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Basic concepts of the theory of geometric objects

ContentsIntroduction............................................................................................................................................................................... 3§ 1. Historical development of the concept of a geometric object..................................................................................4§ 2. Manifold, coordinate system, transformations of the coordinate system............................................................. 7§ 3. Group, pseudogroup,...

Nomographic functions

Warmus M. — 1959

CONTENTS Introduction.............................................................................3 I. Linear dependence and independence of functions............7 II. Bank of a function.............................................................15 III. Nomographic functions ....................................................34 IV. Two fundamental theorems..............................................45 V. Scheme...

On the Schröder equation

M. Kuczma — 1963

CONTENTSPART IIntroduction............................................................................................... 31. General solution.................................................................................. 42. Preliminaries and notation................................................................ 53. C p solutions in *................................................ 74. Change of variables........................................................................... 135. Continuous...

The automorphism groups and endomorphism rings of torsion-free abelian groups of rank two

M. Król — 1967

CONTENTS§ 1. Introduction.......................................................................................................................................... 5§ 2. Definitions and lemmas................................................................................................................... 7§ 3. Theorem on the isomorphism of subdirect sums with the same kernels............................. 15§ 4. The group of automorphisms of a torsion-free abelian group of rank two................................

Relations impartibles

M. Pouzet — 1981

TABLE DES MATIÈRESIntroduction.................................................................................................................................................................................................... 5I. Relation impartible.................................................................................................................................................................................... 6 I-1. Définition.......................................................................................................................................................................................

Cosine operator functions

M. Sova — 1966

CONTENTS0. Introduction............................................................................................................... 31. Preliminaries............................................................................................................ 32. Cosine operator functions..................................................................................... 63. Generation of cosine operator functions............................................................ 234. Cosine operator...

Toric varieties in phylogenetics

M. Michałek — 2015

The paper contains a revised, and extended by new results, part of the author's PhD thesis. The main objects that we study are toric varieties naturally associated to special Markov processes on trees. Such Markov processes can be defined by a tree T and a group G. They are called group-based models. The main, but not unique, motivation to consider these processes comes from phylogenetics. We study the geometry, defining equations and combinatorial description of the associated toric varieties....

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