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The intersite contribution to the ground state energy for the two impurity Anderson model is calculated to first order in 1/N. The dependence of this contribution on the interimpurity separation has an R−1 or R−3 envelope for distances smaller or larger than a length νF/TA ranges from a value equal to the bare ƒ-level position (in the weak valent regime) to the Kondo temperature (in the local moment limit).

Summary. Integral equations are formulated to solve the problem of electromagnetic induction in the Earth in the presence of thin finitely conducting oceans. Unlike earlier models, the oceans are assumed to be in electrical contact with the mantle and leakage of oceanic electric current is therefore possible. A powerful iterative method is developed to solve the very large system of equations and is applied successfully to a model problem. A feature of the integral equations is that they lead to a good first approximation. When fed into the iterative scheme this enhances the rate of convergence. Variable mesh size also appears possible.

(Pentane-2,4-dionato)-tetrafluorophosphorane crystallises in the space group P21/c, Z = 8, with a = 8.896(2), b = 13.760(4), c = 13.316(2) Å, β = 93.42(3)°. The structure was refined to R = 0.053 for 2445 reflections. Small but significant differences are observed in the bond angles at phosphorus and in the chelate ring conformations of the two indepen­dent molecules. These display an approximate mirror plane perpendicular to the chelate rings, which are in the boat form with P and C(3) displaced from the plane of the remaining ring atoms. The average P-O distance of 1.719(2) Å is similar to that for a σ-bond. 19F and 31P NMR and mass spectral data are reported. The basis peak is formed by the cleavage of the two P-0 bonds resulting in the ion PF4+ (m/e 107).

From an exact calculation of the density of states for one electron in the Sherrington-von Molnar model of an s-f resonance coupled to a local optical phonon mode the authors find the conditions necessary for a polaronic reduction in the width of the resonance. With the notation nu for the relaxation shift, Delta 0 for the resonance width in zero coupling, omega 0 the phonon frequency and W the conduction band width, they find for nu in the range W> nu > Delta 0 very little reduction in the resonance width, and obtain the polaronic reduction exp(- nu / omega 0) only if nu >W. This condition is too strong to be satisfied in intermediate-valence systems. However, the model is not an adequate description of intermediate-valence materials as it is an essentially one-site model. The authors generalise the model to include two sites coupled to phonons such that the sites compete a favourable local lattice distortion. In this model they can examine the dependence of the intersite transfer on lattice coupling strength. For w> nu > Delta 0 (the plausible physical region), this intersite transfer is reduced by a polaronic reduction factor leaving the widths of the virtual bound-state resonance almost unaffected.

The antiferromagnetic phase of a narrow energy band material with one electron per atom is studied using the Hubbard model in the 'alloy analogy'. An electron of a particular spin sees the potential due to a 'frozen' configuration of the electrons of opposite spin, these being distributed on two sublattices with probabilities 1/2(1+or-m), where m is the antiferromagnetic order parameter. This problem of a partially ordered alloy is treated within the coherent potential approximation. The order parameter m is determined self-consistently and the detailed calculations are given for an alternant lattice with a semicircular density of states. It is found that, contrary to Hartree-Fock calculations, antiferromagnetism appears only when the intra-atomic Coulomb interaction U exceeds a critical value. The metal-insulator transition occurs at a lower value of U so that antiferromagnetism does not appear in the metallic state. The general features of the electronic density of states in the antiferromagnetic phase are discussed.

Summary An iterative scheme is proposed for numerically solving the integro-differential equations arising in geomagnetic induction problems. The method is tested successfully on two simple models, both involving an infinite strip. The results indicate that for induction problems generally, the iterations should converge rapidly. It is believed that the method will have applications in other fields of interest.

In recent years inelastic neutron scattering experiments have revealed marked variations in the temperature dependence of the rotational tunnelling spectra of molecular groups in various local environments. A new theoretical approach is developed here to explain these results. A microscopic model of a rigid molecular group, whose rotational degree of freedom is coupled to lattice modes, is formulated in terms of standard basis operators for states of the uncoupled system. It is shown that a complete description of the neutron spectrum can be found in terms of the time-dependent correlation functions of these operators. As a preliminary to a fuller treatment of this problem a perturbational approach is developed, which allows the conditions for a treatment-dependent shift to lower tunnelling frequencies, which is commonly observed experimentally, to be thoroughly examined.

