We investigate the parameter plane of the Newton’s method applied to the family of quartic polynomials pa,b(z) = z 4 +az + bz +az+ 1, where a and b are real parameters. We divide the parameter plane (a, b) ∈ R into twelve open and connected regions where p, p′ and p′′ have simple roots. In each of these regions we focus on the study of the Newton’s operator acting on the Riemann sphere.

For integers d ≥ 2 and ε = 0 or 1, let S(ε) denote the sphere product S × S if ε = 0 and the twisted sphere product S1× − S if ε = 1. The main results of this paper are : (a) if d ≡ ε (mod 2) then S(ε) has a unique minimal triangulation using 2d + 3 vertices, and (b) if d ≡ 1− ε (mod 2) then S(ε) has minimal triangulations (not unique) using 2d+ 4 vertices. In this context, a minimal triangulat...

MHC-related protein (MR)1 is an MHC class I-related molecule encoded on chromosome 1 that is highly conserved among mammals and is more closely related to classical class I molecules than are other nonclassical class I family members. In this report, we show for the first time that both mouse and human MR1 molecules can associate with the peptide-loading complex and can be detected at low level...

Let Cm,n be the graph on the vertex set {1, . . . ,m} × {0, . . . , n − 1} in which there is an edge between (a, b) and (c, d) if and only if either (a, b) = (c, d ± 1) or (a, b) = (c ± 1, d), where the second index is computed modulo n. One may view Cm,n as a unit square grid on a cylinder with circumference n units. For odd n, we prove that the Euler characteristic of the simplicial complex Σ...

We have used positron annihilation spectroscopy to study vacancy-type defects in strained phosphorus doped Si12xGex layers grown on Si substrates and irradiated with 2-MeV protons. The results show that the dominant defect in the SiGe layer after irradiation is the E center, the vacancy-phosphorus pair. When the sample is annealed at 150–175 °C, the dominant defect species in the SiGe layer cha...

In this study, we present the work on the physicochemical interaction between the anti-cancer alkaloidberberine (BRB) and DNA with the purpose of designing drugs that interact more with DNA. Molecularmodeling on the complex formed between berberine and DNA presented that this complex was undeniablyfully able of participating in the formation of a stable intercalation site. Besides, the molecula...

Hoogsteen base pairs within duplex DNA typically are only observed in regions containing significant distortion or near sites of drug intercalation. We report here the observation of a Hoogsteen base pair embedded within undistorted, unmodified B-DNA. The Hoogsteen base pair, consisting of a syn adenine base paired with an anti thymine base, is found in the 2.1 A resolution structure of the MAT...

Thin section electron micrographs of rapidly fixed Chlamydomonas cells were used to establish a relationship between flagellar bends and orientation of the central pair microtubule complex. Using conditions that preserve flagellar waveforms during both forward swimming (asymmetric bends) and backward swimming (symmetric bends), we found that central pair orientation differs in bent regions and ...