The proposed algorithm versus the nave method of analogous calculations drastically reduces the number of multipliers required for FPGA implementation of complex-valued constant matrix-vector multiplication. If the fully parallel hardware implementation of nave (schoolbook) method for complex-valued matrix-...
A nonconstant complex-valued function f of a complex variable z is said to be periodic if there is a nonzero complex number ω such that f(z +ω) = f(z) for all z, in which case ω is called a period of f. From: Handbook of Complex Analysis, 2005 ...
We gen- eralize TReLU through three modifications: a) a learned complex-valued scaling factor for each input channel, en- abling the layer to adapt to input magnitude and phase, b) hyperparameter r to control the magnitude threshold, and c) learned scaling constant for the output...
Consider a two-neuron complex-valued neural network with constant delay Global [mu]-stability of complex-valued neural networks with unbounded time-varying delays Xiao-hui, "Synchronization of complex-valued neural network with sliding mode control," Journal of The Franklin Institute, vol. Impulsive ...
The bias is implemented by a constant input 1, and an additional complex-valued variable b is allocated in the weight vector to make the bias trainable. In this task, identity activation function (Supplementary Note 14) is applied to the single neuron. Therefore, Eq. (2) is simplified to ...
YDSE: wavelength\(\lambda = 5 \times 10^{ - 6} m\), distance between two slits\(d = 5 \times 10^{ - 3} m\), distance between the barrier and the projection screen\(L = 1m\), distance between light source and barrier\(I = 0.01m\), constant value\(\delta = 0.38\). ...
The property of self-similarity results into the fBM spectrum to behave as f_X\left( \omega \right) =A^2 \left| \omega \right|^{-2\delta} for frequencies \omega , a constant A and \delta ∈ (1/2, 3/2) . The spectral slope parameter \delta is linked to the aspect ratio of ...
Fundamental theorem of algebra- letp(z)be non-constant complexpolynomial. Then there exists aξ∈\Csuch thatp(ξ)=0. Consequently, a complex polynomial of degree N > 1 has exactly N roots counted with multiplicity. § 2.1 differentiation of complex valued functions ...
(2) |\phi |^2 is constant. (3) \phi (x)\ne 0 for all x\in M. As an obvious consequence we have the following. Corollary 4.3 If \phi :M\rightarrow {{\mathbb {C}}} is a complex-valued (\lambda ,\mu )-eigenfunction on a compact and connected Riemannian manifold (M, g) su...
Sufficient conditions for the existence of orbital motion and non-asymptotic, non-orbital motion in the solutions of constant coefficient complex variable differential equations are obtained through Liapunov''s direct method. Matrix analogues of those conditions assure the corresponding type of motion of ...