bluuebunny/crossref_metadata_2025 huggingface dataset:
STUDIES OF SOME PECULIARITIES OF NONLINEAR DYNAMICS OF FOUR-WAVE MIXING OF LIGHT WAVES PROPAGATING FORWARD IN LIQUID CRYSTAL ON THERMAL NONLINEARITY
Authors: PODOSHVEDOV SERGEY A.
Published: March 2003

Evolution of four waves propagating forward in nematic liquid crystal is studied using Hamiltonian representation of initial equations describing the process. Here we extend theory of the four-wave mixing on thermal nonlinearity of nematic liquid crystal. All types of analytical solutions are found for these equations. The possibilities of observing of optical switching in this mixing are discussed.
OPTICAL NUTATION AND FREE INDUCTION DECAY IN MAGNETOACTIVE INDIUM ANTIMONIDE
Authors: ANDREWS J. THOMAS , SEN PRATIMA
Published: March 2003

Using the density matrix approach, the effect of magnetic field on optical nutation and free induction decay (FID) has been investigated analytically in direct gap semiconductors. The numerical estimations made for a thin sample of bulk InSb duly irradiated by a Lead salt (PbEuSeTe) diode laser exhibit an enhancement in the beat signal intensity of the nutating output at large magnetic fields. The numerical analysis of free induction decay in InSb crystal–laser interacting system yield the results that both the decay time as well as transmitted field amplitude increase with increasing magnetic field.
NUMERICAL ANALYSIS OF NONLINEAR INTERACTIONS
Authors: HSU HSIUNG , LI TONG-NING
Published: March 2003

The theories of parametric and nonlinear interactions are often limited to small signal analysis of ideal lossless systems. We have presented large signal analysis to ideal three1,2 and four3,4 wave parametric interactions, still treating the systems as lossless. The analysis was in terms of Jacobian elliptic functions which are often not readily available. The objective of this paper is to show that the solution of these large signal analysis can be obtained very easily and accurately by numerical analysis, and extended further to include the effect of losses. In this paper, we use stimulated Brillouin scattering and phase conjugation as example for demonstration.
ADVANCED IMAGING METHODS FOR THE ASSESSMENT OF HIP DYSPLASIA
Authors: Frick Steven L. , Kim Hui Taek , Wenger Dennis R.
Published: March 2003

Developmental dislocation of the hip is an important orthopedic condition whose early diagnosis and treatment greatly improves the life of a patient with the condition. Despite a worldwide focus on early diagnosis and treatment, many children and adolescents present with residual hip dysplasia. This group includes those that have not had prior diagnosis or treatment and often present in adolescence, as well as those who have been treated nonoperatively and yet continue to have residual dysplasia.

Decisions determining when hip dysplasia should be surgically corrected have traditionally been dependent upon two-dimensional images (plain radiographs) to analyze the nature and degree of residual deformity. To better understand residual hip dysplasia in children, we have utilized three-dimensional computerized tomographic (3-D CT) methods to evaluate the pathoanatomy of hip dysplasia in children. Careful analysis of these images has allowed us to more fully understand the nature of residual hip dysplasia and to better plan corrective hip osteotomies designed to improve the longevity and function of the hip joint.
ACETABULUM-IMPACTING TOTAL HIP ARTHROPLASTY FOR SEVERE ACETABULAR DYSPLASIA
Authors: Matsumoto Tadami , Kabata Tamon , Nishino Mitsuru , Kaneuji Ayumi , Sugimori T. , Tomita Katsuro
Published: March 2003

We report our experience using the acetabulum-impacting total hip arthroplasty technique and describe the results of short-term follow up. This technique is new method of acetabular plasty for the patients with severe dysplastic hip.
RELIABILITY OF A SIMPLE SHOULDER ENDURANCE TEST
Authors: Hughes Richard E. , Johnson Marjorie E. , Skow Anne , An Kai-Nan , O'Driscoll Shawn W.
Published: March 2003

Reduced shoulder endurance in rotator cuff tear patients has been observed clinically. A simple and inexpensive shoulder endurance test protocol was developed. This study reports the test-retest reliability of the protocol. Twenty healthy volunteers without a history of shoulder pathology participated in the study. Each subject was tested twice, each on a separate day. Test-retest correlation coefficients of the arm endurance times were 0.59 and 0.60 for the dominant and nondominant sides, respectively. The protocol appears promising for assessing shoulder function.
STABILIZATION EFFECTS OF GRAF LIGAMENTOPLASTY
Authors: Hasegawa Kazuhiro , Hirata Yasuharu , Morita Tetsuro , Kobayashi Hiroto
Published: March 2003

