The second-order N-dimensional radial Schrdinger differential equation with the isotropic harmonic oscillator is reduced to a first-order differential equation by means of the Laplace transform, and then, its solutions are directly obtained by means of making use of an integral.

The second-order one-dimensional Schrdinger differential equation for the harmonic oscillator is reduced to a first-order differential equation by means of the Laplace transform,and then,its solutions are obtained by means of directly making use of an integral.

Master equations which normally appear as an infinite set of first-order differential equations coupled with each other are simplified to 4 independent equations, leading to Bloch equations for dressed atoms through which all the coherent interactions of atoms with light can be extended to the case of dressed atoms.

In time series forecasting,a novel criterion has been presented based on the mechanism of first-order differential and minimum variance error under multiple components reconstruction.

In the proposed MPC,the first-order differential equations were derived from the transfer functions of controlling variables and controlled variables in CSC,and the equations were used as predictive control model.

In the proposed MPC,the first-order differential equations were derived from the transfer functions of controlling variables and controlled variables in PWM-CSR,and the equations were used as predictive control model,meanwhile,the uncertain factor reference trajectory was left out. Consequently,considerable computation and inconvenient realization of traditional MPC were avoided and the merits of feedback correction and dynamic optimization of traditional MPC were reserved in the new MPC.

Compared with other similar methods,this algorithm doesn′t need phase estimation. It estimates signal Doppler frequency shift directly by first-order differential structure. This technique may be easily implemented in programmable digital device,and calculate can target-radar radial velocity.

In the paper a method of identifying parameters a, b, c, d, and r in a kind of time-varying linear first-order differential equation system dx(t)dt=ax(t)+br -t y(t),dy(t)dt=cr tx(t)+dy(t) is introduced.

This paper established the existence and uniqueness of periodic solutions for the fully nonlinear first-order differential equations under some natural structure conditions by using viscosity-solutoin method.

In the present paper we obtain an approximate first-order differential equation for the frequency squared, using the filling level as the independent variable.

An ordinary first-order differential equation is obtained for the velocity distribution along the profile in [2].

In the present study, the solution of this type of equation is reduced to the integration of a chain of linear first-order differential equations.

The system of three non-linear first-order differential equations has kinetic energy and circulation integrals representing two ellipsoids with displaced centers in parameter space.

The problem is reduced to two essentially nonlinear first-order differential equations for the velocity and concentration of ions.

Recently, digital computers are gradually used to replace analog or hybrid computations for implement of continuous-system simulations. Digital continuous-system simulation has significant advantages: better man-machine interaction, higher accuracy and reproducibility, more convenient programming and report generation, etc.The simulation user would like to have a more convenient and flexible simulation language, in order to be as free as possible from the details of computer programming and concentrate on his...

Recently, digital computers are gradually used to replace analog or hybrid computations for implement of continuous-system simulations. Digital continuous-system simulation has significant advantages: better man-machine interaction, higher accuracy and reproducibility, more convenient programming and report generation, etc.The simulation user would like to have a more convenient and flexible simulation language, in order to be as free as possible from the details of computer programming and concentrate on his system simulations. An equation-oriented BASIC simulation language which permits the user to enter first-order differential equations in essentially unchanged mathematical form is introduced in this paper. It may run on any machine which supports BASIC. The user does not even have to be familiar with BASIC so long as he follows the simple format specified. A computing example is given to illustrate its application.

In this paper the differential equationis discussed and conditions are found which the functions P1(x), P2(y), Q1(x) and Q2(y) must satisfy for the equation to be integrable. It shows that Bernolli's equation is only a special case of this equation, so that a class of first order differential equations can be reduced to integrable cases and can be solved conveniently by elementary methods.

In this paper, starting from the equations of the nonlinear inertio-internal1 gravity waves in stratified shear fluid, and considering the flow about a class of the progressive waves, the autonomous dynamic systems of the first-order differential equations in two variables are derived. Using the qualitative theory of the differential equations, we analyze qualitatively the topological structure of the integral curves in the neighbourhood of the origin on a phase planewith cartesian axes u, v. On...

In this paper, starting from the equations of the nonlinear inertio-internal1 gravity waves in stratified shear fluid, and considering the flow about a class of the progressive waves, the autonomous dynamic systems of the first-order differential equations in two variables are derived. Using the qualitative theory of the differential equations, we analyze qualitatively the topological structure of the integral curves in the neighbourhood of the origin on a phase planewith cartesian axes u, v. On the du/dz (the velocity shear), L2-L02 (L is thehorizontal scale, L0 is the Rossby radius of deformation) plane, the integral curves divide the plane into some domains of different stability.