For example, a CAPTCHA that just slants the letters and peppers them with dots can be solved by removing dots and then looking for recognizable letters when the image is bent in various directions.
Figure 2 Reflected field amplitude (pmb{vert Rvert }) and absolute error versus the truncation number M. Now, we truncate the infinite system of equations (3.11 - 3.15) by taking (n=1, 2, 3, dots, 5M) and (m=1, 2, 3, dots, M) to solve (F_{n}).
They gave 28 healthy right-handed participants (aged 19 to 63) the nine-dot problem to solve.
The rigorous solution for ( {sigma}_{0i}^2left 1, dots, mright) ) can be delivered by solving the m dimensional equation system.
For computational efficiency, we first solved the derivatives with respect to time of the tsunami velocity components, (dot{M} x,y,t)) and (dot{N} x,y,t)), rather than calculating the tsunami velocity by implicitly solving Eq. 10, where the dots denote derivatives with respect to time.
By solving systems (10) and (11), we obtain the predictor directions (( dot{tilde{x}}, dot{tilde{y}}, dot{tilde{s}})) and ((ddot{tilde {x}},ddot{tilde{y}},ddot{tilde{s}})) and have the following lemma.
(Predictor step) The predictor directions ((dot{tilde{x}}^{k},dot{y}^{k},dot{tilde{s}}^{k})), ((ddot{tilde {x}}^{k},ddot{y}^{k}, ddot{tilde{s}}^{k})) are obtained by solving the linear system (10), (11) and the largest positive (bar{theta}^{k}in 0,pi/2]) is computed by solving (16) and (15).
Step 2: (Predictor step) The predictor directions ((dot{tilde{x}}^{k},dot{y}^{k},dot{tilde{s}}^{k})), ((ddot{tilde {x}}^{k},ddot{y}^{k}, ddot{tilde{s}}^{k})) are obtained by solving the linear system (10), (11) and the largest positive (bar{theta}^{k}in 0,pi/2]) is computed by solving (16) and (15).
Using the dropping shock initial conditions (dot{x}(0) = sqrt{2gh}), the two key parameters A and ω can be obtained by solving equation (20) and equation (22) simultaneously.