Graf ligamentoplasty with or without decompression was performed consecutively in 22 patients of lumbar degenerative diseases with segmental instability. The clinical course of the patients was evaluated using the criteria of the Japanese Orthopaedic Association (JOA) for assessing treatment of low back pain (29 points in total), and radiological alteration in angular and translational displacements were measured in flexion, extension, or neutral position. The change of an intervertebral vacuum phenomenon (Knutsson's sign), as a sign of segmental instability, was observed before and after the surgery.

A preoperative JOA score of 13.7 points was significantly improved to 25.0 points with an improvement rate of 75.7% on average by Graf ligamentoplasty. Radiological measurements revealed that the operation reduced the range of motion of the involved segment in both angular and translational modes with the segment realigned in extension. The short-term results of Graf ligamentoplasty was acceptable for lumbar degenerative diseases. The patients in whom Knutsson's sign was reduced or disappeared after Graf ligamentoplasty had a better outcome than those with the sign unchanged or increased in size. This suggests that Knutsson's sign can be a predictive indicator of the outcome of the surgery.
THE GEOMETRIC TRIANGLE FOR 3-DIMENSIONAL SEIBERG–WITTEN MONOPOLES
Authors: CAREY A. L. , MARCOLLI M. , WANG B. L.
Published: March 2003

In this paper we prove the surgery formula relating the moduli spaces of solutions of suitably perturbed 3-dimensional Seiberg–Witten equations on a homology 3-sphere Y and on the 3-manifolds Y1and Y0obtained, respectively, by +1 and 0-surgery on a knot K in Y.
QUANTUM DEFORMATION AND TABLEAUX REALIZATION OF SIMPLE DENSE ${\mathfrak g} l (n, {\mathbb C})$-MODULES
Authors: MAZORCHUK VOLODYMYR
Published: March 2003

We show that all simple dense [Formula: see text]-modules with finite-dimensional weight spaces admit quantum deformation to the corresponding Drinfeld–Jimbo quantum group. We also realize almost all such modules via Gelfand–Zetlin construction, presenting them by a basis and precise formulae for the action of generators of [Formula: see text]. This construction has a direct analogue on the quantum level, hence for such modules the main result becomes very easy.
First Columnar Monolayer Structure of Bile Acids Inclusion Crystal. Inclusion Compounds of 23-Nordeoxycholic Acid
Authors: Sada Kazuki , Sugahara Michihiro , Nakahata Yoshihiro , Yasuda Yoshitaka , Nishio Akinori , Miyata Mikiji
Published: March 2003

A new host, 23-nordeoxycholic acid, which forms inclusion compounds with many organic compounds, have a novel monolayer columnar structure in spite of a facially amphiphilic molecular structure.
Synthesis of MnMoO4 as High Capacity Anode Material for Li Secondary Battery
Authors: Kim Sung-Soo , Ogura Seiichiro , Ikuta Hiromasa , Uchimoto Yoshiharu , Wakihara Masataka
Published: March 2003

MnMoO4(C2/m) as a new anode material for Li secondary battery has been synthesized by a conventional solid state reaction method and its electrochemical properties have been investigated. Mn L-edge XANES indicates that the energy of the main peak of MnMoO4 is close to that of MnCO3 (Mn2+). Mo L-edge XANES shows that the oxidation state of Mo in MnMoO4 is +6. The reversible amount of Li insertion/removal in MnMoO4 anode during the first cycle was about 1000 Ah/kg. Capacity variation with the current density shows that the rate capability of MnMoO4 is better than that of graphite.
Novel Absorption and Fluorescence Characteristics of l-Lysine
Authors: Homchaudhuri L , Swaminathan R
Published: March 2003

l-Lysine displays new absorption and fluorescence features at high concentrations (∼ 0.5 M) in aqueous medium. A new absorption peak was detected around ∼ 270 nm (ε = 0.34 M−1 cm−1). Blue fluorescence (∼ 435 nm) was visible on excitation at 355 nm. The above features which were concentration dependent are attributed to likely aggregates of l-lysine.
Ordered Mesoporous Materials. Novel Catalyst for Degradation of N′-Nitrosonornicotine
Authors: Zhu Jian Hua , Zhou Shi-Lu , Xu Yang , Cao Yi , Wei Yi-Lun
Published: March 2003

