We establish the first super-logarithmic lower bound for the number of conjugacy classes of a finite nilpotent group. In particular, for any constant c there are only finitely many finite p-groups of order pm with at most c ·m conjugacy classes. This answers a question of L. Pyber.

In this paper, we propose a new height function for a variety defined over a finitely generated field overQ. For this height function, we will prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (Manin-Mumford’s conjecture). CONTENTS Introduction 1 1. Arakelov intersection theory 3 2. Arithmetically positive hermitian line bundles 6 3. Ari...

We show that the isoperimetric function of a nitely generated nilpotent group of class c is bounded above by a polynomial of degree 2c.

Then it follows that mvm = m. Our main goal is to find an analogue of the Möbius transform on MV-algebras [4]. To this end, replace the boolean algebra 2X with a semisimple MV-algebra MX . There is no loss of generality in assuming that X is a compact Hausdorff space and MX is a separating MV-algebra of continuous functions over X. Since every Möbius transform mv corresponds to some finitely-ad...

Parallel implementation of complex computational software is a difficult task. This paper describes the Super Instruction Architecture (SIA) and its application to the implementation of algorithms for electronic structure computational chemistry calculations. The methods are programmed in a domain specific programming language called super instruction assembly language (SIAL), which is based on...

Despite the recent development of several super-resolution fluorescence microscopic techniques, there are still few techniques that can be readily employed in conventional imaging systems. We present a very simple, rapid, general and cost-efficient super-resolution imaging method, which can be directly employed in a simple fluorescent imaging system with general fluorophores. Based on diffusion...

We extend some of the classical connections between automata and logic due to Büchi (1960) [5] and McNaughton and Papert (1971) [12] to languages of finitely varying functions or ‘‘signals’’. In particular, we introduce a natural class of automata for generating finitely varying functions called ST-NFA’s, and show that it coincides in terms of language definability with a natural monadic second...

We extend some of the classical connections between automata and logic due to Büchi [1] and McNaughton and Papert [2], to languages of finitely varying functions or “signals”. In particular we introduce a natural class of automata for generating finitely varying functions called ST-NFA’s, and show that it coincides in terms of language-definability with a natural monadic second-order logic inte...