integral representation वाक्य
उदाहरण वाक्य
मोबाइल
- When the Abel Plana formula is applied to the defining series of the polylogarithm, a Hermite-type integral representation results that is valid for all complex " z " and for all complex " s ":
- The examples listed below follow directly from the integral representation of the Clausen function, and the proofs require little more than basic trigonometry, integration by parts, and occasional term-by-term integration of the Fourier series definitions of the Clausen functions.
- Every other integral representation " H i " at the same level becomes a module for the vertex algebra, in the sense that for each " a " there is a vertex operator on " H i " such that
- Stochastic quantization takes advantage of the fact that a Euclidean quantum field theory can be modeled as the path integral representation of a Euclidean quantum field theory, the path integral measure is closely related to the Boltzmann distribution of a statistical mechanical system in equilibrium.
- Andrianov was an Invited Speaker at the ICM in 1970 in Nice with talk " On the zeta function of the general linear group " and in 1983 in Warsaw with talk " Integral representation of quadratic forms by quadratic forms : multiplicative properties ".
- His research topics include path integral representation of Fractional Brownian motion, ring closing opening dynamics in polymers, first passage time calculation in phase space, energy transfer between molecule and graphene, quantum coherence etc . He introduced what is known as the kink mechanism for the translocation of long chain molecule through a nano-pore.
- As evidenced by Efimov and Ganbold in an earlier work ( Efimov 1991 ), the procedure of tadpole renormalization can be employed very effectively to remove the divergences from the action of the basic field-theoretic representation of the partition function and leads to an alternative functional integral representation, called the Gaussian equivalent representation ( GER ).
- Once this integral representation is obtained, there are various ways to present a succinct and self-contained proof starting from the integral ( as in Cartwright's, Bourbaki's or Niven's presentations ), which Hermite could easily see ( as he did in his proof of the transcendence of " e " ).
- Jost researched quantum-mechanical scattering theory ( also inverse scattering theory : Reconstruction of potentials from scattering data ) and the mathematical quantum field theory, where he in 1958 with the methods of Arthur Strong Wightman proved the PCT theorem and in 1957 introduced " the Jost-Dyson-representation " ( an integral representation of the expectancy value of the commutator of two field operators ).
- All three order types also have integral representations, that is for a particular order A is smaller than B if and only if { \ rm E } [ f ( A ) ] \ le { \ rm E } [ f ( B ) ] for all f : \ mathbb R ^ d \ longrightarrow \ mathbb R in a class of functions \ mathcal G . \ mathcal G is then called generator of the respective order.
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