The Jacobian conjecture is a well-known open problem in affine algebraic
geometry that asks if any polynomial endomorphism of the affine space
ACn (n≥2) with jacobian 1 is an automorphism.
We present a surve...
The Third Evolution Equation for Optimal Control Computation
February 11, 2018
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Computer Science
Mathematics
Systems and Control
Optimization and Control
Systems and Control
Optimization and Control
The Variation Evolving Method (VEM) that originates from the continuous-time
dynamics stability theory seeks the optimal solutions with variation evolution
principle. After establishing the first and the second evolution equations
within it...
The Strange Attractor Model of Bipedal Locomotion and its Consequences
on Motor Control
February 9, 2018
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Computer Science
Robotics
Despite decades of study, many unknowns exist about the mechanisms governing
human locomotion. Current models and motor control theories can only partially
capture the phenomenon. This may be a major cause of the reduced efficacy of
lower l...
A simple example of the weak discontinuity of f↦∫det∇f
February 8, 2018
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Mathematics
Analysis of PDEs
Analysis of PDEs
Verifying lower-semicontinuity of integral functionals in the weak topology
of Sobolev spaces is a central theme in the calculus of variations. For
integral functionals with p-growth, quasiconvexity is a necessary condition
for weak lower...
Existence of augmented Lagrange multipliers: reduction to exact penalty
functions and localization principle
February 8, 2018
Mathematics
Optimization and Control
In this article, we present new general results on existence of augmented
Lagrange multipliers. We define a penalty function associated with an augmented
Lagrangian, and prove that, under a certain growth assumption on the augmenting
functi...
Doubling constructions: Global functoriality for non-generic cuspidal
representations
February 7, 2018
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Mathematics
Number Theory
Representation Theory
We study the generalized doubling method for pairs of representations of
G×GLk where G is a symplectic group, split special orthogonal group
or split general spin group. We analyze the poles of the local integrals, and
prove that...
Variable Modified Newtonian Mechanics III: Milky Way Rotational Curve
February 5, 2018
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Physics
Astrophysics of Galaxies
Astrophysics of Galaxies
A cosmological background dependent Mond-like gravitational acceleration
arises along with the Newtonian aceeleration in a new metric solution for a
point mass residing in an expanding universe. Recently, we study the monolithic
evolution o...
Solve the General Constrained Optimal Control Problem with Common
Integration Method
February 5, 2018
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Electrical Engineering and Systems Science
Computer Science
Mathematics
Systems and Control
Systems and Control
Optimization and Control
Systems and Control
Systems and Control
Optimization and Control
Computation of general state- and/or control-constrained Optimal Control
Problems (OCPs) is difficult for various constraints, especially the
intractable path constraint. For such problems, the theoretical convergence of
numerical algorithm...
The tame fundamental group schemes of curves in positive characteristic
February 4, 2018
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Mathematics
Algebraic Geometry
Algebraic Geometry
The tame fundamental group scheme for an algebraic variety is the maximal
linearly reductive quotient of Nori's fundamental group scheme. In this paper,
we study the tame fundamental group schemes of smooth curves defined over
algebraically...
Lattices with exponentially large kissing numbers
February 2, 2018
Mathematics
Number Theory
Algebraic Geometry
Combinatorics
Metric Geometry
We construct a sequence of lattices {Lni⊂Rni} for
ni⟶∞, with exponentially large kissing numbers, namely,
log2τ(Lni)>0.0338⋅ni−o(ni). We also show that the maximum
lattice...