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Start Over Publication Year Range More than 50 years ago Publisher birkhauser
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3. A Geometrical Isoperimetric Inequality and Applications to Problems of Mathematical Physics

Author

Catherine Bandle

Subjects
Surface (mathematics), Kantorovich inequality, symbols.namesake, General Mathematics, Mathematical analysis, symbols, Symmetrization, Poincaré inequality, Boundary (topology), Isoperimetric inequality, Curvature, Mathematics, Geodesic curvature
Abstract

The classical isoperimetric inequality states that among all closed curves of given circumference the circle encloses the largest area. This inequality has been considerably generalized by A. D. Alexandrow. He derived [1] inequalities for the case where the curve lies on an abstract surface, and obtained lower bounds for the length of the curve in terms of the area of the domain and an expression involving the curvature of the surface. In this paper we consider a curve Fo on an abstract surface whose endpoints lie on a curve F 1. With the help of Alexandrow's inequality we construct lower bounds for the length of Fo. These bounds depend on the area of the domain between Fo and F1, the curvature of the surface and the geodesic curvature of F~. By use of the geometrical inequalities we derive a monotony property of the Green's function. The geometrical inequalities lead also to an estimate for the fundamental frequency of an inhomogeneous membrane with partially free boundary. The result extends the Rayleigh-Faber-Krahn inequality [12] and its generalizations obtained by Nehari [11] and the author [2, 3, 6]. At the end we indicate how to generalize the concept of Schwarz symmetrization [12] for functions which do not vanish at the whole boundary. This symmetrization combines in a certain way the ones defined in [2] and [3]. The principal results of this paper have already been announced in [4].

Published
1974
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4. Homological Methods in Group Varieties

Author

Urs Stammbach

Subjects
Surjective function, Exact sequence, Pure mathematics, Functor, General Mathematics, Group homomorphism, Homology (mathematics), Abelian group, Mathematical proof, Mathematics
Abstract

In papers by Stallings [9] and the author [10], [11] the homology theory of groups has been applied to central series, and meaningful group theoretical results have been obtained. In the present paper we show how similar homological methods can be used to obtain interesting results in arbitrary varieties of groups. It is not surprising that the methods are most successful if applied to problems involving central series. It is the nature of a paper introducing new methods to repeat many well known results. However the approach presented here leads to an interestingly unifying point of view. Also, it is possible to simplify the proofs of many well known results. Given a variety ~ , we first define a functor S o from ~ to abelian groups. This functor is defined in terms of the integral second homology group functor H 2 ( , Z). We then prove that a surjective group homomorphism G ~ Q in ~ , with kernel N, gives rise to an exact sequence

Published
1970
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5. Free Cyclic Actions on Manifolds

Author

Timothy Lance

Subjects
Combinatorics, Covering space, General Mathematics, Lens space, Equivariant map, Cyclic group, Intersection form, Homomorphism, Homology (mathematics), Manifold, Mathematics
Abstract

This paper presents a geometric description and partial classification of smooth or PL oriented closed ( n 1 ) connected 2n manifolds M, n>~3, which support free actions of the cyclic group Zp= Z/pZ (where p ~> 3 is prime) with preferred generator TM and orbit manifold M/Zp. If L (n) is an n-dimensional lens space (or the n-skeleton of the usual CW decomposition of L(n +1) if n = 2k) with nl(L(n))= Zp, universal cover E (n), and fixed generator T r of the induced Zp action on E (n), we define a standard model to be a 2n dimensional smooth or PL thickening N/Zp of L(n) with generator Tn of the Zp action on N corresponding to Tr. Given an equivariant isomorphismf : (dN, TN)~ (dN, TN) (i.e.fTN=TNf, so there is an induced isomorphism f/Zp of ~N/Zp) and a closed ( n 1) connected 2n manifold K, the universal cover of (N/Zp [.Jl/zp)#K (written (NUIN)#zpK) is such a manifold M. The underlying idea of this work is that most of the manifolds M can be obtained in this way. A standard model N/Z~ is untwisted if the homology intersection form on Hn(N) is identically zero, and it is simple if in addition N~-S~x D ~ (not necessarily equivariantly) when n = 2 k + l . The homomorphism (Tu). makes H~(M) a A=ZZp module, and Wall ([35], w defines a A valued intersection form 2 on Hn(M). We say that M has hyperbolic rank >~d if the 2 form orthogonaUy splits off d hyperbolic planes (see 2.9).

