Cross Moments Research Articles

Matching polygon fragments

Many computer vision systems model objects using polygons. If objects occlude each other or do not appear entirely in view, we need to match a polygon scene fragment with the polygon representation of the model objects. In this paper we present a way to match polygon fragments. Using polygon moments and cross moments we can compute a dissimilarity measure between two fragments. In addition, we also find the coordinate transform that maps one fragment onto the other. These polygon moments can be conputed by using just the end points of the line segments. If the dissimilarity measure is less than a small number, then we can preliminarily conclude fragments. Otherwise the polygon fragments are dissimilar and are not considered any further. In computing the dissimilarity measure, we will also find a coordinate transform that maps one fragment to another. By using this coordinate transform, we can develop confirmation tests for determining whether the scene polygon fragments really belong to an occluded object.

Some Problems on Nonparametric Estimation in Gaussian White Noise

Some Problems on Nonparametric Estimation in Gaussian White Noise

First passage probability and probability distribution of level crossings for a nonlinear system to nonwhite excitation.

The level crossing problem is discussed for a multi-dimentional nonlinear system subjected to an amplitude modulated nonwhite random excitation. The first passage probability and the probability distribution of the level crossings are approximately represented by a few low order factorial moments of crossings, which are calculated by using the equivalent linearization technique and assuming the Gaussian probability distribution of the response process. The dependence of occurrence of the level crossing upon the number of events is taken into consideration. Numerical results are compared with the corresponding digital simulation results for a single degree of freedom system with bilinear hysteresis excited by noise with an exponentially decaying harmonic correlation function.

Numerical model of the nonlinear behavior of curved rods

A theoretical model for the nonlinear behavior of curved rods is derived. The model is very general and it allows any combination of geometry, structural properties distribution, load distribution, and boundary conditions. A set of nonlinear equilibrium equations and boundary conditions is obtained. The equations are solved using the Galerkin Method. Two kinds of methods to calculate the cross sectional resultant forces and moments along the rod are described. One method includes differentiation of the displacements along the rod while the other method is based on integration of the loads along the rod. In order to show the use of the model an example is presented. The different nonlinear effects are indicated and discussed.

Estimation of first passage probability and probability distribution of level crossings in random vibration.

An approximate analytical technique is presented to improve the theory of level crossings in random vibration. The first passage probability and the probability distribution of level crossings are determined in therms of the factorial moments of crossings. This technique is a generalization of the conventional one, based on the assumption of independent crossings, and thus applicable for a wide class of random processes. As a numerical example, the displacement response of a single degree of freedom linear system subjected to an amplitude modulated white noise excitation is considered. Comparison with the corresponding digital simulation results demonstrates the usefulness of the present method.

軽鋼構造骨組の耐力と変形能力に関する実験的研究

The objectives of this paper are to understand the plastic behavior of cold formed members and to establish the evaluating method of deformation capacity and ultimate strength for the antiseismic design of these steel structures. In the course of this reserch, a total of 25 specimens of cold formed steel beams and 8 specimens of these protal frames including of the braced frame are tested. The test parameters of beam specimens are the shapes of cross section, slenderness ratio and moment distributions. The parameters of frame tests are the cross section of colum members, the details of connection and the boundary condition of base. Experimental results are discussed comparing with that of the heavy steel members and frames. On the cold formed steel members, the ultimate strength can not exceed full plastic moment M_p and local bucking occures at the early stage. The critical buckling stress are not over the yield stress point. From the above reasons, the deformation angle θ_y at the yield moment M_y are introduced for the base evaluated value. The load deflection capacities enough to insure the safety of structures on the antiseismic design. On these structures, the stiffness of connections have not bad effects on deformation capacity. Finally, from these experimental results, the new evaluated method of deformation capacity and ultimate strength for the antiseismic design of these steel structures that have large wide-thickness ratio are proposed.

Random excitation of magnetic spin systems

The equation of motion of the spin density matrix is treated for nuclear magnetic resonance with random excitation by a δ-correlated Gaussian noise process. Lagged cross moments between the transverse rf magnetization response and powers of the input are derived and their relation with deterministic multidimensional resonance spectra is discussed.

Generalization of Fisher's z-transformation

We deal with the asymptotic expansions of the means and the variances of the correlation coefficients in truncated bivariate normal populations. The Fisher's z -transformation is generalized for stabilizing variance in a truncated normal population. The Hermite moments are introduced, and the relationship among cross moments, central cross moments, and Hermite moments are discussed.

Edge reinforced circular elastic inclusions in cylindrical shells

The effect of having an edge reinforcement around a circular elastic inclusion in a cylindrical shell is studied. The influence of various parameters of the reinforcement such as area of cross section and moment of inertia on the stress concentrations around the inclusion is investigated. It is found that for certain inclusion parameters it is possible to get an optimum reinforcement, which gives minimum stress concentration around the inclusion. The effect of moment of inertia of the reinforcement of SCF is found to be negligible. The results are plotted in a non-dimensional form and a comparison with flat plate results is made which show the curvature effect. In the limiting case of a rigid reinforcement the results tend to those of a rigid circular inclusion. Results are also presented for different values of μ e the ratio of extensional rigidity of shell to that of the inclusion.

