PREPARATION AND SECOND-ORDER OPTICAL NONLINEARITY OF NOVEL PHENOXYSILICON NETWORKS BY SOL-GEL PROCESS

Four phenoxysilicon networks for nonlinear optical (NLO) applications were designed and prepared by an extended sol-gel process without additional H2O and catalyst. All poled polymer network films possess high second-order nonlinear optical coefficients (d(33)) Of 10(-7)similar to 10(-8) esu. The investigation of NLO temporal stability at room temperature and elevated temperature (120 degreesC) indicated that these films exhibit high d(33) stability because the orientation of the chromophores are locked in the phenoxysilicon organic/inorganic networks.

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATION WITH DAMPING

By the generalized Riccati transformation and the integral averaging technique, some sufficient conditions of oscillation of the solutions for second order nonlinear differential equations with damping were discussed.Some sufficient oscillation criteria for previous equations were built up.Some oscillation criteria have been expanded and strengthened in some other known results.

A Theoretical Study of Nonlinear Second-Order Optical Properties of Substituted Silanes

On the basis of ZINDO method and according to the sum over states(SOS) expression, the program is devised for the calculation of nonlinear second order optical susceptibilites β ijk and studying how different substituents on the phenyl ring attached to the atom silicon influence on the nonlinear second order optical properties of substituted silane series of molecules. The properties of (CH 3) 3Si? ?has been studied particularly. The effect of the length of silica chains on the calculated values has been studied too. The regularity summarized from the calculated results has been explained micromechanically.

THE SYNTHESIS OF NEW POLED CROSSLINKED POLYMETHACRYLATES AND THEIR SECOND ORDER NONLINEAR OPTICAL PROPERTIES

Films were prepared from mixtures of copolymers of 4-nitro-4'-[N-methylacryloyloxyethyl, N'-ethyl] amino azobenzene with glycidyl methacrylate (chromophore content: 6 mol%) and copolymers containing anhydride units, which was obtained by the reaction of 4-nitro-4'-[N-hydroxyethyl, N'-ethyl] amino azobenzene with polymethacryloyl chloride (chromophore content: 25 mol %). During thermal poling process the anhydride reacts with the epoxy group and the resulting crosslinked network structure will stabilize the second harmonic generation in the poled film. The second harmonic generation of the poled film shows a maximum with the variation of composition this is presumed to be due to the effects of the increasing of concentration, orientation order as well as orientation stability of chromophore groups during crosslinking.

SECOND ORDER NONLINEAR OPTICAL PROPERTIES OF DICYANOPYRAZINES

Second order nonlinear optical active 2,3-dichloro-5,6-dicyanopyrazine (DCDCP) and its monoamine-substituted derivatives had been synthesized. Their facile synthesis, high melt point, high incidence af substantial SHG activity and increased transparency inthe blue and near infrared make this class compounds appealling for further investigation.

Oscillation Theorems for Second Order Damped Nonlinear Differential Equations

Several oscillation criteria are given for the second order nonlinear differential equation with damped term of the form [α(t)(y'(t))σ]' +p(t)(y'(t))σ+ q(t)f(y(t)) = 0, where α∈C(R, (0,∞)), p(t) and q(t) are allowed to change sign on [t0, ∞), and f∈C1 (R, R) such that xf(x) > 0 for x ≠0. Our results improve and extend some known oscillation criteria. Examples are inserted to illustrate our results.

OSCILLATION THEOREMS FOR SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS WITH DAMPING

Some new oscillation theorems are established for the second order nonlinear differential equations with damping of the form where p（t） and q（t） are allowed to change sign on [t0,∞).

THE SINGULAR SECOND ORDER NONLINEAR EIGENVALUE PROBLEM WITH INFINITELY MANY POSITIVE SOLUTIONS

In this paper we consider the existence of infinitely many positive solutions for second order nonlinear eigenvalue problem with singular coefficient function. By the use of Krasnosel'skii fixed point theorem of cone expansion-compression type we give several sufficient conditions.

