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A lower bound for the dimension of tetrahedral splines in large degree
Splines are piecewise polynomial functions which are continuously differentiable to some order r . For a fixed integer d the space of splines of...
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Some Properties of Coefficients of the Kolchin Dimension Polynomial
This paper presents a formula expressing Macaulay constants of a numerical polynomial through its minimizing coefficients. From this, we obtain that...
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On the packing dimension of Furstenberg sets
We prove that if α ∈ (0, 1/2], then the packing dimension of a set E ⊂ ℝ 2 for which there exists a set of lines of dimension 1 intersecting E in...
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Fractal Dimension of Random Attractor for a Stochastic Lattice System with White Noise
In this paper, it was studied the finite fractal dimension of random attractor for the stochastic Klein-Gordon-Schrödinger (KGS) lattice equation...
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On Generalized Nonparametric Minimal Hyperfurfaces in High Dimension
Nonparametric g-surfaces in Euclidean space have recently been characterized by Bildhauer–Fuchs in terms of closure of a 1-form associated to the so...
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Hausdorff dimension regularity properties and games
The Hausdorff δ -dimension game was introduced in [2] and shown to characterize sets in ℝ d having Hausdorff dimension ≤ δ . We introduce a variation of...
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A dimension expanded Newton-type method for absolute value equations
By expanding the dimension of the absolute value equations, we construct two almost equivalent augmented quadratic polynomial systems, for which the...
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Uniformly Perfect Sets, Hausdorff Dimension, and Conformal Capacity
Using the definition of uniformly perfect sets in terms of convergent sequences, we apply lower bounds for the Hausdorff content of a uniformly...
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Regularity of Sets Under a Reformulation in a Product Space with Reduced Dimension
Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms...
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Zufallsvariablen in unendlicher Dimension
In diesem Kapitel behandeln wir Zufallsvariablen in unendlicher Dimension. Wir werden unter anderem das Bochner-Integral und Gauß’sche...
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On Second-Order Derivatives of Boolean Functions and Cubic APN Permutations in Even Dimension
The big APN problem is one of the most important challenges in the theory of Boolean functions, i.e. finding a new APN permutation in even dimension....
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Federated Sufficient Dimension Reduction Through High-Dimensional Sparse Sliced Inverse Regression
Federated learning has become a popular tool in the big data era nowadays. It trains a centralized model based on data from different clients while...
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On the Zarankiewicz Problem for Graphs with Bounded VC-Dimension
The problem of Zarankiewicz asks for the maximum number of edges in a bipartite graph on n vertices which does not contain the complete bipartite...
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Symmetric cooperative motion in one dimension
We explore the relationship between recursive distributional equations and convergence results for finite difference schemes of parabolic partial...
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An Algebraic Geometric Foundation for a Classification of Second-Order Superintegrable Systems in Arbitrary Dimension
Second-order (maximally) superintegrable systems in dimensions two and three are essentially classified. With increasing dimension, however, the...
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The Simultaneous Fractional Dimension of Graph Families
For a connected graph G with vertex set V , let R G { x, y } = { z ∈ V : d G ( x, z ) ≠ d G ( y, z )} for any distinct x, y ∈ V , where d G ( u, w ) denotes the length...
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Extremality and rigidity for scalar curvature in dimension four
Following Gromov, a Riemannian manifold is called area-extremal if any modification that increases scalar curvature must decrease the area of some...
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Some Variational Principles for the Metric Mean Dimension of a Semigroup Action
In this manuscript, we show that the metric mean dimension of a semigroup action satisfies three variational principles: (a) in our first result, we...