The silylated compounds, N-trimethylsilyl-pyrrole, 1, N-trimethylsilyl-2-methylpyrrole, 2, and N-trimethylsilyl-2,5-dimethylpyrrole, 3, react with the fluorophosphoranes R n PF5-n (n = 0,1) to give N-substituted and C-2-substituted fluorophosphoranyl-pyrrole derivatives. The preparation of the corresponding difluorophosphoranyl-pyrrole compounds was carried out by the reaction of the lithium salts of the pyrroles with diphenyltrifluorophosphorane. N-substituted phenyldifluorophosphoranyl - bis(2,5-dimethylpyrrole), 13, was obtained from the reaction of phenyltetrafluorophosphorane with the lithium salt of 2,5-dimethylpyrrole, the reaction also producing the monosubstituted phenyltrifluorophosphoranyl-pyrrole derivative, 11. The N-bonded diphenyl-difluorophosphoranyl derivatives, 10 and 12, were found to rearrange thermally to give the corresponding C-bonded derivatives, 18 and 19. The structures of the compounds are deduced from 1H, 19F, 31P n.m.r. spectral data and infrared data. Mass spectral a...

The spin-orbit degenerate Anderson model is investigated in the limit of large spin-orbit degeneracy (N). Low-temperature properties are discussed, yielding the full range of intermediate to local moment behaviour. The relation between ground state susceptibility and valence is examined to leading and next-leading orders in 1/N.

The author derives a general solution of the linear dispersion s-d exchange model which is not based on the Bethe ansatz. The spectrum of energy levels is the same as that obtained by Wiegmann but the solutions are shown to be very general. This derivation clarifies certain assumptions made by Wiegmann (1980) and the recent controversies on the completeness of the Wiegmann states.

The model ocean used in previous papers in this series is refined to allow for five separate land masses. The ocean is taken to be of uniform depth, and insulated from the mantle which is modelled by an infinitely conducting core at uniform depth. The fast method of solution introduced in Paper IV enables the electric currents induced by Sq to be calculated on a 2° x 2° global mesh. The 'outer' solution away from the coast is calculated. The 'inner' solution will be a coastal correction different for every coastal configuration. The current is allowed to circulate round isolated land masses, giving markedly different patterns from those in Paper IV. For some harmonics it appears necessary to differentiate even between Australia and New Zealand, although the world-wide effect of the remote island of Spitz­ bergen is minimal. Current distributions are shown for periods of 6, 8, 12 and 24 hr, and a value is set on the current streaming between the various land masses for all the Legendre harmonics considered.

Recent experimental measurements such as susceptibility, specific heat, thermopower, and UPS on a wide range of intermetallic intermediate valence systems, e.g. YbCuAl, CeSn3, support a high degree of universality in the properties of such materials which apparently form a unique class of metallic compounds. The ratio χ(0)/γ≂g2μ2B (J+1) (J+1/2)/π2k2B is a good constant for compounds of a given rare earth (though g and J are rare earth dependent). A class of compounds of a given IV rare earth ion shows scaling of properties in terms of an effective temperature, or energy, scale TF, which is strong function of valence. We review the success of theoretical approaches such as perturbation theory, local Fermi liquid theory, the Bethe Ansatz technique, and large‐N perturbation theory in understanding these experimental facts. A challenge continues to be the understanding of the ground state, in which lattice periodicity plays a fundamental role, giving rise to ραT2 in some metallic, and a several meV gap in ins...

The effects produced by a coastline on geomagnetic variations in the oceans have recently received considerable attention. In an attempt to clarify some of the salient physical characteristics, we presented a short note (Hewson-Browne, Hutson & Kendall 1973) in which we outlined several factors occurring when oceans of variable depth, modelled by spherical caps, were subjected to external time-periodic magnetic fields. We called attention to the possible existence of sign changes in the vertical components of the induced magnetic field Br' and the total magnetic field Br. (Throughout this work the steady geomagnetic field is omitted.) The simplest situation occurs when electric currents are induced by an external spatially uniform time-periodic field in a uniform ocean which forms a complete sphere. in this case Br has a sign change for all time across the equator. However, the existence of land masses complicates the situation. In our note referred to above we concentrated on a study of Br in this more complicated case, and showed that Br has sign changes, but that their positions move with time. It was clear both from our own computations and from published graphs (Ashour 1971) that this was also the case for Bri. The motions of these sign changes are interesting and have been further studied by Hewson-Browne & Kendall (1 973). Recently Ashour (1973) has published a note which is in essence a serious criticism of our contribution. His most important contention is that in the cases considered by himself there is a position in the ocean (fixed for all time) at which Bri vanishes. It will be the main aim of this note to show that this assertion is not true, and that both Bri and Br change sign only at points which move with time. To avoid misinterpretation it will be helpful to adopt the following detailed notation. As usual 6' will denote the co-latitude and t the time. Both Br(6', t ) and B,i(O, t ) are real continuous functions of 6' and t. Br is the sum of Bri and the vertical component of external field. This external field is assumed to be periodic with frequency w and we can therefore define complex quantities br(6') and brt(6'), both functions of 0 only, such that

