First-order necessary conditions for quadratically optimal, steady-state, fixed-order dynamic compensation of a linear, time-invariant plant in the presence of disturbance and observation noise are derived in a new and highly simplified form. In contrast to the pair of matrix Riccati equations for the full-order LQG case, the optimal steady-state fixed-order dynamic compensator is characterized...

Abstract Proton emission from deformed nuclei is described within the non-adiabatic weak coupling model which takes into account the coupling to γ-vibrations around the axially-symmetric shape. The coupled equations are derived within the Gamow state formalism. A new method, based on the combination of the R-matrix theory and the oscillator expansion technique, is introduced that allows for a s...

In this paper, we investigate synchronization of coupled second-order linear harmonic oscillators with random noises and time delays. The interaction topology is modeled by a weighted directed graph and the weights are perturbed by white noise. On the basis of stability theory of stochastic differential delay equations, algebraic graph theory and matrix theory, we show that the coupled harmonic...

The evolution of six-quark color-singlet state distribution amplitudes is formulated as an application of perturbative quantum chromodynamics to nuclear wave functions. We derive and solve a set of coupled evolution equations for the deuteron S-wave amplitude. The solution of the evolution equations leads to a general matrix representation of anomalous dimensions which can be used to analyze th...

A Riccati-equation based state-space solution to the H 1-optimal control problem for periodic multirate sampled-data systems is presented. The solution is characterized by two standard discrete algebraic Ric-cati equations with a set of associated matrix positive deeniteness conditions and coupling criteria. The equations are derived by discretizing a pair of coupled periodic Riccati diierentia...

Level-spacing distributions of the Gaussian Unitary Ensemble (GUE) of random matrix theory are expressed in terms of solutions of coupled differential equations. Series solutions up to order 50 in the level spacing are obtained, thus providing a very good description of the small-spacing part of the level-spacing distribution, which can be used to make comparisons with experimental or numerical...

A new approach to fitting coupled geometric objects, such as concentric circles, is presented. The objects can be coupled via common Grassmannian coefficients or through a correlation constraint on their coefficients. The implicit partitioning and partial block diagonal structure of the design matrix enables an efficient orthogonal residualization based on a generalized Eckart-Young-Mirsky matr...

Ionization, pair creation, and electron excitations in relativistic heavy-ion collisions are investigated in the framework of the coupled-channel formalisrn. Collisions between heavy projectiles and pb8*+ are considered for various bombarding energies in the region E =500 up to 2000 MeV/u. Useful symmetry relations for the matrix elements are derived and the influence of gauge transformations o...

in this paper we investigate the existence and uniqueness for volterra-fredholm type integral equations and extension of this type of integral equations. the result is obtained by using the  coupled fixed point theorems in the framework of banach space $ x=c([a,b],mathbb{r})$. finally, we  give an example to illustrate the applications of our results.

Fuzzy liner systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of inconsistent fuzzy matrix equation. Also some numerical examples are considered.