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Generalized Reduced Modulus in Euclidean Space
AbstractIn an Euclidean space, we study condensers with variable potential levels and the presence of a free part at the boundary. The asymptotic...
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A Characterization of Separable Hypersurfaces in Euclidean Space
AbstractAs generalizations of classical translation hypersurfaces, in this note we introduce the notion of separable hypersurfaces in an
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Embedding Dimensions of Matrices Whose Entries are Indefinite Distances in the Pseudo-Euclidean Space
A finite set of the Euclidean space is called an s -distance set provided that the number of Euclidean distances in the set is s . Determining the...
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The Fermat–Steiner Problem in the Space of Compact Subsets of the Euclidean Plane
The Fermat–Steiner problem is the problem of finding all points of a metric space Y such that the sum of the distances from them to points of a...
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New bounds for the Euclidean operator radius of two Hilbert space operators with applications
In this work, we present some new upper and lower bounds for the Euclidean operator radius of a pair of Hilbert space operators. Some of these bounds...
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Pedal and Contrapedal Curves of Framed Immersions in the Euclidean 3-Space
In this paper, we define pedal and contrapedal curves of framed immersions, which can have singularities, in the Euclidean 3-space and investigate...
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Highly Non-contractive Iterated Function Systems on Euclidean Space Can Have an Attractor
Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. Moreover,...
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Binary Differential Equations Associated to Congruences of Lines in Euclidean 3-Space
We study quotients of quadratic forms and associated polar lines in the projective plane. Our results, applied pointwise to quadratic differential...
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Boundary value problems in Euclidean space for bosonic Laplacians
A bosonic Laplacian is a conformally invariant second order differential operator acting on smooth functions defined on domains in Euclidean space...
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Euclidean Spaces
In order to introduce concepts like “distance”, “angle” or “orthogonality” in a real affine space...
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Bertrand and Mannheim curves of framed curves in the 4-dimensional Euclidean space
A Bertrand curve in the 4-dimensional Euclidean space is a space curve whose first normal line is the same as the first normal line of another curve....
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Surfaces of Osculating Circles in Euclidean Space
The aim of this paper is to define a new class of surfaces in Euclidean space using the concept of osculating circle. Given a regular curve C , the...
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Grand Morrey Spaces and Grand Hardy–Morrey Spaces on Euclidean Space
We define and study the grand Morrey spaces and the grand Hardy–Morrey spaces on Euclidean space. We also introduce the small block space and study...
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Classification of complete 3-dimensional self-shrinkers in the Euclidean space ℝ4
In this paper, we completely classify 3-dimensional complete self-shrinkers with the constant norm S of the second fundamental form and the constant f
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On the existence of geodesics connecting Lagrangian graphs in Euclidean space
Existence theory for geodesics in the space of Lagrangian submanifolds plays an important role in a program for studying the existence and uniqueness...
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Solving Hermite Interpolation Problem in Finite-Dimensional Euclidean Space
The Hermite problem in the Euclidean space is considered, where the value of a function of several variables and its first-order Gateaux...
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Agent-Based Model of Cultural Landscape Evolution in Euclidean Space
The cultural landscape determines the cultural agent’s diversity. It is believed that the cultures space can be represented as a Hilbert space, in...
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Side effects of learning from low-dimensional data embedded in a Euclidean space
The low-dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately)...
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Spaces Over Algebras with Euclidean Metric
In this paper, we propose a new approach to the real realization of spaces over algebras, in which a space over an algebra and the space of its...