Recently, Khomskii and Kocharjan have considered a local mixed valence model and, in a generalized linear Hartree-Fock approximation, found solutions which, when generalized to the many site problem, displayed continuous and discontinuous transitions from ground states of integral to intermediate valence. The transitions were due to an energy dependence of the virtual bound state width and persisted in the limit of zero hybridization. We examine the model of Khomskii and Kocharjan and demonstrate that in the limit of zero hybridization an exact solution may be found for the valence behaviour. The generalization of this result to the case of a small but finite concentration of localized level sites, exhibits intermediate valence only as a consequence of the pinning of the Fermi level to the narrow localized levels and the transitions between the ground states of integral and intermediate valence are continuous.

The authors calculate the ground state susceptibility chi 0, to leading and next-leading order in a 1/n expansion, for the N-fold degenerate Anderson model in the integral valent limit. From this and perturbational results they are able to calculate the Wilson numbers W(N), which relate to chi 0 and TK, to first order in 1/N.

The authors give a brief outline of a 'poor man's' scaling approach as applied to locally coupled electron-phonon systems. For these systems they show that the retardation of the effective interactions have to be taken into account. The approach is extended to the calculation of one-electron Green functions and applied to the spinless Anderson model coupled to phonons. A general expression is obtained for the renormalisation of the resonance width due to phonons. This gives the results of Hewson and Newns (1979, 1980) in the appropriate limits but is more general in being applicable to a continuum spectrum of local phonons and for all values of the coupling strength.

Caesium fluoride reacts with tetrafluorophosphoranes, RPF4(R = Me, Ph, or Me2N), and trifluorophosphoranes, R1R2PF3(R1= Me, R2= Ph, and R1= R2= Ph, but not R1= R2= Me), to give the anionic species Cs+[RPF5]–and Cs+[R1R2PF4]– respectively. In the aminolysis of trifluorophosphoranes, R1R2PF3, the novel difluorophos-phoranes, R1R2PF2NR32. were obtained. The characterisation of the fluorophosphate anions and difluorophosphoranes by n.m.r. spectroscopy is described.

A fluid of infinite electrical conductivity without an internal magnetic field and at uniform pressure is in equilibrium outside an infinitely long irregular cylindrical cavity. The cavity is prevented from collapsing by the magnetic field of a finite number of line currents parallel to the axis of the cylinder. The systematic method of solution of this problem is given in the case when the trace of the cavity is a single, simply connected region. The character of the solution is governed by the number of magnetic neutral points inside the cavity, as well as the nature of the magnetic singularities. The method is illustrated by considering the case of two unequal line currents, and the case of a dipole with equal and oppositely-directed line currents at equal distances on either side. It is shown that the solution can be extended to cases when the external hydrostatic pressure is nonuniform. In illustration, the cases of a line current and a line dipole immersed in an exponential atmosphere are considered. (Author)

The induction of electric currents in general arrays of conductors was recently considered by Hutson et al. (1972). It was shown that a certain technique permits the iterative solution of wide classes of problems, and it was proved by a functional analytic argument that the sequence of iterations converged. In the case of an ocean, Price (1949) has shown that a stream function ψ exists. The problem may then be reduced to solving the integro-differential equation: (D + iν0L)ψ = g, where D is a partial differential operator, L is essentially an integral operator, g is a known function derived from the external field and ν0 is a constant. For low frequency and/or low conductivity, ν0 is small and an expansion in powers of ν0 is valid. However, in the case of high frequency (ν0 ⪢ 1) such an expansion does not converge. Moreover an expansion in powers of ν0−1 is generally unsatisfactory since difficulties are encountered when the conductivity is zero over a non-vanishing region bordering the ocean. A “one-step” iterative method (as opposed to effectively inverting D and L alternately), believed to be new in the present context, is proposed for the solution of the above equation for the stream function. The method is tested on a class of high-frequency problems and is shown to be efficient in computational time. Essentially the range of convergence of Price's first method (1949) is extended to include those values of ν0 for which methods other than those presented here are likely to meet with serious difficulties.

