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We give the proofs of some simple facts on parahoric subgroups and on Iwahori Weyl groups
used in [H], [PR] and in [R].
Fermat numbers and integers of the form a k + a l + p
Fermat numbers generalized Fermat numbers Erdos problems Zsigmondy’s theorem covering systems
2015/8/25
In 1849, A. de Polignac [20] conjectured that every odd number larger than 3 can be written as the sum of an odd prime and a power of 2. He found a counterexample 959 soon. In 1934, N. P. Ro- manoff [...
The range of a rotor walk
range rotor walk
2015/8/14
In a rotor walk the exits from each vertex follow a prescribed periodic sequence. On an infinite Eulerian graph embedded periodically in Rd, we show that any simple rotor walk, regardless of rotor mec...
In 2006, the fourth author of this paper proposed a graph-theoretic model of interface dynamics called competitive erosion. Each vertex of the graph is occupied by a particle that can be either red or...
COEULERIAN GRAPHS
COEULERIAN GRAPHS
2015/8/14
We suggest a measure of “Eulerianness” of a finite directed graph and define a class of “coEulerian” graphs. These are the graphs whose Laplacian lattice is as large as possible. As an application, we...
On parametric H_infinity optimization
Parameters the transfer matrix the Hamiltonian matrix eigenvalue the implicit function
2015/8/13
The problem of optimizing the H_infinity norm of a rational transfer matrix with respect to a finite number of design parameters is considered. The H_infinity norm is characterized as a value of a par...
Linear controller design: Limits of performance via convex optimization
Linear controller design convex optimization linear control system the convex optimization algorithm the controller the transfer matrix
2015/8/12
In this tutorial, an approach to the analysis and design of linear control systems based on numerical convex optimization over closed-loop maps is presented. Convexity makes numerical solution effecti...
Design of stablizing state feedback for delay systems via convex optimization
A linear system functional convex optimization techniques
2015/8/12
For linear systems with delays, we define a new class of Lyapunov-like functionals that may be used to prove stability. We also show how we may design a stabilizing (delayed) state feedback for delay ...
A primal-dual potential reduction method for problems involving matrix inequalities
Interior point algorithms Linear matrix inequaliües Semidefinite programming
2015/8/11
We describe a potential reduction method for convex optimization problems involving matrix inequalities. The method is based on the theory developed by Nesterov and Nemirovsky and generalizes Gonzaga ...
A global BMI algorithm based on the generalized Benders decomposition
Linear matrix inequalities Robust control Numerical Methods
2015/8/11
We present a new algorithm for the global solution of optimization problems involving bilinear matrix inequalities (BMIs). The method is based on a technique known in large-scale and global optimizati...
Semidefinite programming relaxations of non-convex problems in control and combinatorial optimization
Applications of semidefinite programming combinatorial optimization quadratic semi-definite programming bilinear matrix inequality
2015/8/11
We point out some connections between applications of semidefinite programming in control and in combinatorial optimization. In both fields semidefinite programs arise as convex relaxations of NP-hard...
FIR filter design via spectral factorization and convex optimization
Finite impulse response filter filter coefficient variables spectral decomposition linear and nonlinear convex programming
2015/8/11
We consider the design of finite impulse response (FIR) filters subject to upper and lower bounds on the frequency response magnitude. The associated optimization problems, with the filter coefficient...
Control applications of nonlinear convex programming
semidefinite programming linear programming convex optimization interior-point methods robust optimal control
2015/8/11
Since 1984 there has been a concentrated effort to develop efficient interior-point methods for linear programming (LP). In the last few years researchers have begun to appreciate a very important pro...
Disciplined convex programming
Convex programming automatic verification symbolic compu-tation modelling language
2015/8/10
Convex programming is a subclass of nonlinear programming (NLP) that unifies and generalizes least squares (LS), linear programming (LP), and convex quadratic programming (QP). It has become quite pop...
Learning the kernel via convex optimization
Convex optimization kernel methods machine learning support vector machine
2015/8/10
The performance of a kernel-based learning algorithm depends very much on the choice of the kernel. Recently, much attention has been paid to the problem of learning the kernel itself from given train...