We recall from [1] that a line segment in Rmax, and consiquently Rmax has a similar case, has one of the three following forms: When X ≤ Y and x1 − y1 ≤ x2 − y2, then [X,Y ] = [X, (y1 + x2 − y2, x2)] ∪ [(y1 + x2 − y2, x2), Y ] (2) When X ≤ Y and x2 − y2 ≤ x1 − y1, then [X,Y ] = [X, (x1, y2 + x1 − y1)] ∪ [(x1, y2 + x1 − y1), Y ] (3) When X Y and Y X, then [X,Y ] = [X,max(X,Y )] ∪ [max(X,Y ), Y ]...

We consider the stability problem of reconstructing lattice sets from their noisy X-rays (i.e. line sums) taken along two directions. Stability is of major importance in discrete tomography because, in practice, these X-rays are affected by errors due to the nature of measurements. It has been shown that the reconstruction from noisy X-rays taken along more than two directions can lead to drama...

Recent results using inverse scattering techniques interpret every solution φ(x, y) of the sine-Gordon equation as a non-linear superposition of solutions along the axes x = 0 and y = 0. This has a well-known geometric interpretation, namely that every weakly regular surface of Gauss curvature K = −1, in arc length asymptotic line parametrization, is uniquely determined by the values φ(x, 0) an...

We present results from a 20 ksec XMM-Newton observation of Mrk 231. EPIC spectral data reveal strong line emission due to Fe Ka, which has rarely been detected in this class, as BAL QSOs are very faint in the X-ray band. The line energy is consistent with an origin in neutral Fe. The width of the line is equivalent to a velocity dispersion 18,000 km s-l and thus the line may be attributed to t...

We report on variations in important X-ray emission lines in a series of Chandra grating spectra of the supermassive colliding wind binary star η Car, including key phases around the X-ray minimum/periastron passage in 2003.5. The X-rays arise from the collision of the slow, dense wind of η Car with the fast, low-density wind of an otherwise hidden companion star. The X-ray emission lines provi...

Inactivation of the X chromosome in the male germ line has been suggested to contribute to the excess of gene movement off the X chromosome and the paucity of X-linked male-biased genes that have been observed in Drosophila species. Recent experimental work has demonstrated the transcriptional inactivation of the X chromosome during spermatogenesis, but it is not known if some regions of the X ...

Logic Rule 0 No unstated assumptions may be used in a proof. Logic Rule 1 Allowable justifications. 1. “By hypothesis . . . ”. 2. “By axiom . . . ”. 3. “By theorem . . . ” (previously proved). 4. “By definition . . . ”. 5. “By step . . . ” (a previous step in the argument). 6. “By rule . . . ” of logic. Logic Rule 2 Proof by contradiction (RAA argument). Logic Rule 3 The tautology ∼ (∼ S)⇐⇒ S L...

Logic Rule 0 No unstated assumptions may be used in a proof. Logic Rule 1 Allowable justifications. 1. “By hypothesis . . . ”. 2. “By axiom . . . ”. 3. “By theorem . . . ” (previously proved). 4. “By definition . . . ”. 5. “By step . . . ” (a previous step in the argument). 6. “By rule . . . ” of logic. Logic Rule 2 Proof by contradiction (RAA argument). Logic Rule 3 The tautology ∼ (∼ S)⇐⇒ S L...