Asymptotic Calculation of the Wave Trough Exceedance Probabilities in A Nonlinear Sea

This paper concerns the calculation of the wave trough exceedance probabilities in a nonlinear sea. The calculations have been carried out by incorporating a second order nonlinear wave model into an asymptotic method. This is a new approach for the calculation of the wave trough exceedance probabilities, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. The proposed asymptotic method has been applied to calculate the wave trough depth exceedance probabilities of a sea state with the surface elevation data measured at the coast of Yura in the Japan Sea. It is demonstrated that the proposed new method can offer better predictions than the theoretical Rayleigh wave trough depth distribution model. The calculated results by using the proposed new method have been further compared with those obtained by using the Arhan and Plaisted nonlinear distribution model and the Toffoli et al.’s wave trough depth distribution model, and its accuracy has been once again substantiated. The research findings obtained from this study demonstrate that the proposed asymptotic method can be readily utilized in the process of designing various kinds of ocean engineering structures.

Density Functional Studies on Isonicotinato Lead(II) Complex [Pb(C_5H_4NCOO)_2]

The title compound of isonicotinato lead（Ⅱ） [Pb（C5H4NCOO）2] has been optimized at B3LYP/LANL2DZ level of theory and calculated results show that the lead（Ⅱ） ion adopts 4-coordinate geometry. Atomic charge distributions indicate that during forming the title compound, each isonicotinic acid ion transfers -0.452 e to lead（Ⅱ） ion. The electronic spectra calculations show that there exist two absorption bands and the electronic transitions are mainly derived from the contribution of intraligand π→π^＊ transition and ligand-to-metal charge transfer （LMCT） transition. The thermodynamic properties of the title compound at different temperatures have been calculated and corresponding relations between property and temperature have also been obtained. The calculation of the second order optical nonlinearity was carried out, and the molecular hyperpolarizability was 3.62365^＊10^-30 esu.

Quasiperiodic Solutions for Nonlinear Differential Equations of Second Order with Symmetry

In this paper,we study the existence of quasi-periodic solutions and the bound- edness of solutions for a wide class nonlinear differential equations of second order.Using the KAM theorem of reversible systems and the theory of transformations,we obtain the existence of quasi-periodic solutions and the boundedness of solutions under some reasonable conditions.

OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR NEUTRAL PERTURBED DYNAMIC EQUATIONS ON TIME SCALES

In this paper,we discuss the oscillatory behavior of a class of nonlinear neutral perturbed dynamic equations on time scales.Some new oscillation criteria are obtained for such dynamic equations.Finally,an example that dwells upon the sharp conditions of our result is also included.

Modulation of the Second Order Nonlinear Optical Properties of Helical Graphene Nanoribbons Through Introducing Azulene Defects or/and BN Units

The current study has obtained excellent potential nonlinear optical(NLO)materials by combining density functional theory methods with sum-over-states model to predict the second order NLO properties of helical graphene nanoribbons(HGNs)through introducing azulene defects or/and BN units.The introduction of these functional groups deforms the pristine HGN(compression or tension)and enhances obviously the static first hyperpolarizability(〈β0〉)of system by up to two orders of magnitude.The tensor components along the helical axis of HGNs play a dominant role in the total〈β0〉.The azulene defects and the BN units polarize the pristine HGN to different degrees,and the azulenes and contiguous benzenes are involved in the major electron excitations with significant contributions to〈β0〉but the BN units are not.The BN-doped chiral HGNs have good kinetic stability and strong second order NLO properties(6.84×10^(5)×10^(−30) esu),and can be a potential candidate of high-performance second order NLO materials.The predicted two-dimensional second order NLO spectra provide useful information for further exploration of those helicenes for electro-optic applications.

