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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....

Symmetric function spaces on atomless probability spaces

CONTENTSIntroduction....................................................................................................................................51. Sequences of elements in separable Banach spaces...............................................................82. Maharam's theorem.................................................................................................................163. Symmetric function spaces......................................................................................................214....

The homology of tensor products

M. W. Warner — 1969

CONTENTS1. Introduction............................................................................................................................... 52. Definitions and preliminaries............................................................................................... 73. Main Theorem......................................................................................................................... 104. The groups D, D’, ∆ and ∆’.....................................................................................................

Existence and regularity of solutions of some elliptic system in domains with edges

CONTENTS1. Introduction.......................................................................52. Notation and auxiliary results............................................93. Statement of the problem (1.1)-(1.3)..............................204. The problem (3.14).........................................................225. Auxiliary results in D ϑ ...............................................346. Existence of solutions of (3.14) in H μ k ( D ϑ ) ............417. Green function................................................................528....

Stationary subsets, stabilizers and transitive representations of semigroups

B. M. Schein — 1970

CONTENTS0. Introduction........................................................................................................ 51. Main definitions......................................................................................................... 62. Characterizations of stabilizers and stationary subsets................................... 93. Transitive representations..................................................................................... 244. Symmetric representations and...

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