A Note on Fuzzy Automorphism and Inner Automorphism of Groups
September 20, 2019
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Mathematics
Group Theory
The fuzzification of classical set theory came into existence when Zadeh [1]
laid down the concept of a fuzzy set as a generalization of a crisp set. The
objective of this paper is to extend the concept of fuzzy endomorphism to fuzzy
automo...
Good Lambda Inequalities and Variable Orlicz Hardy Spaces
September 20, 2019
Mathematics
Complex Variables
We prove a general theorem showing that local good-λ inequalities
imply bounds in certain variable Orlicz spaces. We use this to prove results
about variable Orlicz Hardy spaces in the unit disc....
Neutralization of low energy Na+ scattered from InAs(001)
September 20, 2019
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Physics
Materials Science
Mesoscale and Nanoscale Physics
The neutralization probability of low energy Na+ ions scattered from In-
and As-rich InAs(001) surfaces is measured by time-of-flight spectroscopy. It
is found that the neutralization probability for projectiles scattered from As
sites...
Small MMI with simplified coherent coupling branches used to develop a
lower footprint power splitter on SOI platform
September 20, 2019
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Physics
Optics
In this paper, we introduce a new approach to fabricate under the Silicon on
Insulator (SOI) platform a 1x2 power splitter and scale it to 1xN system device
from the proposed model. The current strategy of design is based on the
well-known ...
Elementary Methods for Persistent Homotopy Groups
September 19, 2019
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Mathematics
Algebraic Topology
In this paper, we study the basic properties of persistent homotopy groups.
We show that the persistent fundamental group benefits from the Van Kampen
theorem, and the interleaving distance between total spaces is less than or
equal to the ...
Homogenization of quadratic convolution energies in periodically
perforated domains
September 18, 2019
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Mathematics
Analysis of PDEs
Analysis of PDEs
We prove a homogenization theorem for quadratic convolution energies defined
in perforated domains. The corresponding limit is a Dirichlet-type quadratic
energy, whose integrand is defined by a non-local cell-problem formula. The
proof reli...
A sharper Ramsey theorem for constrained drawings
September 18, 2019
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Mathematics
Combinatorics
Combinatorics
Given a graph G and a collection C of subsets of Rd
indexed by the subsets of vertices of G, a constrained drawing of G is a
drawing, where each edge is drawn inside some set from C, in such a
way tha...
Robust statistical modeling of monthly rainfall: The minimum density
power divergence approach
September 17, 2019
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Statistics
Applications
Statistical modeling of monthly, seasonal, or annual rainfall data is an
important research area in meteorology. These models play a crucial role in
rainfed agriculture, where a proper assessment of the future availability of
rainwater is n...
Counterfactual restrictions and Bell's theorem
September 14, 2019
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Physics
Quantum Physics
History and Philosophy of Physics
Quantum Physics
History and Philosophy of Physics
We show that the ability to consider counterfactual situations is a necessary
assumption of Bell's theorem, and that, to allow Bell inequality violations
while maintaining all other assumptions, we just require certain measurement
choices b...
Special Orthogonal Group SO(3), Euler Angles, Angle-axis, Rodriguez
Vector and Unit-Quaternion: Overview, Mapping and Challenges
September 14, 2019
Mathematics
Computer Science
Electrical Engineering and Systems Science
Optimization and Control
Systems and Control
Systems and Control
The attitude of a rigid-body in the three dimensional space has a unique and
global definition on the Special Orthogonal Group SO (3). This paper gives an
overview of the rotation matrix, attitude kinematics and parameterization. The
four m...