Conversion Matrices Research Articles

An Analysis of the Output and Employment Conversion Matrices of Australia’s Economy

Based on two snapshots taken from the Australian economy, this study quantifies the impacts of final demand aggregates on output and employment in various sectors using the 1989 and 1997 conversion matrices. The sectoral output and employment are linked with final demand deliveries in such a way that one can measure the impacts on changes in each component of aggregate demand, other components remaining unchanged, on output and employment. A comparison of the aggregate output and employment multipliers in 1989 to 1997 indicates that while the output multipliers have increased, the employment multipliers have declined. This means that through time, due to rising labour productivity, the various components of aggregate demand would need to grow at a faster rate in order to achieve a certain employment growth. It was also found that almost all employment generated between 1989 to 1997 was in three service industries, namely community, social and personal services; wholesale retail; restaurants and property: and business services. These are industries that are least likely to have benefited from the productivity gains that resulted from the microeconomic reforms that characterised the Australian economy during this period. On a relative basis, a rise in various components of aggregate final demand can lead to a higher employment generation in these three industries.

Phase noise: whether identical at all nodes in free-running oscillator circuit

Many years ago it was analytically demonstrated that phase noise in free-running oscillators might be different on the different circuit nodes. Recently this result was questioned. It was claimed that phase noise is identical at all nodes, and characterised by a single scalar constant for white noise sources. Using the time domain Monte Carlo method, which is the only method which does not treat the large signal and the noise signals separately, it is demonstrated that in free-running oscillator circuits the phase noise could be different on the nodes of the circuit and cannot be represented by a single scalar constant. This result is confirmed by simulations performed in the frequency domain using the conversion matrices method.

The conversion matrix between uniform B-spline and Bézier representations

In computer-aided design it is both convenient and practical to use the matrix form in representing parametric curves and surfaces. One of the reasons is that the matrix notation allows an easy conversion between different shape representations and provides a convenient implementation in either hardware or software with available matrix facilities. In this work we propose a very simple and efficient procedure for computing in a recursive way the conversion matrices which provide the direct transformation between uniform B-spline and Bézier representations of arbitrary degrees.

A Note on Mathematical Relationships Among Bond-Torsion Force Fields

A set of mathematical relationship between torsion potential functions such as trigonometric and Fourier series is presented herein. A harmonic approximation form is also introduced, and its stiffness constant is related to the parameters of trigonometric and Fourier series. Mathematical relationships between various force field parameters are presented in the form of conversion matrices.

Multitone signal harmonic balance method

A novel approach for generating the frequency/time conversion matrices of multitone signals is presented. Conversion matrices are normally used in the harmonic balance method to evaluate currents/voltages of nonlinear devices. The conditioning number of these matrices is a fundamental aspect and the proposed approach always generated matrices with the best conditioning number.

Noise modeling in MESFET and HEMT mixers using a uniform noisy line model

The aim of this paper is to present a noise model which predicts the noise performance of MESFET and HEMT mixers. The conversion and noise correlation matrices of a FET mixer are calculated using a uniform nonlinear noisy active line concept to describe the FET. This calculation is based on a perturbation analysis of the large-signal noiseless steady state, making it a microscopic nonlinear noise model. This method is applied to the case of a hot HEMT gate mixer and we show that the theoretical results are in agreement with experimental data.

Comparison between simulations and measurements of large signal and nonlinear noise behaviors of MMIC analog frequency divider by two

For the first time, the large signal and nonlinear noise behaviors of an analog frequency divider has been fully simulated and measured: comparisons between predicted and measured results of this circuit are given. The circuit designed is a monolithic microwave integrated circuit (MMIC) X-band 8.2-4.1 GHz analog frequency divider by two. The large signal analysis relies on the open-loop method extended to synchronous systems. The simulation of noise behavior of such a circuit has been performed by means of the nonlinearities conversion matrices and noise generators correlation matrices analysis.

Fields as a framework for integrating GIS and environmental process models. Part 2: Specifying field variables

In Part 1 of this paper, the concept of a field variable was described. In Part 2, the way in which a field variable might be specified is outlined. Field variables can be declared like other data types in any standard computing language. Specifications of field variables must include several special properties which are used to express the relationship between the physical field and the discrete data model. Field variable properties determine how the spatial data can be manipulated. For example, specifying a cellgrid spatial data model requires information about grid orientation and origin and the size of cells, while specifying a polygon data model requires information about the minimum distance over which variation is recorded. In either case, this information can be used to select appropriate conversion procedures between spatial data models using similarly specified conversion matrices and rules. The use of field variables has pedagogic as well as practical value. New operations allowed include field functions such as those for determining integrals, slope, and aspect, and reserved variables such as latitude and longitude.

