his paper gives a method of obtaining the general solution of the equations to be U(x,y) = C through properly decomposing M(x,y) and N(x,y) in a total differential equation M(x,y)dx + N(x,y)dy = 0, and having indefinite integrals to get the binary function U(x, y).
Based on the definitions of real and reactive currents into a bus due to a generator, a new method is derived theoretically to determine branch's complex loss components induced by individual generators' active- and reactive-power, respectively, using the concepts of total differential and definite integral.
We compare the integral of a functions complete differential expression along limit cycle and reduction to absurdity and obtain a limit cycle uniqueness theorem of system (1) under certain conditions.
The expression of energy margin is given using full differential formula. And the energy margin sensitivity is calculated by state variable sensitivity computation in fault clearing point and controlling UEP.
Deformation induced grain growth (DIGG) is an important characteristics of micro-deformation evolution during superplastic deformation. Based on the idea that full differential of superplastic grain growth is the partial sum of net micro-deformation deformation of grain switching and static growth of grain, a modified model of Campenni DIGG model and a newly extended grain growth rate model have been obtained. Model predictions are proved by experimental evidence of DIGG in superplastic Mg-8.4Li alloy.
Regarding seeking solution of three kinds of first order differential equations,usually the reference book introduces some methods of looking for integral factor ,then transforms integral factor into full differential equation ,finally through which the solutien is found.
According to the transient hydrodynamics theory, an one dimension non stable flow mathematic model was evolved and with a special full differential equation,the outburst gas affected to the incoming air flow and practices were calculated.
A Maximum Principle for Linear Total Differential Control Systems with One-Parametric Input
The Zhikov-Bronshtein theorems concerning asymptotically almost periodic solutions of ordinary differential equations are extended toβ-differential equations (in particular, to total differential equations).
It has been adapted to a direct determination of sulfide by both common spectrophotometric method and total differential spectrophotometric method.
In total differential spectrophotometric method, the calibration curve is A=9.25ρ + 0.004 and the correlation coefficient is 0.9996.
The limit of detection is found to be 1.0 ng·mL-1 by both common spectrophotometric method and total differential spectrophotometric method.