A Pascal's triangle-like approach for the determination of characteristic polynomial coefficients of reciprocal graphs

Characteristic polynomial coefficients of three classes of graph, namely L_n + n(p), C_n + n(p) and K _1,n-1 + n(p), which are known to have reciprocal pairs of eigenvalues, have been shown to be generated by simple manipulation of the Pascal's triangle.     

A comparative study on dual colour soft aperture cascaded second-order mode-locking with different nonlinear optical crystals

A comparative study in terms of optimized output power and stability is made on cascaded second-order nonlinear optical mode-locking with KTP, BBO and LBO crystals for both 1064 nm and 532 nm. Large nonlinear optical phase shift achieved in a non-phase-matched second harmonic generating crystal, is transformed into amplitude modulation through soft aperturing the nonlinear cavity mode variation at the laser gain medium to mode-lock a Nd:YVO4 laser. The laser delivers stable dual wavelength cw mode-locked pulse train with pulse duration 10.3 ps and average power of 1.84 W and 255 mW at 1064 nm and 532 nm respectively for the optimum performance in type-II KTP crystal. The exceptional stability achieved with KTP is accounted by simulating the mode-size variation with phase mismatch.     

DYNAMIC STABILITY OF CURVED PANELS WITH CUTOUTS

The parametric instability behaviour of curved panels with cutouts subjected to in-plane static and periodic compressive edge loadings are studied using finite element analysis. The first order shear deformation theory is used to model the curved panels, considering the effects of transverse shear deformation and rotary inertia. The theory used is the extension of dynamic, shear deformable theory according to Sanders' first approximation for doubly curved shells, which can be reduced to Love's and Donnell's theories by means of tracers. The effects of static and dynamic load factors, geometry, boundary conditions and the cutout parameters on the principal instability regions of curved panels with cutouts are studied in detail using Bolotin's method. Quantitative results are presented to show the effects of shell geometry and load parameters on the stability boundaries. Results for plates are also presented as special cases and are compared with those available in the literature.     

Iterative approach for the eigenvalue problems

An approximation method based on the iterative technique is developed within the framework of linear delta expansion (LDE) technique for the eigenvalues and eigenfunctions of the one-dimensional and three-dimensional realistic physical problems. This technique allows us to obtain the coefficient in the perturbation series for the eigenfunctions and the eigenvalues directly by knowing the eigenfunctions and the eigenvalues of the unperturbed problems in quantum mechanics. Examples are presented to support this. Hence, the LDE technique can be used for nonperturbative as well as perturbative systems to find approximate solutions of eigenvalue problems.     

Rapidity dependence of multiplicity fluctuations and correlations in high-energy nucleus–nucleus interactions

The multiplicity fluctuations of the produced pions were studied using scaled variance method in ¹⁶O–AgBr interactions at 2.1 AGeV, ²⁴Mg–AgBr interactions at 4.5 AGeV, ¹²C–AgBr interactions at 4.5 AGeV, ¹⁶O–AgBr interactions at 60 AGeV and ³²S–AgBr interactions at 200 AGeV at two different binning conditions. In the first binning condition, the rapidity interval was varied in steps of one centring about the central rapidity until it reached 14. In the second case, the rapidity interval was increased in steps of 1.6 up to 14.4. Multiplicity distributions and their scaled variances were presented as a function of the dependence on the rapidity width for both the binning conditions. Multiplicity fluctuations were found to increase with the increase of rapidity interval and later found to saturate at larger rapidity window for all the interactions and in both the binning conditions. Multiplicity fluctuations were found to increase with the energy of the projectile beam. The values of the scaled variances were found to be greater than one in all the cases in both the binning conditions indicating the presence of correlation during the multiparticle production process in high-energy nucleus–nucleus interactions. Experimental results were compared with the results obtained from the Monte Carlo simulated events for all the interactions. The Monte Carlo simulated data showed very small values of scaled variance suggesting very small fluctuations for the simulated events. Experimental results obtained from ¹⁶O–AgBr interactions at 60 AGeV and ³²S–AgBr interactions at 200 AGeV were compared with the events generated by Lund Monte Carlo code (FRITIOF model). FRITIOF model failed to explain the multiplicity fluctuations of pions emitted from ¹⁶O–AgBr interactions at 60 AGeV for both the binning conditions. However, the experimental data agreed well with the FRITIOF model for ³²S–AgBr interactions at 200 AGeV.     

Hall Effects on Hydromagnetic Flow and Heat Transfer in a Rotating Channel

An exact solution has been obtained for the fully developedflow of a conducting fluid within a rotating channel due toaconstant pressure gradient in the presence of a uniform transversemagnetic field, taking Hall currents into account. The effectsof Hall current and rotation on the velocity and the magneticfield have been discussed. The shear stress at theplate decreasesdue to an increase in either the Hall parameter for the rotationparameter. Hall effects on the heat transfer have also beenconsidered. For small values of rotation parameter, the rateof heat transfer at the upper plate decreases while for largevalues of rotation parameter the rate of heat transfer firstdecreases, reaches a minimum and then increases with the increasein the Hall parameter. This result is reversed for the lowerplate whose temperature is below that of the upper plate.     

RELIABILITY ANALYSIS OF SUSPENSION BRIDGES AGAINST FLUTTER

A reliability analysis of suspension bridges against flutter failure is presented using the basic theory of reliability. For the purpose of analysis, uncertainties considered are those arising from the variations in geometric and mechanical properties of bridge, modelling, damping and experimentally obtained flutter derivatives. These uncertainties are incorporated by multiplying the computed flutter wind speed with a number of independent factors, which are considered as random variables. Each factor is assumed to follow log-normal distribution. The wind environment at the site, which may cause flutter failure, is considered as the other uncertainty necessary for computing the reliability against flutter failure. The flutter wind speed for the bridge is determined using a finite element approach and a multimode analysis. The effect of some important parameters such as the mean wind speed at the site, coefficients of variation of the multiplying factors associated with damping, modelling and flutter derivatives on the reliability estimates is investigated. The results of the study show that the reliability against flutter failure is sensitive to the variation of the above parameters.     

硅胶硫酸:一种在温和及无溶剂条件下一锅法合成1,4-二氢吡啶的高效多相催化剂(英文)

A series of 1,4-dihydropyridines have been prepared by a one-pot condensation of aldehydes,ethyl acetoacetate,and ammonium acetate in the presence of a heterogeneous catalyst silica sulfuric acid at room temperature under solvent-free condition. This new protocol has the advantage of short reaction time and excellent yields,and is an environmentally benign route to the synthesis of 1,4-dihydropyridines.