bluuebunny/crossref_metadata_2025 huggingface dataset:
PRECLINICAL STUDIES OF ALENDRONATE
Authors: Zhao Jenny , Jiang Yebin , Genant Harry K.
Published: March 2003

Alendronate has been developed for the treatment of diseases characterized by increased bone resorption, such as osteoporosis. It increases metaphyseal bone density, bone volume, femoral bending strength and vertebral compressive strength, in a dose-dependent manner, in growing, intact rats. In ovariectomized (OVX) rats, alendronate increases femoral bone mass and tibial trabecular bone volume in a dose-dependent manner, and increases femoral midshaft bending strength. In rats immobilized by unilateral sciatic neurectomy, it inhibits bone loss and is dose-dependent. In rats, alendronate prevents high-turnover osteopenia induced by hyperthyroidism or by administration of immunosuppressant agent cyclosporin-A. Also in rats, treatment with prostaglandin E 2 and alendronate does not inhibit prostaglandin E 2-induced stimulation of bone formation on endocortical and periosteal surfaces. It does, however, prevent prostaglandin E 2-induced cortical bone porosity as a result of increased bone resorption, leading to an increase in cortical thickness and an increase in three-point bending strength of the femoral midshaft. At up to five times the dose used for treatment of osteoporosis in clinical trials, alendronate causes no abnormalities in bone remodeling, bone structure, or structural mechanical properties of the femur or vertebrae in intact beagles. Treatment with alendronate before or during fracture healing, or both, has no adverse effects on the union, strength, bone formation or mineralization of bone in mature beagle dogs. In intact minipigs, sodium fluoride increases and alendronate decreases bone turnover, while sodium fluoride, but not alendronate, decreases L4 strength and femoral stiffness. Small-angle X-ray scattering and backscattered electron imaging show that the trabecular bone matrix is more uniformly mineralized after alendronate treatment. In OVX baboons, which show bone changes similar to those seen in postmenopausal women, alendronate prevents an increase in bone turnover, and increases both bone volume and strength in vertebrae, in a dose-dependent manner. Alendronate also reduces the bone loss of alveolar support associated with periodontitis in monkeys. Thus, alendronate inhibits bone resorption and bone turnover, increases bone quantity accompanied by improved bone quality in some of the intact animals and in the animal models.
A SURGICAL GUIDE TO ACCURATELY PLACE PINS OR NAILS WITHIN THE FEMORAL HEAD
Authors: Anderson David A. , Schnieders Michael J. , Heiner Anneliese D. , Pedersen Douglas R. , Brown Thomas D. , Brand Richard A.
Published: March 2003

The purpose of this study was to demonstrate the accuracy of a novel, surgically useful guide that could place a drill or pin within the femoral head. The radiolucent guide for attachment to the lateral femoral cortex was tested for reproducibility on cadaveric specimens simulating a surgical procedure. The guide allows selection of the three-degree freedom angle of insertion of a drill or pin via two circular channels allowing anterior–posterior or superior–inferior adjustment. The guide can accurately place a pin tip within 2.5–3.8 mm of a desired location. We conclude this guide could be used to accurately place a fibular graft in an osteonecrotic lesion, or place pins or nails during many different surgical procedures such as fractures or slipped capital femoral epiphysis.
A CASE REPORT OF CONGENITAL ABSENCE OF THE PATELLA ANALYZED WITH MAGNETIC RESONANCE IMAGING
Authors: Sakamoto Keizo , Munechika Hirotsugu , Ishikawa Satoshi , Fujimaki Etsuo
Published: March 2003

Congenital absence of the patella is extremely rare, and there are very few reports on this condition. We describe our experience of congenital, bilateral absence of the patella in a 17-year-old girl. Her chief complaint was an inability to run, jump, or extend her back in the standing position. Plain X-rays showed complete absence of the patella, but bones involving the pubis were present and intact. Magnetic resonance (MR) images were acquired, and this report focuses on our MR-based analysis. MR T2-weighted and proton-enhanced imaging showed a dark, low-signal band, between the quadriceps tendon and the patellar tendon with cartilaginous tissue surrounded by tendon at the junction of both tendons, 2 mm thick and 18 mm long, in place of the patella. On T1-weighted axial images, a hypoplastic patellar groove was observed, and the patella was absent. A low-signal band involved with a relatively high-signal band was noted. We concluded this to be cartilaginous tissue that may indicate cartilaginous patellar dysplasia, allowing for non-rupture of the patellar tendon.
STALLED REFORM: FAMILY LAW IN POST-UNIFICATION YEMEN
Authors: Würth Anna
Published: March 2003

I examine here the conditions that have impacted on family law reform in unified Yemen. I will argue that during the early 1990s, the political climate of post-unification Yemen was polarized between supporters of the status quo ante— advocates of laissez-faire in the North and state intervention in the South. This division rendered any meaningful debate on family law impossible. Drawing on urban court records from the 1980s to the mid-1990s, I will show that courts are frequented mainly by women of modest origins who sue for divorce and maintenance, but who are discriminated against by judicial interpretation. Elite women use the courts only rarely and are comparatively better served by current judicial interpretation; thus, they have little concern for changing provisions on divorce and maintenance. Evaluating debates on women's rights in the late 1990s, I will briefly introduce some governmental and non-governmental initiatives with respect to family law to gauge current possibilities for reform.
RECENT DEBATES ON FAMILY LAW REFORM IN MOROCCO: ISLAMIC LAW AS POLITICS IN AN EMERGING PUBLIC SPHERE
Authors: Buskens Léon
Published: March 2003