Published
1975
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6. Trees of Homotopy Types of Two-Dimensional CW-Complexes

Author

Allan J. Sieradski and Micheal N. Dyer

Subjects
Homotopy group, Pure mathematics, n-connected, Homotopy sphere, Homotopy category, General Mathematics, Homotopy, Whitehead theorem, Cofibration, Regular homotopy, Mathematics
Abstract

This paper is concerned with the homotopy theory and simple homotopy theory of connected finite 2 dimensional CW complexes with finite cyclic fundamental group. The main theorem presents a complete classification of such complexes up to homotopy type, and this theorem has the corollary that homotopy type and simple homotopy type coincide for these complexes. This work is motivated by the general problem of describing the sets HT(n) and SHT(n) of homotopy types and simple homotopy types of n-complexes, that is, connected finite 2 dimensional CW-complexes with a given fundamental group n. A visually satisfying description of HT (n) or SHT (n) is that of either set as a graph whose edges connect the type of each n-complex X to the type of its sum X v S 2 with the 2-sphere S 2. These graphs are actually trees; they clearly contain no circuits, and they are connected because any two n-complexes have the same type once each is summed with an appropriate number of copies of the 2-sphere S 2. To re establish this latter observation ofJ. H. C. Whitehead ([20, Theorem 12]), note that each n-complex has the simple homotopy type of one modeled in an obvious fashion on some finite presentation of the fundamental group ~z (see Proposition 1). But two finite presentations of the same group n differ by a finite sequence of Tietze operations, two of which leave the simple homotopy type of the associated topological model unchanged, while two alter the simple homotopy type by an S 2 summand. Of special interest in each of these trees are the roots and the junctions. The roots are the (simple) homotopy types that do not admit a factorization involving an S 2 summand; they generate the rest of the types in the tree under the operation of forming sum with S 2. The junctions are the (simple) homotopy types that admit two or more inequivalent factorizations involving an S 2 summand; they determine the shape of the tree. Each junction is a 2-dimensional instance of non-cancellation of the 2-sphere S 2 with respect to the sum operation. When the group n is a free group F of finite rank or is the finite cyclic group Z~ of prime order q, complete descriptions of the trees HT (n) and SHT (n) can be derived from the literature, as follows. A result of C. T. C. Wall ([17, Proposition 3.3]) can be specialized to read that for a free group F of finite rank r every F-complex has the homotopy type of a sum of r

Published
1973
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7. The Central Connection Problem at Turning Points of Linear Differential Equations

Author

Wolfgang Wasow

Subjects
Matrix (mathematics), Pure mathematics, Linear differential equation, Simple (abstract algebra), General Mathematics, Diagonal, Mathematical analysis, Holomorphic function, Point (geometry), Connection (algebraic framework), Eigenvalues and eigenvectors, Mathematics
Abstract

A system of linear differential equations of the vectorial form edy/dx=A (x, e) y is considered, where e is a positive parameter, and the matrixA (x, e) is holomorphic in |x|⩽x 0, 0 < e ⩽ e0 , with an asymptotic expansionsA (x, e) ∼ ∑ =0 ∞ A r (x) e r , as e→0. The eigenvalues ofA 0(x) are supposed to coalesce atx=0 so as to make this point a simple turning point. With the help of refinements of the representations for the inner and outer asymptotic solutions, as e→0, that were introduced in the articles [9] and [10] by the author (see the references at the end of the paper), explicit connection formulas between these solutions are calculated. As part of this derivation it is shown that only the diagonal entries of the connection matrix are asymptotically relevant.