Temperature-programmed surface reaction (TPSR) of N′-nitrosonornicotine (NNN) was firstly reported on zeolite and ordered mesoporous materials. Among the catalysts SBA-15 and MCM-48 exhibited an activity much higher than zeolite NaY. They could also adsorb nitrosamines without interference of organic solvent, which will be helpful for environmental protection.
Microbial contamination of non-disposable instruments in otolaryngology out-patients
Authors: Powell Steven , Perry John , Meikle David
Published: March 2003

Nosocomial infections are an important cause of morbidity and contaminated equipment may contribute to this. There has been little work concerning contamination of non-disposable equipment in Otolaryngology. This study investigates the efficacy of the cleaning regimen for non-disposable instruments in an Otolaryngology out-patients clinic. Instruments were swabbed before each clinic, when they had been autoclaved, then after use on patients, when they had been washed with detergent and chlorhexidine. Swabs of 86 instruments were cultured using standardized microbiological techniques. Fifteen instruments (17 per cent) were contaminated, most with coagulase negative staphylococci. Two specimens of Micrococcus luteus were cultured and one each of Pseudomonas aeruginosa, Acinetobacter lwoffii and Aureobacterium spp. Micrococcus luteus and coagulase negative staphylococci may represent skin contaminants, but Aureobacterium spp. and Acinetobacter lwoffii can be sources of nosocomial infection. Pseudomonas aeruginosa is a potentially serious pathogen and is implicated in the aetiology of otitis externa. These findings question the efficacy of the current cleaning techniques.
Singularities for fluids with p=ω equation of state
Authors: Letelier P. , Tabensky R.
Published: March 2003

The structure of singularities is discussed for some exact solutions of Einstein equations for irrotational perfect fluids with equation of state pressure equal to energy density, p=ω. It is found that all singularities studied are velocity−dominated of the semi−Kasner class. It is also found that data on the singularity are not enough to generate space−time for all times.
Four examples of the inverse method as a canonical transformation
Authors: McLaughlin D. W.
Published: March 2003

The Toda lattice, the nonlinear Schrödinger equation, the sine−Gordon equation, and the Korteweg−de Vries equation are four nonlinear equations of physical importance which have recently been solved by the inverse method. For these examples, this method of solution is interpreted as a canonical transformation from the initial Hamiltonian dynamics to an ’’action−angle’’ form. This canonical structure clarifies the independence of an infinite number of constants of the motion and indicates the special nature of the solution by the inverse method.
Dual trees and resummation theorems
Authors: Friedberg R.
Published: March 2003

Various resummation theorems known for graphical expansions in statistical physics and field theory are exhibited as special cases of a single symmetrical, easily remembered theorem on a generalized structure we call a dual tree.
A new derivation of some fluctuation theorems in statistical mechanics
Authors: Vezzetti David J.
Published: March 2003

A simple derivation is given of some of the fluctuation theorems of statistical mechanics which relate integrals of molecular distribution functions to thermodynamic properties. The derivation employs the generating function for the probability Pω(n) that a domain ω contains n particles. Various forms of the generating function are derived, and each leads to a different form of the fluctuation theorems.
A stochastic Gaussian beam. II
Authors: McLaughlin D. W.
Published: March 2003

The propagation of a Gaussian beam in a strongly focusing medium is considered. The medium is subject to random deformations of the beam axis. The average intensity and the intensity fluctuations on the beam axis and the mean population remaining in the fundamental mode are computed when the random inhomogeneities are weak and the distance between the source and observation points is large. All results for random axis deformations are compared to those obtained earlier for random width perturbations. The mean intensity off the beam axis and the mean population transfer into higher modes are also discussed.
Lorentz covariance of the Yukawa2 quantum field theory
Authors: McBryan Oliver A. , Park Yong Moon
Published: March 2003

We prove Lorentz covariance of the field algebras in the Yukawa2 quantum field theory, thus completing the verification of the Haag−Kastler axioms for this model. We also study the energy−momentum tensor of the theory. In particular, we prove an estimate of the form P (f)2 ?const(H (g)+I)2 dominating local momenta by local Hamiltonians. Most of the results are a consequence of this estimate. These methods apply also to the (φ4)2 model.
Lattice Green’s function for B−site lattice in spinel
Authors: Inoue Michiko
Published: March 2003

