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In this paper, we study a pair of unified and extended fractional integral operator involving the multivariable I-functions and general class of multivariable polynomials. Here, we use Mellin transforms to obtain our main results. Certain properties of these operators concerning to their Mellin-transforms have been investigated. On account of the general nature of the functions involved herein, a large number of known (may be new also) fractional integral operators involved simpler functions can be obtained. We will also quote the particular case of the multivariable H-function.

We present the EPR spectra of two new phosphorus centred free radicals in solutions. The spectra were performed in solid state frozen solutions and were interpreted with a simple model allowing to determine the isotropic and anisotropic parts of both the g factors and the hyperfine coupling. The high value of the isotropic hyperfine constant (A ∼ 650 MHz) shows that these systems seem particularly suitable for low field measurements performed by Dynamic Nuclear Polarization (DNP) magnetometers.

One particular application of DNP (1,2) between solvent protons and the electron of a free radical is its use for NMR earth field magnetometers (3), whose sensitivity increases with the DNP Factor (DPF). This factor is proportional to the so-called leakage factor f; f = 1 - T1/T10 where T1, T10, are the nuclear relaxation times of the radical solution and of the pure solvent respectively. More than just leakage phenomena, f expresses the efficiency of the Abragam-Overhauser electron-proton coupling, and then we prefer to call it the “Efficiency Factor”. In this paper, we describe an experimental determination of this factor and its interpretation in terms of DNP, for several M/1000 radical solutions; perdeuterated 2,2,6,6 tetramethyl-4-pipe- ridone 15N-oxide in CH3OH, CH3OD, CD3OH.

A unique ESR spectrum of an 27 O-enriched diarylphosphonyl radical, (2,4,6-Bu 3 t C 6 H 2 ) 2 ṖO, is presented and explained. Marked multiplet linewidth variation is attributed to the temporal correlation of the phosphorus-31 and oxygen-17 anisotropic hyperfine interactions. It is demonstrated that the linewidth variation can be helpful in ascertaining the electronic structure of this free radical. In particular, it is argued that the canonical structure, (2,4,6-Bu 3 t C 6 H 2 ) 2 PȮ symbolizing the delocalized nature of the unpaired electron, is an important resonance structure. This thesis is supported by the finding that the 27 0 isotropic hyperfine coupling constant is of negative sign.

Soft gels contained in rigid rectangular cells are observed to give rise to low‐frequency mechanical oscillations under zero displacement boundary conditions. The ratio of the bulk to shear modulus in such gels is very large, and the medium can be considered to be incompressible. We derive a modified form of the equation of motion for the shear waves, and solve, using a variational technique, for the fundamental modes in two two‐dimensional cases, the infinite ribbon and the square. In three dimensions, long cells of square cross sections are investigated. Two types of waves arise: motion transverse to the cell axis and motion parallel to the axis. It is shown, both by a variational calculation and by Fourier decomposition, that the axial modes show a pronounced cellular structure, as in the case of the two‐dimensional ribbon. The predicted fundamental frequency of the transverse waves is in good agreement with the experimental observations.

Nous avons etudie le coefficient de polarisation dynamique des protons de solutions contenant des radicaux libres du type nitroxyde lorsque le champ magnetique directeur est faible. . Nous avons, pour cela, examine les differents processus susceptibles d'intervenir dans la relaxation des spins electroniques des radicaux, qui sont : l'effet spin-rotationnel, la modulation du couplage hyperfin entre le spin electronique et le spin du noyau d'azote du meme radical, l'interaction dipolaire magnetique et l'echange de Heisenberg entre les spins electroniques de deux radicaux. Les matrices de relaxation obtenues montrent qu'il existe deux types de processus : ceux qui ramenent les populations initiales a leurs valeurs a l'equilibre thermique (processus propres) et ceux qui ne peuvent le faire (processus impropres). On donne une expression formelle simple du coefficient de polarisation dynamique immediatement exploitable lorsqu'une seule transition electronique est excitee; un formalisme plus complexe est mis au point dans le cas ou le champ directeur est assez faible pour que plusieurs transitions soient simultanement excitees.

Dans un processus diffusionnel, on remplace le temps par une quantite definie au moyen d'une integrale sur la trajectoire parcourue par le point migrant, le temps, fictif. Le nuage de points migrants pris au meme instant fictif a une densite obeissant a une equation aux derivees partielles, que l'on applique a la theorie de l'elargissement par echange des raies R.P.E. des radicaux libres azotes en solution, dans le cas ou l'integrale d'echange est fonction de la distance entre les centres des radicaux, par exemple, une fonction exponentielle. On a un bon accord avec l'experience dans le cas du tanone dans le methanol entre — 30° et + 90 °C. Un autre modele, base sur la possibilite de formation fugitive d'un biradical, est egalement traite.

