A generalization of the riemann zeta-function

A generalization of the Riemann zeta-function which has the form

On the zeros ofζ (1)(s) — a (on the zeros of a class of a generalized Dirichlet series — XVII)

Some very precise results (see Theorems 4 and 5) are proved about thea-values of thelth derivative of a class of generalized Dirichlet series, forl≥l _o =l _o(a) (l _o being a large constant). In particular for the precise results on the zeros ofζ ⁽¹⁾ (s) —a (a any complex constant andl≥l _o) see Theorems 1 and 2 of the introduction.     

2pi ambiguity-free optical distance measurement with subnanometer precision with a novel phase-crossing low-coherence interferometer

We report a highly accurate phase-based technique for measuring arbitrarily long optical distance with subnanometer precision. The method employs a Michelson interferometer with a pair of harmonically related light sources, one cw and the other low coherence. By slightly detuning (~2 nm) the center wavelength of the low-coherence source between scans of the target sample, we can use the phase relationship between the heterodyne signals of the cw and the low-coherence light to measure the separation between reflecting interfaces with subnanometer precision. As this technique is completely free of 2pi ambiguity, an issue that plagues most phase-based techniques, it can be used to measure arbitrarily long optical distances without loss of precision. We demonstrate one application of this technique, the high-precision determination of the differential refractive index.     

Isotopic sum rules and compliance scheme

It is known that compliance scheme does not provide simple linear isotopic sum rules in λ^?1 similar to the ones in λ in the force constant scheme. The advantage of not having such sum rules in the compliance scheme is discussed in relation to the uniqueness problem of the molecular force field.Incidentally, for the molecules H₂O, D₂O, and HDO, two quadratic relations in terms of the inverse frequency parameters λ^?1 are obtained. These supplement the three obvious product rule relations.     

Synthesis and study of electrical and magnetic properties of vanadium oxide micro and nanosized rods grown using pulsed laser deposition technique

Vanadium oxide micro and nanosized rods were grown using pulsed laser deposition technique under different oxygen pressures. X-ray diffractogram shows a predominant mixture of vanadium dioxide, VO₂ and Magneli phase, V₃O₇. The diameters of the rods were found to increase from 300 nm to 2.3 μm with increase in oxygen pressure from 0.1 mbar to 0.5 mbar as seen from high resolution scanning electron microscope images. Raman spectra of the rods show peaks at all the characteristic vibrations corresponding to that of V O_x phase. The 0.5 mbar oxygen deposited sample shows a semiconducting behavior from 300 to 77 K and is paramagnetic down to 5 K. Using versatile pulsed laser deposition we have established the tunability of the dimensions of V O_x nanorods which can find numerous potential applications in electrochemistry, catalysis, etc.     

Palladium–Schiff base–triphenylphosphine catalyzed oxidation of alcohols

Novel palladium(II)‐N‐(2‐pyridyl)‐N′‐(5‐R‐salicylidene) hydrazine triphenylphosphine complexes were synthesized and characterized by UV, IR, ¹H NMR and ³¹P NMR spectral analysis, C, H, N analysis and magnetic susceptibility measurements. The complexes were effective in the catalytic oxidation of primary and secondary alcohols in presence of N‐methyl‐morpholine‐N‐oxide as oxidant. The oxidation reactions were carried out in dichloromethane. A mechanistic study of the above reactions has been proposed. Copyright © 2010 John Wiley & Sons, Ltd.     

Hilbert phase microscopy for investigating fast dynamics in transparent systems

We introduce Hilbert phase microscopy (HPM) as a novel optical technique for measuring high transverse resolution quantitative phase images associated with optically transparent objects. Because of its single-shot nature, HPM is suitable for investigating rapid phenomena that take place in transparent structures such as biological cells. The potential of this technique for studying biological systems is demonstrated with measurements of red blood cells, and its ability to quantify dynamic processes on a millisecond scale is exemplified with measurements of evaporating micrometer-sized water droplets.     

Volatile oil composition of Pogostemon heyneanus and comparison of its composition with patchouli oil

The volatile oil of the leaves of Pogostemon heyneanus Benth. (Lamiaceae) was analyzed by GC and GC-MS. Twenty-six components representing 96.0% of the oil were identified. The major components of the oil were acetophenone (51.0%), beta-pinene (5.3%), (E)-nerolidol (5.4%), and patchouli alcohol (14.0%). Comparison of the compositions of the oils of P. heyneanus and P. cablin (Blanco) Benth. (Patchouli oil) showed wide variation between them. Though 13 sesquiterpenes and oxygenated sesquiterpenes were detected in both oils, their concentrations in the oils differed widely. Acetophenone, benzoyl acetone and (E)-nerolidol present in the oil of P. heyneanus were not detected in patchouli oil.