Time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of n line currents are considered. The general problem is formulated and solved in the case of an initially flat-faced cloud of flux approaching and passing the magnetic field of n line currents. The special case of a line dipole is analysed in some detail.

Burbot are common in Lake Winnipeg; 886 were taken as a sample. Trap-net and otter-trawl catches are more representative of the population than gill-net catches. A significant difference in length-weight relationship exists between two localities. Ages were determined from otoliths. Heavier exploitation in the northern part of the lake probably accelerated the growth rate. Age-6 burbot there weighed 3.4 pounds compared with 2.6 pounds in the southern part. Spawning begins about January 31 and lasts 3 weeks. The smaller burbot feed mainly on insect larvae, the larger burbot on fish and crayfish.

This paper concerns the time-dependent motions of the cavity formed when a uniform corpuscular flux is incident on the magnetic field of a line current. The two-dimensional problem is formulated and solved with two particular classes of solutions being given; namely, the steady-state solutions and the time-history of the interaction with a cloud of flux.

Over the past few years a number of theoretical investigations have been carried out in an attempt to assess the effect of a coastline on geomagnetic variations. Several model oceans have been used together with a variety of inducing magnetic fields. In this connection we have recently been considering shelving oceans modelled by plane strips or spherical caps. A number of calculations have been made of the azimuthal electric current J and the normal magnetic field component B, inter a h , induced at the cap (or strip) by an external magnetic field B, exp (iwt) parallel to its axis (or plane of symmetry). In this note we shall primarily be concerned with

A representative section of the Lake Winnipeg whitefish fishery was studied during seven summers. The average size of whitefish in samples numbering from 100 to 3,500 fish yearly varied with time and place, but trends were absent. Ages of whitefish in commercial catches, determined by scale reading, revealed three main age groups each year during six summers. Fishing success varied during 7 years and showed no indication of a trend toward better or worse fishing. Some parts of the fishing ground are but lightly exploited. Temperature changes in inshore water masses affected catches in some fishing gear.

The problem of determining the conditions for the occurrence of localized moments in dilute alloys on the basis of Anderson's model is re-examined. From a coupled set of Green's-function equations an approximate solution is found which includes the electron correlation in the impurity levels and which passes over to the exact solution in the limiting case of an isolated impurity. The Hartree-Fock theory is obtained only if the Coulomb repulsion $U$ is relatively small. When $U$ is large the correlation effects are important, and magnetic states are found only if the energy shift caused by the impurity-band electron scattering satisfies certain fairly restrictive conditions. Possible modifications when the degeneracy of the impurity levels, the intra-atomic exchange interactions, and the electron interactions in the host metal are taken into account are qualitatively discussed.

Electrochemical machining is the name given to the process of eroding metal by electrolysis. The anode in this process is a workpiece from which metal is eroded and the cathode is a shaped machine tool which is fed towards the work-piece (see Fig. 1). Erosion takes place when an electric potential is applied across the electrolyte filled gap between the tool and the workpiece. The electrolyte is pumped through the gap in order to remove the products of erosion.

