nils-herrmann/clean_scirepeval huggingface dataset:
The computational complexity of the parallel knock-out problem
We consider computational complexity questions related to parallel knock-out schemes for graphs. In such schemes, in each round, each remaining vertex of a given graph eliminates exactly one of its neighbours. We show that the problem of whether, for a given bipartite graph, such a scheme can be found that eliminates every vertex is NP-complete. Moreover, we show that, for all fixed positive integers k>=2, the problem of whether a given bipartite graph admits a scheme in which all vertices are eliminated in at most (exactly) k rounds is NP-complete. For graphs with bounded tree-width, however, both of these problems are shown to be solvable in polynomial time. We also show that r-regular graphs with r>=1, factor-critical graphs and 1-tough graphs admit a scheme in which all vertices are eliminated in one round.

title: Amalgamations of connected k-factorizations
abstract: In this paper, necessary and sufficient conditions are found for a graph with exactly one amalgamated vertex to be the amalgamation of a k-factorization of Kkn+1 in which each k factor is connected. From this result, necessary and sufficient conditions for a given edge-coloured Kt to be embedded in a connected k-factorization of Kkn+1 are deduced.

title: The Computational Complexity of the Parallel Knock-Out Problem
abstract: We consider computational complexity questions related to parallel knock-out schemes for graphs. In such schemes, in each round, each remaining vertex of a given graph eliminates exactly one of its neighbours. We show that the problem of whether, for a given graph, such a scheme can be found that eliminates every vertex is NP-complete. Moreover, we show that, for all fixed positive integers k ≥ 2, the problem of whether a given graph admits a scheme in which all vertices are eliminated in at most k rounds is NP-complete. For graphs with bounded tree-width, however, both of these problems are shown to be solvable in polynomial time.

title: Characterization of graphs with hall number 2
abstract: Hall’s condition is a simple condition that a graph G and list assignment L must satisfy if G has a proper L-colouring. The Hall number of G is the smallest integer m such that whenever each list has size m and Hall’s condition is satisfied a proper L-colouring exists. Hilton and P.D. Johnson introduced the parameter and showed that a graph has Hall number 1 if and only if every block is a clique. In this paper we characterize graphs with Hall number 2. ∗Current address: London School of Economics, Houghton Street, London WC2A 2AE, U.K.
Using metaballs to modeling and animate clouds from satellite images
1 Hiroshima City University, Faculty of Information Sciences, 3-4-1 Ozukahigashi, Asaminami-ku, Hiroshima, 731-3194, Japan E-mail: {doba, okita}@im.hiroshima-cu.ac.jp 2 The University of Tokyo, Department of Information Science, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan E-mail: nis@is.s.u-tokyo.ac.jp 3 Hiroshima University, Faculty of Engineering, 1-4-1 Kagamiyama, Higashi-Hiroshima, 739-8527, Japan E-mail: yama@eml.hiroshima-u.ac.jp

title: A simple, efficient method for realistic animation of clouds
abstract: This paper proposes a simple and computationally inexpensive method for animation of clouds. The cloud evolution is simulated using cellular automaton that simplifies the dynamics of cloud formation. The dynamics are expressed by several simple transition rules and their complex motion can be simulated with a small amount of computation. Realistic images are then created using one of the standard graphics APIs, OpenGL. This makes it possible to utilize graphics hardware, resulting in fast image generation. The proposed method can realize the realistic motion of clouds, shadows cast on the ground, and shafts of light through clouds.

title: Modeling of clouds from satellite images using metaballs
abstract: The paper proposes an image based modeling of clouds where realistic clouds are created from satellite images using metaballs. The intention of the paper is for applications to space flight simulators, the visualization of the weather information, and the simulation of surveys of the Earth. In the proposed method, the density distribution inside the clouds is defined by a set of metaballs. Parameters of metaballs, such as center positions, radii, and density values, are automatically determined so that a synthesized image of clouds modeled by using metaballs is similar to the original satellite image. We also propose an animation method for clouds generated by a sequence of satellite images taken at some interval. The usefulness of the proposed method is demonstrated by several examples of clouds generated from satellite images of typhoons passing through Japan.

title: Load Balance Protocol of Cluster on Grid: Pervasive Maximum Algorithmic Parallelism
Modeling of clouds from satellite images using metaballs
The paper proposes an image based modeling of clouds where realistic clouds are created from satellite images using metaballs. The intention of the paper is for applications to space flight simulators, the visualization of the weather information, and the simulation of surveys of the Earth. In the proposed method, the density distribution inside the clouds is defined by a set of metaballs. Parameters of metaballs, such as center positions, radii, and density values, are automatically determined so that a synthesized image of clouds modeled by using metaballs is similar to the original satellite image. We also propose an animation method for clouds generated by a sequence of satellite images taken at some interval. The usefulness of the proposed method is demonstrated by several examples of clouds generated from satellite images of typhoons passing through Japan.

