Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform

New filtering scheme is investigated and implemented on digital speckle pattern interferometric fringes to enhance the signal-to-noise ratio (SNR) in the speckle interferograms. To establish the potential of new filtering scheme the experiment was conducted on the vibrating cantilever beam. Experimental results revealed that the new filtering scheme is more powerful than other known filtering schemes (Kumar et al. Opt Laser Eng 2004;41:81–93. Kumar et al. Opt Laser Technol 2001;33:567–571. Shakher et al. Opt Eng 2002;41:176–180. Shakher et al. Proceedings ICICS, Singapore, 9–12 September 1997, p. 953–956. Bowler et al. Proceedings of IEE second international conference on image processing, London, 1986, p. 24–26. Lim. Opt Eng 1981;20:670–678. Devila et al. J Mod Opt 1995;42:1795–1804; Kaufmann et al. Opt Eng 1996;35:9–14). The new scheme reduced the speckle noise and improved SNR in speckle interferograms. Further, the new investigated filtering scheme is implemented to study the mode shapes of square plates under two different boundary conditions. In the first condition all the edges of the square plate were fixed while in the second condition two adjacent edges were fixed and the remaining two edges were free. From the experimental results it is clear that the mode shapes are more distinctly visible with the implementation of the new filtering scheme as compared to other known schemes. Under both the boundary conditions the recorded resonance frequencies were compared with the calculated values of resonance frequencies based on classical theory. The results obtained form DSPI show good agreement with classical theory.     

Efficient allylation of aldehydes with allyltributylstannane catalyzed by CuI

Cuprous iodide has been found to be a very effective catalyst for allylation of aldehydes with allyltributylstannane. The catalytic system efficiently promotes the allylation reaction in DMF to produce homoallylic alcohols in high yield.     

Surface and catalytic properties of Cu–Ce–O composite oxides prepared by combustion method

Surface and catalytic properties of Cu–Ce–O composite materials prepared by solution combustion method have been investigated. The materials are characterized by X-ray diffraction (XRD), temperature programmed reduction (TPR) and electron paramagnetic resonance spectroscopy (EPR). The results of EPR and TPR show finely dispersed Cu²⁺ species on ceria matrix with low copper content. The Cu²⁺ species exists in the form of dimers and clusters which are not evident in XRD. In addition CuO is also present as small clusters which grow to larger size at higher Cu content. There is no evidence of CuO forming a solid solution with fluorite CeO₂ in combustion method. The Cu²⁺ species mostly appear on surface rather than in the bulk. Hydrogen peroxide decomposition kinetics has been carried out on Cu–Ce–O composite materials to investigate the effect of crystalline and well-dispersed copper oxide phases on CeO₂. From kinetic results, the catalyst materials can be grouped into highly dispersed as well as crystalline CuO phases present on CeO₂ matrix. Two parallel compensating lines for dispersed and crystalline CuO phases on CeO₂ are observed in ln A versus E_a plot indicating the compensation effect in H₂O₂ decomposition. This observation is consistent with XRD and EPR results.     

Structural studies on fullerenes

Amongst the other physical properties, the structure of fullerene solids, and the structural transformations with temperature, pressure and doping have all evoked considerable interest and during the last two years tremendous progress has been made in this area. This paper provides a brief review of the studies on the structural properties of pristine and doped fullerenes. The results of our own investigations are also presented.     

Positive values of non-homogeneous indefinite quadratic forms of type (1, 4)

Let Г_r,n—r denote the infimum of all number Г > 0 such that for any real indefinite quadratic form inn variables of type (r, n—r), determinantD ≠ 0 and real numbers c₁; c₂,…, c_n, there exist integersx ₁,x₂,…,x_n satisfying 0 < Q(x₁+c₁,x₂ + c₂,…,x_n + c_n) ≤(Г|Z > |)^1/n. All the values of Г_r,n—r are known except for г_1,4. Earlier it was shown that 8 ≤Г_1,4 ≤16. Here we improve the upper bound to get Г_1,4 < 12.     

Studies in nickel(IV) chemistry. Electron transfer kinetics of the reaction between tris(dimethylglyoximato)nickelate(IV) and hexacyanoferrate(II) in aqueous medium

The kinetics of electron transfer from hexacyanoferrate(II) to tris(dimethylglyoximato)-nickelate(IV), Ni(dmg)₃^2?, to produce Fe(CN)₆^3? and Ni(dmgH)₂, follows a pseudo-first-order disappearance in the Ni(IV). The pseudo-first-order rate constants k_obs are linearly dependent on [Fe(CN)₆^4?]₀ in a fiftyfold range of 2 × 10^?4?1 × 10^?2M, and the average values of k_obs/[Fe(CN)₆^4?]₀ range from 194M^?1·s^?1 at pH = 5.20 to 0.2M^?1·s^?1 at pH = 9.07 in aqueous medium at 35°C and μ = 0.57M. Results are interpreted in terms of a probable mechanism involving rate-determining outer sphere one-electron transfer steps from the reductant and one-protonated reductant species to the unprotonated and one-protonated Ni(IV) species present in solution. The more electrophilic one-protonated reductant species apparently reacts several orders of magnitude faster than the unprotonated one.     

Equivalence of the angular forces in the lattice dynamics of fcc metals

The expressions for the Clark, Gazis and Wallis type of angular forces are rederived in the caseof fcc metals. These expressions are now foundtobe equivalent to the deLauney type of angular forces.     

Torsional vibrations of non-uniform rotating blades with attachment flexibility

The torsional vibrations of non-uniform pretwisted rotating blades are studied by using finite element methods based on both the Rayleigh-Ritz and Galerkin formulations. The apparent differences between the matrices obtained from these formulations are explained and, as obtained by using three different orders of elements, results are presented for blades with flexibly attached roots and for a non-uniform blade representative of a bearingless rotor. A parametric study is carried out to resolve a controversy regarding the relative importance of certain terms in the equations of motion of pretwisted rotating blades. In Appendix I, an exact solution is presented for the torsional vibrations of flexibly attached rotating blades with piecewise constant inertia and elastic properties, which serves as a benchmark solution for the finite element results.     

Investigation of anomalons in He fragments

We have studied the mean free path of He fragments from projectile beams of Ar, Fe and Kr of energy 1 ? E ?2A GeV at different distances $\text{(L ? 2.5}\text{cm}\text{)}$ from their production point and found that they are the same, independent of their (i) energy, (ii) target size, (iii) target excitation, (iv) He multiplicities and (v) production angles.