An experimental and theoretical study of transient frequency distributions of spontaneously decaying phonons is reported. After pulsed phonon excitation by phonon-combination absorption of infra-red radiation, a decay cascade of acoustic phonons is observed in a CaF2 crystal at low temperature. As long as the phonons do not escape from the crystal, the cascade can be described by a scaling function that is characteristic for spontaneous phonon decay in a crystal containing mode-mixing elastic scattering centres.

Elastomers and gels are characterised by a large ratio of the bulk to the shear modulus, and are consequently capable of propagating shear waves of very low velocity. The authors have elsewhere examined the normal modes excited in gels contained in rectangular cells of infinite length with rigid boundary conditions, and have shown that the fundamental mode consists of a roller structure which is periodic along the long axis of the cell. Here they extend the variational analysis to include gels of semi-infinite length and of square cross-section with one end free; it is found that the fundamental is a localised mode, in which the motion of the gel is confined to the vicinity of the free surface. Gels of finite length with a free end are also investigated. Experimental observations are made both of quasi-longitudinal and of quasi-transverse modes in polyacrylamide gels; good agreement is found between the measured frequencies of the first few modes and the calculated eigenfrequencies for this system.

In cubic symmetry, the description of a scalar anisotropic physical quantity $E$ relative to a static property of a given material can be made with the help of various expansions in terms of symmetrical polynomials or cubic harmonics. A general method for generating the relevant symmetrical polynomials up to an arbitrary order is presented and a new set of cubic harmonics particularly suitable to this problem is tabulated up to order $l=36$. The relations of the latter with the symmetrical polynomials are set up. A careful study of the very important case where $E$ can be accurately measured only in the planes {100} and {110} is made. From the knowledge of the Fourier expansions of $E$ in these planes the conditions for deriving $E$ in a unique way for arbitrary directions are given. It is also shown that some of the coefficients appearing in the former expansions of $E$ may always be determined unambiguously whatever the order up to which these expansions have to be performed. Practical applications of these results are developed with specific reference to the magnetic anisotropy energy of nickel at low temperatures. This study demonstrates the advantages of this method of analysis over the usual procedures.

The ESR spectra of tetra-aryldiphosphine radical cations exhibit dramatic multiplet linewidth differences. This curious effect is a manifestation of the correlated temporal behavior of the two electron-phosphorus anisotropic hyperfine interactions. The strength of the observed correlation suggests a gauche conformation for these radical cations.

It is shown that the use of pseudo-cubic crystal field Hamiltonian enables to interpret susceptbility and magnetization curves of terbium gallium garnet at low temperatures.

The NMR spectrum of a linear chain containing two types of spin 12 nuclei, with slightly different chemical shifts, and coupled by a scalar exchange interaction between nearest neighbors, is examined theoretically. Analytical expressions for the first even moments of the spectrum are given and the dependence of the moments on the number of spins in the chain is analyzed. After a brief review of the Liouville representation, a Green's function theory in this representation is developed allowing the study of the line shape. It is shown that in the central region of the spectrum, one obtains an approximately Lorentzian shape whose width is calculated for a weak field experiment. The theory also provides an approximate value for the line intensity at the center of the spectrum for an arbitrary resonance frequency.

We develop a theory for the width of the proton resonance lines of the water molecules in zeolites. It is based on a model in which the angular migrations of the H — H bond are governed by a diffusion equation. This model leads us to consider an equation of the Fokker-Planck type, which is solved in a " prefered direction " approximation. Our calculated results are in agreement with experimental ones.

Le modele de champ cristallin qui a permis l'interpretation des spectres d'absorption optique du gallate d'erbium, permet egalement d'expliquer les proprietes magnetiques de ce corps, et en particulier l'aimantation en fort champ et a basse temperature. On prevoit egalement la valeur de l'aimantation a saturation. On indique, en appendice, une methode pratique d'integration approchee pour calculer l'aimantation d'une poudre d'un corps anisotrope.

The NMR spectrum of a linear chain containing two types of spin 1/2 nuclei, with slightly different chemical shifts 2δ, and coupled by a scalar exchange interaction J between nearest neighbors is studied theoretically. Expressions for the first ten moments of the spectrum are given. Spectra for a cyclic chain limited to eight spins are computed and the results are compared with those of a previous Green's function theory of the line shape giving an approximately Lorentzian shape in the weak field region. The case where J = δ, for which the line is almost Gaussian, is also analyzed.

A closed and analytical formula is given for the free Green’s function in a harmonic oscillator basis. It is very useful for solving the Lippman–Schwinger equation for the scattering of two clusters within the resonating group method formula.

We have studied transient frequency distributions of spontaneously decaying phonons in CaF2 at low temperature. After pulsed phonon excitation by phonon-combination absorption of infrared radiation, we observed a decay cascade of acoustic phonons. We present a theoretical description of the cascade by a scaling function, that is characteristic for spontaneous phonon decay in a crystal containing mode-mixing elastic scattering centers.