nils-herrmann/clean_scirepeval huggingface dataset:
Zappa products

title: Bilateral semidirect products of transformation semigroups

title: Existence of Solutions for Degenerate Sweeping Processes
abstract: cf. e.g. , and also [11]. In this formulation, every E(x) ⊂ IR is a closed convex set (sometimes called the ”rigidity set”), t ≥ 0 denotes the process time, x ∈ Ω ⊂ IR is the material point, q ∈ IR an internal variable (like plastic strain or hardening), and W denotes a (modified) stored energy function. For our purpose of motivation, the main thing to note is that for every fixed x, the inclusion (2) is of type (1).

title: Yosida–Moreau Regularization of Sweeping Processes with Unbounded Variation
abstract: Lett↦C(t) be a Hausdorff-continuous multifunction with closed convex values in a Hilbert spaceHsuch thatC(t) has nonempty interior for allt. We show that the Yosida–Moreau regularizations of the sweeping process with moving setC(t), i.e., the solutions of[formula]are strongly pointwisely convergent asλ→0+to the solution of the corresponding sweeping process, formally written as[formula]
Yosida–Moreau Regularization of Sweeping Processes with Unbounded Variation
Lett↦C(t) be a Hausdorff-continuous multifunction with closed convex values in a Hilbert spaceHsuch thatC(t) has nonempty interior for allt. We show that the Yosida–Moreau regularizations of the sweeping process with moving setC(t), i.e., the solutions of[formula]are strongly pointwisely convergent asλ→0+to the solution of the corresponding sweeping process, formally written as[formula]

title: Unbounded Solutions in Non-Smooth Dynamical Systems at Resonance
abstract: We consider periodically forced non-smooth dynamical systems at resonance, described by differential inclusions, and we show that analogously to the case of ODEs all solutions are unbounded in the (x)-phase plane, if the first Fourier coefficient of the forcing is large compared to a certain quantity related to the nonlinearity.

title: Bilateral semidirect products of transformation semigroups
A note on generalizations of strict diagonal dominance for real matrices
We investigate classes of real square matrices possessing some weakened from of strict diagonal dominance of a real matrix whose diagonal entries are all positive. The intersection of each one of these classes with the set of all real matrices, with nonpositive off-diagonal elements, coincides with the set of all nonsingular M - matrices.

title: On bounds for the convergence of the SSOR method for H-matrices
abstract: In  G. Alefeld and R S. Varga show that if A is an H-matrix, then where and JA are, respectively, the SSOR and the Jacobi iteration matrices associated with A. We investigate the possibility for[M0001] when Ais an H-matrix and show that unless does not hold. Comparison is made with the sharpness of a similar bound on the ω's for which the SOR iteration matrix associated with A converges.

title: A maximality theorem concerning extreme points

title: Beschränktheitsaussagen für sublineare und bisublineare Funktionale

title: On the Strassen disintegration theorem
On the transformation group for diabolic magic squares of order four
A superposed wafer is separated to a processing target wafer and a supporting wafer while being heated. Then, an adhesive on a joint surface of the processing target wafer is removed by supplying an organic solvent onto the joint surface of the processing target wafer. Then, an oxide film formed on the predetermined pattern on the joint surface of the processing target wafer is removed by supplying acetic acid to the joint surface of the processing target wafer. Then, the joint surface of the processing target wafer is inspected. Then, based on an inspection result, the adhesive on the joint surface of the processing target wafer is removed and the oxide film formed on the predetermined pattern on the joint surface of the processing target wafer is removed.

title: The algebraic theory of diabolic magic squares

title: Almost periodic factorization of block triangular matrix functions revisited
abstract: Let G be an n×n almost periodic ( AP ) matrix function defined on the real line R . By the AP factorization of G we understand its representation in the form G = G + ΛG − , where G + ±1 ( G − ±1 ) is an AP matrix function with all Fourier exponents of its entries being non-negative (respectively, non-positive) and Λ ( x )=diag[e i λ 1 x ,…,e i λ n x ], λ 1 ,…,λ n ∈ R . This factorization plays an important role in the consideration of systems of convolution type equations on unions of intervals. In particular, systems of m equations on one interval of length λ lead to AP factorization of matrices (0.1) G(x)= e i λx I m 0 f(x) e − i λx I m . We develop a factorization techniques for matrices of the form (0.1) under various additional conditions on the off-diagonal block f . The cases covered include f with the Fourier spectrum Ω(f) lying on a grid ( Ω(f)⊂−ν+h Z ) and the trinomial f (( Ω(f)={−ν,μ,α} ) with − ν μ α , α +| μ |+ ν ⩾ λ .
Evolution equations with a free boundary condition
In this paper we consider the heat flow of harmonic maps between two compact Riemannian Manifolds M and N (without boundary) with a free boundary condition. That is, the following initial boundary value problem ∂1,u −Δu = Γ(u)(∇u, ∇u) [tT TuuN, on M × [0, ∞), u(t, x) ∈ Σ, for x ∈ ∂M, t > 0, ∂u/t6n(t, x) ⊥u Tu(t,x) Σ, for x ∈ ∂M, t > 0, u(o,x) = uo(x), on M, where Σ is a smooth submanifold without boundary in N and n is a unit normal vector field of M along ∂M.Due to the higher nonlinearity of the boundary condition, the estimate near the boundary poses considerable difficulties, even for the case N = ℝn, in which the nonlinear equation reduces to ∂tu-Δu = 0.We proved the local existence and the uniqueness of the regular solution by a localized reflection method and the Leray-Schauder fixed point theorem. We then established the energy monotonicity formula and small energy regularity theorem for the regular solutions. These facts are used in this paper to construct various examples to show that the regular solutions may develop singularities in a finite time. A general blow-up theorem is also proven. Moreover, various a priori estimates are discussed to obtain a lower bound of the blow-up time. We also proved a global existence theorem of regular solutions under some geometrical conditions on N and Σ which are weaker than KN <-0 and Σ is totally geodesic in N.

