Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

An X-band time domain electron paramagnetic resonance spectrometer

A computer-controlled X-band time domain electron paramagnetic resonance (EPR) spectrometer, with a time resolution of the order of 0.5μsec, has been constructed with many of the crucial microwave components designed and fabricated by the Microwave Engineering Group of TIFR. The spectrometer operates either in a microwave power pulsed mode for determination of spin-lattice relaxation times by the saturation recovery technique or in the kinetic mode for determination of the time dependence of EPR signal after laser excitation. It has an automatic frequency control, an automatic phase control and, most importantly, a field-frequency lock which ensures good stability of the EPR line positions enabling signal averaging for extended periods. The constructional details of the spectrometer and its performance in both the modes are described here by reporting results on certain typical systems.     

Initially and eventually dominating nonoscillatory solutions in integro-differential difference equations

For the system T′(t) + p(t) T(t) + q(t) T(t ? τ) = ∝₀^tK(t ? μ) T(μ) dμ for t ? 0, T(t) = g(t) for t ∈ [?τ, 0], conditions have been obtained which ensure that a solution of this system is dominated by a nonoscillatory solution in the interval ¦τ, ∞).     

Spin resonances in amorphous Y-Fe alloys

We present spin resonance measurements on amorphous Y_1?xFe_x alloys using both bulk (a-YFe₂) and thin film (x = 0.70, 0.77, 0.83) samples. At 300 K, in every sample, we have found one strong line (S₁) whose frequency and angular dependances imply that it is a uniform mode ferromagnetic resonance in a very thin (≈20–40 nm) surface layer. Previous static measurements indicate that these alloys have no long range order at 300 K. The effective magnetization of the surface layer is a non-monotonic function of the Fe content. Rutherford back scattering experiments on bulk samples are used to demonstrate that there is no significant variation in composition, with depth. We show that S₁ cannot be attributed to segregation, surface contamination or crystallinity. We propose that the surface layer is another amorphous phase of the alloy. A second resonance (S₃) has been ascribed to some of the superparamagnetic spin clusters known to be present in these systems. As reported earlier, we observe other resonances whose origin is not fully understood.     

Stereospecific synthesis and antibiotic activity of some cephalosporin analogs

The strategy used for the stereospecific synthesis of benzofused octams as cepham analogs was the conversion of a 3,4-dihydrothioisocarbostyril to a thioimidate, cycloaddition reaction to form a fused β-lactam and subsequent removal of the alkylthio group by Raney nickel hydrogenolysis. Using azidoacetyl chloride for forming the β-lactam and following known procedures, an amido side chain was generated. Two of the carba analogs of cephalosporin so produced showed low levels of antibacterial activity against a number of gram positive and gram negative organisms.     

AB-initio effective potentials derived from many-body green's function theory: Application to Li

The many-body Green's function technique, developed by Schneider, Taylor and Yaris for electron scattering problems, is applied to the calculation of ab-initio effective potentials (pseudo-potentials) in atoms and molecules. Computational results on the ionization potentials, excitation energies and bound-bound oscillator strengths in lithium show quantitative agreement with experiment and contain all the heuristically expected physical effects.     

Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.     

Most recent strategies targeting estrogen receptor alpha for the treatment of breast cancer

Molecular Diversity - Breast cancer is the most prominent, frequently diagnosed and leading cause of death among women. Estrogen is an agonist of estrogen receptor alpha (ER-α), expressed in...     

Impedance matching in RF excited fast axial flow CO2 laser: The role of the capacitance due to laser head

Impedance matching in an indigenously developed 2 kW RF-excited fast axial flow (RF-FAF) CO₂ laser was seen to be significantly influenced by the capacitance formed between the laser head and the electrodes. We find in the published literature that this capacitance is generally assumed to be negligible while designing the matching network in the RF-FAF CO₂ lasers. It is shown that this capacitance could have a significant value and consequently would modify the design of the matching network remarkably for a specific laser design studied in the present case. The widely used discharge load model for capacitively coupled RF (CCRF) discharge excited CO₂ laser plasma is extended to include this capacitance. The method of measurement of this capacitance using a bridge and the ANSYS software based simulation of its formation due to the laser head structure are discussed.