title: A simple, efficient method for realistic animation of clouds
abstract: This paper proposes a simple and computationally inexpensive method for animation of clouds. The cloud evolution is simulated using cellular automaton that simplifies the dynamics of cloud formation. The dynamics are expressed by several simple transition rules and their complex motion can be simulated with a small amount of computation. Realistic images are then created using one of the standard graphics APIs, OpenGL. This makes it possible to utilize graphics hardware, resulting in fast image generation. The proposed method can realize the realistic motion of clouds, shadows cast on the ground, and shafts of light through clouds.

title: Load Balance Protocol of Cluster on Grid: Pervasive Maximum Algorithmic Parallelism
On conjugacy of homomorphisms of topological groups II

title: On faithful representations of the holomorph of Lie groups
abstract: Let G be a Lie group and let Aut(G) denote the group of all automorphisms of the Lie group G, endowed with its natural structure of a Lie group. The natural semidirect product G >~ Aut(G) is called the holomorph of G. In , Hochschild has shown that if the nilradical (that is, the maximum nilpotent analytic normal subgroup) N of a real or complex analytic group G is simply connected, then the holomorph of G is faithfully representable. Moreover, one of the authors in  has given an intrinsic characterization of those complex analytic groups whose holomorph is faithfully representable. In this paper, we are interested in determining when the holomorph of a Lie group G is faithfully representable (that is, admits a faithful finite-dimensional continuous representation). Our first result (Theorem 1) answers this question when G is an f.c.c. Lie group. Also in this work, we extend the result of  to real analytic groups (Theorem 2). Our method is entirely different from that of [4] and may be adapted to cover the complex case as well. We would like to thank the referee for making valuable suggestions for improvements of this paper.

title: A Note on the all Nearest-Neighbor Problem for Convex Polygons
On parabolic quasi-variational inequalities and state-dependent sweeping processes
(1.2) C(t, u) ⊂ H is nonempty, closed, and convex for t ∈ [0, T ], u ∈ H. In (1.1), NC(t,u)(x) denotes the normal cone to C(t, u) at x ∈ C(t, u), cf. Section 2 below. We will treat the case of (t, u) 7→ C(t, u) being Lipschitz continuous w.r. to the Hausdorff distance dH with constants L1, L2 ≥ 0, i.e., we require (1.3) dH(C(t, u), C(s, v)) ≤ L1|t− s|+ L2|u− v|, t, s ∈ [0, T ], u, v ∈ H. Note that a solution of (1.1) in particular has to satisfy u(t) ∈ C(t, u(t)) for t ∈ [0, T ].

title: ON THE DISCRETIZATION OF DEGENERATE SWEEPING PROCESSES
abstract: We prove existence theorems for evolution equations of the form −u(t) ∈ ∂δC(t)(Au(t)) with some maximal monotone and strongly monotone operator A : D(A)→ 2 . 1 – Introduction and main results We study the evolution problem (1) −u(t) ∈ ∂δC(t)(Au(t)) a.e. in [0, T ], u(0) = u0 ∈ D(A) , where A is a maximal monotone and strongly monotone operator in the real Hilbert space H, and t 7→ C(t) is a Hausdorff-continuous multifunction with closed convex values. Equations of this form arise from problems of the type −x(t) ∈ ∂δC(g(t, x(t))), which play an important rôle in elasticity theory, cf. [8, 3, 4] for more information. To solve (1) means that we have to find u ∈W 1,1([0, T ];H) and v ∈ L2([0, T ];H) such that u(0) = u0, u(t)∈D(A) a.e., v(t)∈Au(t)∩C(t) a.e. and −u′(t)∈∂δC(t)(v(t)) a.e. in [0, T ] . Our general assumptions are (H1) A:D(A)→2H\{∅} is a maximal monotone operator (abbreviated mmop) such that A = ∂ψ for some lsc, convex and proper ψ : H → R ∪ {∞}, and there exists a β > 0 such that (2) 〈Ax−Ay, x− y〉 ≥ β |x− y| for x, y ∈ D(A) .  December 31, 1996;  April 4, 1997.  (1991): 34A60, 35K22.