In 1957-1958 Moroccan family law was codified in the Mudawwana, a text known for its close adherence to the classical Maliki tradition. Since the early 1980s the debate about reform has become more intense and widespread. The relatively limited reform of the Mudawwana in 1993 was closely linked to the beginnings of a process of cautious democratization. Since then the discussions have become more vehement, especially since the coming to power of a new government in 1998 consisting of former opposition parties. A year later this government presented a plan for extensive family law reforms. The plan has provoked considerable public debate over key concepts such as democracy, development, human rights, civil society, and ijtihād. Upon closer inspection, larger issues are at stake: Who may speak out in public and participate in politics? This new turn in the discussions is related to the emergence of a public sphere.
Territorialization, science and the colonial state: the case of Highway 55 in Minnesota
Authors: Wainwright Joel , Robertson Morgan
Published: March 2003

This paper examines a recent conflict over the rerouting of Highway 55 in the city of Minneapolis, Minnesota. During a three-year struggle over the project, a group of indigenous people argued that the space where the highway would pass was sacred and of historical importance. We analyse a Cultural Resource Assessment prepared by a team of scientists that responded to these claims and cleared the way for the reroute. Our reading, which draws from the literatures of postcolonial studies and sociology of science, examines the way scientific claims are made to evaluate the sacredness of the site. We find that science works to produce the effect of state territorialization - or the iterative making of the space of the state - by placing ecological phenomena and indigenous testimony ‘within’ a non-sacred Minnesotan space.
The art of nation-building: (re)presenting political transition at the South African National Gallery
Authors: Crampton Andrew
Published: March 2003

This paper examines the relationship between museums and representations of national identity in South Africa. From their early development in Western Europe in the nineteenth century there has been a close relationship between museums and other exhibitionary spaces and the production of national identities. In South Africa, museum displays have historically supported colonial and apartheid ideologies, but with the transition to a post-apartheid society museums have reassessed their divisive roles and repositioned themselves within South Africa’s contemporary nation-building project, organized around building unity from diversity. The development of this new relationship between museums and democratic nation-building is examined here through discussing the attempts of South Africa’s museums to become more inclusive in their exhibitions, and analysing debates in the museological community concerning the challenges facing museums in a post apartheid society. These issues then inform an analysis of an exhibition at the South African National Gallery titled Contemporary South African art 1985-1995. The exhibition attempted to use art to document the political transition and contribute to building national unity. However, by discussing the political operation of classification in museums I argue that the exhibition ultimately fails to represent this period inclusively, and I question, more generally, the possibility of art museums engaging in a properly inclusive nation-building project.
An acoustic method for in-line particle size measurement in flowing bulk solids
Authors: Tallon S , Davies C E , Kirkegaard M
Published: March 2003

The propagation velocity of acoustic waves through a packed bed of particles depends on, among other things, the wave frequency and the size of the particles. In this paper, theory is developed to describe the propagation velocity based on consideration of viscous interactions between the gas and solid phases. Experimental measurements in the frequency range 50–10 000Hz, and for particles ranging in mean size from 65 to 6000μm, agree well with the theory, particularly at low frequencies. The propagation velocity also correlates strongly with measurements of the surface mean particle diameter, independently of changes in particle density, and a method is described using this relationship as the basis of an in-line particle size measurement instrument for flowing bulk solid systems. Measurements using different size fractions of sand suggest that changes in mean particle size of less than 1.5 per cent can be resolved using the simple prototype developed for this work.
A design—decision support framework for evaluation of design options/proposals using a composite structure methodology based on the approximate reasoning approach and the evidential reasoning method
Authors: Sii H S , Wang J
Published: March 2003

With the cost of construction, operation and maintenance estimates in the multi-millions of pounds, the offshore industry is seeking ways of reducing both the time and money spent in providing the high-quality offshore structures needed to support oil and gas extraction and production. Most real world design evaluation and risk-based decision support combine quantitative and qualitative (linguistic) variables. Decision making based on conventional mathematics that combines qualitative and quantitative concepts always exhibits difficulty in the modelling of actual problems. The successful selection process for choosing a design/procurement proposal is based on a high degree of technical integrity, safety levels and low costs in construction, corrective measures, maintenance, operation, inspection, as well as preventive measures. However, the objectives of maximizing the degree of technical performance, maximizing the safety levels and minimizing the costs incurred are usually in conflict, and the evaluation of the technical performance, safety and costs is always associated with uncertainty, especially for a novel system at the initial concept design stage. In this paper, a design—decision support framework using a composite structure methodology grounded in an approximate reasoning approach and an evidential reasoning method is suggested for design evaluation of offshore engineering products at the initial stages. It is a multiple attribute decision-making (MADM) or multiple-criteria decision-making framework, which provides a juxtaposition of cost, safety, and technical performance and other objectives of a system during evaluation to assist decision makers in selecting the winning design/procurement proposal that best satisfies the requirement in hand. It has also been shown that the formal decision-making techniques such as the Analytical Hierarchy Process (AHP) and the Delphi method can be incorporated with the proposed framework in carrying out design support evaluation. An illustrative example is used to demonstrate the application of the proposed framework.
Vestibular-evoked myogenic potential in patients with unilateral vestibular neuritis: abnormal VEMP and its recovery
Authors: Ochi Kentaro , Ohashi Toru , Watanabe Shoji
Published: March 2003

