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Approximate Lattices in Higher-Rank Semi-Simple Groups
We show that strong approximate lattices in higher-rank semi-simple algebraic groups are arithmetic.
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Rank Properties and Computational Methods for Orthogonal Tensor Decompositions
The orthogonal decomposition factorizes a tensor into a sum of an orthogonal list of rank-one tensors. The corresponding rank is called orthogonal...
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Equivariant Grothendieck ring of a complete symmetric variety of minimal rank
We describe the G -equivariant Grothendieck ring of a regular compactification X of an adjoint symmetric space G / H of minimal rank. This extends the...
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On the stability of the representation of finite rank operators
The stability of the representation of finite rank operators in terms of a basis is analyzed. A conditioning is introduced as a measure of the...
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Estimate of the Spectrum of Discrete Sequences in Ill-Posed Problems Based on the Study of the Numerical Rank of the Trajectory Matrix
In this paper, we discuss properties of the singular value decomposition (SVD-decomposition) within the framework of the analysis of the numerical...
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Topological reducibilities for discontinuous functions and their structures
In this article, we give a full description of the topological many-one degree structure of real-valued functions, recently introduced by...
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Taylor Polynomials of Rational Functions
A Taylor variety consists of all fixed order Taylor polynomials of rational functions, where the number of variables and degrees of numerators and...
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Horizontally Affine Functions on Step-2 Carnot Algebras
In this paper, we introduce the notion of horizontally affine, h-affine in short, function and give a complete description of such functions on...
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An infinite family of vector-valued mock theta functions
We exhibit an infinite family of vector-valued mock theta functions indexed by positive integers coprime to 6. These are built from specializations...
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Bounds for theta sums in higher rank. I
Theta sums are finite exponential sums with a quadratic form in the oscillatory phase. This paper establishes new upper bounds for theta sums in the...
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Monogenic Functions with Values in Commutative Complex Algebras of the Second Rank with Unit and a Generalized Biharmonic Equation with Simple Nonzero Characteristics
Among all two-dimensional algebras of the second rank with unit e over the field of complex numbers ℂ , we find a semisimple algebra 𝔹 0 := {c 1 e + c 2 𝜔...
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The Minimal Sum of Squares Over Partitions with a Nonnegative Rank
Motivated by a question of Defant and Propp (Electron J Combin 27:Article P3.51, 2020) regarding the connection between the degrees of...
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Constant rank theorems for curvature problems via a viscosity approach
An important set of theorems in geometric analysis consists of constant rank theorems for a wide variety of curvature problems. In this paper, for...
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A global exact penalty for rank-constrained optimization problem and applications
This paper considers a rank-constrained optimization problem where the objective function is continuously differentiable on a closed convex set....
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A new complexity metric for nonconvex rank-one generalized matrix completion
In this work, we develop a new complexity metric for an important class of low-rank matrix optimization problems in both symmetric and asymmetric...
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Single-pass randomized QLP decomposition for low-rank approximation
As a special UTV decomposition, the QLP decomposition is an effective alternative of the singular value decomposition (SVD) for the low-rank...
