EXISTENCE AND UNIQUENESS FOR THIRD ORDER NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper, the existence and uniqueness of solutions for boundary valueproblem x′′′=f(t, x, x′, x″), x(0)=A, x′(0)=B, g(x′(1), x″(1))=0 are studied byusing Volterra type operator and upper and lower solutions. Our results improve someknown works.

Crystal Structure and Third order Nonlinear Optical Properties of cis-Configuration Biferrocene Trinuclear Complexes

The syntheses and characterization of novel biferrocene trinuclear complexes of Schiff base ligand, S methyl N (ferrocenyl 1 methyl methylidene)dithiocarbazate [hereafter abbreviated as HL (1)], are described. The X ray diffraction studies have established the structures of PdL 2 (3) and CuL 2 (4). The geometry of Pd(Ⅱ) in (3) is close to a square plane and in the novel cis configuration the two ferrocene moieties are in cis configuration, while that of Cu(Ⅱ) in (4) is close to a tetrahedral configuration. The electrochemical measurements suggested that the square planar configuration of Ni(Ⅱ) and Pd(Ⅱ) moieties can effectively transmit the redox effects of the ferrocene moieties, while the tetrahedral configuration of the Cu(Ⅱ) complex can not transmit the redox effects. The degenerate four wave mixing (DFWM) measurements showed that the complexes exhibit obviously nonlinear optical (NLO) response. The magnitude of their third order NLO susceptibility can be explained by their structure and electrochemical properties.

Synthesis and Characterization of Nonlinear Optical Material of Substituted Diacetylenes with Azophenyl Group and Pyrimidine Ring

?-(2-methylthio -4 -methyl -5 -pyrimidinyl)-2. 4 - pentadiyn- 1 -ol- (4- N. N-dimethylamino-azobenzene -4' -sulfonate) (PDABS - 1 ). ②5 -(2 -methylthio -4 -methyl -5-pyrimidinyl)- 2.4 -pentadiyn- 1 -ol - (azobenzene - 4 -sulfonate) (PDABS -2 ). ③2. 4 -hexadiyn - 1 -ol-6- (4 - N, N-dimethylamino-azobenzene-4'-sulfonate) (HDABS - 1 ), ④2. 4 -hexadiyn - 1-ol -6 - (azobenzene4-sulfonate) (HDABS-2), the four new compounds are synthesize. The structures of the new compounds have been demonstrdted by elemental analysis. IR(KBr). 1H-NMR (CD3CO/TMS),MS. Their X(3), d33. βμ and the fabrication of their polarization orientated thin film also have ben reported in this paper.

Hybrid silicon slotted photonic crystal waveguides:how does third order nonlinear performance scale with slow light?

We investigate in this paper the influence of slow light on the balance between the Kerr and two-photon absorption(TPA) processes in silicon slotted hybrid nonlinear waveguides. Three typical silicon photonic waveguide geometries are studied to estimate the influence of the light slow-down factor on the mode field overlap with the silicon region, as well as on the complex effective nonlinear susceptibility. It is found that slotted photonic crystal modes tend to focalize in their hollow core with increasing group index(n_G) values. Considering a hybrid integration of nonlinear polymers in such slotted waveguides, a relative decrease of the TPA process by more factor of 2 is predicted from n_G=10 to n_G=50. As a whole, this work shows that the relative influence of TPA decreases for slotted waveguides operating in the slow light regime, making them a suitable platform for third-order nonlinear optics.

Synthesis of End Functional Polymers via Atom Transfer Radical Polymerization in Immobilized Catalytic System

Cross-linked polystyrene with azo-crown ether functional side chain (PSt-1, 10-dicarbonyl-3,6,9-trizaoeylcode-cane) was prepared under microwave irradiation and the structure was characterized through FT-IR and element analysis. The functionalized cross-linked polystyrene (cross-link degree, 3.5%) combining with immobilized catalyst system (CuBr and ethylα-bromo-isobutyrate) can catalyze atom transfer radical polymerization of Styrene. Neat polymer products can be obtained then. Complex of La and the polymer end group (EBiB) was synthesized. The third order nonlinear optical property of the polymer-La complex was investigated and the structure was also characterized by FT-IR and XPS.

CONVERGENCE OF SOLUTIONS OF CERTAIN SYSTEM OF THIRD ORDER NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

The object of this paper is to give an n-dimensional analogue of a convergence result of Tejumola [8] for some third-order differential equations. The result extends earlier results of Afuwape [1] and Ezeilo [4] to some system of third-order differential equations.