scholarly journals A decomposition of the Schwartz class by a derivative space and its complementary space

2019 ◽  
Author(s):  
Takahide Kurokawa
Keyword(s):  
Schwartz Class ◽  
Complementary Space

A representation of distributions supported on smooth hypersurfaces of Rn

1995 ◽  
Vol 117 (1) ◽  
pp. 153-160
Author(s):  
Kanghui Guo
Keyword(s):  
Gaussian Curvature ◽  
Dual Space ◽  
Smooth Hypersurface ◽  
Zero Gaussian Curvature ◽  
Schwartz Class ◽  
Image Position

Let S(Rn) be the space of Schwartz class functions. The dual space of S′(Rn), S(Rn), is called the temperate distributions. In this article, we call them distributions. For 1 ≤ p ≤ ∞, let FLp(Rn) = {f:∈ Lp(Rn)}, then we know that FLp(Rn) ⊂ S′(Rn), for 1 ≤ p ≤ ∞. Let U be open and bounded in Rn−1 and let M = {(x, ψ(x));x ∈ U} be a smooth hypersurface of Rn with non-zero Gaussian curvature. It is easy to see that any bounded measure σ on Rn−1 supported in U yields a distribution T in Rn, supported in M, given by the formula

Fourier restriction theorems for curves with affine and Euclidean arclengths

1985 ◽  
Vol 97 (1) ◽  
pp. 111-125 ◽  
Author(s):  
S. W. Drury ◽  
B. P. Marshall
Keyword(s):  
Fourier Transform ◽  
Smooth Manifold ◽  
Fourier Restriction ◽  
Survey Article ◽  
Restriction Theorems ◽  
Schwartz Class ◽  
The Fourier Transform ◽  
Image Position

Let M be a smooth manifold in . One may ask whether , the restriction of the Fourier transform of f to M makes sense for every f in . Since, for does not make sense pointwise, it is natural to introduce a measure σ on M and ask for an inequalityfor every f in (say) the Schwartz class. Results of this kind are called restriction theorems. An excellent survey article on this subject is to be found in Tomas[13].

Self-Formation of the Spatial Planar Object. Topological Approach

2004 ◽  
Vol 97-98 ◽  
pp. 85-90
Author(s):  
Stepas Janušonis
Keyword(s):  
Euclidean Space ◽  
Topological Space ◽  
Anisotropic Medium ◽  
Topological Approach ◽  
Spatial Objects ◽  
General Approximation ◽  
Complementary Space ◽  
Self Formation ◽  
Homogeneous Anisotropic Medium

Eight-dimensional topological space providing an object evolution in time, including causes of evolution is presented. Part of Euclidean space separated by any close surface from complementary space, where any Euclidean point of space is juxtaposed with parameter, is being felt as an object. Coplanar approximation of flat planar devices is based on the flat, homogeneous, isotropic planar object and chaotic medium. The new, more general approximation of the topological space by equidistant surfaces, suitable for spatial planar objects, is presented. Selfformation of spatial objects (homogeneous, non-homogeneous, anisotropic), medium (chaotic, chaotic oriented, homogeneous oriented, structural) based on non-homeomorpheous mapping in peculiar points and evolution irreversibility, is discussed.

Chinese Hα Solar Explorer (CHASE) – a complementary space mission to the ASO-S

2019 ◽  
Vol 19 (11) ◽  
pp. 165 ◽  
Author(s):  
Chuan Li ◽  
Cheng Fang ◽  
Zhen Li ◽  
Ming-De Ding ◽  
Peng-Fei Chen ◽  
...  
Keyword(s):  
Space Mission ◽  
Complementary Space

Observation and analysis of extended dislocations in an Al–Pd–Mn icosahedral quasicrystal by transmission electron microscopy

1995 ◽  
Vol 10 (11) ◽  
pp. 2742-2748 ◽  
Author(s):  
Jianglin Feng ◽  
Renhui Wang ◽  
Mingxing Dai
Keyword(s):  
Physical Space ◽  
Stacking Fault ◽  
Icosahedral Quasicrystal ◽  
Burgers Vector ◽  
Partial Dislocations ◽  
Transmission Electron ◽  
Perfect Dislocation ◽  
Complementary Space ◽  
Convergent Beam ◽  
First Time

Extended dislocations including partial dislocations and a stacking fault in Al70Pd20Mn10 icosahedral quasicrystal have been observed and identified for the first time. The diffraction contrast and defocus convergent-beam electron diffraction experiments show that the dissociation of the extended dislocations is of the form 1/2<1 −2 0 0 −2 1> → 1/4<1 −3 1 −1 −1 1>+ 1/4<1 −1 −1 1 −xs3 1> with a stacking fault between these two partial dislocations. For the partial dislocations, the Burgers vector components in physical space b¶part are along different fivefold axes with a magnitude of 0.17 nm, which is about one seventh of that in complementary space. For the perfect dislocation, the Burgers vector component in physical subspace b¶perf is along a twofold axis with a magnitude of 0.183 nm, which is about an eleventh of that in complementary space.

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