It is very complicated to calculate the secondorder aberrations of complex analyser systems and mistakes are liable to be made. Even if the matrix method is used the tediousness of the calculation is not altered. The usefulness of the matrix representation comes from the fact that the over-all transfer matrix of the total system is easily written as a product of the transfer matrices of various...

Two matrix equations, Pascal matrix equation and inverse Pascal matrix, are derived and demonstrated in this work. These matrix equations are used for making a conversion and inversion between the coefficients of an analog low pass filter transfer function H(s) and a digital transfer function H(z). The involving of the Pascal’s triangle in both matrix equations is helpful, easier to transform b...

[1] We investigate the effects of the porosity (and thus permeability) of porous matrix and the fracture aperture on transport in fractured porous media. We do so with detailed lattice Boltzmann simulations on constructed porous media with a single fracture. Both plume spatial moments (the average plume velocity and the dispersion coefficients) and mass transfer coefficients between the facture...

A matrix approach is proposed for determining the coefficients of maximally flat (m.f.) FIR filter transfer functions expressed in terms of cosine of multiple angles. In this, a transformation matrix maps a functional vector, the entries of which are either 0 or 1, into the coefficient vector of the m.f. filter transfer function. It is shown that the transformation matrix could be generated eit...

We present a systematic way of constructing boundary quantum group generators associated to non-diagonal solutions of the reflection equation for the XXZ model. This is achieved by studying the asymptotics of the corresponding open transfer matrix. Linear intertwining relations for the K matrix and Sklyanin’s operator are also obtained, and the symmetry of the transfer matrix is investigated. L...

We consider a variational problem for the two-dimensional (2D) Heisenberg and XY models, using a trial state which is constructed as a 2D product of local weights. Variational energy is calculated by use of the the corner transfer matrix renormalization group (CTMRG) method, and its upper bound is surveyed. The variational approach is a way of applying the density matrix renormalization group m...

The transfer functions of discrete-time SISO compartmental systems whose compartments are connected either in series or in parallel are characterized, and then the corresponding realization problem is studied. The obtained results are extended to the transfer matrix of N-periodic compartmental systems.

Knowledge of the dynamic performance of turbopumps is essential for the prediction of instabilities in hydraulic systems; the necessary information i s in the form of a transfer function relating the instantaneous pressures and mass flow rates at inlet and discharge. Cavitation has a significant effect on this transfer function since dynamical changes in the volume of cavitation contribute to t...