nils-herrmann/clean_scirepeval huggingface dataset:
Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields

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: 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: Singularities of smooth mappings with additional structures : collected papers
A mathematical trivium
Topological problems of the theory of wave propagation V I Arnold International Conference on Differential Equations and Related Questions In honour of the 90th anniversary of the birth of Academician I.G. Petrovskii (1901-1973), Rector of Moscow State University from 1951 to 1973 (14th joint session of the Petrovskii Seminar and the Moscow Mathematical Society, 29 May-3 June 1991) O A Oleinik Some unsolved problems in the theory of differential equations and mathematical physics Vladimir I Arnol'd, M I Vishik, Yu S Il'yashenko et al. Dulac's memoir “On limit cycles” and related problems of the local theory of differential equations Yu S Il'yashenko Aleksandr Adol'fovich Bukhshtab (obituary) I P Kubilis, V I Nechaev, A B Shidlovskii et al. The geometry of spherical curves and the algebra of quaternions Vladimir I Arnol'd A mathematical trivium

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
The Vassiliev Theory of Discriminants and Knots
The study of the discriminant variety in a functional space of smooth mappings is a traditional and fundamental part of the theory of singularities. The discriminant variety is the set of those points of the functional space which represent the mappings having nongeneric singularities. The topological, homotopical and even homological invariants of the complement to the discriminant variety (that is, of the space of generic mappings) are important for many applications. However, progress in these difficult global problems of singularity theory was rather slow until Vassiliev  over the last few years has demonstrated the new perspectives opened up by the singularity theory approach in knot theory.

title: Spaces of functions with moderate singularities

title: Wave front evolution and equivariant Morse lemma

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: 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
Wave front evolution and equivariant Morse lemma

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: 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: Some remarks on symplectic monodromy of Milnor fibrations
abstract: There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions. One of the manifestations of these relations is the Wahl-Neumann theorem, according to which the Euler characteristics of the Floer homology of the boundary of a Milnor fiber of a quasi-homogeneous function of 3 variables is proportional to the signature of the Milnor fiber, provided that the boundary is a homological 3-sphere .

title: Spaces of functions with moderate singularities

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

title: A PROBABILITY PROBLEM OF OPTIMAL CONTROL

title: Topological content of the Maxwell theorem on multiple representation of spherical functions
abstract: Theorem 1. The nth derivative of the function 1/r along n constant (translation-invariant) vector fields in R coincides on the sphere with a spherical function of degree n. Any nonzero spherical function of degree n can be obtained by this construction from some n-tuple of nonzero vector fields. These n fields are uniquely defined by the function (up to multiplication by nonzero constants and permutation of the n fields).
Dynamics of Intersections
Publisher Summary This chapter explains the dynamics of intersections. A smooth mapping A: M → M is considered of a compact manifold M into itself and two compact smooth submanifolds X and Y of M. This chapter presents the study of the intersections of the images of one of the submanifolds transformed by the iterates of A with the other submanifold. The main result states that the measure of this intersection grows generically more slowly than some exponent |Zn| ≤ cean. In the most important case, in which the dimensions of X and Y are complementary, the inequality is an exponential estimate of the number of intersection points.

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: 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: Spaces of functions with moderate singularities

title: Wave front evolution and equivariant Morse lemma

title: Singularities of smooth mappings with additional structures : collected papers
On some problems in singularity theory

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: 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: Wave front evolution and equivariant Morse lemma

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

title: Singularities of smooth mappings with additional structures : collected papers
Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques
Resume On etudie la structure des relations de comportement d'un milieu elastique-plastique ou elastique-viscoplastique en transformation finie. On montre que les discontinuites qui sont a l'origine de la deformation plastique se traduisent par l'influence de vecteurs directeurs caches, qu'on fait intervenir par le moyen de: 1. 1. Variables internes dans la definition de l'etat; 2. 2. Un triedre directeur dans la definition de l'orientation. La transformation thermoelastique-viscoplastique est decomposee en introduisant une configuration intermediare relâchee. Un fait important est que, sauf dans le cas d'isotropie dans les configurations relâchees, les relations de comportement doivent faire intervenir non seulement la vitesse de deformation (et les variables internes) mais encore la vitesse de rotation du triedre directeur par rapport a l'element de matiere.

title: Ondes de choc longitudinales dans un milieu elastoplastique

title: Plasticité classique et viscoplasticité

title: The Analysis of Two‐Way Tables with Missing Values
abstract: A method is given for calculating missing values in a two-way table that conforms to a row linear model. Verification of conformance to the model and analysis of the data are explained with an example of real data.