The incidence of inferior vestibular nerve disorders in patients suffering from unilateral vestibular neuritis and the recovery of these disorders were evaluated by monitoring the vestibular-evoked myogenic potential (VEMP). Eight patients ranged from 21 to 73 years that suffered from unilateral vestibular neuritis underwent VEMP and caloric testing. Abnormal VEMP was observed in two of the eight patients with unilateral vestibular neuritis. Two patients were diagnosed as having an inferior vestibular nerve disorder. One of these patients showed recovery of the inferior vestibular nerve function as assessed by the VEMP. Disorders of the inferior vestibular nerve function and their recovery was confirmed by our current results. The time course of recoveries of the superior and inferior vestibular nerve systems were similar in the two patients.
Permanent bilateral acoustic trauma due to air bag deployment in a young female adult
Authors: Kastanioudakis Ioannis , Exarchakos Georgios , Ziavra Nausica , Skevas Antonios
Published: March 2003

Air bag safety systems have significantly reduced the number of occupant injuries from road traffic accidents (RTA). However air bag deployment is also associated with unavoidable risks.

We report the acoustic trauma incurred by a young female driver who was a heavy smoker as a consequence of air-bag deployment in a low speed RTA and the sparing of her child seated in the rear.
Delayed diagnosis of laryngeal foreign body
Authors: Jesudason W. V. , Luff D. A. , Rothera M. P.
Published: March 2003

Aspiration of a foreign body is a recognized cause of accidental death in children. Paediatricians are aware of the symptoms of inhaled foreign bodies in the lower respiratory tract. However, symptoms which suggest impaction in the larynx do not appear to raise the same index of suspicion of a foreign body. One case of laryngeal foreign body is described with a delay in diagnosis of five days. The clinical presentation, investigations and management are discussed.
Canonical transformation and accidental degeneracy. III. A unified approach to the problem
Authors: Moshinsky M. , Patera J. , Winternitz P.
Published: March 2003

We continue the discussion of the groups of canonical transformations responsible for accidental degeneracy in quantum mechanical problems. A general unified treatment is provided for a wide class of two−dimensional physical systems, having an energy spectrum which is a linear combination of two quantum numbers. The general method involves the use of both nonorthonormal and orthonormal sets of states to construct groups of complex or real canonical transformations, mapping the problem under consideration onto the two−dimensional isotropic harmonic oscillator. The group responsible for the accidental degeneracy is then quite obviously SU (2). The problem of an isotropic oscillator in a sector π/q (q integer) was discussed previously using a nonorthonormal basis. In the present paper we carry the analysis in an orthonormal basis to establish the general procedure mentioned above. We also analyze in detail the Calogero problem for three particles which has a spectrum of the type given above, and obtain explicitly the canonical transformation that maps it on the anisotropic oscillator whose ratio of frequencies is 2/3 and subsequently on the isotropic one.
On the exact solutions of the Wick−rotated fermion−antifermion Bethe−Salpeter equation
Authors: zum Winkel D.
Published: March 2003

Exact solutions of the fermion−antifermion Bethe−Salpeter equation with harmonic kernels are given for bound states with zero mass. The
Equilibrium states for the infinite ideal Bose gas
Authors: Moya R. P.
Published: March 2003

We construct a set of equilibrium states for the ideal Bose gas at temperature β−1 and chemical potential μ. Our choice for the equilibrium states is based on the Kubo−Martin−Schwinger conditions. In particular, we define ℰβ,μ to be the set of states which satisfy the KMS conditions suitably defined. In the condensed phase a certain subset Δβ,μ of ℰβ,μ correspond to states whose mean local densities are not uniformly bounded with respect to the volume. We, therefore, propose that ℰβ,μ Δβ,μ ≡ ?β,μ corresponds to the set of equilibrium states. Then it is shown that ?β,μ contains, as special cases, the equilibrium states obtained via thermodynamical limit arguments by Araki−Woods and Lewis−Pulé. The extremal elements of the convex set ℰβ,μ are obtained explicitly.
Imbedding of Segal systems
Authors: Deliyannis Platon C.
Published: March 2003

It is shown that any distributive Segal quantum system satisfying a certain continuity condition on the squaring operation can be represented as a space of Mackey observables based on some logic derived from the original system.
Prolongation structures of nonlinear evolution equations
Authors: Wahlquist H. D. , Estabrook F. B.
Published: March 2003

