Both the radial shear stress and the normal stress exhibit a usual square-root singularity ahead of and behind the crack front, respectively.
Under uniform radial shear stress, normal and shear stresses have a usual square-root singularity behind and ahead of the crack front, respectively, and the induced normal stress exhibits a logarithmic singularity at the crack center.
Their baklava is dense, neat, flatter-than-usual squares that go for $2. Poseidon Bakery, one of the few members of the old guard that survives in the ethnic food paradise of Hell's Kitchen, has a more riotous Greek version, messy and loaded with almonds and walnuts and drenched in honey ($3), and big enough for two people or one glutton.
We introduce a new criterion based on sequentially minimized squared deviations, which are smaller than both the usual least squares and the squared prediction errors used in PLS.
Let ¿2 be the usual 2D square lattice with sites u = (u1, u2), equipped with the l1-norm: || u || = | u1 | + | u2 |.
New formulations for the recursive residuals for models having uncorrelated errors with equal variances are given in terms of the observation vector or the usual least-squares residuals, which do not require the computation of least-squares parameter estimates and for which the transformation matrices are expressed wholly in terms of the rows of the Theil Z matrix.
All other programs show the usual, 2.2-square-inch, low-resolution displays.
These three cases can easily be solved by the usual least-squares algorithms, e.g., normal equations.
In many of the packings found, the circles form the usual regular square-grid or hexagonal patterns or their hybrids.