We show that the lattice Green’s function at an arbitrary site of a B−site lattice in a spinel with nearest neighbor interactions can be expressed in terms of Green’s functions for a face−centered cubic lattice. Results of numerical calculations of the B−site lattice Green’s functions at the origin and over the third neighboring sites are presented.
Analytic vector harmonic expansions on S
U (2) and S2
Authors: Beers Brian Lee , Millman Richard S.
Published: March 2003

Irreducible vector fields (vector harmonics) are introduced on SU (2). It is shown that an arbitrary vector field can be expanded in terms of these vector harmonics, and tight convergence conditions are derived for analytic vector fields. These expansions are related to well−known vector harmonic expansions on the two−sphere. The generalization to arbitrary tensor fields is discussed. A connection between the Lie algebra of vector fields on SU (2) and the Virasoro algebra is noted.
Some solutions of the Einstein field equations for a rotating perfect fluid
Authors: Krasiński Andrzej
Published: March 2003

The equations of isentropic rotational motion of a perfect fluid are investigated with use of Darboux’ theorem. It is shown that, together with the equation of continuity, they guarantee the existence of four scalar functions on space−time, which constitute a dynamically distinguished set of coordinates. It is assumed that in this coordinate system the metric tensor is constant along the lines tangent to velocity and vorticity fields. Under these assumptions a complete set of solutions of the field equations with Tij = (ε + p)uiuj − pgij is found. They divide into three families, first of which contains six types of new solutions with nonzero pressure. The second family contains only the Gödel’s solution, and the third one, only the Lanczos’ solution. Symmetry groups, exterior metrics, type of conformal curvature, geometrical and physical properties of the new solutions are investigated. A short review of other models of rotating matter is given.
On some nonlinear evolution equations in quantum field theory
Authors: Tesei A.
Published: March 2003

The field equations of a fermion field with a scalar self−interaction are studied in a three− and four−dimensional space−time. The Faedo−Galerkin method is used to prove the existence of a sequence of approximated solutions which converges in a suitable topology. In a different topology, the existence and uniqueness of a local solution
Structural equations for Killing tensors of order two. I
Authors: Hauser I. , Malhiot R. J.
Published: March 2003

For any Killing tensor Kαβ of order two, a system of linear homogeneous first−order differential equations of the form (FA);α = 𝒥B(ΓαABFB) is derived. F1, F2, ... are the components of the tensors Kαβ, Lαβγ = 2Kγ[β;α], and Mαβγδ = (1/2)(Lαβ[γ;δ] + Lγδ[α;β]). The coefficients ΓαAB are linear expressions in the Riemann tensor and its covariant derivative. These equations are analogous to those satisfied by a Killing vector Kα and the Killing bivector ωαβ = Kβ;α, with Lαβγ and Mαβγδ playing roles analogous to ωαβ. The tensor Lαβγ has the symmetries Lαβγ = − Lβαγ and L[αβγ] = 0, and Mαβγδ has the symmetries of the Riemann tensor. Several relations similar to those satisfied by covariant derivatives of Killing vectors are derived. Perspectives for further work are briefly discussed with the idea of using the equations to investigate space−times which admit Killing tensors of order two.
The rest frame in stationary space−times with axial symmetry
Authors: Greene Richard D. , Schucking Engelbert L. , Vishveshwara C. V.
Published: March 2003

A rest frame in a stationary, axially symmetric space−time is defined as a synchronizable frame which is as nearly Killing as possible. This is a possible generalization of the Newtonian rest frame. A kinematical theorem giving the condition for the existence of a rest frame whose time vector is a linear combination of the Killing vectors is proved. The frame is also unique. The condition is shown to be weaker than the assumption of orthogonal transitivity. The surfaces of simultaneity of the rest frame are the surfaces of constancy of a particular Killing time coordinate, and its time vector is the component of the time Killing vector orthogonal to the angular Killing vector. Some properties of the rest frame are then discussed; it is shown that the frame is well−behaved down to the event horizon, where its time vector becomes null. Under a suitable condition on the event horizon, the time vector coincides with a Killing vector there. The gravitational redshift relation in the rest frame is derived. There is a dependence on the angular momentum of the geodesic. Furthermore, the event horizon is shown to be an infinite redshift surface for the rest frame observers. Finally, the three−vector potential of Landau and Lifshitz is interpreted and shown to be closely related to the rest frame, and a corresponding four−vector potential is invariantly defined.
A dispersion series for nonlocal potentials
Authors: Yao T. H.
Published: March 2003

