Undecidability of translational tiling of the 4-dimensional space with a set of 4 polyhypercubes
Sign Up to like & getrecommendations! Published in 2024 at "Science China Mathematics"
DOI: 10.1007/s11425-024-2365-2
Abstract: Recently, Greenfeld and Tao (2024) disproved the conjecture that translational tilings of a single tile can always be periodic. In another paper (Greenfeld and Tao (2025)), they also showed that if the dimension n is… read more here.
Keywords: tiling dimensional; space set; undecidability translational; translational tiling ... See more keywords
Fractal-type sets in the four-dimensional space using bicomplex and hyperbolic numbers
Sign Up to like & getrecommendations! Published in 2020 at "Analysis and Mathematical Physics"
DOI: 10.1007/s13324-020-00356-5
Abstract: In the first part of this work we study the set of bicomplex numbers from the point of view of a hyperbolic module. We make use of the partial order defined on the set of… read more here.
Keywords: fractal type; sets four; four dimensional; hyperbolic numbers ... See more keywords
Identification of a multi-dimensional space-dependent heat source from boundary data
Sign Up to like & getrecommendations! Published in 2018 at "Applied Mathematical Modelling"
DOI: 10.1016/j.apm.2017.09.029
Abstract: We investigate the linear but ill-posed inverse problem of determining a multi-dimensional space-dependent heat source in the parabolic heat equation from Cauchy boundary data. This model is important in practical applications where the distribution of… read more here.
Keywords: dependent heat; space dependent; multi dimensional; boundary data ... See more keywords
The relationship between diversity and productivity from a three-dimensional space view in a natural mesotrophic lake
Sign Up to like & getrecommendations! Published in 2021 at "Ecological Indicators"
DOI: 10.1016/j.ecolind.2020.107069
Abstract: Abstract The relationship between diversity and productivity (DPR) is a hot topic in ecology, whereas most evidence comes from studies of manipulated terrestrial ecosystems or from two-dimensional space views. In this study, we determined DPR… read more here.
Keywords: space; productivity; water; relationship diversity ... See more keywords
Analysis of a metafilm in non-integer dimensional space
Sign Up to like & getrecommendations! Published in 2020 at "Optik"
DOI: 10.1016/j.ijleo.2019.163498
Abstract: Abstract Properties of electromagnetic field, reflected and transmitted from a planar metafilm placed at the interface of two non integer dimensional (NID) mediums are studied. For this purpose, the metafilm is excited by a TE/TM… read more here.
Keywords: metafilm; non integer; metafilm non; dimensional space ... See more keywords
The principles of a new method, MNF-3D, for concentration of magnetic particles in three-dimensional space
Sign Up to like & getrecommendations! Published in 2017 at "Measurement"
DOI: 10.1016/j.measurement.2017.08.034
Abstract: Abstract The paper describes a new method, Magnetic Nanoparticles Focusing 3D (MNF-3D), for focusing of magnetic particles at any point in a three-dimensional space 3D in aqueous solutions. The method is based on a rotating… read more here.
Keywords: three dimensional; space; new method; method ... See more keywords
Expansion Kinetics of Flexible Polymers upon Release from a Disk-Shaped Confinement
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DOI: 10.1021/acsomega.3c08378
Abstract: A general theory is developed to explain the expansion kinetics of a polymer released from a confining cavity in a d-dimensional space. At beginning, the decompressed chain undergoes an explosive expansion while keeping the structure… read more here.
Keywords: polymers upon; expansion kinetics; kinetics flexible; expansion ... See more keywords
A general theory of polymer ejection tested in a quasi two-dimensional space
Sign Up to like & getrecommendations! Published in 2021 at "Scientific Reports"
DOI: 10.1038/s41598-021-94054-2
Abstract: A general ejection theory of polymer is developed in a two- and three-dimensional space. A polymer is confined initially in a cavity and ejects spontaneously to the outer space through a nanopore channel without the… read more here.
Keywords: space; theory; ejection; polymer ... See more keywords
A relationship between two-dimensional and four-dimensional space-time by comparing generalized two-dimensional Yang–Mills theory and Maxwell construction
Sign Up to like & getrecommendations! Published in 2024 at "Scientific Reports"
DOI: 10.1038/s41598-024-69554-6
Abstract: Some important problems in science do not have analytical solutions in four dimensions including QCD, but they are integrable in two dimensions. For many years, scientists have been trying to find a relation between two-dimensional… read more here.
Keywords: usepackage; dimensional space; two dimensional; space time ... See more keywords
The Eigenvalue Properties of a Kind of Singular Differential Equations in 3-Dimensional Space
Sign Up to like & getrecommendations! Published in 2024 at "Wuhan University Journal of Natural Sciences"
DOI: 10.1051/wujns/2024293257
Abstract: In this paper, we consider the eigenvalue problem of the singular differential equation [see formula in PDF] in a bounded open ball with Dirichlet boundary condition in 3-dimensional space, where, [see formula in PDF][see formula… read more here.
Keywords: eigenvalue properties; formula pdf; singular differential; dimensional space ... See more keywords
Two-dimensional space charge limited current in regime between accelerating diode and drift space for sheet and circular beam
Sign Up to like & getrecommendations! Published in 2024 at "Physics of Plasmas"
DOI: 10.1063/5.0208823
Abstract: We develop a general electrostatic steady-state model to calculate the two-dimensional (2D) space-charge-limited current (SCLC) with an initial velocity v0 (i.e., kinetic energy eKV=mv02/2) injected from a cathode into a vacuum diode with a spacing… read more here.
Keywords: space charge; drift space; space; beam ... See more keywords