Moment Criterion Research Articles

A cascade decomposition theory with applications to Markov and exchangeable cascades

A multiplicative random cascade refers to a positive T T -martingale in the sense of Kahane on the ultrametric space T = { 0 , 1 , … , b − 1 } N . T = { \{ 0,1,\dots ,b-1 \} }^{\mathbf {N}}. A new approach to the study of multiplicative cascades is introduced. The methods apply broadly to the problems of: (i) non-degeneracy criterion, (ii) dimension spectra of carrying sets, and (iii) divergence of moments criterion. Specific applications are given to cascades generated by Markov and exchangeable processes, as well as to homogeneous independent cascades.

Failure of an axially compressed beam with uncertain initial deflection of bounded strain energy

Energy-bound convex models are used to represent uncertainty in the initial deformation of a uniform beam. The main result is to relate these convex models of uncertainty to the maximum bending moment failure criterion for the axially loaded beam. While the maximum-moment concept is a local failure criterion, it is governed by global energetic considerations. The initial deformation energy specifies the degree of uncertainty in the initial beam shape, as well as the greatest bending moment which can be attained in the loaded beam. Analytical relations are obtained which determine the maximum allowable, critical, initial deformation energy as a function of the applied load. This theoretical critical load is compared against and seems consistent with allowed engineering data. Considerable simplification is attained by exploiting a single physical parameter—the deformation energy—for specifying both the shape uncertainty and the failure criterion. The ability of the initial deformation energy to serve as a failure criterion, equivalent to the maximum bending moment criterion, is given a physical interpretation.

Raman scattering investigation of the orientational dynamics of methyl iodide

A Raman scattering study of the v 3 vibration—rotation band in methyl iodide as a function of temperature and dilution (in cyclohexane) has been performed. All the data satisfy the second moment criterion. Detailed information about rotational correlation function, angular velocity correlation function, various correlation times and mean-square torque has been obtained. The correlation function, in the pure liquid, decays slowly with decrease in temperature whereas it decays faster with decreasing concentration in cyclohexane. It has been shown, from a consideration of the second moment as a function of concentration, that the contribution of collision-induced scattering to the v 3 band of methyl iodide is negligible. Applicability of a simple “damped librator model”, with a view to understanding certain aspects of the rotational motion in methyl iodide, is discussed.

A biomechanical analog of curve progression and orthotic stabilization in idiopathic scoliosis

A biomechanical analog of curve progression and orthotic stabilization in idiopathic scoliosis has been developed using the classical theory of curved beam-columns. The interaction of the spinal musculature and other supporting structures is incorporated in the model using an equivalent flexural rigidity. The stability of a given scoliotic curve relative to a normal spine is described in terms of the so-called critical load ratio ( P c P e ). This dimensionless quantity appears in the exact solution of the governing differential equation and boundary conditions. It is defined as the ratio of the load bearing capacity of a scoliotic spine ( P c ) to that of a normal spine where the load bearing capacity of a normal spine is defined as Euler's buckling load ( P e ). The computation of P c P e is based upon a maximum allowable moment criterion. This model is used to study the effect of the degree of initial curvature and curve pattern in the frontal plane on the stability of untreated idiopathic scoliosis. Although restricted to two-dimensions, the model appears to demonstrate the synergistic effects of end support, transverse loading, and curve correction on improvement in relative stability of an orthotically supported scoliotic curve. The results of this study are in qualitative agreement with clinical findings that are based on long-term studies of natural history of idiopathic scoliosis and of patients undergoing orthotic management for scoliosis.

Shakedown analysis of plates

A numerical approach for shakedown analysis of laterally loaded elasto-plastic plates is presented. The normal moment criterion and the Tresca criterion are considered. Shakedown criteria are applied at a set of nodes distributed throughout the plate. Apart from the elastic analysis, the main computing work involves solving of a primal dual pair of linear programming problems. The analysis provides the shakedown limit and indicates the mode of failure (incremental collapse or alternating plasticity). Whenever incremental collapse is the critical mode the collapse mechanism is determined.

Two moment structural safety analysis

In this paper the two moment criteria proposed by Hasofer and Lind, Paloheimo and Hannus, Ditlevsen and Skov, and the European Joint Committee on Structural Safety are reviewed. Numerical results for several examples are presented and compared. Special attention is given to situations involving counteracting forces where serious difficulties with simple approaches are demonstrated. The problem of design with specified indices is discussed briefly through two examples. It is concluded that simplified criteria may often be used but that a more basic approach must be followed in certain situations.

