The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. An example is finally given to illustrate the application of the results.

This paper deals with a non-Noether conserved quantity constructed directly by u sing the form invariance for the Nielsen equation of a non-conservative mechanic al system. The definition and the criterion of a non-point form invariance of th e equation, of which the Noether conserved quantity is studied, are established by relying on the total time derivative along the trajectory of the equation. T he condition under which the form invariance can lead to a non-Noether conserved quantity and the form of the conserved quantity are deduced, and three corollar ies in special cases are presented. Two examples are finally given to illustrate the application of the results.

Unlike chlorination fluorination of ammine complexes of platinum(IV) in aqueous solution does not lead to haloamido complexes. Instead, the triammine complexes [Pt(NH3)3Cl3]Cl and [Pt(NH3)3(NCl2)2Cl]Cl yield no definite main product, and the tetrammine and pentammine complexes trans-[Pt(NH3)4C12]C12, [Pt(NH3)4(NCl2)Cl]Cl2, [Pt(NH3)5Cl]Cl3, and [Pt(NH3)5(OH)]Cl3 form the sparingly soluble complex trans -[Pt (NH3 )4C12] (H2F3 )2 • 2 H-20 as the main product.

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A Hojman conserved quantity constructed by using the special Lie symmetry, or the Noether symmetry, or the form invariance for a holonomic system in the event space is studied. First, the differential equations of motion of the system are established. Second, the critera of three kinds of symmetries, such as the Lie symmetry, the Noether symmetry and the form invariance, and the relation among them are obtained. Third, the conservation law theorem gained by Hojman is generalized and applied to the system, and a non-Noether conserved quantity is obtained. Two examples are finally given to illustrate the application of the results.