title: BV Solutions to Evolution Problems with Time-Dependent Domains
abstract: In a Hilbert space H we consider evolution problems -du(t) ε A(t)u(t) on some interval [0, T], where every A(t): D(A(t))→ 2 H is a maximal monotone operator, and the correspondence t↦ A(t) is – in a suitable sense – of bounded variation or absolutely continuous.

title: On the Uniqueness and Asymptotic Behaviour of Plasma Corners

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: 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]

title: Bilateral semidirect products of transformation semigroups

title: Zappa products
On the Uniqueness and Asymptotic Behaviour of Plasma Corners

title: BV Solutions to Evolution Problems with Time-Dependent Domains
abstract: In a Hilbert space H we consider evolution problems -du(t) ε A(t)u(t) on some interval [0, T], where every A(t): D(A(t))→ 2 H is a maximal monotone operator, and the correspondence t↦ A(t) is – in a suitable sense – of bounded variation or absolutely continuous.

title: ON THE DISCRETIZATION OF DEGENERATE SWEEPING PROCESSES
abstract: We prove existence theorems for evolution equations of the form −u(t) ∈ ∂δC(t)(Au(t)) with some maximal monotone and strongly monotone operator A : D(A)→ 2 . 1 – Introduction and main results We study the evolution problem (1) −u(t) ∈ ∂δC(t)(Au(t)) a.e. in [0, T ], u(0) = u0 ∈ D(A) , where A is a maximal monotone and strongly monotone operator in the real Hilbert space H, and t 7→ C(t) is a Hausdorff-continuous multifunction with closed convex values. Equations of this form arise from problems of the type −x(t) ∈ ∂δC(g(t, x(t))), which play an important rôle in elasticity theory, cf. [8, 3, 4] for more information. To solve (1) means that we have to find u ∈W 1,1([0, T ];H) and v ∈ L2([0, T ];H) such that u(0) = u0, u(t)∈D(A) a.e., v(t)∈Au(t)∩C(t) a.e. and −u′(t)∈∂δC(t)(v(t)) a.e. in [0, T ] . Our general assumptions are (H1) A:D(A)→2H\{∅} is a maximal monotone operator (abbreviated mmop) such that A = ∂ψ for some lsc, convex and proper ψ : H → R ∪ {∞}, and there exists a β > 0 such that (2) 〈Ax−Ay, x− y〉 ≥ β |x− y| for x, y ∈ D(A) .  December 31, 1996;  April 4, 1997.  (1991): 34A60, 35K22.

title: Periodic Solutions of Conservative Non‐Smooth Dynamical Systems
abstract: We consider conservative non-smooth dynamical systems of the type ẍ+e+a sgn(x) = p(t) with an w-periodic forcing p, and we first prove the existence of periodic solutions in the non-resonant case for the corresponding differential inclusion. Moreover, in the resonant case w = 2π, we gave necessary and sufficient conditions on a and the first Fourier coefficient of p for periodic solutions to exist.

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]

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: Zappa products

title: Bilateral semidirect products of transformation semigroups
ON THE DISCRETIZATION OF DEGENERATE SWEEPING PROCESSES
We prove existence theorems for evolution equations of the form −u(t) ∈ ∂δC(t)(Au(t)) with some maximal monotone and strongly monotone operator A : D(A)→ 2 . 1 – Introduction and main results We study the evolution problem (1) −u(t) ∈ ∂δC(t)(Au(t)) a.e. in [0, T ], u(0) = u0 ∈ D(A) , where A is a maximal monotone and strongly monotone operator in the real Hilbert space H, and t 7→ C(t) is a Hausdorff-continuous multifunction with closed convex values. Equations of this form arise from problems of the type −x(t) ∈ ∂δC(g(t, x(t))), which play an important rôle in elasticity theory, cf. [8, 3, 4] for more information. To solve (1) means that we have to find u ∈W 1,1([0, T ];H) and v ∈ L2([0, T ];H) such that u(0) = u0, u(t)∈D(A) a.e., v(t)∈Au(t)∩C(t) a.e. and −u′(t)∈∂δC(t)(v(t)) a.e. in [0, T ] . Our general assumptions are (H1) A:D(A)→2H\{∅} is a maximal monotone operator (abbreviated mmop) such that A = ∂ψ for some lsc, convex and proper ψ : H → R ∪ {∞}, and there exists a β > 0 such that (2) 〈Ax−Ay, x− y〉 ≥ β |x− y| for x, y ∈ D(A) .  December 31, 1996;  April 4, 1997.  (1991): 34A60, 35K22.