An algorithm for the calculation of distribution parameters in an analysis of the dose-effect curve

An algorithm is proposed for calculating the parameters of the statistical distribution of the dose-effect curve on the basis of the principle of piecewise-linear approximation. The computer program enables an estimate of the mean dose (equivalent to the value ED50 as applied to a normal distribution) and the error of its determination to be obtained; a check on the hypothesis of the normality of the statistical distribution is carried out by the method of moments and Kolmogorov's criterion; if this hypothesis is correct, the values of ED025 and ED975 are calculated. Since the algorithm is not connected with any a priori hypothesis concerning the nature of the distribution of the probability of the effect, the estimate obtained by using it is free from the distortions inherent in the method of probit anaylsis [1]. At the same time, the possibility of approximating the empirical distribution by the normal distribution is taken into account and is checked by the extremely strict criterion of moments and Kolmogorov's criterion. The corresponding check has shown that some of the empirical distributions of the probability of a lethal effect of antibiotics that we have encountered in acute experiments on mice definitely do not belong to the normal type. In this case, the estimate of the mean dose cannot be expressed by the idea of ED50, which is quite permissible for a normal distribution in which the mathematical expectation and the median coincide. In addition to the variance of the distribution of the probability of the effect, we also calculated the variance of the summed binomial distribution of the tests of various doses, which estimates the error in the estimate of the mean dose. This estimate is weakly connected with the nonuniformity of the distribution of the symptom of sensitivity to the preparation in the population and therefore permits the approximation of the binomial distributions to the normal distribution to a considerably greater extent. It is proposed to calculate the confidence intervals for the estimate of the mean dose for the 5% level of significance on the basis of the latter program.

Monotonicity Properties of the Moments of Truncated Gamma and Weibull Density Functions

Moments of truncated Weibull and gamma density functions exhibit monotonicity properties with respect to the parameters of these density functions under the assumption of a known truncation value. Using these properties, we then apply the melhod of moments criterion to get estimates of the parameter of the truncated exponential density function.

Monotonicity Properties of the Moments of Truncated Gamma and Weibull Density Functions

Moments of truncated Weibull and gamma density functions exhibit monotonicity properties with respect to the parameters of these density functions under the assumption of a known truncation value. Using these properties, we then apply the melhod of moments criterion to get estimates of the parameter of the truncated exponential density function.

Yield-line theory and limit analysis of plates and slabs

Synopsis The usual geometrical, statical and physical conditions for the anisotropic, perfectly plastic plate are given. It is demonstrated that the normal moment criterion usually employed in modern yield-line theory is identical with the ‘stepped’ criterion of the classical theory, and that they both correspond to a yield surface, called the upper yield surface, which satisfies the requirements of limit analysis. When the actual yield surface of the plate is different from the upper yield surface, then the yield load predicted by limit analysis can generally not be determined by yield-line theory. It is not even possible to approach the solution by successive refinement of the yield-line pattern. The common yield surfaces of metal plates are compared with the upper yield surface, and the yield surface of the arbitrarily reinforced concrete slab is derived. Finally, the relationship between yield-line theory and limit analysis is discussed, and it is concluded that the two theories are consistent in their foundation.

A consistent limit-analysis theory for reinforced concrete slabs

Summary The paper aims to show that a consistent limit-analysis theory for reinforced concrete slabs can include the recent advances in yield-line theory. It starts by accepting a physical yield criterion for an element of a slab (a bending moment criterion), derives the yield surface in moment space, assumes plastic potential (normality law) and shows that yielding can occur in the form of yield lines and also of yielding regions. The fundamental theorems of limit analysis are then stated. Nodal-force theory is defined and the concept of upper-bound moment field is examined. Connexions between various approaches to nodal-forces formulae are noted, and particular aspects, such as the intersection of yield lines and the existence of torque in the yield lines, are discussed.

The Galton-Watson Process with Mean One and Finite Variance

The Galton-Watson Process with Mean One and Finite Variance

Development of Arch Action in Arch Dams

Considering hydrostatic pressure as the only external load on an arch dam, the influence of the reservoir elevation and the elastic deformability of the foundations is investigated using the crown cantilever method. The arch and cantilever action are evaluated on the basis of a shear and moment criterion, representing the relative magnitude of the hydrostatic loads carried by arches and cantilevers. The structural behavior of the dam has been studied on the basis of the radial displacement of the crown cantilever, hydrostatic load distribution, and stresses in the arches and cantilevers. The arch action increases with the deformability of the foundations and generally with an increase in the level of the reservoir. The lower levels of the reservoir result in noticeable increase in cantilever tensile stresses. Conversely, only compressive stresses appear to increase with overpressures.