Exact solutions of sixth and fifth degree equations

The real problematic with algebraic polynomial equations is how to exactly solve any sixth and fifth degree polynomial equations. In this study, we give a new absolute method that presents a new decomposition to exactly solve a sixth degree polynomial equation, while the corresponding fifth degree equation can be easily transformed into a sixth degree equation of this kind (sixth degree equation solvable by this method), then the sextic equation (sixth degree equation) obtained will be solved by applying the principles of this method; moreover, the solutions of the quintic equation (fifth degree equation) will be easily deduced.

The Idea of Cognition and Absolute Method

Chapter 8 completes the interpretation of the Logic offered in this book by taking up the final chapters of that text on “The Idea of Cognition” and “The Absolute Idea.” The logical form of life enables and constrains the activities of theoretical and practical cognition, and this chapter argues that cognition is understood by Hegel to be the result of life’s self-division from itself, a result of the Idea “doubled.” As self-conscious life, theoretical and practical cognition produce various self-conceptions, which have various limitations and powers. These limitations are overcome by the unity of theoretical and practical cognition. The chapter concludes with a discussion of absolute method as the ongoing dialectic between life and cognition. It argues that method is “unbounded,” and provides a discussion of the role of beginning and dialectic in Hegel’s method.

True absolute determination of photoluminescence quantum yields by coupling multiwavelength thermal lens and photoluminescence spectroscopy

A novel true absolute method to determine photoluminescence quantum yields by coupling thermal lens and photoluminescence spectroscopy is demonstrated.