For a class of short−range nonlocal potentials, and for the energy variable E in a certain part of the complex plane, we obtain a generalized subtracted dispersion relation which relates the forward scattering amplitude to contributions from negative energy pole terms, a usual dispersion integral along the positive real axis of the complex energy plane, and a uniformly convergent infinite series, apart from subtraction terms, subject to the condition that no bound state exists with energy less than −γ2, where γ is some parameter of
Neutrinos in cylindrically−symmetric spacetimes
Authors: Davis Talmadge M. , Ray John R.
Published: March 2003

An exact solution to the Einstein−Dirac equations is presented for a static, cylindrically−symmetric spacetime. The neutrino field is nonzero and corresponds to a neutrino current in the radial direction. The neutrinos yield a zero energy−momentum tensor and therefore the gravitational field is the same as for the vacuum case. The neutrinos in these static cylindrically−symmetric spacetimes can exist only if the spacetimes are locally equivalent to static plane−symmetric spacetimes. This type of ’’ghost neutrino’’ solution is already known to exist in plane−symmetric spacetimes.
Semisimple graded Lie algebras
Authors: Pais A. , Rittenberg V.
Published: March 2003

The concept of metric is introduced for graded Lie algebras. Semisimple graded Lie algebras are defined in terms of metric conditions of nonsingularity. It is shown that for this class of algebras the metric tensor generates a quadratic Casimir operator. Also for this class, the grading representation is irreducible and its weights are related to the roots of the Lie algebra (’’root-weight theorem’’). The problem is solved to find all semisimple graded Lie algebras. For SU(N), N≳2, for O(N), N≳5, and for all exceptional groups there are none. For all other semisimple Lie algebras there is one and only one. These are explicity constructed in terms of a convenient realization of Sp(2N) matrices. SU(2) is discussed in some detail and a new group [GSU(2)] is found which leaves a mixed c-number/q-number quadratic form invariant. We also define irreducible tensor operators for this group. SU(N), N≳2, provides examples of nonsemisimple gradings.
Gauge transformations and normal states of the CCR
Authors: Fannes M. , Verbeure A.
Published: March 2003

Let ω be any normal state on the CCR-algebra, and τχ the gauge transformation corresponding to the continuous character χ on the test function space as an Abelian group; denote by K the set of these characters; then we prove that the linear hull of {ω0τχ‖χ-K} is norm dense in all normal states. It is also proved that the theorem is in general false if we take the convex hull.
Exact recursive evaluation of 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta
Authors: Schulten Klaus , Gordon Roy G.
Published: March 2003

Algorithms are developed for the exact evaluation of the 3j-coefficients of Wigner and the 6j-coefficients of Racah. These coefficients arise in the quantum theory of coupling of angular momenta. The method is based on the exact solution of recursion relations in a particular order designed to guarantee numerical stability even for large quantum numbers. The algorithm is more efficient and accurate than those based on explicit summations, particularly in the commonly arising case in which a whole set of related coefficients is needed.
Semiclassical approximations to 3j- and 6j-coefficients for quantum-mechanical coupling of angular momenta
Authors: Schulten Klaus , Gordon Roy G.
Published: March 2003

The coupling of angular momenta is studied using quantum mechanics in the limit of large quantum numbers (semiclassical limit). Uniformly valid semiclassical expressions are derived for the 3j (Wigner) coefficients coupling two angular momenta, and for the 6j (Racah) coefficients coupling three angular momenta. In three limiting cases our new expressions reduce to those conjectured by Ponzano and Regge. The derivation involves solving the recursion relations satisfied by these coefficients, by a discrete analog of the WKB method. Terms of the order of the inverse square of the quantum numbers are neglected in the derivation, so that the results should be increasingly accurate for larger angular momenta. Numerical results confirm this asymptotic convergence. Moreover, the results are of a useful accuracy even at small quantum numbers.
An inverse problem in statistical mechanics
Authors: Fesciyan S. , Frisch H. L.
Published: March 2003

We study some one-dimensional systems specified by their nearest neighbor distribution. It is found that systems exhibiting second order phase transitions can be constructed. This paradoxical situation is resolved by a consideration of the peculiarities of the underlying potential. It is shown that the usual compressibility equation is not satisfied for these systems.
Direct determination of the Iwasawa decomposition for noncompact semisimple Lie algebras
Authors: Cornwell J. F.
Published: March 2003