Aerodynamic Coupling between Lateral and Longitudinal Degrees of Freedom

An oscillatory technique for routine measurement of the direct, cross, and cross-coupling moment derivatives due to pitching and yawing has been developed and a series of comprehensive results at Mach numbers 0.7 and 0.25 and at angles of attack up to 40 deg has been obtained in a large wind tunnel. It was found that some of the dynamic cross-coupling derivatives, which at low angles of attack were all insignificant, at higher angles of attack could reach values that rendered the pertinent cross-coupling terms in the equations of motion comparable in magnitude to the well-established damping terms. This applied in particular to results obtained at Mach number 0.7. Large nonlinear variations with angle of attack were observed in many of the measured derivatives including the important damping-in-pitch and damping-in-yaw derivatives. It was concluded that it may be desirable to include certain dynamic cross-coupling derivatives in the equations of motion, and to consider all of these equations simultaneously, rather than in separate longitudinal and lateral groups.

Study of the [formula omitted] scattering amplitude (I). Threshold to 1 GeV mass region

Kπ scattering from threshold to 1 GeV in Kpi; mass is studied by modified Chew-Low extrapolation in the reactions K −p→K − π +n and K +n→K + π −p. Although the cross section and moments of these two reactions differ significantly in the physical region, similar values are found for the Kπ phases in the two processes. The necessary modifications of one pion exchange are sizeable and although they do not agree quantitatively with the poor man's absorption model, they can be understood in a more general absorption framework. The experimental Kπ s-wave scattering length is much larger than naive current algebra predictions but consistent with a straight forward dispersion theory method of extrapolating current algebra to the physical region.

Post-Elastic Behavior of Wide-Flange Steel Beams

Relationship of flexural strength and fully plastic strength of wide flange steel sections is explained; based on tests on 21 simple beams of various cross sectional dimensions and moment gradients, semi-empirical expressions for strengths and deformations are established and expressions for effective moment curvature relationships for any rolled steel section are obtained; results are compared with rigid plastic and elastic theories.

The Library Shelf

The author is Professor of Aeronautical Engineering and Applied Mechanics at the Brooklyn Polytechnic. He is well known to the British aero‐nautical world not only for his writings but as a fluent and stimulating speaker. In this volume Professor Hoff develops a system of analysis starting from the principle of virtual displacements. In the first of the four Parts this principle is explained and, after a brief glance at its application to mechanisms, is used to find the forces and displacements in jointed frameworks. The principle is applicable to both simply stiff and redundant frames. An engine mounting under torque loads from a radial engine is discussed in full detail to illustrate the application to a redundant space frame with the aid of tension coefficients. This Part ends with the treatment of beams by virtual displacements, the Hardy Cross moment distribution method and the analysis of the rigid unbraced frame.

The Analysis of Shear Distribution for Multi-Cell Beams in Flexure by means of Successive Numerical Approximations

The determination of shear distributions for multi-cell sections can conveniently be considered as two separate problems.(i)the shear flow arising from a pure torsional couple applied in the plane of the section, and(ii)the shear flow arising from a resultant shear force acting on the section so as to produce no resultant twist per unit length of that section,i.e. through the shear centre of that section.Both problems involve finding the value of one unknown shear flow for each cell, so that in multi-cell construction a set of simultaneous equations is obtained, which must be solved to obtain the shear pattern.The solution of problem (i) by successive numerical approximations has been dealt with completely by Benscoter. The present paper gives a method for problem (ii).The usefulness of the method becomes more apparent with increasing numbers of spar webs as may be envisaged for future wing sections of small thickness chord ratios. It is analogous in the procedure used to the Hardy Cross moment distribution method for continuous beams, and has similar advantages. An approximate solution of any required degree of accuracy is quickly obtainable at the design stage and the method is readily adaptable for use by a computer with no knowledge of the structural or mathematical theory involved.

Stresses in Ring Structures

The simple ring frames which are a common feature of metal fuselage construction are being superseded in some large aircraft by more complicated frames in which one or more cross members are added to stiffen the frame. The stress distribution in simple rings is readily analysed by the standard methods for redundant structures, but the direct extension of these methods to more complicated cases leads normally to the solution of a number of simultaneous equations. The method now proposed avoids this difficulty by breaking down the calculation into a number of simple steps and then applying the principle of superposition to combine the results so obtained. In this respect it is equivalent to the Hardy Cross moment distribution method (1) or to Southwell's method of the systematic relaxation of constraints (2) though in many applications the final superposition of loadings is so simple that the full moment distribution or relaxation procedure is not required.

Stress Analysis of Aircraft Frameworks

SummaryIt is shown that the calculation of the critical loads of a plane framework is superfluous if the bending moments in the bars due to external moments and to lateral loads are determined by the Hardy Cross moment distribution method as extended by James. Convergence of this method is a proof of the stability of the framework. In Section 1 methods of determining stresses and critical loads in frameworks are discussed. Section 2 deals with the distortion patterns of beam columns on several supports below and above the critical loads. In Section 3 the method of proof of the convergence is outlined, and regular and particular cases are discussed with the aid of numerical examples. The final proof is given in Section 4.