An electro-optic holographic technique for the measurement of the components of the strain tensor on three-dimensional object surfaces

An electro-optic holographic technique (also called electronic speckle pattern interferometry or TV holography) for the measurement of displacements and strains on three-dimensional object surfaces is presented. The three components of the displacement vector, in a fixed coordinate system, are separated using four independent illumination beams. The interferometric phase for each illumination beam is extracted using the phase stepping technique. Displacements in the fixed coordinate system are projected on to the object surface using the tensor transformation law. Equations for the computation of surface strains using the projected displacements and the surface geometry are developed. The technique is applied for the measurement of strains on the surface of a cylindrical vessel subjected to internal pressure.     

Zirconyl-alizarin blue s complex a spectrophotometric study

Alizarin blue S in 0.5N hydrochloric acid and 10% acetone gives a coloured complex with zirconium salts, which is used for the estimation of zirconium. Measurements were made at 625 mμ and the interference of several cations and anions was studied     

Measurement of <Superscript>99</Superscript>Mo production cross-section from the <Superscript>100</Superscript>Mo(n,2n) reaction with quasi monoenergetic neutron based on the <Superscript>9</Superscript>Be(p,n) reaction

The production cross-section of the medical isotope, ⁹⁹Mo from the enriched ¹⁰⁰Mo(n,2n) reaction with the average neutron energies of 21.9 and 26.5 MeV has been determined for the first time by using an off-line γ-ray spectrometric technique. The average neutron energies were generated by using the ⁹Be(p,n) reaction with the proton energies of 35 and 45 MeV from the MC50 cyclotron of the Korea Institute of Radiological and Medical Sciences (KIRAMS) at Seoul, South Korea. The ¹⁰⁰Mo(n,2n) reaction cross-section as a function of neutron energy was also calculated theoretically by using the computer code TALYS-1.8 and EMPIRE-3.2 Malta. The experimental results are in close agreement with the theoretical values from TALYS-1.8. However, the present data at the neutron energy of 21.9 MeV is slightly lower and at 26.5 MeV is higher than the values from EMPIRE-3.2 Malta.     

Super‐heptazethrene

The challenging synthesis of a laterally extended heptazethrene molecule, the super‐heptazethrene derivative SHZ‐CF3 , is reported. This molecule was prepared using a strategy involving a multiple selective intramolecular Friedel–Crafts alkylation followed by oxidative dehydrogenation. Compound SHZ‐CF3 exhibits an open‐shell singlet diradical ground state with a much larger diradical character compared with the heptazethrene derivatives. An intermediate dibenzo‐terrylene SHZ‐2H was also obtained during the synthesis. This study provides a new synthetic method to access large‐size quinoidal polycyclic hydrocarbons with unique physical properties.     

Studies towards the total synthesis of hygrocins A and B

The western segment of hygrocins A–B has been synthesized through the coupling of a chiral C5–C13 synthon with the sterically demanding hexasubstituted naphthalenic core. The C5–C13 chiral fragment has been assembled via a stereoselective Johnson orthoester rearrangement of an optically pure allylic alcohol derived from d-glucose. Our studies lay the platform for the determination of the absolute configuration of the unassigned C8-stereocenter of the title compounds in addition to the completion of the total synthesis of the unique ansamacrolides hygrocins A and B.     

Synthesis of on resin poly(propylene imine) dendrimer and its use as organocatalyst

Solid phase synthesis of poly(propylene imine) dendrimer is described. An iterative synthesis including double Michael addition of acrylonitrile to the primary amino groups on crosslinked polystyrene support followed by reduction of nitrile groups to amino groups give poly(propylene imine) dendrimers up to third generation attached to the polystyrene support. The supported dendrimer is used as an organocatalyst to Knoevenagel condensations. The supported catalyst showed good selectivity and the product was obtained in excellent yield under green reaction conditions. Densely packed amino groups enhance catalysis by a co-operative effect. The catalyst is recoverable and reusable.     

Porphyrin/Quinoidal-Bithiophene-Based Macrocycles and Their Dications: Template-Free Synthesis and Global Aromaticity

We report the template-free synthesis and characterization of a new type of porphyrin/quinoidal-bithiophene-based conjugated macrocycle. X-ray crystallographic analysis of the dimer ( 2MC ) revealed a cyclophane-like geometry with large dihedral angles between the porphyrin and the neighboring thiophene rings, and NMR measurements and theoretical calculations confirmed a localized aromatic character of the porphyrin/thiophene rings and quinoidal character of the bithiophene linkers. Restricted rotation of the thiophene rings linked to the porphyrin unit was observed by variable-temperature NMR measurements. The dication ( 2MC²⁺ ) adopts a chair-shaped conformation to facilitate π-electron delocalization around the whole macrocycle. As a result, the molecule is globally aromatic, with a dominant 54 π conjugation pathway. The trimer ( 3MC ) also shows localized aromatic character of porphyrin rings and conformational flexibility, but its dication ( 3MC²⁺ ) is rigid and globally aromatic with a dominant 82 π conjugation pathway.     

A Stable All‐Thiophene‐Based Core‐Modified [38]Octaphyrin Diradicaloid: Conformation and Aromaticity Switch at Different Oxidation States

A soluble and stable core‐modified [38]octaphyrin, MC‐T8 , containing eight thiophene rings was synthesized by Yamamoto coupling followed by oxidative dehydrogenation. X‐ray crystallographic analysis revealed a nearly planar backbone, and the molecule is globally aromatic with a dominant 38π conjugation pathway. The dication MC‐T8²⁺ is antiaromatic, and the backbone is distorted, with a different orientation of the thiophene rings. The tetracation MC‐T8⁴⁺ becomes aromatic again, with a shallow‐bowl‐shaped geometry. Both the neutral compound and the dication demonstrated open‐shell diradical character with a small singlet–triplet energy gap (?2.70 kcal mol^?1 for MC‐T8 and ?3.78 kcal mol^?1 for MC‐T8²⁺ ), and they are stable owing to effective spin delocalization.     

Ramanujan-Fourier series and the conjecture D of Hardy and Littlewood

We give a heuristic proof of a conjecture of Hardy and Littlewood concerning the density of prime pairs to which twin primes and Sophie Germain primes are special cases. The method uses the Ramanujan-Fourier series for a modified von Mangoldt function and the Wiener-Khintchine theorem for arithmetical functions. The failing of the heuristic proof is due to the lack of justification of interchange of certain limits. Experimental evidence using computer calculations is provided for the plausibility of the result. We have also shown that our argument can be extended to the m-tuple conjecture of Hardy and Littlewood.     

Ramanujan — Fourier series and a theorem of Ingham

Given two arithmetical functions f, g, we derive, under suitable conditions, asymptotic formulas for the convolution sums ∑ _n≤N f (n) _g (n + h) for a fixed number h. To this end, we develop the theory of Ramanujan expansions for arithmetical functions. Our results give new proofs of some old results of Ingham proved by him in 1927 using different techniques.