title: BV Solutions to Evolution Problems with Time-Dependent Domains
abstract: In a Hilbert space H we consider evolution problems -du(t) ε A(t)u(t) on some interval [0, T], where every A(t): D(A(t))→ 2 H is a maximal monotone operator, and the correspondence t↦ A(t) is – in a suitable sense – of bounded variation or absolutely continuous.

title: Periodic Solutions of Conservative Non‐Smooth Dynamical Systems
abstract: We consider conservative non-smooth dynamical systems of the type ẍ+e+a sgn(x) = p(t) with an w-periodic forcing p, and we first prove the existence of periodic solutions in the non-resonant case for the corresponding differential inclusion. Moreover, in the resonant case w = 2π, we gave necessary and sufficient conditions on a and the first Fourier coefficient of p for periodic solutions to exist.

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: A Note on A Paper of Cellina Concerning Differential Equations in Banach Spaces

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]

title: Bilateral semidirect products of transformation semigroups

title: Zappa products
Periodic Solutions of Conservative Non‐Smooth Dynamical Systems
We consider conservative non-smooth dynamical systems of the type ẍ+e+a sgn(x) = p(t) with an w-periodic forcing p, and we first prove the existence of periodic solutions in the non-resonant case for the corresponding differential inclusion. Moreover, in the resonant case w = 2π, we gave necessary and sufficient conditions on a and the first Fourier coefficient of p for periodic solutions to exist.

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]

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: BV Solutions to Evolution Problems with Time-Dependent Domains
abstract: In a Hilbert space H we consider evolution problems -du(t) ε A(t)u(t) on some interval [0, T], where every A(t): D(A(t))→ 2 H is a maximal monotone operator, and the correspondence t↦ A(t) is – in a suitable sense – of bounded variation or absolutely continuous.

title: On parabolic quasi-variational inequalities and state-dependent sweeping processes
abstract: (1.2) C(t, u) ⊂ H is nonempty, closed, and convex for t ∈ [0, T ], u ∈ H. In (1.1), NC(t,u)(x) denotes the normal cone to C(t, u) at x ∈ C(t, u), cf. Section 2 below. We will treat the case of (t, u) 7→ C(t, u) being Lipschitz continuous w.r. to the Hausdorff distance dH with constants L1, L2 ≥ 0, i.e., we require (1.3) dH(C(t, u), C(s, v)) ≤ L1|t− s|+ L2|u− v|, t, s ∈ [0, T ], u, v ∈ H. Note that a solution of (1.1) in particular has to satisfy u(t) ∈ C(t, u(t)) for t ∈ [0, T ].

title: A Note on A Paper of Cellina Concerning Differential Equations in Banach Spaces

title: Zappa products

title: Bilateral semidirect products of transformation semigroups
A Note on A Paper of Cellina Concerning Differential Equations in Banach Spaces

title: BV Solutions to Evolution Problems with Time-Dependent Domains
abstract: In a Hilbert space H we consider evolution problems -du(t) ε A(t)u(t) on some interval [0, T], where every A(t): D(A(t))→ 2 H is a maximal monotone operator, and the correspondence t↦ A(t) is – in a suitable sense – of bounded variation or absolutely continuous.

title: On parabolic quasi-variational inequalities and state-dependent sweeping processes
abstract: (1.2) C(t, u) ⊂ H is nonempty, closed, and convex for t ∈ [0, T ], u ∈ H. In (1.1), NC(t,u)(x) denotes the normal cone to C(t, u) at x ∈ C(t, u), cf. Section 2 below. We will treat the case of (t, u) 7→ C(t, u) being Lipschitz continuous w.r. to the Hausdorff distance dH with constants L1, L2 ≥ 0, i.e., we require (1.3) dH(C(t, u), C(s, v)) ≤ L1|t− s|+ L2|u− v|, t, s ∈ [0, T ], u, v ∈ H. Note that a solution of (1.1) in particular has to satisfy u(t) ∈ C(t, u(t)) for t ∈ [0, T ].

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]

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: On the Uniqueness and Asymptotic Behaviour of Plasma Corners

title: Zappa products

title: Bilateral semidirect products of transformation semigroups
BV Solutions to Evolution Problems with Time-Dependent Domains
In a Hilbert space H we consider evolution problems -du(t) ε A(t)u(t) on some interval [0, T], where every A(t): D(A(t))→ 2 H is a maximal monotone operator, and the correspondence t↦ A(t) is – in a suitable sense – of bounded variation or absolutely continuous.

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]

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: Zappa products

title: Bilateral semidirect products of transformation semigroups