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The system with partial unknown structure, parameters and characteristics is called a grey system. Grey system theory is a newly developed theory to deal with the problem of uncertainties in the case with “poor” information and has widely been used in many fields. The grey prediction SCGM(1,1) model has been used widely. In this paper, the characteristics of SCGM(1,1) model are systematically studied. Some new existing forms of SCGM(1,1) are derived including exponential form, α, β parameter form, scale form and recursive form. The parameter range suitable for SCGM(1,1) modeling has been studied based on strict proof. The prohibited area and the area not suitable or suitable for modeling of SCGM(1,1) model are divided clearly according to the developing coefficient a. Then, the discrete form of developing coefficient a is given. Based on the discrete form of developing coefficient a, a new grey modeling method avoiding complex matrix calculation is presented.

The purpose of this paper is to propose an extending correlation analysis method to deal with the correlation analysis between the sequences with incomplete information.

Based on the axiomatic definition of a grey number and its greyness degree in grey system theory, the whitenization mean, whitenization difference, whitenization covariance of sequences with interval grey numbers and their greyness degrees are defined in turn. In addition, the whitenization correlation coefficient and its greyness degree of sequences with interval grey numbers are also defined. By using the relationship between the greyness degree and kernel for a grey number, the transformation formula from the whitenization value and greyness degree of correlation coefficient to form of interval grey numbers are put forward further.

The whitenization value of correlation coefficient efficient of two arbitrary sequences with interval grey numbers have symmetry, with same greyness degree but without normalization in the interval [−1, 1]; the mean, difference, covariance and correlation coefficient defined in statistics are all the special cases of those in sequences with interval grey numbers.

Due to the complexity of operation of grey numbers, the reliability of correlation coefficient of interval numbers sequence is difficult to be tested by constructing statistics at present. The further research is needed.

The correlation analysis method of interval grey numbers can contribute to the further researches on the incomplete information system in the real world.

On the basis of grey system theory, a correlation analysis method for analyzing information incomplete sequences is proposed.

Provision must be made on all aeroplanes for the rapid egress of passengers and crew in emergency. Fulfilment of the requirements detailed below will normally be regarded as sufficient, but departures may be permitted or required in particular cases.

THIS paper presents a summary of the method and results of a general investigation into the performance characteristics of ‘single’ autogyro and helicopter rotors, which was a preliminary to the establishment, by the firm the author serves, of a helicopter division.

This study aims to deal with the performance of symmetric/asymmetric slot entry hybrid journal bearing system considering the effect of three dimensional irregularities in the analysis.

The asperity profile of three-dimensional irregularities has been modeled in both circumferential and axial directions. To compute the bearing performance characteristics parameter, finite element formulation of governing Reynolds equation has been derived using Galerkin’s technique.

Based on the numerically simulated results, it has been observed that the three-dimensional irregularities enhance the value of minimum fluid film thickness (h̄_min), lubricant flow (Q̄) and fluid film damping coefficients (C̄₁₁,C̄₂₂) approximately by order of magnitude of 24-26, 43-51 and 18-66 per cent, respectively, for the case of asymmetric slot entry configuration. Whereas, the values of fluid film stiffness coefficients (S̄₁₁,S̄₂₂) and threshold speed (ω̄_th) reduces approximately by order of 1-6 and 0-3 per cent, respectively, for the case of symmetric slot entry configuration.

The present paper describes that the influence of three-dimensional irregularities on bearing surface on the performance of slot entry hybrid journal bearing is original in literature gaps. The numerically simulated results presented in this study are expected to be quite useful to the bearing designers.

CONSIDER a single rotor helicopter disturbed from the hovering condition as in FIG. 16. It has acquired a small forward velocity V ft./sec. and a nose‐up angular velocity of q rads./sec. For simplicity we consider the centre of gravity of the fuselage to be on the shaft axis, since its actual position can be shown to have a negligible effect in hovering. Resolving moments about the centre of gravity, the important terms are

The multi-quadrics (MQ) function is a kind of radial basis function. And the MQ method has been successfully adopted as a type of meshless method in solving electromagnetic boundary value problems. However, the accuracy of MQ interpolation or solving equations is severely influenced by shape parameter. Thus the purpose of this paper is to propose a case-independent shape parameter selection strategy from the aspect of coefficient matrix condition number analysis.

The condition number of coefficient matrix is investigated. It is shown that the condition number is only a function of shape parameter and MQ node number, and is irrelevant to the interpolated function which means case-independent. The effective condition number which takes into account the interpolated function is introduced. Then, the relation between the relative root mean square error and condition number is analyzed. Three numerical experiments as transmission line, cable channel and grounding metal box model were carried out.

In the numerical experiments, there is an approximate linear relationship between the logarithm of the condition number and shape parameter, an approximate quadratic relationship with node number. And the optimal shape parameter is corresponding to the early stage of condition number oscillation.

This paper proposed a case-independent shape parameter selection strategy. For a finite precision computation, the upper limit of the condition number is predetermined. Therefore, the shape parameter can be chosen where condition number oscillates in early stage.

Applies an error‐correction model to demand for money in five African economies: Congo, Côte d′Ivoire, Mauritius, Morocco and Tunisia. Attention is given to a set of opportunity cost variables including expected inflation, domestic interest rate, foreign interest rate and expected exchange‐rate depreciation. The empirical results show that the domestic interest rate plays a significant role in the demand for money functions for three of the five countries and external opportunity cost variables are significant for one of the others. The results show some diversity in money demand behaviour in the countries studied, but the error correction mechanism is always significant and in four out of five cases there is a short‐run inflation impact. The equations are subjected to a battery of tests and found to be statistically well‐behaved.

This paper presents a computationally efficient numerical solution scheme to solve transient heat conduction problems using the boundary element method (BEM) without volume discretization. Traditionally, a transient solution using BEM is very computer intensive due to the excessive numerical integration requirements at each time increment. In the present work a numerical solution scheme based on the separation of time and space integrals in the boundary integral equation through the use of an appropriate series expansion of the integrand (incomplete gamma function) is presented. The space integrals are evaluated only once in the beginning and within each time increment the additional integrals are obtained from the previously evaluated space integrals by a simple calculation. Three‐dimensional applications are provided to compare the proposed strategy with that used traditionally. The CPU requirements are reduced substantially. The solution scheme presented allows for dynamically changing the time step size as the solution evolves. This feature is not practical in the traditional schemes based on boundary discretization only.