Summary Geomagnetic induction in the oceans at high frequencies, corresponding to periods of less than 12 hr, say, for a typical ocean, is explained and analysed in terms of the transport and merging of magnetic field lines. The explanation helps our physical understanding of problems of induction in the oceans by micropulsations. The complete time-varying part of the electromagnetic field, excluding the Earth’s main field, is able to penetrate the conductor at high frequencies by transport of magnetic field lines through the agency of a large electric field near the edge. This electric field also tends to cause a large electric current there when the ocean has no edge slope. Magnetic neutral points in the time-varying part of the field form within the small thickness of the conductor. This enables the magnetic topology to pass through its various changes. The explanation leads to an analysis which applies to oceans of non-uniform depths, and in particular to oceans with an edge slope. A description is given of the way in which the electric current concentrates near the edge of the ocean and the width for this ‘ boundary layer’ is derived. In a previous paper (Hutson, Kendall & Malin 1972, henceforth referred to as HKM) an iterative method, believed to be new in the context of geomagnetism, has been suggested for dealing with the theoretical solution of model induction problems involving wide ranges of frequencies. Here we concentrate upon a physical analysis of the effects to be expected, particularly in the neighbourhood of a coastline. In keeping with HKM we shall try to retain a general approach, in the hope that the results will be found applicable to a wide range of problems with common features. Throughout this paper we exclude the Earth’s main magnetic field from the configuration. As the Earth’s main field varies very slowly with time, its effect on geomagnetic induction problems of the type considered here is negligible. When we refer to neutral points we therefore mean neutral points in the time-varying part of the magnetic field. In the next section we analyse induction phenomena for a particular example in terms of the merging and disappearance of magnetic field lines. In the later sections we shall draw general conclusions and make predictions. Throughout Sections 2-5 we restrict ourselves to the case of an isolated thin conductor with an inducing magnetic field imposed upon it whilst in Section 6, we examine the effects of an underlying superconducting layer. To discuss magnetic merging we shall have to take some account of the finite thickness of the conductor, but we shall otherwise assume that its thickness is negligible.

The preparation of a series of methyl-substituted piperidyl-fluorophosphoranes is described, of general formula RR′NPF4-nPhn (where RR′N = 2-Me-piperidyl-, 3-Me-piperidyl-, or 4-Me-piperi-dyl; n = 0, 1, or 2), from the cleavage of silicon-nitrogen bonds in methyl-substituted piperidyl silanes by fluorophosphoranes. The structures of the new compounds are deduced from 19F and 31P n.m.r. data.

In this paper a complex variable method of solution to problems in electrochemical machining, developed in an earlier paper, is extended to cover a wider class of two-dimensional tool shapes. In particular the case of a straight sided tool with a finite land width is considered.

The evolution of the Lake Winnipeg whitefish fishery with respect to location, catch, boats and gear is traced from 1883 to 1958. Economic factors affecting fishing techniques and which have implications in management are indicated.

Summary In studying the electric currents and magnetic fields arising from induction in the oceans a number of numerical procedures have been devised by various authors. In all of these methods difficulties arise at the edge of the oceans where the electric currents and magnetic fields change appreciably over a small distance. A physical explanation of these phenomena has been given in the preceding paper in terms of magnetic merging. In the present paper estimates are obtained for the electric currents and magnetic fields near the coast. These depend partly upon the induced currents which are enhanced near the ocean'smargin and partly upon the currents far from the edge of the ocean. A two-dimensional model is formulated and related to more general models. The orders of magnitude which are obtained are believed to have certain generality, and are tested against exact calculations.

The zero temperature impurity magnetization as a function of magnetic field strength has been calculated numerically for the SU(4) and SU(6) Kondo models using the integral equations derived from recent exact results for the linear dispersion model.

The extensive data on YbCuAl is examined, on the assumption it lies close to the Kondo limit, using the results for the j = 7/2 Coqblin-Schrieffer model. Features well explained with a single parameter fit are χ(0), γ, M ( H ) curves, position of the maximum in χ( T ) and the reduction of the high T moment. The apparent success of the impurity model is discussed in the large N approach to the lattice model.

We give an exact calculation for the magnetic isotherm for YbCuAl based on an impurity model which treats the valence fluctuations as virtual. With a single parameter derived from χ(0) we can fit χ(0), γ and the magnetic isotherm extremely accurately.

The Problem.?Recent literature on the psychology of learning has displayed an en couraging tendency to emphasize the points of agreement rather than the differences among learning theories. Insight was for merly taken to mean immediate solution of a problem without any tentative exploration, and many disputes have raged over its role in learning. There now seems to be general agreement that insight should be described as the perception of essential relationships in the learning situation, that it may occur in greater or lesser degree along with trial-and error learning, and that it may be "foresight" or "hindsight" (i, 2, 3). With this agreement on the crucial role of insight in learning, particularly in that kind of learning called problem solving, the way is cleared for constructive research in finding the best means of gaining insight in learning situations. This study attempts to test at three levels of maturity the relative efficiency of three methods of learning in aiding the learner to gain insight in a learning situation in which a complex mental problem must be solved. Specifically, the study attempts to answer experimentally the following ques tions: 1. Are memorizing, the use of a simple verbal principle or rule, and the use of non verbal clues that may aid the learner to formulate the principles of the problem effi cient methods of learning to solve problems? 2. What is the relative efficiency of these methods at the junior high school level, the senior high school level, and the college level, as measured by the ability to make an imme diate transfer to new but similar problems? 3. What is the relative efficiency of these methods at each level as measured by the retention of learned material? 4. What is the relative efficiency of these methods as measured by the ability to make a delayed transfer to new problems? 5Is the mental age of the learner a more important factor in learning than the method of learning? The Experimental Material.?The learning material used in the experiment consisted of nine mathematical puzzles, one of which is shown in Figure i with one of its four pos sible solutions. The problem is to change a D D D D Figure 1 Mathematical Puzzle and Solution

