The Rubin–Stark Conjecture for imaginary abelian fields of odd prime power conductor

We build upon ideas developed in [9], as well as results of Greither on a strong form of Brumers Conjecture ([2]–[4]), and prove Rubins integral version of Starks Conjecture for imaginary abelian extensions of Q of odd prime power conductor.Mathematics Subject Classification (1991): 11R42, 11R58, 11R27Research on this project was partially supported by NSF grants DMS–9801267 and DMS–0196340Revised version: 11 October 2002     

Structural influence of erbium centers on silicon nanocrystal phase transitions

Two different types of erbium-doped silicon nanocrystals, along with undoped, oxide-capped Si dots, are employed to probe the impact of the impurity center location on phase transition pressure. Using a combination of high pressure optical absorption, micro-Raman, and x-ray diffraction measurements in a diamond anvil cell, it is demonstrated that the magnitude of this phase transition elevation is strongly dictated by the average spatial location of impurity centers introduced into the nanocrystal along with the interfacial quality of the surrounding oxide.     

Deterministic automata simulation, universality and minimality

Finite automata have been recently used as alternative, discrete models in theoretical physics, especially in problems related to the dichotomy between endophysical/intrinsic and exophysical/ extrinsic perception (see, for instance [3, 6, 18–21]). These studies deal with Moore experiments; the main result states that it is impossible to determine the initial state of an automaton, and, consequently, a discrete model of Heisenberg uncertainty has been suggested. For this aim the classical theory of finite automata — which considers automata with initial states — is not adequate, and a new approach is necessary. A study of finite deterministic automata without initial states is exactly the aim of this paper. We will define and investigate the complexity of various types of simulations between automata. Minimal automata will be constructed and proven to be unique up to an isomorphism. We will build our results on an extension of Myhill-Nerode technique; all constructions will make use of “automata responses” to simple experiments only, i.e., no information about the internal machinery will be considered available.     

Synthesis and characterization of phenoxarsin-10-yl 2-R2N-cyclopent-1-ene-1-carbodithioate (R = H,C2H5, cyclo-C6H11CH2) and the crystal and molecular structure of the 2-amino (R = H) derivative

Phenoxarsin-10-yl derivatives of 2-amino-cyclopent-1-ene-1-carbodithioic acid, (ACDA), and its N-alkyl derivativesO(C₆H₄)₂ AsS₂C—C₅H₆— NHR-2 (R = H, CH₂CH₃, CH₂C₆H₁₁,), have been prepared by reacting O(C₆H₄)₂AsCI with the corresponding ACDA 1,1-dithioic acid. The compounds were obtained by stirring stoichiometric amounts of the reagents in ethanol, over 24 h, at room temperature. The scale of the preparations were in the order of 2 mmol and the yields of the compounds ca 75%. The reactions were carried out in absolute ethanol. The compounds were characterized by IR, mass and NMR (¹H, ¹³C) spectroscopy. The molecular structure of O(C₆H₄)₂AsS₂C—C₅H₆—NH₂-2 was determined using X-ray diffractometry, achieving an R-value of 6.3%; this compound is monomeric and contains an asymmetric monometallic biconnective 1,1-dithiolato ligand [As—S(1) 2.272(2) å, As … S(2) 3.125(2) å]. An intramolecular hydrogen bond is established between one hydrogen atom of the NH₂ group and the sulfur [S(2)] atom involved in the secondary interaction to arsenic. The dihedral angle (150.3(3)°) of the phenoxarsine moiety is practically unaffected by substitution of chlorine on arsenic by the carbodithioato ligand.     

Lagrange Inversion and Schur Functions

Macdonald defined an involution on symmetric functions by considering the Lagrange inverse of the generating function of the complete homogeneous symmetric functions. The main result we prove in this note is that the images of skew Schur functions under this involution are either Schur positive or Schur negative symmetric functions. The proof relies on the combinatorics of Lagrange inversion. We also present a q-analogue of this result, which is related to the q-Lagrange inversion formula of Andrews, Garsia, and Gessel, as well as the operator of Bergeron and Garsia.