The common characteristic features of this method is to deal with the working conditions of the designed maximum discharge of closed circuit and then to determine the pipe diameters and water head.

In order to strengthen the energy density of wind flowing through the wind turbine, a system which can highly collect wind energy is presented and the author analysed the optimal conversion rate of wind energy under various working conditions.

Secondly, the topology optimization problem under multiple loading conditions is mathematically stated as a nonsmooth programming problem and the latter is then transformed into a smooth one by means of variable transformation, so that the solution of primary problem is finally changed into the solution of several linear programming problems.

The paper presents an effective method of topology optimization for truss structures under multiple loading conditions, by which the member force and structural weight are considered as a design variable and an objective function respectively, while the topology optimization is described as a non-smoothing programming problem at first, and then, transfromed into a smoothing one by means of the variable transformation.

As a consequence, the action is linearizable if certain topological conditions are satisfied.

An algebraicG-varietyX is called "wonderful", if the following conditions are satisfied:X is (connected) smooth and complete;X containsr irreducible smoothG-invariant divisors having a non void transversal intersection;G has 2r orbits inX.

Here we provide certain conditions (more general than those in [Ka1]) which guarantee preservation of the topology under a modification.

We express the vanishing conditions satisfied by the correlation functions of Drinfeld currents of quantum affine algebras, imposed by the quantum Serre relations.

We discuss the relation of these vanishing conditions with a shuffle algebra description of the algebra of Drinfeld currents.

In this paper some cases of optimum control are studied when the conditions at the ends of trajectories are constrainted. The boundary conditions of the system of the differential equations (19), (22), etc. are determined; the formulae of functional variation (20) are derived; and the sufficient conditions of optimality and necessary conditions in some cases are proved.

The problem of large deflection of a clamped circular plate under uniform pressure is studied by the method of successive approximation in terms of the parameter representing the ratio of the center deflection to the thickness. The tedious numerical computations, involved in Way's power series solution are thus avoided. The yielding condition at the edge checks very well with the experimental results given by McPherson, Ramberg and Levy. The method may be easily extended to any other boundary conditions...

The problem of large deflection of a clamped circular plate under uniform pressure is studied by the method of successive approximation in terms of the parameter representing the ratio of the center deflection to the thickness. The tedious numerical computations, involved in Way's power series solution are thus avoided. The yielding condition at the edge checks very well with the experimental results given by McPherson, Ramberg and Levy. The method may be easily extended to any other boundary conditions and loading details.

The dependence of the entropy of a homogeneous system on the composition is investigated with the help of a reversible adiabatic process which allows the change of composition by means of a semipermeable wall. The conditions of equilibrinm for phase transition and for homogeneous chemical reaction are derived in a new way. Next the criterion of minimum energy for constant entropy and volume is derived from the principle of increase of entropy. This criterion is then applied to obtain the conditions...

The dependence of the entropy of a homogeneous system on the composition is investigated with the help of a reversible adiabatic process which allows the change of composition by means of a semipermeable wall. The conditions of equilibrinm for phase transition and for homogeneous chemical reaction are derived in a new way. Next the criterion of minimum energy for constant entropy and volume is derived from the principle of increase of entropy. This criterion is then applied to obtain the conditions of equilibrium and stability with the help of Lagrange's multipliers. The conditions of stability are expressed in several alternative forms. Next the equilibrium properties of a binary system arc considered, and some types of phase diagram are explained by means of equations. The theory is extended to the general heterogeneous equilibrium of a system consisting of any number of independent components. A system of equations for the change of temperature, pressure, and composition are obtained and are solved by means of determinants. Next Planck's theory of a binary solution is extended to a solution consisting of several solnte components, with the same conclusion regarding the lowering of freezing point as for a binary solution. Finally Planck's theory on the number of coexisting phases for aone-component system is extended to a system consisting of k components with the result that a state with, σ coexisting phases is more stable than one with σ-1 phases: where σ is an integer not greater than k + 2.