This brief paper presents findings of 17 (3.4 per cent) of the patients involved in the ARMS research programme which is investigating the role of nutrition and physiotherapy in the management of MS. These 17 were following gluten-free diets. Our findings support the view that there is no conclusive evidence that GF diets are universally beneficial in the management of MS.

The theoretical description of thermodynamic properties of intermediate valence Cerium systems which we adopt here derives from the simple local Fermi liquid picture put forward in 1980 [1], This approach neglects intersite correlations which at very low temperatures can lead to coherence effects like a T3ln(T) term in the specific heat [2], There is a theoretical justification for this neglect within the 1/N expansion that shows [3] that intersite terms are smaller than onsite ones by a factor of 1/N. There has also been considerable success in the comparison with experiment of theoretical results obtained from local models [4], We concentrate here on Cerium intermetallie compounds in the nearly integral limit. Since they all show the characteristic Kondo behaviour in the resistivity they are also called concentrated Kondo systems or Kondo lattices. The appropriate local model is the Coqblin-Schrieffer model [5]. It describes the exchange interaction between conduction electrons and highly localised f-electrons. Due to the large spin-orbit splitting the f-electron states |j,m> are restricted to the lowest (N=2j+1 fold degenerate) multiplet of angular momentum j (j = 5/2 for Ce): Open image in new window The characteristic energy scale, the Kondo temperature TK ∝ D exp(−1/N|J|), determines the linear specific heat coefficient γ = (N−1K)π/(3TK).

For sometime now there has been a group of us at Imperial College (increasing in number but now dispersing) concerned with the theoretical problems of intermediate valency and Kondo lattices. Some of our recent results based on the 1/N expansion, the Bethe ansatz and mean field approach with applications to cerium and ytterbium will be presented here. However, by way of introduction I shall review some of the earlier work concentrating on its motivation and the way the early ideas have been developed and clarified with time.

We present calculations of t he electric currents induced in a model ocean by the 24 hr Sq variation. The model has realistic bathymetry and represents a further step of a consistent approach to oceanic induction in which we have introduced various complexities in order of priority. The solution obtained is compared with our previously published results for the case of an ocean of realistic shape and uniform depth. It is found that the major shelf-seas considerably modify the pattern of elect ric current circu­ lation in the oceans of the southern hemisphere. The consistent nature of the method of matched outer and inner expansions which we have used is also discussed. It seems probable that other methods, not limited to finding an outer solution and consequently more complicated, will at best only produce an outer solution since, in practice, the relatively coarse mesh necessarily used in the computation of realistic global problems precludes a fine resolution of the coastal bathymetry. Finally , the meaning of the internal and external Legendre coefficients and their relationship to Sq over the oceans is briefly discussed.

NMR-spektroskopische Daten der Diazadiphosphetidine (III) werden ermittelt und im Hinblick auf mogliche Isomerie diskutiert.

The usual dietary intake of 142 people with multiple sclerosis (MS), from different areas of Great Britain, has been assessed using the 7-day weighed intake method. This sample represents those subjects who said they had not altered their diets since diagnosis, ie, one-third of those who originally joined the management programme. Despite the low energy intakes of the subjects, intakes of other nutrients were similar to values of the general British population. The relationship of disability to energy and nutrient intake was studied. The relevance of dietary fatty acid intakes in MS is discussed with reference to epidemiological data and regional variations. The possibility that people with MS have specific requirements is considered and the need for nutritional guidance in MS is stressed.

Intermediate Valence (IV) materials are rare earth (RE) materials in which electrons are partially free to hop in and out of the f shell, in contrast to their core-like behaviour in normal RE compounds. They include many normal metals (YbCuAl, CeSn3) and a few normal insulators (SmB6, gap 3 mewl), and we shall discuss only such nonmagnetic compounds here.