For the elliptic partial differential equations of variable coefficient,we obtain the product theorem of asymptotic expansions of energy integral as follows:B(w,v_h)=∑ni=1h~(2i)_e∫_ΩF_i(D~(2i-2)_x(v_(xx)φ))v_hdxdy+∑nj=1k~(2j)_e∫_ΩG_j(D~(2j-2)_y(u_(yy)φ))u_hdxdy+∑ni+j=2h~(2i)_ek~(2j)_e∫_Ω[F_(ij)(D~(2i-2)_xD~(2j)_y(u_(xx)φ))+G_(ij)(D~(2i)_xD~(2j-2)_y(u_(yy)φ))]v_hdxdy+R_(n,h).

In this paper,we prove the product theorems of the infinite matrix operator algebra (λ,μ), with respect to the left (right) strong or K convergence.

Based on the perturbative QCD predictions of gluonic distributions and branch cross section of the J/(?) decay via hadronic, electromagnetic,and radiative channels, the strict solutions of LUND area law of string fragmentation had-ronization are used to treat nonperturbative hadronic production processes, a possible description and Monte Carlo packet for the J/(?) hadronic decay are obtained.

In the teaching of central field, we should pay attention to turning the relative motion of two - body into one dimentuonal radial motion by introducing two physical concepts of reduced mass and effective potential energy, and we should also pay attention that the area law is the geometrical description of the conservation of angular momentum in the central field.

Designing a special math test proved that different problems contexts make effect to using the multiplicative concepts.