In order to improve the compatibility of flame retardant and epoxy resin, a phosphorus nitrogen flame retardant curing agent poly(p-xylylenediamine spirocyclic pentaerythritol bisphosphonate) (PPXSPB) was synthesized. FTIR, 1 HNMR, and mass spectroscopy were used to identify the chemical structure of PPXSPB. Epoxy resin (E-44) and PPXSPB as the raw material, a series of thermosetting systems were prepared. The effects of PPXSPB on flame retardancy, water resistance, thermal degradation behavior, mechanical properties and the adhesive strength of EP/PPXSPB thermosets were investigated. The results show that with the increase of phosphorus content, the oxygen index and carbon residue of the system both increased significantly, and the heat release rate gradually decreased, which is of great significance in delaying the occurrence of fire. When the phosphorus content is 3.24% in EP/PPXSPB thermosets, EP-2 can successfully pass the UL94 V-0 flammability rating, the LOI value of EP-2 can reach 31.4%, the impact strength and tensile strength was 6.58 kJ/m 2 and 47.10 MPa respectively, and the adhesive strength was 13.79 MPa, the system presents a good overall performance. Abstract: Let F denote a eld and let V denote a vector space over F with nite positive dim a pair A, A * of diagonalizable F-linear maps on V, each of which acts on an eigenbasis for irreducible tridiagonal fashion. Such a pair is called a Leonard pair. We consider the self-d there exists an automorphism of the endomorphism algebra of V that swaps A and A * . Such is unique, and called the duality A ↔ A * . In the present paper we give a comprehensive duality. In particular, we display an invertible F-linear map T on V such that the map X → T A ↔ A * . We express T as a polynomial in A and A * . We describe how T acts on ags, and 24 bases for V.