A technique is developed for systematically deriving a ’’prolongation structure’’—a set of interrelated potentials and pseudopotentials—for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg−de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear ’’inverse scattering’’ equations for auxiliary functions, Bäcklund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.
Fields and radiation due to a charge incident on a conducting plane
Authors: Maresca Neal J. , Liboff Richard L.
Published: March 2003

The exact fields of a uniformly moving charged particle which passes through a point hole at t = 0 in a grounded, infinitely conducting plane are obtained. Calculation of the fields for all time (− ∞ ⩽ t ⩽ + ∞) reveals a singular spherical pulse emanating from the origin at t = 0 which destroys fields within its sphere in the left half−space, and generates them within its sphere in the right half−space. Further calculation exposes a reversible exchange of reactive field energy between the left and right half−spaces, together with a dissipative radiation loss. A review of techniques which employ the integral ∫E⋅jdV to obtain radiation energy is given. For the problem at hand (− ∞ ⩽ t ⩽ + ∞) it is found that this integral represents radiation alone while in the restricted problem (−∞ ⩽ t ⩽ 0), the integral contributes both reactive and radiative (resistive) energy with reactive gain exceeding radiative loss by the factor β2.
Preliminary results in the Banach space formulation of master equation and subdynamics theory in quantum statistics
Authors: Alberti M. A. , Cotta−Ramusino P. , Ramella G.
Published: March 2003

The Liouville−von Neumann equation and a useful decomposition of the resolvent of the generator of the time evolution operators are obtained in the formulation of quantum statistics by means of the pair of Banach spaces (τc, B), where τc is the space of the ’’trace−class’’ operators and B is the space of all bounded operators, defined on a Hilbert space.
A minimum principle for von Neumann’s equation
Authors: Golden Sidney
Published: March 2003

A minimum principle is described which has von Neumann’s equation of motion of the statistical operator as its ultimate solution. When the statistical operator is initially restricted to be a projection of trace unity, the minimum principle has Schrödinger’s time−dependent equation as its ultimate solution. As a result, the present minimum principle is shown to be a generalization of one first introduced by McLachlan, with a modification of the Dirac−Frenkel variational principle as a necessary consequence. In physical terms, the quantity that is minimized is shown to be the mean−squared deviation of an effective time−dependent Hamiltonian, which can be attributed to a time−dependent statistical operator initially chosen to describe a system, from the actual time−dependent Hamiltonian of the system. Examples of approximate solutions to von Neumann’s equation and Schrödinger’s equation that are obtained by use of the minimum principle confirm this identification.
Gravitational and electromagnetic radiation in Kerr−Maxwell spaces
Authors: Lind Robert W.
Published: March 2003

The class of Kerr−Maxwell spaces is defined. This class consists of regular electrovac spacetimes in which a geodesic, diverging, shear−free principal null vector field of the Weyl tensor coincides with a principal null vector field of the Maxwell tensor. It is shown that this class admits no Petrov−Penrose type III or type N solutions. It is also shown that the most general nonradiative solution is the Kerr−Newman metric.
Stationary Kerr−Maxwell spaces
Authors: Lind Robert W.
Published: March 2003

We consider algebraically special electrovac spacetimes in which a diverging, geodesic, shear−free (but twisting) degenerate principal null direction of the Weyl tensor coincides with a principal null direction of the Maxwell tensor. All stationary solutions of this class are solved exactly and found to be of Petrov−Penrose type D, the most general regular stationary solution being the Kerr−Newmann metric.
An exact determination of the gravitational potentials g
i
j in terms of the gravitational fields R
l
i
j
k
Authors: Ihrig Edwin
Published: March 2003

Under a certain asymmetry assumption, the gravitational potentials gij are determined up to a conformal factor from the field Rlijk. This constitutes a partial solution to Einstein’s equations in the general case. Moreover, the solutions are simple in that the gij are expressed as polynomial functions of the Rlijk.
On resonance and stability of conservative systems
Authors: Dysthe K. B. , Gudmestad O. T.
Published: March 2003

Resonance and stability of conservative systems are considered by means of a perturbation method similar to the averaging method of Bogoliubov. The accuracy of the method is tested by numerical simulations and by comparing the conditions for stability derived here with the well−known conditions given by Moser and Arnold.
Ghost neutrinos in plane−symmetric spacetimes
Authors: Davis Talmadge M. , Ray John R.
Published: March 2003

An exact solution to the Einstein−Dirac equations is presented for a plane−symmetric spacetime generated by neutrinos. The neutrino field is nonzero and corresponds to a neutrino current along the symmetry axis of the space. The neutrinos yield a nonzero energy−momentum tensor, which we specialize to Tij = 0 for ’’ghost’’ neutrinos. We show that, since the energy−momentum tensor vanishes, the time−dependent ’’ghost’’ neutrino metric reduces to the static case. The time−dependent ’’ghost’’ current is then reduced to the static current through a Lorentz transformation and the ’’ghost’’ wavefunction reduced to the static wavefunction through a spinor transformation. The ’’ghost’’ neutrino current is geodesic and the spacetime is classified by the expansion, rotation, and shear of these geodesics. From previous results it follows that our plane−symmetric ’’ghost’’ solution is the most general solution to the Einstein−Dirac equations for a vanishing energy−momentum tensor and a neutrino current that is expanding. The solution is Petrov type D.
Transport equations for the Stokes parameters from Maxwell’s equations in a random medium
Authors: Papanicolaou G. C. , Burridge R.
Published: March 2003

