nils-herrmann/clean_scirepeval huggingface dataset:
Weak asymptotics for the numbers of solutions of diophantine problems

title: Singularities, bifurcations, and catastrophes
abstract: The first information on catastrophe theory appeared in the western press in the late sixties. In magazines like “News-week” there were reports of a revolution in mathematics, comparable perhaps to Newton’s invention of the differential and integral calculus. It was claimed that the new science, catastrophe theory, was much more valuable to mankind than mathematical analysis: while Newtonian theory only considers smooth, continuous processes, catastrophe theory provides a universal method for the study of all jump transitions, discontinuities, and sudden qualitative changes. There appeared hundreds of scientific and popular science publications in which catastrophe theory was applied to such diverse targets as, for instance, the study of heart beat, geometrical and physical optics, embryology, linguistics, experimental psychology, economics, hydrodynamics, geology, and the theory of elementary particles. Among the published works on catastrophe theory are studies of the stability of ships, models for the activity of the brain and mental disorders, for prison uprisings, for the behaviour of investors on the stock exchange, for the influence of alcohol on drivers and for censorship policy with respect to erotic literature.

title: Wave front evolution and equivariant Morse lemma

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Spaces of functions with moderate singularities

title: Topologically Necessary Singularities on Moving Wavefronts and Caustics
abstract: In his posthumous Vorlesungen Uber Dynamik Jacobi claimed that the caustic (formed by the conjugate points of a given initial point along all the geodesics) on the surface of an ellipsoid has four cusps.

title: Singularities of smooth mappings with additional structures : collected papers
Distribution of ovals of the real plane of algebraic curves, of involutions of four-dimensional smooth manifolds, and the arithmetic of integer-valued quadratic forms

title: Wave front evolution and equivariant Morse lemma

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Spaces of functions with moderate singularities

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: Singularities of smooth mappings with additional structures : collected papers
Sur la topologie des écoulements stationnaires des fluides parfaits
On considere les ecoulements stationnaires d’un fluide parfait, incompressible et non visqueux, dans un domaine borne D. On suppose que le vecteur vitesse n’est pas partout colineaire au vecteur rotation. On demontre alors que le domaine D est divise, par certaines surfaces et courbes, en un nombre fini de « cellules » ouvertes, fibrees en tores ou en cylindres engendres par des lignes de courant. Les lignes de courant sont fermees sur les cylindres, fermees ou denses sur les tores.

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Wave front evolution and equivariant Morse lemma

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Spaces of functions with moderate singularities

title: Singularities of smooth mappings with additional structures : collected papers
On the interior scattering of waves, defined by hyperbolic variational principles
The Transformation of waves of different kinds at some interior points of nonhomogeneous media is studied for waves defined by linear hyperbolic variational systems. A formal normal form is given for the light hypersurface (i.e. for the dispersion relation) at its generic singular points in terms of the contact geometry. This normal form describes the behaviour of the rays and of the wavefronts at the singular points corresponding to the multiple eigenvalues of the principal symbol of a generic hyperbolic variational problem.

title: Spaces of functions with moderate singularities

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Wave front evolution and equivariant Morse lemma

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Singularities of smooth mappings with additional structures : collected papers
Topological Problems of the Theory of Asymptotic Curves
An asymptotic curve on a surface in a three-dimensional Euclidean or projective space is an integral curve of a vector field of asymptotic directions (directions along which the second fundamental form vanishes {reviewer: this means that asymptotic directions are a projective phenomenon, not a metric one}). We prove that the (generic) asymptotic curves on hyperbolic surfaces are precisely the (generic) space curves without flattening points. These curves can also be defined as those curves that are smooth and have smooth dual curves (called rotational curves). Rotational curves have inflection points.

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Spaces of functions with moderate singularities

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: Wave front evolution and equivariant Morse lemma

title: Singularities of smooth mappings with additional structures : collected papers
Integrals of rapidly oscillating functions and singularities of projections of Lagrangian manifolds

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Spaces of functions with moderate singularities

title: Wave front evolution and equivariant Morse lemma

title: Singularities of smooth mappings with additional structures : collected papers
Spectral sequence for reduction of functions to normal form

title: Spaces of functions with moderate singularities

title: Wave front evolution and equivariant Morse lemma

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: Singularities of smooth mappings with additional structures : collected papers
Remark on the branching of hyperelliptic integrals as functions of the parameters

title: Wave front evolution and equivariant Morse lemma

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Spaces of functions with moderate singularities

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: Singularities of smooth mappings with additional structures : collected papers
Remarks on quasicrystallic symmetries
Quasicrystallic symmetries are encountered not only in experimental crystallography, but also in some mathematical theories related to quite different physical situations — in the study of singularities of optical ray symmetries, in the Sinai construction of Markov partitions of the ergodic theory of dynamical systems, in computer experiments with iterations of mappings of the plane and in the statistical study of the topology of the level lines of quasiperiodic Hamiltonian functions. In this article, I shall explain some of these relations between such seemingly unrelated topics.

title: Wave front evolution and equivariant Morse lemma

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Spaces of functions with moderate singularities

title: Singularities of smooth mappings with additional structures : collected papers
Galina Nikolaevna Tyurina (obituary)

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Spaces of functions with moderate singularities

title: Wave front evolution and equivariant Morse lemma

title: Singularities of smooth mappings with additional structures : collected papers
A correction to: Wave front evolution and equivariant morse lemma

title: The Theory of Singularities and its Applications
abstract: Part I. The Zoo of Singularities: 1. Morse theory of functions 2. Whitney theory of mappings 3. The Whitney-Cayley umbrella 4. The swallowtail 5. The discriminants of the reflection groups 6. The icosahedron and the obstacle by-passing problem 7. The unfurled swallowtail 8. The folded and open umbrellas 9. The singularities of projections and of the apparent contours Part II. Singularities of Bifurcation Diagrams: 10. Bifurcation diagrams of families of functions 11. Stability boundary 12. Ellipticity boundary and minima functions 13. Hyperbolicity boundary 14. Disconjugate equations, Tchebyshev system boundaries and Schubert singularities in flag manifolds 15. Fundamental system boundaries, projective curve flattenings and Schubert singularities in Grassmann manifolds.

title: Spaces of functions with moderate singularities

title: Weak asymptotics for the numbers of solutions of diophantine problems

title: Wave front evolution and equivariant Morse lemma

title: Poisson structures on the plane and other powers of volume forms
abstract: The hierarchy of formsf(dx1∧...∧dxn)α (α fixed) starts with the series A, D, and E. Their singular hypersurfaces admit quasihomogéneous polynomials g as representatives. The dimension of the space of moduli of forms with fixed g is calculated; it is equal to the number of monomials h, for which g(hx)α has weight zero. For Poisson structures on the plane (α=−1, n=2) this dimension is one less than the number of irreducible components of the curve g=0, i.e., is equal to the number h1,0 of mixed Hodge structures.

title: Singularities of smooth mappings with additional structures : collected papers