A direct method for the determination of the Iwasawa decomposition of any noncompact semisimple real Lie algebra is described in detail. It is based on the canonical form of the Lie algebra. The physically important Lie algebras so (3,1), so (4,1), so (3,2), and so (4,2) are treated as illustrative examples.
Higher-dimensional unifications of gravitation and gauge theories
Authors: Cho Y. M.
Published: March 2003

We give a comprehensive geometric treatment of Kaluza–Klein type unifications of non-Abelian gauge theories with gravitation. The appearance of a cosmological term is noted.
Exact quantization of the nonlinear Schrödinger equation
Authors: Kaup D. J.
Published: March 2003

By means of an ’’inverse scattering transform,’’ we can exactly quantize the one-dimensional nonlinear Schrödinger equation ih/Ψt=−(h/2/2m) Ψxx−ε2(Ψ*Ψ) Ψ for any value of ε2=real. When ε2<0, the eigenvalues of the number operator, field momentum operator, and the Hamiltonian are found to be exactly the same as the linear case. In other words, by quantizing the exact theory, no effects corresponding to ’’renormalization’’ are found, and the zero point energy is independent of ε2. When ε2<0, the Hamiltonian is unbounded from below, and, in addition to the above spectra of eigenvalues, bound states can occur. Each bound state can be interpreted to be a bound state of n ’’excitations,’’ moving in a coherent fashion and with a binding energy proportional to the cube of the number of excitations. This problem is also formally equivalent to the N-body problem with a delta-function interaction solved by Bethe, with which we shall contrast our results, and we shall conclude by making certain remarks concerning ordinary field quantization versus ’’scattering space’’ quantization.
Perturbative solution to order βε of the Percus–Yevick equation for the square-well potential
Authors: Henderson Douglas , Chen Masao
Published: March 2003

The radial distribution function (RDF) of a fluid is considered for the case of the square-well potential. If the RDF is expanded in powers of the depth of the square-well, ε, the first two terms are, in most applications, the most important. The Percus–Yevick (PY) integral equation for the RDF is examined and the resulting integral equations for these terms obtained. The first set of equations are just the PY equations for hard spheres which have been solved analytically. In this paper, the remaining equations for the terms of order βε, where β=1/kBT, are solved analytically and the results examined. We have speculated in the past that the PY theory could be used to obtain estimates of higher-order terms in a perturbation expansion of the RDF. We find that the PY theory cannot give reliable estimates of these higher-order terms for the square-well potential at high densities.
Internal-labeling operators
Authors: Sharp R. T.
Published: March 2003

A simple method is described for finding all possible ’’missing label’’ operators when a semisimple group is reduced according to a maximal semisimple subgroup. The operators may be chosen to be Hermitian and hence lead to an orthonormal basis. The solution is worked out for all seven cases of one missing label. In each case two independent subgroup scalars are found in the enveloping algebra of the group; either of them can be used as the missing label.
On some geometrical aspects of classical nonconservative mechanics
Authors: Djukic Dj. , Vujanovic B.
Published: March 2003

It is shown that a scleronomous, holonomic dynamical system with nonconservative forces moves in such a way that the differential equations of motion are geodesic lines in a linear connected space Ln. The space Ln is semimetric and semisymmetric. The geodesic line on which the tangent at a point remains tangent if it is parallel displaced along the curve is simultaneously the curve of stationary length between two points in the space Ln. A necessary condition for the stationary length is derived by making use of the noncommutation rule for the differential of variation and the variation of differential. The noncommutation rule is obtained from a quadrilateral, which is called the fundamental quadrilateral of variational calculus. By using the noncommutation rule, the variational principles of Maupertius and Hamiltonian type for nonconservative mechanical systems are presented.
Cores for operators in quantum mechanics
Authors: Schroeck F. E.
Published: March 2003

It is shown that the set of finite linear combinations of the harmonic oscillator functions as well as the set of (Schwartz) functions of fast decrease form cores for a large class of operators on the space ℒ2μ(Rn), where μ is nice relative to Lebesgue measure. The results are applied to a variety of classes of classical potentials and their second-quantized analogs.
An exact spherically symmetric local solution in a class of ’’strong’’ and ’’weak’’ two-tensor gravity theories
Authors: Hammel William C.
Published: March 2003