title: The Distribution of Eigenvalues of Covariance Matrices of Residuals in Analysis of Variance
abstract: A rigorous definition is given for the concept of an interaction matrix (Z* lij*s) where i=1 to m and j=1 to n, in terms of two idempotent matrices A*lr*s and B*ls*s of rank r and s, respectively. It is then shown that the frequency distribution of the eigenvalues of (Z)(Z)' depends only on r and s. Applications are given to matrices of residuals arising from two-way data, either by removing row and/or column-means, or by applying any number of sweeps of the vacuum cleaner. The theorems are important in the theory of the analysis of two-way tables of nonadditive data.
Ondes de choc longitudinales dans un milieu elastoplastique

title: Plasticité classique et viscoplasticité

title: The Analysis of Two‐Way Tables with Missing Values
abstract: A method is given for calculating missing values in a two-way table that conforms to a row linear model. Verification of conformance to the model and analysis of the data are explained with an example of real data.

title: The Distribution of Eigenvalues of Covariance Matrices of Residuals in Analysis of Variance
abstract: A rigorous definition is given for the concept of an interaction matrix (Z* lij*s) where i=1 to m and j=1 to n, in terms of two idempotent matrices A*lr*s and B*ls*s of rank r and s, respectively. It is then shown that the frequency distribution of the eigenvalues of (Z)(Z)' depends only on r and s. Applications are given to matrices of residuals arising from two-way data, either by removing row and/or column-means, or by applying any number of sweeps of the vacuum cleaner. The theorems are important in the theory of the analysis of two-way tables of nonadditive data.
Alternative proofs of a theorem of Moyls and Marcus on the numerical range of a square matrix
Moyls and Marcus  showed that for n⩽4,n×n an complex matrix A is normal if and only if the numerical range of A is the convex hull of the eigenvalues of A. When n⩾5, there exist matrices which are not normal, but such that the numerical range is still the convex hull of the eigenvalues. Two alternative proofs of this fact are given. One proof uses the known structure of the numerical range of a 2×2 matrix. The other relies on a theorem of Motzkin and Taussky stating that a pair of Hermitian matrices with property L must commute.

title: Simultaneous block triangularization and block diagonalization of sets of matrices
abstract: We consider the problem of simultaneously putting a set of square matrices into the same block upper triangular form with a similarity transformation, and obtain a result linking the size of the largest block to polynomial identities. This is used to yield a new proof of a theorem of Watters [20] which gives a necessary and sufficient condition for a set of matrices to be simultaneously, unitarily similar to block diagonal matrices with blocks of sizes one or two.

title: INTEGRATION OVER HILBERT SPACE AND OUTER EXTENSIONS.

title: A counterexample in harmonic analysis

title: SOME REMARKS ON WEIGHTED POLYNOMIAL APPROXIMATIONS OF HOLOMORPHIC FUNCTIONS
abstract: Production of oxidation resistant, thermal shock resistant and high strength composites, produced by hot pressing at high temperatures, e.g., about 2,100 DEG C, a mixture preferably of a boride such as hafnium diboride, a silicide such as tungsten disilicide, and a minor portion of discrete carbon particles such as graphite, e.g., a mixture of 66 percent hafnium diboride, 20 percent tungsten disilicide and 14 percent graphite fibers, by weight, against a high temperature resistant substrate, e.g., a metal such as tantalum, to form an integral bonded composite coating on said substrate.

title: The modulus of continuity of an analytic function
SOME REMARKS ON WEIGHTED POLYNOMIAL APPROXIMATIONS OF HOLOMORPHIC FUNCTIONS
Production of oxidation resistant, thermal shock resistant and high strength composites, produced by hot pressing at high temperatures, e.g., about 2,100 DEG C, a mixture preferably of a boride such as hafnium diboride, a silicide such as tungsten disilicide, and a minor portion of discrete carbon particles such as graphite, e.g., a mixture of 66 percent hafnium diboride, 20 percent tungsten disilicide and 14 percent graphite fibers, by weight, against a high temperature resistant substrate, e.g., a metal such as tantalum, to form an integral bonded composite coating on said substrate.

title: INTEGRATION OVER HILBERT SPACE AND OUTER EXTENSIONS.

title: Simultaneous block triangularization and block diagonalization of sets of matrices
abstract: We consider the problem of simultaneously putting a set of square matrices into the same block upper triangular form with a similarity transformation, and obtain a result linking the size of the largest block to polynomial identities. This is used to yield a new proof of a theorem of Watters [20] which gives a necessary and sufficient condition for a set of matrices to be simultaneously, unitarily similar to block diagonal matrices with blocks of sizes one or two.

title: The modulus of continuity of an analytic function

title: A counterexample in harmonic analysis
The modulus of continuity of an analytic function

title: A counterexample in harmonic analysis

title: INTEGRATION OVER HILBERT SPACE AND OUTER EXTENSIONS.

title: Simultaneous block triangularization and block diagonalization of sets of matrices
abstract: We consider the problem of simultaneously putting a set of square matrices into the same block upper triangular form with a similarity transformation, and obtain a result linking the size of the largest block to polynomial identities. This is used to yield a new proof of a theorem of Watters [20] which gives a necessary and sufficient condition for a set of matrices to be simultaneously, unitarily similar to block diagonal matrices with blocks of sizes one or two.