title: Partial regularity for weak heat flows into spheres
abstract: In this paper we show that a weak heat flow of harmonic maps from a compact Riemannian manifold (possibly with boundary) into a sphere, satisfying the monotonicity inequality and the energy inequality, is regular off a closed set of m-dimensional Hausdorff measure zero.

title: Global Classical Solutions for Nonlinear Evolution Equations
abstract: This text represents the results originally obtained by S. Lainerman, D. Christodoulou, Y. Choquet-Bruhat, T. Nishida and A. Matsumara on the global existence of classical solutions to the Cauchy problem with small initial data for nonlinear evolution equations.

title: On the Vibration of Beams or Rods Carrying a Concentrated Mass

title: Der Satz von Miquel in der Möbiusebene

title: On existence theorems of periodic traveling wave solution to the generalized forced Kadomtsev-Petviashvili equation
abstract: T uts PAPER is concerned with periodic travcling wave solutions of the generalized forced KadomtsevPetviashvili equation in the form ( u 1 + If( tt)lx + o u x.rx )"' + {3uyy = ho. The basic approach to this problem is to establish an equivalence relat ionship between a periodic boundary value problem and nonlinear integral equations wirh symrnerric kernels by using the Green's function method. The integral representations generate compact operators in a Banach space of real-valued continuous periodic functions with a given period 2T. Schauder's fixed point theorem is then used to prove the existence of no nconstant periodic traveling wave solutions.
Global Classical Solutions for Nonlinear Evolution Equations
This text represents the results originally obtained by S. Lainerman, D. Christodoulou, Y. Choquet-Bruhat, T. Nishida and A. Matsumara on the global existence of classical solutions to the Cauchy problem with small initial data for nonlinear evolution equations.

title: Partial regularity for weak heat flows into spheres
abstract: In this paper we show that a weak heat flow of harmonic maps from a compact Riemannian manifold (possibly with boundary) into a sphere, satisfying the monotonicity inequality and the energy inequality, is regular off a closed set of m-dimensional Hausdorff measure zero.

title: On the Vibration of Beams or Rods Carrying a Concentrated Mass

title: Der Satz von Miquel in der Möbiusebene

title: On existence theorems of periodic traveling wave solution to the generalized forced Kadomtsev-Petviashvili equation
abstract: T uts PAPER is concerned with periodic travcling wave solutions of the generalized forced KadomtsevPetviashvili equation in the form ( u 1 + If( tt)lx + o u x.rx )"' + {3uyy = ho. The basic approach to this problem is to establish an equivalence relat ionship between a periodic boundary value problem and nonlinear integral equations wirh symrnerric kernels by using the Green's function method. The integral representations generate compact operators in a Banach space of real-valued continuous periodic functions with a given period 2T. Schauder's fixed point theorem is then used to prove the existence of no nconstant periodic traveling wave solutions.
Hyperbolic polynomials and Vandermonde mappings

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

title: Wave front evolution and equivariant Morse lemma

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: 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
Instability of dynamical systems with several degrees of freedom

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

title: Singularities of smooth mappings with additional structures : collected papers
Algebraic unsolvability of the problem of lyapunov stability and the problem of topological classification of singular points of an analytic system of differential equations

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

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: Wave front evolution and equivariant Morse lemma

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: Singularities of smooth mappings with additional structures : collected papers
Dynamics of complexity of intersections
The topological complexity of the intersection of a submanifold, moved by a dynamical system, with a given submanifold of the phase space, can increase with time. It is proved that the Morse and Betti numbers of the transversal intersections “generically” grow at most exponentially, while for some special infinitely smooth systems the topological complexity of the intersections can become larger than any given function of time (for a growing sequence of integer time moments).

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: 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: Singularities of smooth mappings with additional structures : collected papers
REMARKS ON THE STATIONARY PHASE METHOD AND COXETER NUMBERS
We study integrals of rapidly oscillating functions. Such integrals tend to zero when the length of the oscillation wave tends to zero through wave fronts of constant form. The asymptotic decrease of the integral is determined by the character of the critical points of the function describing the front. If all of these critical points are non-degenerate (Morse), then the integral tends to zero like the wave length raised to the power of half the dimension of the space, and indeed this is the asymptotic behaviour of the integral for functions in general position.However, if the integral depends on additional parameters, then for certain caustic parameter values there arise non-Morse critical points and the integral decreases slowly. The investigation of the asymptotic behaviour of the integral of an oscillating function in caustic cases can be regarded as a generalization of the theory of Airy functions; it is closely connected with Artin's braid theory, and the answer in the case of few parameters is expressed in terms of the Coxeter numbers of the Weyl groups of the series A, D, E, and in the case of many parameters it is expressed in terms of generalizations of them.

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
ON MATRICES DEPENDING ON PARAMETERS
1. Классические результаты (Аполлоний, Декарт, Ньютон, Харнак). Шестнадцатая проблема Гильберта.

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

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: Spaces of functions with moderate singularities

title: Singularities of smooth mappings with additional structures : collected papers
CONGRUENCES FOR EULER, BERNOULLI, AND SPRINGER NUMBERS OF COXETER GROUPS
The classical and generalized Euler numbers, reduced with respect to an odd modulus, are represented as sums of exponentials. From this representation there follow congruences modulo powers of an odd prime p between elements of the Euler-Bernoulli triangles and the values of certain polynomials in two variables on sublattices with step p–1.

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: 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