Inflation with hyperbolic potential in the braneworld model

In this paper we study inflationary dynamics with a scalar field in an inverse coshyperbolic potential in the braneworld model. We note that a sufficient inflation may be obtained with the potential considering slow-roll approximation in the high energy limit. We determine the minimum values of the initial inflaton field required to obtain sufficient inflation and also determine the relevant inflationary parameters. The numerical values of spectral index of the scalar perturbation spectrum are determined by varying the number of e-foldings for different initial values of the inflaton field. The result obtained here is in good agreement with the current observational limits.      

Analysis of noncircular fluid-filled boreholes in elastic formations using a perturbation model

This paper presents a perturbation model to obtain flexural mode dispersions of noncircular fluid-filled boreholes in homogeneous elastic formations. The perturbation model is based on Hamilton's principle with a modified procedure for the reference state selection in order to handle the directional sensitivity of the flexural modes. The accuracy of the perturbation model has been confirmed by comparison to boundary integral solutions. Numerical results confirm that for a fast formation, even modes, and for a slow formation, odd modes are more sensitive to changes in the borehole elongation and azimuth. Even though the focus of this work is on elliptical boreholes and breakouts, the formulation is valid for any kind of noncircular borehole.     

Binuclear spin state selective detection of 1H single quantum transitions using triple quantum coherence: a novel method for enantiomeric discrimination

In the present work a novel methodology is developed for the unambiguous discrimination of enantiomers aligned in chiral liquid crystalline media and the simultaneous determination of 1H-1H and 13C-1H couplings in a single experiment. An INEPT transfer and back transfer of magnetization to protons retain the 13C edited 1H magnetization which is utilized to generate spin selective homonuclear triple quantum coherence of dipolar coupled methyl protons. Spin selective correlation of triple quantum to single quantum coherence results in spin state selective detection by 13C spin and the remaining passive protons. The difference between the successive transitions in the triple quantum dimension pertains to sum of the passive couplings and results in enhanced resolution by a factor of three. This results in unambiguous chiral visualization. The masked 13C satellite transitions in the single quantum spectrum are extracted for chiral discrimination. The technique retains all the passive homo- and heteronuclear couplings in the triple quantum dimension by the application of non-selective refocusing pulse on 1H as well as on 13C spins. This, however, refocuses the chemical shift evolution in the triple quantum dimension, and also overcomes the problem of field inhomogeneity. The method enables the determination of spectral information which is otherwise not possible to derive from the broad and featureless proton spectra. The elegant experimental technique has been demonstrated on different chiral molecules.     

On the boundedness result of wavelet transform associated with fractional Hankel transform

This article is concerned with the study of the continuity of wavelet transform involving fractional Hankel transform on certain function spaces. The n-dimensional boundedness property of the fractional wavelet transform is also discussed on Sobolev type space. Particular cases are also considered.     

Real‐Time Band‐Selective Homonuclear Proton Decoupling for Improving Sensitivity and Resolution in Phase‐Sensitive J‐Resolved Spectroscopy

Real‐time band‐selective homonuclear ¹H decoupling during data acquisition of z‐filtered J‐resolved spectroscopy produces ¹H‐decoupled ¹H NMR spectra and leads to sensitivity enhancement and improved resolution, and thus aids the measurement of J couplings and residual dipolar couplings in crowded regions of ¹H NMR spectrum. High quality spectra from peptides, organic molecules, and also from enantiomers dissolved in weakly aligned chiral media are reported.     

Spin selective multiple quantum NMR for spectral simplification, determination of relative signs, and magnitudes of scalar couplings by spin state selection

In the present work we demonstrate a novel method for spectral simplification and determination of the relative signs of the scalar couplings using a spin selective multiple quantum NMR experiment. A spin selective excitation of double quantum coherence of A and M spins in a weakly coupled three spin system of the type AMX, results in a doublet in the double quantum dimension whose separation corresponds to the sum of couplings of the active spins to the passive spin X. One component of the doublet has the passive spin X in mid R:alpha state while the other component has the passive spin X in mid R:beta state. The spin selective conversion of double quantum coherence to single quantum coherence does not disturb the spin states of the passive spin thereby providing the spin state selection. There will be two domains of single quantum transitions in single quantum dimension at the chemical shift positions of A and M spins. The mid R:alpha domain of A spin is a doublet because of mid R:alpha and mid R:beta states of M spin only, while that of mid R:beta domain is another doublet in a different cross section of the spectra. The scalar coupling J(AM) can be extracted from any of the mid R:alpha and mid R:beta domain transitions while the relative displacements of the two doublets between the two domains at the two chemical shifts provides the magnitude and sign of the scalar coupling J(AX) relative to the coupling J(MX). Similar result is obtained for zero quantum studies on AMX spin system. The proposed technique is discussed theoretically using product operator approach. The new spin state selective double quantum J-resolved sequence has also been developed. The methodology is confirmed experimentally on a homonuclear weakly coupled three spin system and applied to two different heteronuclear five spin systems.     

Spin state selective detection of single quantum transitions using multiple quantum coherence: simplifying the analyses of complex NMR spectra

NMR spectra of molecules oriented in liquid-crystalline matrix provide information on the structure and orientation of the molecules. Thermotropic liquid crystals used as an orienting media result in the spectra of spins that are generally strongly coupled. The number of allowed transitions increases rapidly with the increase in the number of interacting spins. Furthermore, the number of single quantum transitions required for analysis is highly redundant. In the present study, we have demonstrated that it is possible to separate the subspectra of a homonuclear dipolar coupled spin system on the basis of the spin states of the coupled heteronuclei by multiple quantum (MQ)-single quantum (SQ) correlation experiments. This significantly reduces the number of redundant transitions, thereby simplifying the analysis of the complex spectrum. The methodology has been demonstrated on the doubly 13C labeled acetonitrile aligned in the liquid-crystal matrix and has been applied to analyze the complex spectrum of an oriented six spin system.     

Solving Linear Systems of Equations by Using the Concept of Grover’s Search Algorithm: an IBM Quantum Experience

International Journal of Theoretical Physics - Quantum algorithm, as compared to classical algorithm, plays a notable role in solving linear systems of equations with an exponential speedup. Here,...