Published
1971
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8. Architekturpsychologie

Author

David V. Canter and David V. Canter

Abstract

Editorship Elisabeth Blum, Jesko Fezer, Günther Fischer, Angelika Schnell Not unjustly referred to as legendary, this series of books on the history and theory of architecture and urban development was founded in 1963 by Ulrich Conrads, who was joined by Peter Neitzke as a co-editor of the series in the early 1980s. Now numbering over 150 titles, it is the most comprehensive German-language book series covering these fields. Following the deaths of the two longtime editors Ulrich Conrads (2013) and Peter Neitzke (2015), a new editorial committee was formed to continue their work: Elisabeth Blum, Jesko Fezer, Günther Fischer and Angelika Schnell. As the future editors of this series, it is our aim to maintain the course set by our forerunners. The series has fulfilled its original aim of taking stock of the constructional and urban planning ideas and realizations formulated and achieved over the twentieth century in exemplary fashion. The Bauwelt Fundament series actually represents a history of ideas in the fields of planning and building that extends from the beginning of the twentieth century into the present. The second objective of the series, one that is anchored in its very name, will also continue to guide the development of the series, namely the publication of foundational thought – authoritative and fundamental – rather than passing opinion, of theses and polemics relating to the burning architectural and urban planning themes of the time. Penetrating complex interrelationships and probing them with systematic analysis provides the prerequisite for fruitful discourse and ongoing debate. As a forum for such discourses and contributions, the Bauwelt Fundamente series is maintaining its focus on the areas of architecture and urbanism, supplementing it with the always necessary historical　investigation of important questions and texts and its extension into other cultural and social fields. A strong international orientation and the desire for more female authors are self-evident in such a context. The original graphic design approach taken by Helmut Lortz to the series is being maintained. As is fitting for a working library, Bauwelt Fundamente titles remain simply designed, using black and white for the logo, the images on the front and back, and the eleven-line summary of the volume's contents. This is indicative of the broad orientation of Bauwelt Fundamente to all those interested in the cultural and social development that provides the context for the creation of cities, houses and other objects, which in turn create contexts for the world.'Architects, it is said – or hoped – have always been interested in the world beyond the boundaries of their profession.'(1) (1) Peter Neitzke, manuscript of his address Nicht mit dem Rücken zur Gesellschaft (Not with one's back to society) given to mark the fiftieth anniversary of Bauwelt Fundamente in Berlin, 2013.

Published
1972

9. Materialien zur Ökonomie der Stadtplanung

Author

Jörn Barnbrock and Jörn Barnbrock

Subjects
Urban economics, City planning
Abstract

Editorship Elisabeth Blum, Jesko Fezer, Günther Fischer, Angelika Schnell Not unjustly referred to as legendary, this series of books on the history and theory of architecture and urban development was founded in 1963 by Ulrich Conrads, who was joined by Peter Neitzke as a co-editor of the series in the early 1980s. Now numbering over 150 titles, it is the most comprehensive German-language book series covering these fields. Following the deaths of the two longtime editors Ulrich Conrads (2013) and Peter Neitzke (2015), a new editorial committee was formed to continue their work: Elisabeth Blum, Jesko Fezer, Günther Fischer and Angelika Schnell. As the future editors of this series, it is our aim to maintain the course set by our forerunners. The series has fulfilled its original aim of taking stock of the constructional and urban planning ideas and realizations formulated and achieved over the twentieth century in exemplary fashion. The Bauwelt Fundament series actually represents a history of ideas in the fields of planning and building that extends from the beginning of the twentieth century into the present. The second objective of the series, one that is anchored in its very name, will also continue to guide the development of the series, namely the publication of foundational thought – authoritative and fundamental – rather than passing opinion, of theses and polemics relating to the burning architectural and urban planning themes of the time. Penetrating complex interrelationships and probing them with systematic analysis provides the prerequisite for fruitful discourse and ongoing debate. As a forum for such discourses and contributions, the Bauwelt Fundamente series is maintaining its focus on the areas of architecture and urbanism, supplementing it with the always necessary historical　investigation of important questions and texts and its extension into other cultural and social fields. A strong international orientation and the desire for more female authors are self-evident in such a context. The original graphic design approach taken by Helmut Lortz to the series is being maintained. As is fitting for a working library, Bauwelt Fundamente titles remain simply designed, using black and white for the logo, the images on the front and back, and the eleven-line summary of the volume's contents. This is indicative of the broad orientation of Bauwelt Fundamente to all those interested in the cultural and social development that provides the context for the creation of cities, houses and other objects, which in turn create contexts for the world.'Architects, it is said – or hoped – have always been interested in the world beyond the boundaries of their profession.'(1) (1) Peter Neitzke, manuscript of his address Nicht mit dem Rücken zur Gesellschaft (Not with one's back to society) given to mark the fiftieth anniversary of Bauwelt Fundamente in Berlin, 2013.

