Generalization of five q-series identities of Ramanujan and unexplored weighted partition identities

The Ramanujan Journal - Ramanujan recorded five interesting q-series identities in a section that is not as systematically arranged as the other chapters of his second notebook. These five...     

Pb/Al codoped germano-silicate optical fiber with high non-resonant third-order nonlinearity

A germano-silicate optical fiber codoped with Pb²⁺ and Al³⁺ was developed by modified chemical vapor deposition and solution doping techniques. The non-resonant third-order optical nonlinearity was measured to be 6.9105 × 10⁻²⁰ m²/W by using the continuous-wave self-phase modulation method. The enhanced non-resonant nonlinearity was ascribed to the increasing number of non-bridging oxygens due to the incorporation of the glass modifiers Pb²⁺ and Al³⁺, the large molar refraction from heavy metal ions Pb²⁺, and the enhanced hyper-polarization from PbO doped into the core of the made fiber.     

Direct determination of large in-plane strains using high-resolution moiré shearography

A high-resolution moiré shearography method is described which allows direct measurement of in-plane strain and in-plane shearing strain.     

Continuous Miscibility from Dilute Solution to Fused Salt: Volumetric Properties of Binary Solutions of Nitrobenzene, 1-Butanol, and Anisole with Tetra-n-Butylammonium Picrate from 298.15 to 371.1 K

The densities and speeds of sound of binary solutions of nitrobenzene, 1-butanol, and anisole with tetra-n-butylammonium picrate have been measured over the full composition range from 298.15 to 371.1 K, in order to study the volumetric behavior of continuously miscible systems, made from an organic fused salt and a molecular organic liquid, at just above the melting point of the salt. The calculated apparent molar volumes and compressibilities are analyzed by using the equations of Petrenko and Pitzer. The thermal expansion coefficients of the above systems are also reported.     

Generalized linear prediction method in phase-shifting interferometry in the presence of noise

The effectiveness of phase-shifting interferometry (PSI) techniques employing piezoelectric device PZT in the estimation of phase depends largely on the accuracy with which the phase shifts are imparted to the device and the noise influencing the measurement. Several effective algorithms have been proposed to compute the phase shifts imparted to the device and subsequently obtain the phase using least-squares estimation technique. In this paper, we propose a generalized approach, which accurately estimates the phase shifts in the presence of noise. The method is based on the idea of linear prediction and explores the fact that sampling more data frames yields a reliable phase step estimate in a least-squares sense. We also compare our method with a commonly used generalized phase-shifting method based on histogram analysis and show that our proposed approach is highly effective. We also present simulation and experimental validations of our proposed method.     

Phase shifting interferometry using a robust parameter estimation method

The paper proposes a maximum-likelihood (ML) method based on spectral estimation theory for the estimation of phase distribution in interferometry in the presence of nonsinusoidal waveforms, noise, and the miscalibration of the piezoelectric device. The proposed method also allows the use of arbitrary phase steps. ML estimators are asymptotically efficient for large number of data samples. The method is complemented well by the incorporation of global search algorithm known as Probabilistic Global Search Lausanne for minimizing the ML function. The performance of the proposed method is studied in the presence of noise.     

Generalized phase-shifting interferometry by use of a direct stochastic algorithm for global search

A new phase-shifting interferometric technique that uses an unknown phase step is described in which the phase step is determined by use of an algorithm called Probabilistic Global Search Lausanne (PGSL). One of the main sources of error in phase stepping is piezoelectric device (PZT) nonlinearity. The PGSL algorithm identifies the characteristics of the response of the PZT to the applied voltage through matching predicted and measured responses. The unknown phase step is also calculated with 0.097% error. This approach overcomes the limitations of existing techniques to determine unknown phase steps. Linear regression is subsequently applied for interference phase determination.     

Model-based processing of a holographic moiré

A state space model for the determination of dual phase distributions in a holographic moiré in the presence of nonsinusoidal waveforms, random noise, and miscalibration of the piezoelectric (PZT) devices is proposed. The extraction of these phase terms requires incorporating two PZTs into the moiré setup. A Toeplitz approximation method (TAM) is applied for phase determination, and modification to the Toeplitz covariance matrix formed from the phase-shifted moiré fringes by application of a denoising step in the state-feedback matrix is proposed. This step ensures that the phase terms can even be estimated at a signal-to-noise ratio much lower than that of the original TAM or by our previously suggested polynomial based method.     

2,5-Dialkyl cyclohexenones by Fe(CO)5-mediated carbonylation of alkenyl cyclopropanes: functional group compatibility

The preparation of alkenyl cyclopropanes 1 with a variety of common organic functionalities is reported. These substrates were subjected to the Fe(CO)(5)-mediated carbonylation process under a CO atmosphere, leading to the formation of 2,5-disubstituted cyclohexenones 2, important intermediates for target-directed synthesis.