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The Mayan calendar is proposed to derive from an arithmetical model of naked-eye astronomy. The Palenque and Copan lunar equations, used during the Maya Classic period (200 to 900 AD) are solution of the model and the results are expressed as a function of the Xultun numbers, four enigmatic Long Count numbers deciphered in the Maya ruins of Xultun, dating from the IX century AD, providing strong arguments in favor of the use of the model by the Maya. The different Mayan Calendar cycles can be derived from this model and the position of the Calendar Round at the mythical date of creation 13(0).0.0.0.0 4 Ahau 8 Cumku is calculated. This study shows the high proficiency of Mayan mathematics as applied to astronomy and timekeeping for divinatory purposes.

The Maya were known for their astronomical proficiency. This is demonstrated in the Mayan codices where ritual practices were related to astronomical events/predictions. Whereas Mayan mathematics were based on a vigesimal system, they used a different base when dealing with long periods of time, the Long Count Calendar (LCC), composed of different Long Count Periods: the Tun of 360 days, the Katun of 7200 days and the Baktun of 144000 days. There were two other calendars used in addition to the LCC: a civil year Haab' of 365 days and a religious year Tzolk'in of 260 days. Another cycle was also in use: a 3276-day cycle (combination of the 819-day Kawil cycle and the 4 directions-colors). Based on the hypothesis that Mayan astronomers had a good knowledge of naked-eye astronomy, we propose here an explanation of the origin of the LCC, the Haab', the Tzolk'in and the 3276-day cycle. This study sheds more light on the connection between arithmetic, astronomy and religion in Maya civilization.

The electronic and magnetic properties of neutral substitutional transition-metal dopants in dia- mond are calculated within density functional theory using the generalized gradient approximation to the exchange-correlation potential. Ti and Fe are nonmagnetic, whereas the ground state of V, Cr and Mn are magnetic with a spin entirely localized on the magnetic ion. For Co, Ni, and Cu, the ground state is magnetic with the spin distributed over the transition-metal ion and the nearest-neighbor carbon atoms; furthermore a bound state is found in the gap that originates from the hybridization of the 3d-derived level of the dopant and the 2p-derived dangling bonds of the nearest-neighbor carbons. A p{d hybridization model is developed in order to describe the origin of the magnetic interaction. This model predicts high-spin to low-spin transitions for Ni and Cu under compressive strain.

The electronic and magnetic properties of a neutral substitutional nickel (Ni$_s^0$) impurity in diamond are studied using density functional theory in the generalized gradient approximation. The spin-one ground state consists of two electrons with parallel spins, one located on the nickel ion in the $3d^9$ configuration and the other distributed among the nearest-neighbor carbons. The exchange interaction between these spins is due to $p-d$ hybridization and is controllable with compressive hydrostatic or uniaxial strain, and for sufficient strain the antiparallel spin configuration becomes the ground state. Hence, the Ni impurity forms a controllable two-electron exchange-coupled system that should be a robust qubit for solid-state quantum information processing.

We have calculated the chemical trend of magnetic exchange parameters ($J_{dd}$, $N \alpha$, and $N \beta$) of Zn-based II-VI semiconductors ZnA (A=O, S, Se, and Te) doped with Co or Mn. We show that a proper treatment of electron correlations by the LSDA+$U$ method leads to good agreement between experimental and theoretical values of the nearest-neighbor exchange coupling $J_{dd}$ between localized 3$d$ spins in contrast to the LSDA method. The exchange couplings between localized spins and doped electrons in the conduction band $N \alpha$ are in good agreement with experiment as well. But the values for $N \beta$ (coupling to doped holes in the valence band) indicate a cross-over from weak coupling (for A=Te and Se) to strong coupling (for A=O) and a localized hole state in ZnO:Mn. That hole localization explains the apparent discrepancy between photoemission and magneto-optical data for ZnO:Mn., Comment: 19 pages, 4 figures

We calculate the magnetic interactions between two nearest neighbor substitutional magnetic ions (Co or Mn) in ZnO by means of density functional theory and compare it with the available experimental data. Using the local spin density approximation we find a coexistence of ferro- and antiferromagnetic couplings for ZnO:Co, in contrast to experiment. For ZnO:Mn both couplings are antiferromagnetic but deviate quantitatively from measurement. That points to the necessity to account better for the strong electron correlation at the transition ion site which we have done by applying the LSDA+U method. We show that we have to distinguish two different nearest neighbor exchange integrals for the two systems in question which are all antiferromagnetic with values between -1.0 and -2.0 meV in reasonable agreement with experiment.

Discusses how collaborative learning (CL) can be used in a computer-assisted learning (CAL) environment for language learning, reviewing research in the fields of applied linguistics, educational psychology, and artificial intelligence. An application of CL and CAL in the learning of French as a Second Language, focusing on interrogative sentences, is proposed. (28 references) (MDM)