Showing papers on "Affine involution published in 2017"
1 Jan 2017
TL;DR: In this paper, pseudo-differential operators on the affine group were defined using the Fourier inversion formula for Fourier transform on affine groups and the Weyl transform was given.
Abstract: Pseudo-differential operators are defined on the affine group using the Fourier inversion formula for the Fourier transform on the affine group. The Weyl transform on the affine group is given and so are the L2-L p estimates for pseudo-differential operators on the affine group.
15 citations
TL;DR: With this method, a family of differentially 4-uniform involutions with optimal algebraic degree and high nonlinearity is constructed, and it is shown with the help of computer that such involutions which are CCZ-inequivalent to the known same-sex permutations in small number of even dimensions are constructed.
10 citations
TL;DR: In this paper, the total classification of Weingarten affine translation surfaces in three dimensional Euclidean space is given. But the classification is restricted to the minimal affine Scherk surface or the surface with flat metric.
Abstract: By solving certain (partial) differential equations we give the total classification of Weingarten affine translation surfaces in three dimensional Euclidean space $$\mathbb {E}^3$$
. Explicitly, a Weingarten affine translation surface in Euclidean 3-space is the minimal affine Scherk surface or the surface with flat metric.
7 citations
TL;DR: An unsupervised learning algorithm that computes low dimensional data from complex high dimensional data using affine transformation and neighborhood preserving embedding, which is affine invariant where each point is being represented by an affine combination of its neighboring points.
Abstract: Dimensional reduction is a primary way to analyze and work with complex and large amount of multidimensional data by avoiding the effect of curse of dimensionality. This problem of constructing low dimensional embedding gains importance in number of fields like artificial intelligence, image processing, geographical research and lot more. In this paper, we introduce a modified locally linear embedding, an unsupervised learning algorithm that computes low dimensional data from complex high dimensional data using affine transformation and neighborhood preserving embedding. Unlike novel locally linear embedding, our method is affine invariant where each point is being represented by an affine combination of its neighboring points. At the end, we conduct the experiment to evaluate our proposed method and compare its performance with existing methods. Results show that our proposed method is unaffected by affine transformation, specifically shear while existing methods fail to produce correct results in case of shear.
4 citations
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TL;DR: In this paper, endpoint Lebesgue space bounds for convolution and restricted X-ray transforms along curves satisfying fairly minimal differentiability hypotheses, with affine and Euclidean arclengths.
Abstract: We establish endpoint Lebesgue space bounds for convolution and restricted X-ray transforms along curves satisfying fairly minimal differentiability hypotheses, with affine and Euclidean arclengths. We also explore the behavior of certain natural interpolants and extrapolants of the affine and Euclidean versions of these operators.
1 citations
23 Sep 2017
TL;DR: In this article, the polynomial affine translation surfaces in E3 with constant curvature were studied and some non-existence results for such surfaces were derived. Several examples are also given by figures.
Abstract: In this paper we study the polynomial affine translation surfaces in E3 with constant curvature. We derive some non-existence results for such surfaces. Several examples are also given by figures.
1 citations
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TL;DR: A two-party wire-tap channel of type II in the framework of almost affine codes is described, its cryptological performance is related to some relative profiles of a pair of almost Affine codes, which are analogues of relative generalized Hamming weights in the linear case.
Abstract: We describe a two-party wire-tap channel of type II in the framework of almost affine codes. Its cryptological performance is related to some relative profiles of a pair of almost affine codes. These profiles are analogues of relative generalized Hamming weights in the linear case.
1 citations
TL;DR: In this article, the affine Toda models in the homogeneous higher grading case were derived and the main example of the homogenous higher grading sine-Gordon equation was discussed.
1 citations
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TL;DR: In this article, the authors focus on the differential geometric approach to the study of nonlinear systems that are affine in control and develop normal forms for nonlinear system affine-in-control.
Abstract: The note focuses on the differential geometric approach to the study of nonlinear systems that are affine in control. We first develop normal forms for nonlinear system affine in control. Based on these normal forms, we then address the problems of global stabilization, semi-global stabilization and disturbance attenuation.
1 Jan 2017
TL;DR: Affine and euclidean space are discussed primarily in view of their use as models for physical space as mentioned in this paper, and affine mappings and coordinate charts generated by them are examined.
Abstract: Affine and euclidean space are discussed primarily in view of their use as models for physical space. Affine mappings and coordinate charts generated by them are examined. Furthermore, topological aspects are addressed.
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TL;DR: In this paper, it was shown that on closed manifolds of odd Euler characteristic fixed point sets of involutions, the set is smooth and non-nondisplaceable.
Abstract: We prove that on closed manifolds of odd Euler characteristic fixed point sets of involutions are smoothly nondisplaceable.
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TL;DR: In this article, the affine Orlicz Polya-Szego principle for log-concave functions was shown to be applicable to star bodies and an affine ORlicz-Petty projection inequality for star bodies was established.
Abstract: The author established the affine Orlicz Polya-Szego principle for log-concave functions and conjectured that the principle can be extended to the general Orlicz Sobolev functions. In this paper, we confirm this conjecture completely. An affine Orlicz Polya-Szego principle, which includes all the previous affine Polya-Szego principles as special cases, is formulated and proved. As a consequence, an Orlicz-Petty projection inequality for star bodies is established.