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to an equation with double periodic kernel. Effective solutions having integrable singularities at the end-points of the line of integration are obtained. ...
, for very small values of |$R$| it is necessary to pass the contour over the double pole at |$s=0$| and instead perform the integration on a line |$\Re (s)=-c_0,$| say. Then the expressions for the |$d_j(s ...
with a multinomial distribution with identity covariance matrix and zero mean; p ∼ N(0, I). The equations of motion are then integrated with starting conditions (q, p) for some time period to produce new coordinates ...
either in impulse (force integrated over time) or work (force integrated over distance), respectively. Fig 2A and 2B depict the average work and impulse produced by the manipulator as a function of force ...
for integral constraints on |${{\dot{\boldsymbol \Gamma }}}$| using a low-frequency approximation. If the displacement field is low-pass filtered to wavelengths |$\lambda$| and periods |$\tau$| that are long ...
that there exists a heat source which is significantly dependent on space, time and temperature, and hence it cannot be neglected. This gives rise to a non-characteristic Cauchy inverse boundary value problem ...
specified by a scalar moment density, and the integral of that density over the source volume—the Aki (ordinary) seismic moment—is equal to the total moment. The mechanism of an extended seismic source ...
into a product or taken from one water body and returned to another or is returned to the same basin but in a time period different from that of the analysis being carried out (WFBlue). The grey component ...
}= (x_1, x_2) \in \mathbb{R}^2$|. Introduce the double Fourier transform |$\mathfrak{F}$| and its inverse |$\mathfrak{F}^{- 1}$| defined by $$\begin{eqnarray*} \mathfrak{F} [\phi] (\boldsymbol{\xi}, x_3 ...
=1,...,m \rbrace$| are the integrals of the first kind and each is uniquely determined, up to an additive constant, by its periods around the |$a$| and |$b$|-cycles. The functions |$\lbrace v_j(\zeta ...
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