We start with introducing a hyperbolic version of the reflection principle that parallels the one with the standard Brownian motion in "Hyperbolic reflection principle" section.
Finally, by introducing a hyperbolic realization and constructing auxiliary systems, a sufficient and generically necessary condition for the existence of the unknown functions is obtained.
In this paper, in view of application to pricing of Barrier options under a stochastic volatility model, we study a reflection principle for the hyperbolic Brownian motion, and introduce a hyperbolic version of Imamura-Ishigaki-Okumura's symmetrization.
By proposing a new transformation of the final control signal, using the sector-bound property of the quantizer and introducing a hyperbolic tangent function, the effects from input quantization and external disturbance are effectively compensated and the Lipschitz condition required for the nonlinear functions in the systems is removed.
In this paper we introduce a hyperbolic (Poincaré Bergman type) distance δ on the noncommutative open ball[B(H n]1:="{ X1,…,Xn)∈B(H n:‖X1X1∗+⋯+XnXn∗‖1/2<1}, where B(H) is the algebra of all bounded linear operators on a Hilbert space H.
They make the same QSS assumption as Thattai and Van Oudenaarden to introduce a hyperbolic term for the repression and also linearize the system about its steady state.
We take care of this effect by introducing a hyperbolic time dependence for the siRNA-concentration: (23) [ siRNA ] (t ) = [ siRNA ] MAX · (1 − exp (− r siRNA t ) ).
The first part of the analysis proceeds in the same way as Thattai and Van Oudenaarden by making the QSS approximation and introducing a hyperbolic term for the production of mRNA.
The present work successfully achieves a strong enhancement in performance of a near-field thermophotovoltaic (TPV) system operating at low temperature and large-vacuum-gap width by introducing a hyperbolic-metamaterial (HMM) emitter, multilayered graphene, and an Au-backside reflector.
Stakhov and Tkachenko [14] introduced a new class of hyperbolic functions called hyperbolic Fibonacci functions replacing the discrete variable n in equation (9) with the continuous variable x that takes its values from the set of real numbers.
