3,770 research outputs found
On Witten multiple zeta-functions associated with semisimple Lie algebras IV
In our previous work, we established the theory of multi-variable Witten
zeta-functions, which are called the zeta-functions of root systems. We have
already considered the cases of types , , , and . In
this paper, we consider the case of -type. We define certain analogues of
Bernoulli polynomials of -type and study the generating functions of them
to determine the coefficients of Witten's volume formulas of -type. Next
we consider the meromorphic continuation of the zeta-function of -type and
determine its possible singularities. Finally, by using our previous method, we
give explicit functional relations for them which include Witten's volume
formulas.Comment: 22 pag
Strong first order S-ROCK methods for stochastic differential equations
Explicit stochastic Runge–Kutta (SRK) methods are constructed for non-commutative Itô and Stratonovich stochastic differential equations. Our aim is to derive explicit SRK schemes of strong order one, which are derivative free and have large stability regions. In the present paper, this will be achieved by embedding Chebyshev methods for ordinary differential equations in SRK methods proposed by Rößler (2010). In order to check their convergence order, stability properties and computational efficiency, some numerical experiments will be performed
Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise
A new class of third order Runge-Kutta methods for stochastic differential
equations with additive noise is introduced. In contrast to Platen's method,
which to the knowledge of the author has been up to now the only known third
order Runge-Kutta scheme for weak approximation, the new class of methods
affords less random variable evaluations and is also applicable to SDEs with
multidimensional noise. Order conditions up to order three are calculated and
coefficients of a four stage third order method are given. This method has
deterministic order four and minimized error constants, and needs in addition
less function evaluations than the method of Platen. Applied to some examples,
the new method is compared numerically with Platen's method and some well known
second order methods and yields very promising results.Comment: Two further examples added, small correction
Observation of the Ettingshausen effect in quantum Hall systems
Evidence of the Ettingshausen effect in the breakdown regime of the integer
quantum Hall effect has been observed in a GaAs/AlGaAs two-dimensional electron
system. Resistance of micro Hall bars attached to both edges of a current
channel shows remarkable asymmetric behaviors which indicate an electron
temperature difference between the edges. The sign of the difference depends on
the direction of the electric current and the polarity of the magnetic field.
The results are consistent with the recent theory of Akera.Comment: 4 pages, 6 figures, submitted to Phys. Rev.
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