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Algebra of Pseudodifferential Operators with Piecewise Smooth Symbols on a Smooth Manifold
On a smooth compact m-dimensional manifold \(\mathcal {M}\)...
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Galerkin-based quasi-smooth manifold element (QSME) method for anisotropic heat conduction problems in composites with complex geometry
The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance...
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Generalization of a Theorem on the Equivalence of the Coordinate and Algebraic Definitions of a Smooth Manifold
In this paper, we generalize the theorem on the equivalence of the coordinate and algebraic definitions of a smooth manifold. Within the framework of...
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Structural Stability for 2-Dimensional Piecewise Smooth Vector Fields Where the Switching Manifold is a Double Discontinuity
The main purpose of this work is exhibit the canonical forms for 2D codimension zero piecewise smooth vector fields where the switching manifold is a...
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Manifold Theory
Curves and surfaces are the fundamental concepts of studying geometry in a 3-dimensional space. The quest for studying these two concepts in a space...
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On smooth functions with two critical values
We prove that every smooth closed connected manifold admits a smooth real-valued function with only two critical values such that the set of minima...
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On the Solvability of Linear Differential Operators on Vector Bundles over a Manifold
AbstractA necessary and sufficient condition is established for the closedness of the range or surjectivity of a differential operator acting on...
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On the Duality in the Theory of Smooth Manifolds
In this paper, we discuss an important and nontrivial theorem on evaluation homomorphisms. We state this theorem as a canonical duality between the...
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Space of Affine Connections of an Almost Hermitian Manifold
We consider affine connections determined by an almost Hermitian structure of a smooth manifold. We prove that the affine space of connections...
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Smooth Maps
A real-valued function on an open subset $$U\subseteq \mathbb...
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A collection of efficient retractions for the symplectic Stiefel manifold
This article introduces a new map on the symplectic Stiefel manifold. The operation that requires the highest computational cost to compute the novel...
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Proximal gradient algorithm with trust region scheme on Riemannian manifold
We consider the problem of minimizing the sum of a smooth function and nonsmooth function over a Riemannian manifold. We develop a Riemannian...
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Intrinsic sub-Laplacian for hypersurface in a contact sub-Riemannian manifold
We construct and study the intrinsic sub-Laplacian, defined outside the set of characteristic points, for a smooth hypersurface embedded in a contact...
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Hermite multiwavelets for manifold-valued data
In this paper we present a construction of interpolatory Hermite multiwavelets for functions that take values in nonlinear geometries such as...
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Accelerating inexact successive quadratic approximation for regularized optimization through manifold identification
For regularized optimization that minimizes the sum of a smooth term and a regularizer that promotes structured solutions, inexact...
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Statistical manifold with degenerate metric
A statistical manifold is a pseudo-Riemannian manifold endowed with a Codazzi structure . This structure plays an important role in Information...
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A Grassmann manifold handbook: basic geometry and computational aspects
The Grassmann manifold of linear subspaces is important for the mathematical modelling of a multitude of applications, ranging from problems in...
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Minimal extensions in smooth dynamics
A classical result of Fathi and Herman from 1977 states that a smooth compact connected manifold without boundary admitting a locally free action of...
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Generalization of the Notion of Completeness of a Riemannian Analytic Manifold
In this paper, we discuss the concept of an analytic prolongation of a local Riemannian metric. We propose a generalization of the notion of...