutative and associative algebra
    Advances in Mathematics, 1997
    Co-Authors: Paul S Pedersen
    Abstract:

    LetR[α]=R[α1, α2, …, αn] (whereα1=1) be a real, unitary, finitely generated, commutative, and associative algebra. We consider functionsf(z)=f(∑ni=1 xiαi) which mapR[α]n={∑ni=1 aiαi | 1⩽i⩽n,ai∈R} intoR[α]=finite dimensional subspaces of {∑k∈Nn0 bkαk | bk∈R,k=(k1, …, kn)∈Nn0} whereN0={0, 1, 2, …}. We impose a total order on an algorithmically defined basisBforR[α]. The resulting algebra and ordered basis will be written as (R[α], <). We then use this basis to define a norm ‖·‖ on (R[α], <). Continuous functions, differentiable functions, and the concept of Riemann integration will then be defined and discussed in this new setting. We then show that ∫γ f(z) dz=0 whenf(z) is a continuous and differentiable function defined in a simply connected regionG⊂R[α]n⊂(R[α], <) containing the closed pathγ.

  • Cauchy's Integral Theorem on a Finitely Generated, Real, Commutative, and Associative Algebra
    Advances in Mathematics, 1997
    Co-Authors: Paul S Pedersen
    Abstract:

    LetR[α]=R[α1, α2, …, αn] (whereα1=1) be a real, unitary, finitely generated, commutative, and associative algebra. We consider functionsf(z)=f(∑ni=1 xiαi) which mapR[α]n={∑ni=1 aiαi | 1⩽i⩽n,ai∈R} intoR[α]=finite dimensional subspaces of {∑k∈Nn0 bkαk | bk∈R,k=(k1, …, kn)∈Nn0} whereN0={0, 1, 2, …}. We impose a total order on an algorithmically defined basisBforR[α]. The resulting algebra and ordered basis will be written as (R[α],

Sergey G. Fedosin - One of the best experts on this subject based on the ideXlab platform.

  • The Integral Theorem of the field energy
    gazi university journal of science, 2019
    Co-Authors: Sergey G. Fedosin
    Abstract:

    The Integral Theorem of the vector field energy is derived in a covariant way, according to which under certain conditions the potential energy of the system’s field turns out to be half as large in the absolute value as the field’s kinetic energy associated with the four-potential of the field and the four-current of the system’s particles. Thus, the Integral Theorem turns out to be the analogue of the virial Theorem, but with respect to the field rather than to the particles. Using this Theorem, it becomes possible to substantiate the fact that electrostatic energy can be calculated by two seemingly unrelated ways, either through the scalar potential of the field or through the stres energy-momentum tensor of the field. In closed systems, the Theorem formulation is simplified for the electromagnetic and gravitational fields, which can act at a distance up to infinity. At the same time for the fields acting locally in the matter, such as the acceleration field and the pressure field, in the Theorem formulation it is necessary to take into account the additional term with Integral taken over the system’s surface. The proof of the Theorem for an ideal relativistic uniform system containing non-rotating and randomly moving particles shows full coincidence in all significant terms, particularly for the electromagnetic and gravitational fields, the acceleration field and the vector pressure field .

  • The Integral Theorem of generalized virial in the relativistic uniform model
    Continuum Mechanics and Thermodynamics, 2019
    Co-Authors: Sergey G. Fedosin
    Abstract:

    In the relativistic uniform model for continuous medium, the Integral Theorem of generalized virial is derived, in which generalized momenta are used as particles’ momenta. This allows us to find exact formulas for the radial component of the velocity of typical particles of the system and for their root-mean-square speed, without using the notion of temperature. The relation between the Theorem and the cosmological constant, characterizing the physical system under consideration, is shown. The difference is explained between the kinetic energy and the energy of motion, the value of which is equal to half the sum of the Lagrangian and the Hamiltonian. This difference is due to the fact that the proper fields of each particle have mass–energy, which makes an additional contribution into the kinetic energy. As a result, the total energy of motion of particles and fields is obtained.

Blake A Richard - One of the best experts on this subject based on the ideXlab platform.

  • the helmholtz kirchoff 2 5d Integral Theorem for sign bit data
    Journal of Geophysics and Engineering, 2004
    Co-Authors: Louis M. Houston, Blake A Richard
    Abstract:

    The Helmholtz–Kirchoff Integral Theorem is the basis for Kirchoff migration of seismic data. Essentially, Kirchoff migration is a solution to the wave equation in the presence of obstacles. In practice, prestack migration of typical seismic data sets can be very computer intensive. Consequently, it is beneficial to consider more efficient migration algorithms. The theory presented here offers, potentially, a much more compact Kirchoff migration scheme by reducing the seismic data into its residual sign bits, prior to migration. Sign-bit processing in the seismic industry has historically been limited to stacking, but the theory presented in this paper extends sign-bit data to wave equation processing. Included in this paper is a refinement of prior treatments of sign-bit processing based on statistical analysis. In other words, this treatment is purely mathematical, while earlier treatments tend to be partially intuitive and partially mathematical. This paper is the theoretical component of a dual presentation, in which the second paper will include computational examples.

  • The Helmholtz–Kirchoff 2.5D Integral Theorem for sign-bit data
    Journal of Geophysics and Engineering, 2004
    Co-Authors: Louis M. Houston, Blake A Richard
    Abstract:

    The Helmholtz–Kirchoff Integral Theorem is the basis for Kirchoff migration of seismic data. Essentially, Kirchoff migration is a solution to the wave equation in the presence of obstacles. In practice, prestack migration of typical seismic data sets can be very computer intensive. Consequently, it is beneficial to consider more efficient migration algorithms. The theory presented here offers, potentially, a much more compact Kirchoff migration scheme by reducing the seismic data into its residual sign bits, prior to migration. Sign-bit processing in the seismic industry has historically been limited to stacking, but the theory presented in this paper extends sign-bit data to wave equation processing. Included in this paper is a refinement of prior treatments of sign-bit processing based on statistical analysis. In other words, this treatment is purely mathematical, while earlier treatments tend to be partially intuitive and partially mathematical. This paper is the theoretical component of a dual presentation, in which the second paper will include computational examples.

Yusuf Ziya Umul - One of the best experts on this subject based on the ideXlab platform.

Fedosin, Sergey G. - One of the best experts on this subject based on the ideXlab platform.

  • The Integral Theorem of generalized virial in the relativistic uniform model
    'Springer Science and Business Media LLC', 2019
    Co-Authors: Fedosin, Sergey G.
    Abstract:

    In the relativistic uniform model for continuous medium the Integral Theorem of generalized virial is derived, in which generalized momenta are used as particles momenta. This allows us to find exact formulas for the radial component of the velocity of typical particles of the system and for their root-mean-square speed, without using the notion of temperature. The relation between the Theorem and the cosmological constant, characterizing the physical system under consideration, is shown. The difference is explained between the kinetic energy and the energy of motion, the value of which is equal to half the sum of the Lagrangian and the Hamiltonian. This difference is due to the fact that the proper fields of each particle have mass-energy, which makes an additional contribution into the kinetic energy. As a result, the total energy of motion of particles and fields is obtained.Comment: 22 page