Efektivní aritmetika eliptických křivek nad konečnými tělesy

The thesis deals with arithmetics of elliptic curves over finite fields and methods to improve those calculations. In the first part, algebraic geometry helps to define elliptic curves and derive their basic properties including the group law. The second chapter seeks ways to speed up these calculations by means of time-memory tradeoff, i.e. adding redundancy. At last, the third part introduces a wholly new curve form, which is particularly effective for such purposes

Cationic Ir(III) Alkylidenes Are Key Intermediates in C–H Bond Activation and C–C Bond-Forming Reactions

This work describes the chemical reactivity of a cationic (η⁵-C₅Me₅)­Ir­(III) complex that contains a bis­(aryl) phosphine ligand, whose metalation determines its unusual coordination in a κ⁴-<i>P</i>,<i>C</i>,<i>C′</i>,<i>C″</i> fashion. The complex (<b>1</b>^<b>+</b> in this paper) undergoes very facile intramolecular C–H bond activation of all benzylic sites, in all likelihood through an Ir­(V) hydride intermediate. But most importantly, it transforms into a hydride phosphepine species <b>4</b>^<b>+</b> by means of an also facile, base-catalyzed, intramolecular dehydrogenative C–C coupling reaction. Mechanistic studies demonstrate the participation as a key intermediate of an electrophilic cationic Ir­(III) alkylidene, which has been characterized by low-temperature NMR spectroscopy and by isolation of its trimethylphosphonium ylide. DFT calculations provide theoretical support for these results

Cationic Ir(III) Alkylidenes Are Key Intermediates in C–H Bond Activation and C–C Bond-Forming Reactions

This work describes the chemical reactivity of a cationic (η⁵-C₅Me₅)­Ir­(III) complex that contains a bis­(aryl) phosphine ligand, whose metalation determines its unusual coordination in a κ⁴-<i>P</i>,<i>C</i>,<i>C′</i>,<i>C″</i> fashion. The complex (<b>1</b>^<b>+</b> in this paper) undergoes very facile intramolecular C–H bond activation of all benzylic sites, in all likelihood through an Ir­(V) hydride intermediate. But most importantly, it transforms into a hydride phosphepine species <b>4</b>^<b>+</b> by means of an also facile, base-catalyzed, intramolecular dehydrogenative C–C coupling reaction. Mechanistic studies demonstrate the participation as a key intermediate of an electrophilic cationic Ir­(III) alkylidene, which has been characterized by low-temperature NMR spectroscopy and by isolation of its trimethylphosphonium ylide. DFT calculations provide theoretical support for these results