Beginning with Maxwell’s equations in a random medium and following a perturbation procedure, we obtain transport equations for the Stokes parameters. We compare our equation with Chandrasekhar’s transport equation and find that they agree when the random medium is specialized appropriately. We also examine the role of degeneracy in the perturbation analysis.
New class of exact solutions of the Dirac equation
Authors: Felber Franklin S. , Marburger John H.
Published: March 2003

A new class of exact solutions of the Dirac equation with external electromagnetic fields is derived by assuming a set of field-dependent solution matrices which obey an algebra isomorphic to the Pauli matrices. The method of exact solution may be applied to any field having a four-vector potential Aμ depending only on kμxμ, but for which the field tensor and initial electron momentum are such that AμAμ, Aμpμ, (σμνFμν)2, and (σμνF′μν)2 are independent of kμxμ. Exact solutions for a circularly polarized propagating electromagnetic wave in an isotropic medium, for a screw symmetric static magnetic field, and for a rotating uniform electric field are given in terms of the roots of a quartic equation. A class of solutions is given explicitly in the weak field limit to lowest order in eA/mc2. The vacuum limit of the solution of a wave propagating in a medium is shown to be the Volkov solution.
Two-point characteristic function for the Kepler–Coulomb problem
Authors: Blinder S. M.
Published: March 2003

Hamilton’s two-point characteristic function S (q2t2,q1t1) designates the extremum value of the action integral between two space–time points. It is thus a solution of the Hamilton–Jacobi equation in two sets of variables which fulfils the interchange condition S (q1t1,q2t2) =−S (q2t2,q1t1). Such functions can be used in the construction of quantum-mechanical Green’s functions. For the Kepler–Coulomb problem, rotational invariance implies that the characteristic function depends on three configuration variables, say r1,r2,r12. The existence of an extra constant of the motion, the Runge–Lenz vector, allows a reduction to two independent variables: x≡r1+r2+r12 and y≡r1+r2−r12. A further reduction is made possible by virtue of a scale symmetry connected with Kepler’s third law. The resulting equations are solved by a double Legendre transformation to yield the Kepler–Coulomb characteristic function in implicit functional form. The periodicity of the characteristic function for elliptical orbits can be applied in a novel derivation of Lambert’s theorem.
On the quantum mechanical treatment of dissipative systems
Authors: Hasse Rainer W.
Published: March 2003

Two types of Hamiltonians are investigated which describe quantum mechanically a particle moving subject to a linear viscous force under the influence of a conservative force: the conventional explicitly time-dependent one and an alternative class of nonlinear Hamiltonians. In the latter group we propose a new form. By Ehrenfest’s theorem the expectation values of the operators of physical observables correspond to the classical quantities. For all Schrödinger equations we derive and discuss wavepacket, wave, stationary, and pseudostationary solutions of force free motion, free fall, and harmonic oscillator.
Nonlinear canonical transformations and their representations in quantum mechanics
Authors: Mello P. A. , Moshinsky M.
Published: March 2003

In the last few years an extensive literature has developed on linear canonical tranformations and their representation in quantum mechanics. Applications of these results have been made to clustering theory in nuclei, problems of accidental degeneracy, etc. In the present paper we wish to turn our attention to nonlinear canonical transformations. We show that by dealing with appropriate functions fα (α=1,...,2n) of xi, pi (i=1,...,n) rather than with these variables themselves, we can in principle set unambiguously the equations that determine the representation in quantum mechanics of the canonical transformation under study. This result holds when the old and new functions fα have the same spectrum. We discuss specific examples when this last condition is satisfied: nonlinear canonical transformations in the radial variable that were obtained from projection of linear ones in higher-dimensional spaces; canonical transformations that take us from one Hamiltonian to another with the same spectrum, be this one continuous or discrete; canonical transformations that relate two sets of integrals of motion (which include the Hamiltonians) when we are dealing with phase spaces of dimensions higher than 2, etc. We discuss briefly, in the concluding section, the possibility of extending our analysis to canonical tranformations that do not conserve the spectrum of the relevant operators.
An asymptotic formula for the twisted product of distributions
Authors: Liu Kuang Chi
Published: March 2003

The expansion theorem for the twisted product associated with the Weyl form of CCR for n degrees of freedom is generalized to involve tempered distributions.
Convergence of the perturbative approach to the N-body problem in the N→∞ limit
Authors: Calogero F. , Palumbo F.
Published: March 2003

