A simple derivation methodology for optimization of linear quadratic controllers is presented, in the discrete time polynomial systems framework. A control law variation, regarded as a potential feedforward from the innovations , is used. Orthogonality is evaluated in the frequency domain, by collectively cancelling unstable poles by zeros. The suggested method, summarized as a three{step schem...

I show that there exist universal constants C(r) < ∞ such that, for all loopless graphs G of maximum degree ≤ r, the zeros (real or complex) of the chromatic polynomial PG(q) lie in the disc |q| < C(r). Furthermore, C(r) ≤ 7.963907r. This result is a corollary of a more general result on the zeros of the Potts-model partition function ZG(q, {ve}) in the complex antiferromagnetic regime |1 + ve|...

We give several descriptions of positive quadrature formulas which are exact for trigonometric-, respectively, Laurent polynomials of degree less or equal to n − 1 − m, 0 ≤ m ≤ n − 1. A complete and simple description is obtained with the help of orthogonal polynomials on the unit circle. In particular it is shown that the nodes polynomial can be generated by a simple recurrence relation. As a ...

In this paper we study the function , for z∈C. We derive a functional equation that relates G(z) and G(1−z) all z∈C, prove: 1) G Riemann zeta ζ have exactly same zeros in critical region D:= {z∈C:ℜz∈(0,1)}; 2) hypothesis, i.e., of D are located on line := {z∈D:ℜz =1/2}; 3) simple.

We derive the soliton matrices corresponding to an arbitrary number of higherorder normal zeros for the matrix Riemann–Hilbert problem of arbitrary matrix dimension, thus giving the complete solution to the problem of higher-order solitons. Our soliton matrices explicitly give all higher-order multisoliton solutions to the nonlinear partial differential equations integrable through the matrix R...

Probabilistic sequence models estimated from large corpora typically require smoothing techniques to reserve some probability mass for unobserved events. These techniques fail to distinguish between events unobserved due to sampling limitations, sampling zeros, and those unobserved due to structural reasons such as syntactic constraints, structural zeros. We investigate the use of statistical t...

where P is a real even polynomial with positive leading coefficient, which is called a potential. The boundary condition is equivalent to y ∈ L(R) in this case. It is well-known that the spectrum is discrete, and all eigenvalues λ are real and simple, see, for example [3, 14]. The spectrum can be arranged in an increasing sequence λ0 < λ1 < . . .. Eigenfunctions y are real entire functions of o...