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    Wyświetlanie 1-4 z 4
    Tytuł:
    Wave-particle duality of a 6D wavicle in two paired 4D dual reciprocal quasispaces of a heterogeneous 8D quasispatial structure
    Autorzy:
    Czajko, Jakub
    Powiązania:
    https://bibliotekanauki.pl/articles/1062921.pdf
    Data publikacji:
    2019
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Wave-particle duality
    multispatial mathematical reality of physics
    wavicle
    Opis:
    According to Louis de Broglie, wave-particle duality can imply presence of a single entity also known as wavicle. Hence, instead of the double solution he proposed to explain the duality, I depict the 6D wavicle in a multispatial mathematical entity represented in two 4D quasigeometric heterogeneous structures comprising two paired 3D dual reciprocal spaces, one of which represents the particle and the other the wave that was supposed to guide the particle in his pilot wave theory. The operational nature of the (2⨯4)D = 8D biquaternionic quasigeometric structure of the wavicle is synthesized from twin operations performed over paired 3D homogeneous dual reciprocal spaces, each of which is immersed in a pair of two 4D asymmetrically overlapping heterogeneous quasigeometric (3+1)D = 4D spatial structures.
    Źródło:
    World Scientific News; 2019, 127, 1; 1-55
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Todorov’s formula involving Stirling numbers of the second kind and Nörlund polynomials
    Autorzy:
    Zúñiga-Segundo, A.
    López-Bonilla, J.
    Vidal-Beltrán, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1165650.pdf
    Data publikacji:
    2018
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Bernoulli numbers
    Duality property
    Generalized chain rule of differentiation
    Hoppe’s formula
    Nörlund polynomials
    Stirling numbers
    Opis:
    We use the Todorov’s formula for the generalized Bernoulli numbers, in terms of Stirling numbers of the second kind, to deduce the Guo-Qi and Schläfli identities. Our approach is based in the duality property between the Stirling numbers, and in the Nörlund polynomials. We also consider the Janjic’s definitions for the Stirling numbers.
    Źródło:
    World Scientific News; 2018, 107; 201-206
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dual Reciprocal Scalar Potentials Paired via Differential Operators in Frenet Frames Make the Operators to Act Simultaneously in Each of Two Paired 3D Reciprocal Spaces
    Autorzy:
    Czajko, Jakub
    Powiązania:
    https://bibliotekanauki.pl/articles/1046557.pdf
    Data publikacji:
    2019
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    3D intraspatial and interspatial duality principles
    3D potentials in inertially moving trihedron
    Paired 3D dual reciprocal spaces
    scalar covariant differential operator SCovar
    Opis:
    Extending the operating domain of 3D geometric differential operator expands also the range of its operations onto paired 3D dual reciprocal spaces as well as the scope of their validity into paired 3D multispatial structures. Intraspatial duality principle for paired 3D dual reciprocal spaces is inferred from differential operations performed on the dual reciprocal 3D spaces. The new scalar differential operator SCovar as multiplicative inverse of the scalar gradient differential operator SGrad is proposed here to deliver scalar components of covariant differentials in order to accommodate both the operational and structural legitimacy of differential and integral operations performed in 3D dual reciprocal spaces. From preliminarily formulated abstract intraspatial duality principle a generalized interspatial duality principle is deduced and the connection of paired multispatial structures established. It is shown that the finegrained geometric differential operator GDiff acts simultaneously in each of the paired dual reciprocal spaces, which is its formerly unknown operational feature.
    Źródło:
    World Scientific News; 2019, 137; 96-118
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Some applications of Noether’s theorem
    Autorzy:
    Montiel-Pérez, J. Yaljá
    López-Bonilla, J.
    López-Vázquez, R.
    Vidal-Beltrán, S.
    Powiązania:
    https://bibliotekanauki.pl/articles/1166045.pdf
    Data publikacji:
    2018
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Complex Riemann-Silberstein vector
    Duality rotations
    Ignorable variable
    Invariance of the action
    Lanczos variational method
    Linear differential equation of second order
    Maxwell equations
    Noether’s theorem
    Variation of parameters
    Variational symmetry
    Opis:
    If the action S= ∫_(t_1)^(t_2)▒〖L(q,〗 (q,) ̇t) dt is invariant under the infinitesimal transformation t ̃=t+ε τ(q,t), q ̃_r= q_r+ε ξ_r (q,t),r=1,… ,n, with ε=constant ≪1, then the Noether’s theorem permits to construct the corresponding conserved quantity. The Lanczos approach employs to ε= q_(n+1) as a new degree of freedom, thus the Euler-Lagrange equation for this new variable gives the Noether’s constant of motion. Torres del Castillo and Rubalcava-García showed that each variational symmetry implies the existence of an ignorable coordinate; here we apply the Lanczos approach to the Noether’s theorem to motivate the principal relations of these authors. The Maxwell equations without sources are invariant under duality rotations, then we show that this invariance implies, via the Noether’s theorem, the continuity equation for the electromagnetic energy. Besides, we demonstrate that if we know one solution of p(x)y''+q(x)y'+r(x)y=0, then this Lanczos technique allows obtain the other solution of this homogeneous linear differential equation.
    Źródło:
    World Scientific News; 2018, 106; 69-80
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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