An N-body system with interparticle forces that are attractive at short range collapses in the limit N→∞, namely in this limit the ground-state energy per particle diverges to negative infinity. If instead the forces are sufficiently repulsive at short range, in the limit N→∞ saturation occurs, leading to a finite ground-state energy per particle ε. This quantity depends, among other things, on the ’’coupling constant’’ g (entering as a factor that multiplies the interaction), and the above remark clearly implies that it is defined in the N→∞ limit only for positive values of g (although, for finite N, it is defined both for positive and negative g). This fact is generally taken to imply that the function ε (g) is nonanalytic in g at g=0 and, therefore, that the perturbative expansion of ε (g), being a power expansion in g, is necessarily nonconvergent (although it might be asymptotic). The purpose of this paper is to demonstrate the lack of cogency of this argument. It is therefore concluded that nonconvergence of the perturbative expansion for ε (g) is thus far an unproven hypothesis. The lack of cogency of analogous current arguments concerning the equilibrium density of many-body systems is also pointed out.
A possible unification of gravitation and electrodynamics both for spinless and spinning media
Authors: Mahanta M. N.
Published: March 2003

It was shown by the author recently that the Einstein–Mayer formalism of 1931–32 can be successfully applied to derive the field equations for a spinning medium. The present article discusses the possibility of obtaining a unified representation of gravitation as well as electromagnetism both for spinless and spinning media with the help of the same formalism. Field equations and equations of motion for a point particle are derived for both cases.
Solutions of a scalar–tensor theory from Einstein’s theory
Authors: Singh T.
Published: March 2003

The vacuum field equations of a scalar–tensor theory proposed by Sen and Dunn are investigated. The metric coefficients are assumed to be functions of three variables only. It is then shown that if one assumes a functional relationship between some one of the metric coefficients and the scalar function, one can find a solution of the vacuum field equations of Sen and Dunn’s scalar–tensor theory in terms of a solution of the vacuum field equations of Einstein’s theory. This result is applied to some well-known solutions, viz., Schwarzschild solution, the static plane symmetric solution of Taub, the conformastat solution of Das, and the static axially symmetric solutions of Levi-Civita and Curzon; and the corresponding solutions of the scalar–tensor theory are obtained.
A Clifford algebraic approach to superfields and some consequences
Authors: Ktorides C. N.
Published: March 2003

Frames provided by Clifford algebras 𝒞n are considered for the purpose of expanding a field multiplet (containing, possibly, both bosons and fermions). After giving a brief—mainly geometrical—description of Clifford algebras, the main tools of the present scheme are introduced: a scalar product in 𝒞n, a conjugation operation, and a ’’Lorentz covariant derivative.’’ It is described how these Clifford algebraic tools can be applied in order to obtain free massless Lagrangian expressions for a number of field theoretical models. It is also shown how gauge fields can arise within this scheme. It appears possible that the suggested formalism can lead naturally to spinor field operators as ’’gauge fields.’’ A specific example which can lead to a two-component ’’gauge spinor’’ is discussed. Possible lines of investigation which could solidify this potentially rich approach are suggested.
A superposition principle for Siegert resonant states
Authors: Huestis David L.
Published: March 2003

The utilization of the Siegert resonant states as a natural basis for the scattering process has been constrained by the lack of a convergent superposition formula. This paper presents such an expansion of the exact scattering wavefunction over the s-wave Siegert resonant states for finite range potentials. Any integral property of the scattering wavefunction can then be calculated from the resonances.
On finite mass renormalizations in the two-dimensional Yukawa model
Authors: Seiler Erhard , Simon Barry
Published: March 2003

In the Mathews–Salam formulas for the (space–time cutoff) Schwinger functions of Y2, no restriction on finite mass renormalizations for the boson is necessary.
Average multiplicity and the zeros of multiparticle generating function
Authors: Kinoshita Toichiro , Maharana Jnanadeva
Published: March 2003

We have obtained several theorems exhibiting relations between the asymptotic behavior of the average multiplicity 〈n〉 and the distribution of zeros of a generating function for multiparticle production cross sections.
Monotonic converging variational approximations to the functional integrals in quantum statistical mechanics
Authors: Bessis D. , Moussa P. , Villani M.
Published: March 2003

We show, by making use of the functional integral technique, that, for a large class of useful quantum statistical systems, the partition function is, with respect to the coupling constant, the Laplace transform of a positive measure. As a consequence, we derive an infinite set of monotonicly converging upper and lower bounds to it. In particular, the lowest approximation appears to be identical to the Gibbs–Bogolioubov variational bound, while the next approximations, for which we give explicit formulas for the first few ones, lead to improve the previous bound. The monotonic character of the variational successive approximations allows a new approach towards the thermodynamical limit.
Self-adjoint operators, derivations and automorphisms on C*-algebras
Authors: Narnhofer Heide
Published: March 2003

We discuss how the concept of C*-algebras with a strongly continuous one parameter group of automorphisms can be realized, if the automorphism is implemented by an unbounded operator.
Normal coordinates and quantization of nonlinear fields by Feynman’s path integral
Authors: Hsue C. S.
Published: March 2003

A simple derivation for the quantization of nonlinear fields by Feynman’s path integral method is given in terms of normal coordinates. The origins of the additional term obtained by DeWitt can be clearly seen in this formalism.
Spectral representation and decomposition of self-adjoint operators
Authors: de Dormale Bernard M. , Gautrin Henri-François
Published: March 2003