After defining simultaneous spherical symmetry for two metrics, the technique of equation splitting is used to produce exact spherically symmetric solutions within the class of two-metric gravity theories introduced in an earlier paper. The nontrivial solutions are found to select the exceptional case, distinguished in previous work. The solutions in this case, however, possess a ’’gauge freedom’’ which apparently leaves the physics ambiguously defined. Nevertheless, we use the gauge freedom to simplify and proceed to local solutions, where 1g⋅⋅ is an empty closed space of positive constant curvature and 0g⋅⋅ is a Schwarzschild solution with a mass. The empty closed space is found to be contained within the Schwarzschild radius.
On the entire solutions of a functional equation in the theory of fluids
Authors: Gross Fred , Osgood Charles F. , Yang Chung-Chun
Published: March 2003

In this paper, we shall give necessary and sufficient conditions for the existence of entire solutions to the functional equation ψ2+gφ2=h, where g and h are given nonzero polynomials in z. This functional equation arises when one studies the Percus–Yevick integral equation of hard sphere mixture. The contruction of all such entire solutions ψ and φ is presented. Also, we shall show that it is possible, in some cases, to prove the existence of solutions with prescribed asymptotic properties at z=∞.
Surface scattering on topological networks
Authors: Budgor Aaron B.
Published: March 2003

The quantum mechanical network model of electrons in solids as introduced by Montroll is used to construct a multiple-scattering formalism for scattering in slightly aperiodic lattices. We examine both the case of Bloch electron scattering and diffractive scattering (as applied to LEED) from surfaces. In the former case the resulting equations are completely analogous to those derived by Koster and Maradudin in their analyses of the scattering of electron and lattice waves by defects. In the latter case the differential cross section functionally resembles Fraunhofer diffraction in optical systems, and is explicitly dependent upon the atomic geometry and the atomic potentials of the surface. All computations are analytic. Since qualitative agreement with experiment is excellent, our results seem to imply that the geometric structure of a material dominates the electronic character of a scattering system.
Positive solution of a time and energy dependent neutron transport problem
Authors: Pao C. V.
Published: March 2003

The purpose of this paper is to give a constructive method for the determination of a solution and an existence–uniqueness theorem for some nonlinear time and energy dependent neutron transport problems, including the linear transport system. The geometry of the medium under consideration is allowed to be either bounded or unbounded which includes the geometry of a finite or infinite cylinder, a half-space and the whole space Rm (m=1,2,⋅⋅⋅). Our approach to the problem is by successive approximation which leads to various recursion formulas for the approximations in terms of explicit integrations. It is shown under some Lipschitz conditions on the nonlinear functions, which describe the process of neutrons absorption, fission, and scattering, that the sequence of approximations converges to a unique positive solution. Since these conditions are satisfied by the linear transport equation, all the results for the nonlinear system are valid for the linear transport problem. In the general nonlinear problem, the existence of both local and global solutions are discussed, and an iterative process for the construction of the solution is given.
The Hamiltonians of the Schrödinger algebra
Authors: Burdet G. , Perrin M.
Published: March 2003

We give a complete characterization of the one-dimensional nonconjugate subalgebras of the extended Schrödinger algebra (and of the Schrödinger algebra). This yields a classification into conjugacy classes of all the Hamiltonians admitting the extended Schrödinger algebra as time dependent invariance algebra in the Schrödinger picture. Moreover, we determine the action of the inner automorphism induced by the general element of the extended Schrödinger algebra from which the explicit time dependence of the generators is deduced, whatever Hamiltonian is considered.
The Gel’fand states of certain representations of U (n) and the decomposition of products of representations of U (2)
Authors: Henrich Christopher J.
Published: March 2003

The representations of U (n), as realized by Bargmann and Moshinsky on spaces of polynomials (’’boson calculus’’), are the main subject of this paper. We consider them from a global point of view, pointing out the connection with induced representations. To compute the detailed structure of the representations, we find the reproducing kernels of the function spaces and the operators that connect them according to Weyl’s branching law. Using these results, we compute the boson polynomials of representations of U (3), and arrange them in a generating function. We extend this generating function to the boson polynomials of representations of U (n) of the form 〈 (m1m20⋅⋅⋅0) 〉. By considering these polynomials from a different viewpoint, we are able to obtain an explicit decomposition of the Kronecker product of n−1 representations of SU (2).
Resonantly coupled nonlinear evolution equations
Authors: Ablowitz Mark J. , Haberman Richard
Published: March 2003

