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The Structure of Differential Invariants for a Free Symmetry Group Action
AbstractIn the paper, we consider the problem of describing the general structure of differential invariants for transformation groups that act...
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Invariants of Finite and Discrete Group Actions via Moving Frames
A new, elementary algorithm for constructing complete, minimal sets of generating invariants for finite or, more generally, discrete group actions,...
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Explicit construction of frames and pairs of dual frames on locally compact abelian groups
Locally compact abelian (LCA) groups form a natural setting for frame theory in signal processing: while classical frame theory was developed in the...
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Classes of explicit phylogenetic networks and their biological and mathematical significance
The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate...
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A Group-Theoretic Approach to the Reducibility Problem of Optimal Processes
The reducibility problem of optimal processes is posed, and a group-theoretic approach to its solution is proposed. This approach is based on the...
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Explicit construction of wavelet frames on locally compact Abelian groups
The aim of this article is to present a novel method for constructing wavelet frames on locally compact Abelian (LCA) groups by employing the frame...
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Regularity Theory of Quasilinear Elliptic and Parabolic Equations in the Heisenberg Group
This note provides a succinct survey of the existing literature concerning the Hölder regularity for the gradient of weak solutions of PDEs of the...
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Logahoric Higgs torsors for a complex reductive group
In this article, a logahoric Higgs torsor is defined as a parahoric torsor with a logarithmic Higgs field. For a connected complex reductive group G ,...
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The Method of Explicit Auxiliary Functions
In this chapter, we consider bounds for various functions defined on conjugate sets of algebraic numbers. These bounds are obtained by the use of...
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Existence of a Minimizer for the Bianchi-Egnell Inequality on the Heisenberg Group
This paper is concerned with the Bianchi-Egnell inequality on the Heisenberg group, which quantifies the stability of the Sobolev inequality. We...
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Helicoidal minimal surfaces in the 3-sphere: an approach via spherical curves
We prove an existence and uniqueness theorem about spherical helicoidal (in particular, rotational) surfaces with prescribed mean or Gaussian...
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Dimension ≥ 2: Some Explicit Cases Beyond the Periodic Setting
We consider nonperiodic homogenization in dimensions d higher than 2. We first consider the deterministic setting in Sect. 4.1, with “local” defects,...
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A heat equation approach to intertwining
In this paper we present anew approach based on the heat equation and extension problems to some intertwining formulas arising in conformal CR...
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A decomposition theorem for unitary group representations on Kaplansky–Hilbert modules and the Furstenberg–Zimmer structure theorem
In this paper, a decomposition theorem for (covariant) unitary group representations on Kaplansky–Hilbert modules over Stone algebras is...
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Global Compactness, Subcritical Approximation of the Sobolev Quotient, and a Related Concentration Result in the Heisenberg Group
We investigate some effects of the lack of compactness in the critical Sobolev embedding in the Heisenberg group.
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New Similarity Solutions of Magnetohydrodynamic Flow Over Horizontal Plate by Lie Group with Nonlinear Hydrodynamic and Linear Thermal and Mass Slips
The viscous laminar magnetohydrodynamic convective boundary layer flow with the combined effects of chemical reaction and nonlinear velocity slip and...