This paper is an extension of results established by Jauch and Misra [Helv. Physica Acta 38, 30 (1965)] concerning finite or countable sets of commuting self-adjoint operators. We have obtained the following results: let 𝒜={Ai}i-I be a set of commuting self-adjoint operators on a separable Hilbert space ℋ. Then (i) for any I (possibly noncountable), there exists a spectral representation for 𝒜 iff 𝒜″ is maximal Abelian. (ii) If I is finite or countable, -i-I,n-N 𝒟 (Ani) is dense in ℋ. As a corollary of a theorem of Maurin [Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 7, 471 (1959)], this implies the existence of a common complete set of generalized eigenvectors.
Expansions for simple cubic lattice Green’s functions
Authors: Jorna S.
Published: March 2003

Expansions in terms of elementary functions are given for the diagonal elements of the simple cubic Green’s function I (l;s) = (1/π3) ℱℱℱπ0 [cos(lφ1) cos(lφ2) cos(lφ3)/ (s+iε−cosφ1−cosφ2−cosφ3)] dφ1dφ2dφ3 in the ranges 0<s<1, 1<s<3, and s≳3 for arbitrary l. The fast convergence of these expansions renders them extremely useful for the rapid determination of numerical values for ReI (l;s) and ImI (l;s) of high accuracy. More slowly converging expansions are given for s=1 and s=3. The expansion for s=1 is particularly useful for large l.
Group theory and propagation of operator averages
Authors: Quesne C.
Published: March 2003

The propagation of operator averages, which is the basis of French’s spectral distribution method, is reformulated in the framework of group theory. The concept of complementary groups is extensively used. It is shown that the possibility of propagating averages is intimately connected with the absence of state labeling problem. The construction of the propagation operators is examined, and for those cases where it is not trivial, a new way of approach is suggested by establishing a link with recent group theoretical advance in the construction of subgroup invariants in the universal covering algebra of a group. Finally the discussion is illustrated by some examples taken, or not, from current literature.
Solutions for the general cylindrically symmetric stationary dust model
Authors: Zimmerman John Charles
Published: March 2003

For a dust-filled space–time possessing cylindrical symmetry, the field equations form an underdetermined set. As demonstrated by King [Commun. Math. Phys. 38, 157 (1974)], by carefully selecting a function it is possible to generate solutions which are either well-behaved or are characterized by one of a number of different types of singularity. The three particular choices for the functions we take produce two nonsingular solutions and one with a Weyl singularity.
Invariance transformations, invariance group transformations, and invariance groups of the sine-Gordon equations
Authors: Kumei Sukeyuki
Published: March 2003

We investigate a structure of continuous invariance transformations connected to the identity transformation. The transformations considered do not necessarily form a group. We clarify the relationship between the infinitesimal invariance transformation and the finite invariance transformation by showing explicitly how the infinitesimal transformations are woven into the finite one. The analysis leads to a new method of finding generators of the invariance group transformation. The results are useful in the study of symmetry properties, or group theoretic structure, of differential equations. We use the results in studying the group properties of the sine-Gordon equation uxt=sinu, and indicate that the equation is invariant under an infinite number of one-parameter groups; the groups obtained are of a more general type than that dealt with by Lie. These findings are used to prove the group theoretic origin of the well-known conservation laws associated with the sine-Gordon equation.
SU(4) Clebsch–Gordan coefficients
Authors: Rabl Veronika , Campbell George , Wali Kameshwar C.
Published: March 2003

We give tables of Clebsch–Gordan coefficients for the products of SU(4) representations 15⊗15 and 20⊗15, decomposed with respect to SU(3).
Lie theory and separation of variables. 8. Semisubgroup coordinates for Ψt
t − Δ2Ψ = 0
Authors: Kalnins E. G. , Miller Willard
Published: March 2003

We classify and study all coordinate systems which permit R-separation of variables for the wave equation in three space–time variables and such that at least one of the variables corresponds to a one-parameter symmetry group of the wave equation. We discuss 33 such systems and relate them to orbits of commuting operators in the enveloping algebra of the conformal group SO (3,2).
The structure of groups with index-3 subgroups and Landau’s second theorem
Authors: Meisel L. V. , Gray D. M. , Brown E.
Published: March 2003

For any group G0 which contains an index-3 subgroup G, it is shown that either (a) G is an invariant subgroup or (b) G contains an index-2 subgroup GA, where GA is an invariant subgroup of G0. For case (a), G and its cosets give rise to three operators which span a stable three-dimensional subspace of the group algebra which further reduces to three one-dimensional stable subspaces. For case (b), GA and its cosets give rise to six operators which span a six-dimensional stable subspace of the group algebra which reduces to two one-dimensional and two two-dimensional irreducible stable subspaces of the group algebra. The irreducible representations and the corresponding basis elements of the group algebra are given for both cases. Landau’s second theorem pertaining to second order phase transitions is proven.
Representations of a local current algebra: Their dynamical determination
Authors: Menikoff Ralph , Sharp David H.
Published: March 2003

