what is scaling factor and flexing factor in watermark embedding ?

hello sir, i apply following formula for watermark embedding. S1= S+ a* w for Combine SVs of the watermark with the SVs of the selected sub-band where S & S1 are singular values of kth sub-band of the host and watermarked images and w shows the singular values of the watermark image. Here what is a ? either scaling factor or flexing factor ? what is the difference between them ? and i want to known that how to decide value of this factor ? what is the range of scaling factor ?