Published
1975

10. Gesellschaftsplanung in kapitalistischen und sozialistischen Systemen

Author

Josef Esser, Frieder Naschold, Werner Väth, Josef Esser, Frieder Naschold, and Werner Väth

Subjects
Economic policy, Social policy, Marxian economics
Abstract

Editorship Elisabeth Blum, Jesko Fezer, Günther Fischer, Angelika Schnell Not unjustly referred to as legendary, this series of books on the history and theory of architecture and urban development was founded in 1963 by Ulrich Conrads, who was joined by Peter Neitzke as a co-editor of the series in the early 1980s. Now numbering over 150 titles, it is the most comprehensive German-language book series covering these fields. Following the deaths of the two longtime editors Ulrich Conrads (2013) and Peter Neitzke (2015), a new editorial committee was formed to continue their work: Elisabeth Blum, Jesko Fezer, Günther Fischer and Angelika Schnell. As the future editors of this series, it is our aim to maintain the course set by our forerunners. The series has fulfilled its original aim of taking stock of the constructional and urban planning ideas and realizations formulated and achieved over the twentieth century in exemplary fashion. The Bauwelt Fundament series actually represents a history of ideas in the fields of planning and building that extends from the beginning of the twentieth century into the present. The second objective of the series, one that is anchored in its very name, will also continue to guide the development of the series, namely the publication of foundational thought – authoritative and fundamental – rather than passing opinion, of theses and polemics relating to the burning architectural and urban planning themes of the time. Penetrating complex interrelationships and probing them with systematic analysis provides the prerequisite for fruitful discourse and ongoing debate. As a forum for such discourses and contributions, the Bauwelt Fundamente series is maintaining its focus on the areas of architecture and urbanism, supplementing it with the always necessary historical　investigation of important questions and texts and its extension into other cultural and social fields. A strong international orientation and the desire for more female authors are self-evident in such a context. The original graphic design approach taken by Helmut Lortz to the series is being maintained. As is fitting for a working library, Bauwelt Fundamente titles remain simply designed, using black and white for the logo, the images on the front and back, and the eleven-line summary of the volume's contents. This is indicative of the broad orientation of Bauwelt Fundamente to all those interested in the cultural and social development that provides the context for the creation of cities, houses and other objects, which in turn create contexts for the world.'Architects, it is said – or hoped – have always been interested in the world beyond the boundaries of their profession.'(1) (1) Peter Neitzke, manuscript of his address Nicht mit dem Rücken zur Gesellschaft (Not with one's back to society) given to mark the fiftieth anniversary of Bauwelt Fundamente in Berlin, 2013.

Published
1972

11. Verhalten in sozialen Situationen

Author

Erving Goffmann and Erving Goffmann

Subjects
Public spaces--Psychological aspects, Social interaction, Interpersonal relations, Social groups
Abstract