Theoretical and Experimental Studies on the Metal Complex of Diethylenetriamino-trioxo-molybdenum(VI) [MoO_3(NH_2C_2H_4NHC_2H_4NH_2)]

For diethylenetriamino-trioxo-molybdenum（Ⅵ）, density functional theory （DFT） method calculations of the structure, atomic charge distributions, electronic spectra, natural population analyses and thermodynamic properties at different temperatures have been performed by B3LYP method using LANL2DZ, CEP-121G and CEP-31G basis sets, respectively. The calculated results show that B3LYP/LANL2DZ method can best reproduce the molecular structure. The atomic charge distribution analyses indicate that during forming the complex, the ligand of diethylenetriamine donates negative charges to MoO3 and these charges are accepted by molybdenum（Ⅵ） atom as well as three oxygen atoms. The electronic spectra calculations indicate that B3LYP/ LANL2DZ results are nearest to experimental data among the three methods and electronic transitions are mainly derived from the contribution of bands π→π^＊. The calculation of the second order optical nonlinearity was carried out, and the molecular hyperpolarizability was 0.7881^＊10^30 esu.

Legendre-Gauss Spectral Collocation Method for Second Order Nonlinear Delay Differential Equations

In this paper, we present and analyze a single interval Legendre-Gaussspectral collocation method for solving the second order nonlinear delay differentialequations with variable delays. We also propose a novel algorithm for the singleinterval scheme and apply it to the multiple interval scheme for more efficient implementation. Numerical examples are provided to illustrate the high accuracy ofthe proposed methods.

Calculations on the Nonlinear Second-Order Optical Polarizabilities for Series of Donor-C_(60) Molecules

The equilibrium geometries and UV visible spectra of a series of donor C 60 molecules were obtained by means of the AM1 and INDO/CI method, on the basis of accurate geometric and electronic structures. The nonlinear second order optical polarizabilities were calculated using the method INDO/SDCI combined with the Sum Over States (SOS) expression. The calculated β ( λ =1 34 μm) values are 28 81, 48 56, 57 33, 66 99, 70 85, 85 84, and 142 14 (×10 -30 esu) for the molecules A, B, C, D, E, F and G, respectively. The frontier orbitals were plot for the representative molecules in order to exhibit the intramolecular charge transfer. The results indicate that introduction of thienylethylene can enhancethe NLO response and the dimethyl^aniline substituted di^thienyl^ethylene C 60 (molecule G) possesses the largest NLO second order optical polarizability. The large β values can be attributed to the charge transfer between the substituents and C 60 , as well as within the three dimensional conjugated sphere of C 60 .

AN EXISTENCE－UNIQUENESS RESULT FOR SECOND ORDER NONLINEAR DIFEERENTIAL EQUATIONSWITH ROBIN BOUNDARY CONDITION

An existence-uniqueness result is given for second order nonlinear differential equations with Robin boundary conditionwhere αi, βi,(i =1,2), α and b are all constants.And the resonant points of this problemare also evaluated.AMS(MOS) Subject classifications 34B15

Limit Boundary Value Problem for Nonlinear Differential Equation of the Second Order

1 .Introduetion Considered in thio PaPer 15 the exi tenoe of the solution of the limit boundaryvalue problem■ which occurs in the study of Physios

Relationship between Dislocation Density in P91 Steel and Its Nonlinear Ultrasonic Parameter

P91 steel is an important bearing material used in nuclear power plants. The study of its mechanical degradation behavior is important for ensuring safe operation. The relationship between the dislocation density of P91 steel under different strains and the corresponding nonlinear ultrasonic parameter β was studied. The dislocation density of strained samples was estimated by X-ray diffraction. Nonlinear ultrasonic testing was conducted to evaluate β, showing that this value increased with increasing dislocation density induced by different tensile elongations. It was shown that the ultrasonic secondharmonic generation technique can effectively evaluate the degradation behavior of metallic materials, and the prediction of the residual life of bearing parts in service can be made based on β and the dislocation density.

OSCILLATION CRITERIA FOR DELAY DIFFERENTIAL EQUATIONS WITH IMPULSES

The present paper is devoted to the investigation of the oscillation of second order nonlinear delay differential equation （DDE） with impulses, sufficient conditions of oscillation for the solutions of DDE with impulses are obtained by using differential inequality. Some known results are improved and generalized.