3,512 research outputs found
Lorentz Transformation in Flat 5D Complex-Hyperbolic Space
The Lorentz transfomation is derived in 5D flat pseudo-complex affine space
or TT Space. The TT space or pseudo-Complex space accomodates one
uncompactified time-like extra dimension. It is shown that the maximum
allowable speed for particles living in TT space exceeds the speed of light, c,
the absolute speed of the Minkowski space.Comment: Removal of non-alpha numeric characters from the title and abstrac
Extra-Dimensional Approach to Option Pricing and Stochastic Volatility
The generalized 5D Black-Scholes differential equation with stochastic
volatility is derived. The projections of the stochastic evolutions associated
with the random variables from an enlarged space or superspace onto an ordinary
space can be achieved via higher-dimensional operators. The stochastic nature
of the securities and volatility associated with the 3D Merton-Garman equation
can then be interpreted as the effects of the extra dimensions. We showed that
the Merton-Garman equation is the first excited state, i.e. n=m=1, within a
family which contain an infinite numbers of Merton-Garman-like equations.Comment: Ease the time-independent restriction on the extra dimensional
coordinates. Fixed typos and expand the conclusio
Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters
A new method of designing linear-phase FIR filters is proposed by minimizing a quadratic measure of the error in the passband and stopband. The method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The proposed design procedure is general enough to incorporate both time- and frequency-domain constraints. For example, Nyquist filters can be easily designed using this approach. The design time for the new method is comparable to that of Remez exchange techniques. The passband and stopband errors in the frequency domain can be made equiripple by an iterative process, which involves feeding back the approximation error at each iteration. Several numerical design examples and comparisons to existing methods are presented, which demonstrate the usefulness of the present approach
A 'trick' for the design of FIR half-band filters
Based on a well-known property of FIR half-band filters, this correspondence shows how the design time for equiripple half-band filters can be reduced by a considerable amount. The observation which leads up to this improved procedure also places in evidence new implementation schemes, which simultaneously ensure low passband and stopband sensitivities. Extension of the method to Mth-band filter design is also outlined
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