A closed-form expression
for the average achievable rates is first derived, and its asymptotic behavior is then shown in the limit of large number of N.
We use the reciprocal gamma distribution proposed by Milevsky and Posner (1998a, 1998b) as an approximation of the state-price density of An and thereby obtain an approximate closed-form expression
for the fair valuation of survivor swaps and survivor floors.
The theoretical calculation often may take the form of numerical integration on an existing tabulation of power spectral density (PSD) obtained from a Monte Carlo simulation or, perhaps, may be evaluated directly from a closed-form expression
In addition, for a Rayleigh fading channel, the closed-form expression
of CDF for SINR is given.
The closed-form expression
for the inverse function [F.sup.-1.sub.i](x) is not easy to derive.
Firstly, a closed-form expression
for the critical buckling load of T-section webs is established using energy conservation approach with the assumption of noncorrelation of the restrain coefficient and buckling half-wavelength.
Hence, we derived an approximate closed-form expression
to evaluate the performance in terms of ergodic capacity using practical satellite channel data for various fading conditions.
Then, we provide a closed-form expression
of the surrender option value in the case of a single-premium policy when its dollar amount is invested in a fixed-term zero-coupon bond of the asset portfolio, and the dynamics of the term structure of interest rates are assumed to be driven by a one-factor model with a deterministic term structure of volatilities.
The following theorem provides new closed-form expression
for Dn in the presence of ideal hardware.
For example,  derived an exact closed-form expression
for the outage probability of a dual-hop AF MIMO relay network where the source and destination have multiple antennas and the relay has only one antenna, while  addressed the case where only one of the nodes is equipped with multiple antennas and the relay node is subjected to a single interferer, and later  extended  to systems with arbitrary number of interferers at the relay node, assuming that the relay is subjected to CCI and additive white Gaussian noise (AWGN) while the destination is corrupted by AWGN only.
Recently, Jeng  derived the new analytic closed-form expression
for the 3-D dyadic DGF in infinite free space based on the ordinary z-transform along with the partial difference operators.
This impedance is difficult to model accurately, especially for W-band IMPATT diodes that operate at high current density.(8) An approximate closed-form expression
for a single drift structure diode has been reported previously.(9) In this work, a modified form of this expression that suits the DDR structure has been used and is given as