Dimensional-directional analysis by a quaternionic representation of physical quantities

The method of dimensional-directional analysis is established by a way which consists of the representation of the physical quantities as quaternions. Two dimensional-directional bases are obtained for the particular case of Newtonian mechanics. The dimensional-directional, the dimensional, the directional and the reduced-dimensional-directional equations are defined. Furthermore, the Principle of Dimensional-directional Homogeneity is established and the Buckingham π theorem is reformulated. Some examples show the powerfulness of the dimensional-directional analysis. Finally, the conversion matrices for a change of dimensional-directional basis are given.

The numerical problem of using Be´zier curves and surfaces in the power basis

The computations of curves and surfaces points for CAD modeling are numerous and important. In the case of modeling using the Be´zier method, these may be achieved either with the De Casteljau algorithm in the Bernstein basis, or with the Horner algorithm in the power basis. The De Casteljau algorithm requires a greater number of operations than Horner's. However, we show that the equations of curves and surfaces in the power basis may be affected by a very important loss of significant digits on the polynomials coefficient; this is due to the required conversion matrices which are ill-conditioned. Examples are given. We conclude that the use of the Horner algorithm should be avoided for the computations of curves and surfaces points with the Be´zier method.

Discrete transforms via the Walsh-Hadamard transform

Even-odd transforms (EOTs) such as the discrete cosine (DCT), the discrete sine (DST), the slant (ST) and the discrete Legendre (DLT) transforms are developed from the Walsh-Hadamard transform (WHT). Conversion matrices for all these EOTs are outlined. Computational requirements for implementing these transforms are listed.

Lattice constant systems and some of their properties

Lattice constants are defined in a general way such that weak lattice constants, strong lattice constants, free multiplicities and coincidable occurrence factors are cases of the generalised lattice constants. A general method to express a lattice constant of one system as a linear combination of lattice constants of another system is described. Some properties of the conversion matrices are discussed. A systematic method to express the lattice constant of a reducible graph in terms of lattice constants of irreducible graphs is also studied.

Some results on conversion matrices

In this paper we prove a theorem concerning weak lattice constants and hence three matricial equations for conversion matrices. Then we introduce a block-partition for conversion matrices and we write matricial equations for this block-partition; from these matricial equations we propose the calculus of conversion matrices by induction on their order.

Lattice constants matricial equations for conversion matrices

In this paper we proof a theorem concerning lattice constants and hence three matricial equations for conversion matricesR: if H=ΔRT we have: i)H 3 =I; ii) HT Σ H= Σ; iii)(DH) 2 =I; where Δ,D, and e are known when we can enumerate all non-isomorphic graphs withn vertices, we know (for Δ and e) their edge-number and (for e) the order of their automorphism group.

Improved tables for the evaluation of sphere size distributions including the effect of section thickness.

The problem of determining the size distribution and population density of a population of spherical particles randomly distributed throughout a transparent matrix from data obtained by transmission microscopy on parallel plane-faced sections of known field area and thickness may be readily solved by the use of matrix algebra. The solution presented in this paper may be used to construct conversion matrices whereby the particle size distribution and the numerical density can be calculated directly from the frequency distribution of the observed diameters; the only mathematical processes necessary being mulitplication and addition. Specimen conversion matrices valid for a wide range of conditions are presented in the appended tables.

Indirect measurements of family size preferences and of abortion

SummaryMatrices are derived for converting the proportions of couples wanting various completed family sizes to proportions attaining given sizes of families at a given time, based on a simulation model in which couples commence the regular use of contraception as soon as the decision is made to have not more than one further child. The matrices are adapted to include a proportion of ‘prospective aborters’ who are prepared to have recourse to abortion if contraception fails. A measure of consistency between the family size preferences estimated for different durations of marriage is introduced. This measure, together with the conversion matrices, is used to estimate the distribution of aborters and of family size preferences among a cohort of women married in England and Wales in 1920–24 at ages 20–24.