Editorship Elisabeth Blum, Jesko Fezer, Günther Fischer, Angelika Schnell Not unjustly referred to as legendary, this series of books on the history and theory of architecture and urban development was founded in 1963 by Ulrich Conrads, who was joined by Peter Neitzke as a co-editor of the series in the early 1980s. Now numbering over 150 titles, it is the most comprehensive German-language book series covering these fields. Following the deaths of the two longtime editors Ulrich Conrads (2013) and Peter Neitzke (2015), a new editorial committee was formed to continue their work: Elisabeth Blum, Jesko Fezer, Günther Fischer and Angelika Schnell. As the future editors of this series, it is our aim to maintain the course set by our forerunners. The series has fulfilled its original aim of taking stock of the constructional and urban planning ideas and realizations formulated and achieved over the twentieth century in exemplary fashion. The Bauwelt Fundament series actually represents a history of ideas in the fields of planning and building that extends from the beginning of the twentieth century into the present. The second objective of the series, one that is anchored in its very name, will also continue to guide the development of the series, namely the publication of foundational thought – authoritative and fundamental – rather than passing opinion, of theses and polemics relating to the burning architectural and urban planning themes of the time. Penetrating complex interrelationships and probing them with systematic analysis provides the prerequisite for fruitful discourse and ongoing debate. As a forum for such discourses and contributions, the Bauwelt Fundamente series is maintaining its focus on the areas of architecture and urbanism, supplementing it with the always necessary historical　investigation of important questions and texts and its extension into other cultural and social fields. A strong international orientation and the desire for more female authors are self-evident in such a context. The original graphic design approach taken by Helmut Lortz to the series is being maintained. As is fitting for a working library, Bauwelt Fundamente titles remain simply designed, using black and white for the logo, the images on the front and back, and the eleven-line summary of the volume's contents. This is indicative of the broad orientation of Bauwelt Fundamente to all those interested in the cultural and social development that provides the context for the creation of cities, houses and other objects, which in turn create contexts for the world.'Architects, it is said – or hoped – have always been interested in the world beyond the boundaries of their profession.'(1) (1) Peter Neitzke, manuscript of his address Nicht mit dem Rücken zur Gesellschaft (Not with one's back to society) given to mark the fiftieth anniversary of Bauwelt Fundamente in Berlin, 2013.

Published
1971

12. Großstadt-Politik. : Texte zur Analyse und Kritik lokaler Demokratie

Author

Rolf-Richard Grauhan and Rolf-Richard Grauhan

Subjects
Municipal government
Abstract

Editorship Elisabeth Blum, Jesko Fezer, Günther Fischer, Angelika Schnell Not unjustly referred to as legendary, this series of books on the history and theory of architecture and urban development was founded in 1963 by Ulrich Conrads, who was joined by Peter Neitzke as a co-editor of the series in the early 1980s. Now numbering over 150 titles, it is the most comprehensive German-language book series covering these fields. Following the deaths of the two longtime editors Ulrich Conrads (2013) and Peter Neitzke (2015), a new editorial committee was formed to continue their work: Elisabeth Blum, Jesko Fezer, Günther Fischer and Angelika Schnell. As the future editors of this series, it is our aim to maintain the course set by our forerunners. The series has fulfilled its original aim of taking stock of the constructional and urban planning ideas and realizations formulated and achieved over the twentieth century in exemplary fashion. The Bauwelt Fundament series actually represents a history of ideas in the fields of planning and building that extends from the beginning of the twentieth century into the present. The second objective of the series, one that is anchored in its very name, will also continue to guide the development of the series, namely the publication of foundational thought – authoritative and fundamental – rather than passing opinion, of theses and polemics relating to the burning architectural and urban planning themes of the time. Penetrating complex interrelationships and probing them with systematic analysis provides the prerequisite for fruitful discourse and ongoing debate. As a forum for such discourses and contributions, the Bauwelt Fundamente series is maintaining its focus on the areas of architecture and urbanism, supplementing it with the always necessary historical　investigation of important questions and texts and its extension into other cultural and social fields. A strong international orientation and the desire for more female authors are self-evident in such a context. The original graphic design approach taken by Helmut Lortz to the series is being maintained. As is fitting for a working library, Bauwelt Fundamente titles remain simply designed, using black and white for the logo, the images on the front and back, and the eleven-line summary of the volume's contents. This is indicative of the broad orientation of Bauwelt Fundamente to all those interested in the cultural and social development that provides the context for the creation of cities, houses and other objects, which in turn create contexts for the world.'Architects, it is said – or hoped – have always been interested in the world beyond the boundaries of their profession.'(1) (1) Peter Neitzke, manuscript of his address Nicht mit dem Rücken zur Gesellschaft (Not with one's back to society) given to mark the fiftieth anniversary of Bauwelt Fundamente in Berlin, 2013.

Published
1972