
 Title: Ball Structures and Colorings of Graphs and Groups 
Authors: I. Protasov, T. Banakh 
ISBN: 9667148998 
Price: 35.00 USD 
The ball structures of different kinds arise naturally in the asymptotic topology, geometric group theory and combinatorics. The book is devoted to systematic investigation of purely combinatorical aspects of ball structures of graphs with accent on their applications to partitions of groups and graphs. A lot of new author’s results are included. An exposition is supplied with a chain of exercises and open problems.

 

 Title: General Asymptology 
Authors: Ihor Protasov, Michael Zarichnyi 
ISBN: 9668849329 
Price: 50.00 USD 
The present monograph is devoted mostly to general properties of the ball structures, which simultaneously generalize the coarse structures introduced in the large scale geometry by J. Roe as well as the uniform structures. Chapter 1 contains the definition of the ball structures (baleans), provides their different examples and briefly discusses their connections with coarse structures. The topological coarse structures are also considered. The different morphisms of balleans and coarse spaces are defined and some categories of balleans and coarse structures are introduced. Chapter 2 is devoted to relations between the ball structures and metric structures, important morphisms between metric spaces. Chapter 3 concerns the property of cellularity of balleans and contains the notion of asymptotic dimension of balleans in the spirit of Gromov. It turns out that cellularity can be described in terms of asymptotic dimension zero, which makes it close to the nonArchimedean (ultrametric) spaces. Chapter 4 is devoted to the property of normality. In Chapters 5 and 6 the graph balleans and the group balleans are investigated. In Chapter 7 the functions on balleans which are slowly oscillating with respect to given filter are studied. The counterpart of the Higson corona in the context of balleans is investigated in Chapter 8. Some cardinal invariants of balleans are introduced and discussed in Chapter 9. The concluding Chapter 10 is devoted to the notion of maximality of balleans. Bibliography: 86 items.

 

 Title: Ultrafilters and Topologies on Groups 
Authors: Mahmoud Filali, Igor V. Protasov 
ISBN: 9667148140 
Price: 75.00 USD 
The book is devoted to the studying of ultrafilters in topological algebra. The main object of investigations is the StoneCech compactification betaG of a topological group G. The set betaG is a right topological semigroup and the continuity of the operation involving the left translation is extensively studied in the book. The richness of algebraic structure, makes the semigroup betaG very useful and with plenty of applications in combinatorics as well as in functional analysis, in particular, to the left convolution algebras. In the book, the algebra in the StoneCech compactification is used to construct and study topologies on groups.

 

 Title: Limit Theorems and Transient Phenomena in the Theory of Branching Processes 
Authors: Soltan Aliev, Yaroslav I. Yeleyko, Iryna B. Bazylevych 
ISBN: 9667148191 
Price: 75.00 USD 
In this monograph, there are presented two directions of the theory of branching processes, namely, the processes with arbitrary numbers types of particles and processes with continuous state space.
The monograph consists of eight chapters. The first one contains a short historical information about branching processes and concise review of literature. The second one is devoted to the basic definition and statements of theorems. The third chapter contains the results of an article by M. Jirina “General branching process with continuous time parameter''.
Further, there are presented the results of Ya. Yeleyko, the limit theorems for processes with arbitrary numbers of particles. The fifth chapter follows the fundamental article of M. Jirina “Stochastic branching processes with continuous state space” as well as Yu. Ryshov and A. Skorohod “Homogeneous branching processes with finite number types of particles and continuously changing mass”'. The final chapters include theorems on convergence of sequences of GaltonWatson processes to a process with continuous state space.

 

 Title: Asymptotical Behaviour of LaplaceStiltjes Integrals 
Authors: Myroslav Sheremeta 
ISBN: 9667148221 
Price: 75.00 USD 
The monograph is devoted to investigation of asymptotic properties of positive functions represented by the LaplaceStiltjes integrals. Important role of such integrals is wellknown in mathematical and complex analysis, probability theory, number theory and in other regions of mathematics. Since the LaplaceStieltjes integrals are direct generalization of the Laplace integral and the Dirichlet series with nonnegative coefficients and exponents, the investigation of the asymptotic properties of the LaplaceStieltjes integrals is necessary and actual. The book is intended for graduate mathematical students, postgraduates and experts in the mathematical analysis and its applications. The necessary mathematical background for reading the monograph is a university course of calculus.

 






