Synthetic,spectroscopic, and structural Studies on Lanthanide Complexes of Diphosphazane Dioxide Ligands

Lanthanide nitrate complexes of diphosphazane dioxides Ph₂P(O)N(Prⁱ)P(O)Ph₂ ( 1 ) and (PhO)₂P(O)N(Me)P(O)(OPh)₂ ( 2 ) have been synthesised and studied by conductometry, IR, multinuclear NMR spectroscopic methods and X-ray diffraction. Ligand 2 is accessible by two different methods, viz., by direct oxidation of the phosp(III)azane ligand or by starting from phosph(V)azane chloro precursor. The structure of 2 is confirmed by X-ray diffraction. Crystallographic data for 2 : Triclinic, Space group P1 , a = 10.078(1), b = 10.575(3), c = 12.364(4) Å, α = 75.70(2)°, α = 75.56(1)°, γ = 77.68(1)°, Z = 2, V = 1 220 ų; structure refined to R_F = 0.0459 on 3 495 data with F > 3σ(F). The diphosphazane dioxide ligand exhibits trans geometry in the solid state. The structure of a lanthanide complex, [Pr(NO₃)₃( 2 )₂] ( 14 ) is also determined by X-ray diffraction. Crystallographic data for 14 : Trigonal, Space group P3₂, a = b = 15.710(2), c = 40.067(2) Å, Z = 6, V = 8 564 ų; structure refined to R_F = 0.0430 on 8 077 data with F > 5σ(F). The two diphosphazane dioxide ligands and the nitrate groups are coordinated to praseodymium in a bidentate chelate fashion. The geometry around the ten coordinated metal is distorted bicapped square antiprism.     

ON THE CRITICAL POINTS OF THE MAP Fp:X→‖AXB-C‖pp

Suppose A,B and C are the bounded linear operators on a Hilbert space H, when A has a generalized inverse A^- such that (AA^-)^*=AA^- and B has a generalized inverse B^- such that (B^-B)^*=B^-B,the general characteristic forms for the critical points of the map F_p:X^→‖AXB-C‖_p^p(1p=2. Similarly, the same question has been discussed for several operators.     

The finite element method based on interpolating with wavelet basis function

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｐｒｏｂｌｅｍｓｗｉｔｈｌａｒｇｅｇｒａｄｉｅｎｔａｒｅｃｏｍｍｏｎｉｎｐｒａｃｔｉｃａｌｅｎｇｉｎｅｅｒｉｎｇｆｉｅｌｄｓ,ｅ．ｇ．ｉｎｍａｔｅｒｉａｌｌｏｃａｌｉｚａｔｉｏｎ,ｗｉｔｈｉｎｔｈｅｌｏｃａｌｉｚａｔｉｏ...     

Periodic boundary value problems for first-order integro-differential equations of mixed type

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4th-order spline wavelets on a bounded interval

ＩｎｔｒｏｄｕｃｔｉｏｎＷａｖｅｌｅｔａｎａｌｙｓｉｓｈａｓｅｘｐｅｒｉｅｎｃｅｄａｎｅｎｏｒｍｏｕｓｄｅｖｅｌｏｐｍｅｎｔｉｎｒｅｃｅｎｔｙｅａｒｓ.Ｏｎｅｏｆｔｈｅｉｍｐｏｒｔａｎｔｆｉｅｌｄｓｉｓｔｈｅｎｕｍｅｒｉｃａｌａｎａｌｙｓｉｓｏｆｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ｔｈｅａｄｖａｎｔａｇｅｏｆａｄｏｐｔｉｎｇｗａｖｅｌｅｔｓｈａｓｂｅｅｎｒｅｐｏｒｔｅｄ[1～ 4].Ｃｌａｓｓｉｃａｌａｐｐｒｏａｃｈｅｓｔｏｗａｖｅｌｅｔｃｏｎｓｔｒｕｃｔｉｏｎｄｅａｌｗｉｔｈｍｕｌｔｉｒｅｓｏ…     

A discrete algorithm for complex frequency-domain convolutions

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Krylov subspace projection method and its application on oil reservoir simulation

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General solutions of coupled thermoelastic problem

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