Torus graphs and simplicial posets

For several important classes of manifolds acted on by the torus, the information about the action can be encoded combinatorially by a regular n-valent graph with vector labels on its edges, which we refer to as the torus graph. By analogy with the GKM-graphs, we introduce the notion of equivariant cohomology of a torus graph, and show that it is isomorphic to the face ring of the associated simplicial poset. This extends a series of previous results on the equivariant cohomology of torus manifolds. As a primary combinatorial application, we show that a simplicial poset is Cohen-Macaulay if its face ring is Cohen-Macaulay. This completes the algebraic characterisation of Cohen-Macaulay posets initiated by Stanley. We also study blow-ups of torus graphs and manifolds from both the algebraic and the topological points of view.Comment: 26 pages, LaTeX2e; examples added, some proofs expande

THE RELATION BETWEEN CHLORINITY AND SILICATE CONCENTRATION OF WATER OBSERVED IN SOME ESTUARIES

The most important problem near the estuaries may be the investigation of the influence of the sea water upon the river water and vice versa. By stochastical analysis of previous data, I found that the concentration of chlorine (dominant in sea water) and that of silicate (dominant in river water) alter near the estuary in a correlated manner which may be represented by a nearly exact linear formula. In this report I want to propose an actual relation formula deduced from the calculated data of 9 observations in two inlet bays, Yosa-naikai and Kojima Bay. I wish to express my sincere thanks to Prof. Dr. D. MIYADI (Biologist) and Prof. Dr. M. ISHIBASHI (Chemist) of Kyoto University and their co-workers for their kind assistance, valuable advices and criticisms given to me

A Method to Optimize the Stability of a Linear Dynamic System : II. With Equality Constraints

A numerical method to optimize the stability of a linear dynamic system which was described in the last paper is generalized to the case of equality constraints in this report. The process is an application of the “steepest-descent method” as well, and it is inclusive of the procedure given in the last paper as a simple case. Hence, with application of this method, problems which are of practical interest but are difficult to treat with the previous method are expected to be solvable. A numerical example is presented for maximizing the damping of the Dutch-Roll mode of motion of an airplane

A Method to Optimize the Stability of a Linear Dynamic System

A systematic and numerical procedure is described for optimizing the stability of a linear dynamic system. The process is an application of the so-called “steepest-descent method”, and since the stability of a linear dynamic system is determined by the real part of the roots of the characteristic equation, the practical procedure is suggested in this paper. A numerical example is presented for maximizing the damping of the perturbed motion of a earth satellite by the use of the gravity-oriented principle

Experimental Methods for Determining Aerodynamic Stability Derivatives of an Airplane in Wind Tunnels

Two methods for determining the aerodynamic stability derivatives of an airplane in wind tunnels are investigated. The principles of measurement are as follows : (1) Determining the stability derivatives from the frequency response characteristics of a second order dynamic system with application of a forced oscillation of constant amplitude ; (2) Determining the stability derivatives from the transient response data of the model to a step control deflection input. The former is suitable for low speed wind tunnel tests, and the latter is mainly for high speed wind tunnel tests. In this paper the theoretical calculation and the preliminary experimental results are reported

Pitching Characteristics of Peripheral Jet Ground Effect Machines

A theory of the pitching characteristics is presented for three-dimensional peripheral jet ground effect machines which are equipped with a compartment partition along the pitch axis. The analysis is separated into two parts, i.e. the longitudinal static stability and the dynamic pitching motion. In both cases, the behaviors of jet are quantitatively treated as the underfed and overfed operation. At the static pitch condition, the cushion pressures in the falling downward and rising upward compartments are first discussed, and applying those results, a simple expression of the static moment about the pitch axis is derived. Next, utilizing the quasistatic principle, a second order nonlinear differential equation is obtained as the equation of pitching motion. Detailed calculations have been carried out for a circular model GEM, and the comparisons with experimental data are encouraging

A Method for Calculating the Dynamic Stability of a Human-Piloted Airplane by the “Root-Locus Method”

A method of treating a human-piloted airplane as one closed-loop system and calculating the dynamic stability of the airplane by the Evans's “Root-Locus Method” has been investigated. Using this method, not only the characteristics of the transient motion but also the control ability of the human-pilot to decrease the residual motion of the airplane can be understood conveniently. In this paper, some results of numerical calculation with this method are described for a typical airplane

Spin Wave Resonance and Exchange Parameters in fcc Fe-Ni Alloys

Spin wave resonance for a series of fcc Fe-Ni alloys has been measured in order to study the exchange stiffness constant D. In general the resonance field vs the square of the spin wave mode number (n) curve is linear for high values of n, whereas some amount of deviation from linearity occurs for low values of n. This is considered to be due to the inhomogeneous demagnetizing field of the sample. We can determine the value of D from the linear part of the curve, provided we have a sufficient number of observed modes. As a supplementary means, we have also made low temperature magnetization measurements from which the value of D was derived. Consistency between these two kinds of measurements is ascertained. The composition dependence of D is not quite coincident with that derived from the neutron small angle scattering experiments by Hatherly et al. The data are discussed both from the standpoint of localized electron model and collective electron model

An Application of Stochastic Control Theory to the Gust-Alleviation System for a Transport Airplane

The optimal control law that minimizes the gust responses of an airplane's longitudinal motion is obtained, making assumptions that the airplane is approximated as a point and that aeroelastic problem is ignored. The airplane gust-alleviation problem has been treated mainly in the frequency domain because of the simplicity of the input-output relations for the power spectra. But in the optimal control problem, the approach in the time domain, applying the optimal stochastic control theory, seems to have more advantages for investigating such a complex control as gust-alleviation. The system state equations consist of the short-period equation of an airplane and the gust shaping filter. The optimal linear control law is derived by applying the Matrix Minimum Principle which minimizes the R.M.S. values of the normal acceleration and the pitch rate at the center of gravity. The results of the numerical calculation for two types of control systems, one being the linkage-control system and the other the independent-control system, are shown in the case of a conventional transport. The latter system is ascertained to have a fairly better performance. The optimal system is also ascertained to have very low sensitivity to the change of the scale of turbulence