This book presents models written as partial differential equations and originating from various questions in population biology, such as physiologically structured equations, adaptive dynamics, and bacterial movement. Its purpose is to derive appropriate mathematical tools and qualitative properties of the solutions. The book further contains many original PDE problems originating in biosciences.
This book presents models written as partial differential equations and originating from various questions in population biology, such as physiolog...
A functional identity (FI) can be informally described as an identical relation involving(arbitrary)elementsinaringtogetherwith( unknown )functions;more precisely, elementsaremultipliedbyvaluesoffunctions.ThegoalofthegeneralFI theory is to determine the form of these functions, or, when this is not possible, to determine the structure of the ring admitting the FI in question. This theory has turnedouttobeapowerfultoolfor solvingavarietyofproblemsindi?erentareas. It is not always easy to recognize that the problem in question can be interpreted through some FI; often this is the most...
A functional identity (FI) can be informally described as an identical relation involving(arbitrary)elementsinaringtogetherwith( unknown )functions;mo...
A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the Desarguesian plane of order 2. It is also equivalent to a flock of a quadratic cone, and hence to a line-spread of 3-dimensional projective space and thus to a translation plane, and more. These geometric objects are tied together by the so-called Fundamental Theorem of q-Clan Geometry. The book gives a complete proof of this theorem, followed by a detailed study of the known examples. The collineation groups of the associated generalized...
A q-clan with q a power of 2 is equivalent to a certain generalized quadrangle with a family of subquadrangles each associated with an oval in the ...
The aim of the present book is a uni?ed representation of some recent results in geometric function theory together with a consideration of their historical sources. These results are concerned with functions f, holomorphic or meromorphic in a domain ? in the extended complex planeC. The only additional condition we impose on these functions is the condition that the range f(?) is contained in a given domain C.Thisfactwillbedenotedby f? A(?, ?). We shall describe (n) how one may get estimates for the derivatives-f (z )-, n?N, f ? A(?, ?), 0 dependent on the position of z in ? and f(z)in?. 0 0...
The aim of the present book is a uni?ed representation of some recent results in geometric function theory together with a consideration of their hist...
The characterization of combinatorial or geometric structures in terms of their groups of automorphisms has attracted considerable interest in the last decades and is now commonly viewed as a natural generalization of Felix Klein s Erlangen program(1872).Inaddition, especiallyfor?nitestructures, importantapplications to practical topics such as design theory, coding theory and cryptography have made the ?eld even more attractive. The subject matter of this research monograph is the study and class- cation of ?ag-transitive Steiner designs, that is, combinatorial t-(v, k,1) designs which admit...
The characterization of combinatorial or geometric structures in terms of their groups of automorphisms has attracted considerable interest in the las...
Problems linking the shape of a domain or the coefficients of an elliptic operator to the sequence of its eigenvalues are among the most fascinating of mathematical analysis. In this book, we focus on extremal problems. For instance, we look for a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. We also consider the case of functions of eigenvalues. We investigate similar questions for other elliptic operators, such as the Schrodinger operator, non homogeneous membranes, or the bi-Laplacian,...
Problems linking the shape of a domain or the coefficients of an elliptic operator to the sequence of its eigenvalues are among the most fascinatin...
In this book we are concerned with the study of a certain class of in?nite matrices and two important properties of them: their Fredholmness and the stability of the approximation by their ?nite truncations. Let us take these two properties as a starting point for the big picture that shall be presented in what follows. Stability Fredholmness We think of our in?nite matrices as bounded linear operators on a Banach space E of two-sided in?nite sequences. Probably the simplest case to start with 2 +? is the space E = of all complex-valued sequences u=(u ) for which m m= 2 -u - is summable over...
In this book we are concerned with the study of a certain class of in?nite matrices and two important properties of them: their Fredholmness and the s...
If H is a Hilbert space and T: H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e., M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails...
If H is a Hilbert space and T: H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ...
Thegoalofthisbookistoinvestigatethebehaviourofweaksolutionstotheelliptic transmisssion problem in a neighborhood of boundary singularities: angular and conic points or edges. We consider this problem both for linear and quasi-linear (very little studied) equations. In style and methods of research, this book is close to our monograph 14] together with Prof. V. Kondratiev. The book consists of an Introduction, seven chapters, a Bibliography and Indexes. Chapter 1 is of auxiliary character. We recall the basic de?nitions and properties of Sobolev spaces and weighted Sobolev-Kondratiev spaces....
Thegoalofthisbookistoinvestigatethebehaviourofweaksolutionstotheelliptic transmisssion problem in a neighborhood of boundary singularities: angular an...
Here is a comprehensive exposition of the key results and ideas connected to the Poncelet theorem, focusing on the mathematics and including the dynamics of integrable billiards and the algebraic geometry of hyperelliptic Jacobians, among other material.
Here is a comprehensive exposition of the key results and ideas connected to the Poncelet theorem, focusing on the mathematics and including the dy...
