By means of the Plemelj formula of extensional Bochner-Martinelli type integral, we obtain the transformation formula of singular integral with extensional Bochner-Martinelli kernel on a closed smooth manifold, and give the corresponding composite formula when the density function is holomorphically extended to domain D.

The another method prove that if φ∈H(α,D), 0<α≤1 , the transformation formula holds, and if φ∈H(α,D) and can be holomorphic extended in to D then the composite formula can be deduced from transformation formula.

Through optimizing the related parameters by modified simplex method, an optimizing conversion formula between hardness and strength for steels has been obtained, and the accurate conversion formula can be described as: σb=208.

In order to test the γ shielding effect of PET special working-boxes to 18F,the conversion formula using calculate formula of γ point-source absorbed dose rate and substitute 137Cs for 18F is deduced.

Derivations have been made with the least square method to have the conversion equation regressed,thus converting the ind.

According to the data of a model pumping station, the present equation is compared with other conversion equations, and its applicability is verified.

We get a new q-series identity by using Bailey′s transformation formula and Ismail′s result.

The transformation formulas of a Gaussian beam through para- bolic diverging GRIN rod lens are derived by using the variationl method and ABCD law.

By using some transfer formulae, we may figure out the control point which is impossible for the surveyors to survey directly in engineering survey.

This paper gives a unified approach to Hsu s two classes of extended GSN pairs in the setting of Hsu-Riordan partial monoid which is a generalization of Shapiro s Riordan group, and moreover Hsu-Wang transfer theorem, Drown-Sprugnoli transfer formula and generalized Brown transfer lemma which display some transfer methods of different kinds of Hsu-Riordau arrays and identities respectively.