Local currents are used to describe nonrelativistic many-body quantum mechanics in the thermodynamic limit. The problem of determining a representation of the local currents corresponding to a given Hamiltonian is studied. We formulate the dynamics in such a way that one solves simultaneously for the ground state and the representation of the local currents. This leads to two coupled functional equations relating the generating functional to a functional which describes the ground state. Together these functionals determine a representation of the local currents in which the Hamiltonian is a well-defined operator. The functional equations are equivalent to a set of integro–differential equations for expansion coefficients of the two functionals.
Singularities in nonsimply connected space–times
Authors: Gannon Dennis
Published: March 2003

Space–times with asymptotically flat nonsimply connected spacelike slices are shown to possess enough intrinsic geometric structure to guarantee the existence of singularities under conditions usually considered insufficient. In particular, it is shown that if the normal geodesics to the spacelike slice are converging on a suitable compact set, and the space–time satisfies a standard energy condition, then it is timelike geodesically incomplete. A similar result holds if the space–time satisfies the chronology and generic conditions.
Note on the computation formula of the boost matrices of SO(n−1,1) and continuation to the d matrices of SO(n)
Authors: Maekawa Takayoshi
Published: March 2003

The general formula of computing the boost matrices of SO(n−1,1), which is valid for the single- and double-valued representations and is similar to that of Vilenkin and Wolf, is given. It is noted that a phase factor of a unit magnitude in the boost matrices must be taken into account in analytic continuation to the d matrices of SO(n), and then the formula of computing the d matrices of SO(n) is given. It is remarked that the d matrices of SO(n) are expressed in terms of those of SO(n−1).
Some solutions of complex Einstein equations
Authors: Plebañski J. F.
Published: March 2003

Complex V4’s are investigated where ΓȦḂ =0 and therefore a fortiori equations Gab=0 are fulfilled. A general theory of spaces of this type is outlined and examples of nontrivial solutions of all degenerate algebraic types are provided.
Exact propagator for a time−dependent harmonic oscillator with and without a singular perturbation
Authors: Khandekar D. C. , Lawande S. V.
Published: March 2003

By using Feynman’s definition of a path integral, exact propagators for a time−dependent harmonic oscillator with and without an inverse quadratic potential have been evaluated. It is shown that these propagators depend only on the solutions of the classical unperturbed oscillator. The relations between these propagators, the invariants, and the Schrödinger equation are also discussed.
Calculation of moments in the harmonic oscillator basis
Authors: Joshi P. C.
Published: March 2003

The matrix element of rk between the eigenstates of harmonic oscillator potential is generally calculated by using the value of an integral listed in available literature for certain specific conditions. Recently, while calculating the matrix elements of deformed spin−orbit potential in the harmonic oscillator basis for nonspherical nuclei, we found that the evaluation of this integral is needed under more general conditions then discussed previously. We discuss the results of the evaluation of this integral for these additional cases.
Disproof of a conjecture of D. Muhlerin and I. Zinnes
Authors: Dollard John D.
Published: March 2003

It is shown that the operator U(±)c(t) defined by Muhlerin and Zinnes [J. Math.Phys.11,1402 (1970)] in their account of Coulomb potential scattering theory is not an isometry when the Coulomb potential is weak enough. It is opined that for this reason their account of Coulomb potential scattering theory does not have a straightforward physical interpretation.
J−matrix method: Extensions to arbitrary angular momentum and to Coulomb scattering
Authors: Yamani Hashim A. , Fishman Louis
Published: March 2003

The J−matrix method introduced previously for s−wave scattering is extended to treat the lth partial wave kinetic energy and Coulomb Hamiltonians within the context of square integrable (L2), Laguerre (Slater), and oscillator (Gaussian) basis sets. The determination of the expansion coefficients of the continuum eigenfunctions in terms of the L2 basis set is shown to be equivalent to the solution of a linear second order differential equation with appropriate boundary conditions, and complete solutions are presented. Physical scattering problems are approximated by a well−defined model which is then solved exactly. In this manner, the generalization presented here treats the scattering of particles by neutral and charged systems. The appropriate formalism for treating many channel problems where target states of differing angular momentum are coupled is spelled out in detail. The method involves the evaluation of only L2 matrix elements and finite matrix operations, yielding elastic and inelastic scattering information over a continuous range of energies.
Acoustic scattering by penetrable homogeneous objects
Authors: Kittappa R. , Kleinman R. E.
Published: March 2003

The scattered field is found when a time harmonic acoustic wave is incident upon a finite object characterized by a density and wavenumber different from that of the surrounding medium. The interface is assumed to be either Lyapunoff or piecewise Lyapunoff. The problem is cast as a pair of coupled surface integral equations for the total field and its normal derivative on the interface. The Neumann series obtained by straightforward iteration is proven to be convergent for ranges of density and wavenumber, and specific bounds on these ranges are given. For small enough wavenumbers, the series converges for all values of the interior density. The iteration appears simpler than the usual Born approximation, which involves volume as well as surface integrals. The method is illustrated in the case of a spherical interface.