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The essence of the new approach to the equation of the monolayer state
      
A new approach to the theory of the equation of state of the adsorption monolayer is elucidated.
      
The influence of the orientational effect on the equation of the monolayer state and phase transitions is discussed.
      
The velocities of an increase in the number of molecules and the radius of two-component droplet with time are found with allowance for the equation ensuring this solution.
      
Calculations are performed on the basis of the equation of rotational diffusion derived previously by the authors.
      
The equation is equivalent to a periodic Hamiltonian system with a single degree of freedom and has a singularity.
      
A New Approach to the Equation of State of a Monolayer
      
It is shown also that the one-dimensional motions of an ideal gas with the equation of state p=ρf(t) and the one-dimensional adiabatic motions of a gas for which p=ρf(τ) are equivalent (t is time,τ is the stream function).
      
Chaplygin [1] obtained a general solution for the equation of motion in the hodograph plane.
      
The fixed surface is given by the equation y=h[1+εf(x/h)], where the functionf(x/h=h) characterizes the deviation of the fixed surface from the plane y=h(h and ε, are constants).
      
Since the equation for χ is very complex, we have considered only two interesting cases, namely: 1) when the motion is irrotational, and 2) when the pressure is constant along the streamlines.
      
All the equation coefficients have been calculated for a cavity in the form of a circular cylinder or two concentric cylinders.
      
The solution of the equation is presented for a five-point system in the form of a power series with respect to time.
      
We consider a system consisting of the equation of motion, the equation for the turbulence energy, the expression relating the turbulence coefficient with the turbulence scale, and the integral formula for determining the turbulence scale.
      
In addition to the usual MHD equations (with additional terms accounting for the magnetization of the medium), this system includes the equation for the rate of change of the magnetic moment.
      
The paper considers the solution of the equation of relative motion of two spherical bubbles in a fluid for high Reynolds numbers.
      
A solution is presented of the equation for the transfer of a vortex in the case of an external flow containing a single largesize vortex in the low-frequency part of the spectrum.
      
For the velocity profile in the mixing zone an expression is used which results from integrating the equation of motion in von Mises variables.
      
The motion of the gas, as shown in [2], can be assumed to be nearly isothermal, and the influence of the inertial terms in the equation of motion for the gas can be neglected.
      
The present study offers a numerical solution of the problem of an underwater explosion based on the equation of state obtained in [9].
      
 

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