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.     

Conformational Study of Spectrin in Presence of Submolar Concentrations of Denaturants

The presence of very low concentrations of the commonly used chemical denaturants, guanidinium chloride (GdmCl) and urea brought about conformational changes in the erythrocyte membrane skeletal protein, spectrin. Evidences in support of changes in the quaternary structure of spectrin have been put forward from quenching study of tryptophan fluorescence, by both steady state and time-resolved measurements, using acrylamide as the quencher. It revealed significant differences between the Stern–Volmer quenching constants (K_SV) and the fraction of accessible tryptophans (f_e) observed in absence and presence of GdmCl and urea concentrations below 1 M at which the association of the two subunits remains intact. The steady state anisotropy of both the spectrin tryptophans and the spectrin-bound fluorescence probe, Prodan also indicate changes in the overall flexibility of the spectrin dimer, originating from changes in the quaternary structure of spectrin. Studies on the binding of Prodan, further indicate that conformational changes also occur in spectrin near the Prodan-binding site at the terminal domain of the protein which is reflected in 3–4 fold decrease in the affinity of binding of Prodan to spectrin in the presence of GdmCl and urea compared to that observed in the absence of the denaturants. The dissociation constant (K_d) of Prodan to spectrin is 0.43 M at 25°C.     

Polarity Estimate of the Hydrophobic Binding Sites in Erythroid Spectrin: A Study by Pyrene Fluorescence

The apparent dielectric constant, , of the hydrophobic pyrene binding sites in erythroid spectrin and human serum albumin (HSA) were estimated using the linear relationship [Turro, N.J., Kuo, P.L., Somasundaran, P. and Wong, K. (1986). J. Phys. Chem. 90, 288–291] between the ratio of the first (373 nm) and the third (384 nm) vibronic peak intensities (l₁/l₃) and the dielectric constant of the bulk medium. Binding of the hydrophobic fluorescent probe, pyrene, to erythroid spectrin and HSA was determined from concentration dependent change in the ratio l₁/l₃ from the emission spectra. Pyrene binds to spectrin (K_app = 6.2 × 10⁶ M^–1) with a higher affinity than that of HSA (K_app = 3.7 × 10⁴ M^–1) and the binding in both cases are saturable. The for spectrin and HSA was estimated to be 7 ± 2.1 and 5.4 ± 1.6 respectively. A case study with spectrin, covalently labeled with pyrene maleimide, have been presented for aging of pyrene-labelled spectrin showing the potential of the use of vibrational peak ratios (l₁/l₃) in the study of polarity of microenvironments in the neighborhood of cysteine residues of a protein. Large changes in the pyrene spectral components indicated conformational changes in the cysteine microenvironment of the protein upon storage at 4°C.     

Borel complexity of the space of probability measures

Using a technique developed by Louveau and Saint Raymond, we find the complexity of the space of probability measures in the Borel hierarchy: if is any non-Polish Borel subspace of a Polish space, then , the space of probability Borel measures on with the weak topology, is always true , where is the least ordinal such that is .

     

Effect of exchangeable cation on the swelling property of 2:1 dioctahedral smectite--a periodic first principle study

We used both localized and periodic calculations on a series of monovalent (Li+, Na+, K+, Rb+, Cs+) and divalent (Mg2+, Ca2+, Sr2+, Ba2+) cations to monitor their effect on the swelling of clays. The activity order obtained for the exchangeable cations among all the monovalent and divalent series studied: Ca2+ > Sr2+ > Mg2+ > Rb+ > Ba2+ > Na+ > Li+ > Cs+ > K+. We have shown that, in case of dioctahedral smectite, the hydroxyl groups play a major role in their interaction with water and other polar molecules in the presence of an interlayer cation. We studied both type of clays, with a different surface structure and with/without water using a periodic calculation. Interlayer cations and charged 2:1 clay surfaces interact strongly with polar solvents; when it is in an aqueous medium, clay expands and the phenomenon is known as crystalline swelling. The extent of swelling is controlled by a balance between relatively strong swelling forces and electrostatic forces of attraction between the negatively charged phyllosilicate layer and the positively charged interlayer cation. We have calculated the solvation energy at the first hydration shell of an exchangeable cation, but the results do not correspond directly to the experimental d-spacing values. A novel quantitative scale is proposed with the numbers generated by the relative nucleophilicity of the active cation sites in their hydrated state through Fukui functions within the helm of the hard soft acid base principle. The solvation effect thus measured show a perfect match with experiment, which proposes that the reactivity index calculation with a first hydration shell could rationalize the swelling mechanism for exchangeable cations. The conformers after electron donation or acceptance propose the swelling mechanism for monovalent and divalent cations.     

A universal coanalytic linear ordering

We construct a linear ordering in which every (coanalytic) linear ordering can be order embedded.

     

Photoinduced Bending of Single Crystals of a Linear Bis-Olefin via Water-Templated Solid-State [2+2] Photopolymerization Reaction

The single crystals of two structural isomers of bis-olefinic molecules were shown to have contrasting properties in terms of their photoreactivity: one exhibits an excellent ability to form polymers, accompanied with bending of crystals upon irradiation, while the other is photostable. The photoreactive crystal is a first example in which [2+2] polymerization leads to bending of the crystals, with implications for the design of photoactuators. The hydrate formation ability of one of these molecular isomers promotes the solid-state reactivity in its crystal, as the H₂O molecules act as a template to bring the olefin molecules into the required arrangement for [2+2] polymerization. Further, the crystals of the polymer exhibited better flexibility and smoothed surfaces compared to those of the monomers. In addition, under UV-light the diene emits bluish violet light while the polymer emits green light, indicating that the luminescence property can be tuned through photoirradiation.