A differential matrix eigenvalue problem is used to generate systems of nonlinear evolution equations. They model triad, multitriad, self-modal, and quartet wave interactions. A nonlinear string equation is also recovered as a special case. A continuum limit of the eigenvalue problem and associated evolution equations are discussed. The initial value solution requires an investigation of the corresponding inverse-scattering problem.
A new solution of the Einstein–Maxwell equations
Authors: McLenaghan Raymond G. , Tariq Nessim
Published: March 2003

A space–time is determined which is a solution of the Einstein–Maxwell equations for a nonsingular electromagnetic field and for which the electromagnetic field tensor is weakly parallelly propagated along its principal null directions. A coordinate system is given in which the metric depends upon one essential arbitrary constant. The space–time admits a four-parameter simply transitive group of motions and its Weyl tensor is of Petrov type I.
Macroscopic and microscopic, coherent and incoherent variables
Authors: Ekstein H.
Published: March 2003

Quantitative figures of merit for microscopicity (resolving power) and for coherence (the necessity of simultaneous observations of large volumes) are defined operationally. Such indices are not assignable to observables (which are equivalence classes of observation procedures) but to observation procedures. As an application, the problem of reversibility is reconsidered. Known qualitative arguments explaining the difficulty of creating certain processes are made quantitative. A conjectured theorem states that the difficulty of preparing a state at t=0 so that a particular target situation is observed at t=τ increases monotonically with τ.
The λφ43 Euclidean quantum field theory in a periodic box
Authors: Park Yong Moon
Published: March 2003

The ultraviolet cutoff (the lattice cutoff) normalized Schwinger functions converge as the ultraviolet cutoff (the lattice cutoff) is removed. The limit Schwinger functions are the moments of the normalized physical measure. As a consequence of the lattice approximation, the Lee–Yang theorem and various correlation inequalities hold for the λφ43 field theory in a periodic box.
New Jacobian ϑ functions and the evaluation of lattice sums
Authors: Zucker I. J.
Published: March 2003

The properties of some infinite series are discussed. They are used to evaluate some two- and higher-dimensional lattice sums.
Calculation of special functional integrals
Authors: Kollmann W.
Published: March 2003

For the integration with respect to a Gaussian weak distribution of a special class of functionals φ defined on L2[0,1] explicit formulas are derived. The φ are defined as nonnegative integer powers of a continuous linear functional B and the integration is performed under the condition that another continuous linear functional A assumes a given value.
The 2:1 anisotropic oscillator, separation of variables and symmetry group in Bargmann space
Authors: Boyer Charles P. , Wolf Kurt Bernardo
Published: March 2003

We present a detailed analysis of the separation of variables for the time-dependent Schrödinger equation for the anisotropic oscillator with a 2:1 frequency ratio. This reduces essentially to the time-independent one, where the known separability in Cartesian and parabolic coordinates applies. The eigenvalue problem in parabolic coordinates is a multiparameter one which is solved in a simple manner by transforming the system to Bargmann’s Hilbert space. There, the degeneracy space appears as a subspace of homogeneous polynomials which admit unique representations of a solvable symmetry algebra s3 in terms of first order operators. These representations, as well as their conjugate representations, are then integrated to indecomposable finite-dimensional nonunitary representations of the corresponding group S3. It is then shown that the two separable coordinate systems correspond to precisely the two orbits of the factor algebra s3/u (1) [u (1) generated by the Hamiltonian] under the adjoint action of the group. We derive some special function identitites for the new polynomials which occur in parabolic coordinates. The action of S3 induces a nonlinear canocical transformation in phase space which leaves the Hamiltonian invariant. We discuss the differences with previous works which present su (2) as the algebra responsible for the degeneracy of the two-dimensional anisotropic oscillator.
G-Hilbert bundles
Authors: Abbati Maria C. , Cirelli Renzo , Gallone Franco
Published: March 2003

A notion of Hilbert bundle is proposed which leads to the construction of a ’’big’’ Hilbert space ℋ starting from a family of Hilbert spaces. For this, such a family is equipped with a suitable structure, called Borel field structure. A meaningful relationship is established between the Borel structures which can be defined on the union of the Hilbert spaces of the family and the Borel field structures with which the family can be equipped. For a topological group G, the structure of G-Hilbert bundle is defined linking in a suitable way a Hilbert bundle with actions of G. In the framework of a G-Hilbert bundle, a continuous unitary representation of G in ℋ can be constructed. The transitive G-Hilbert bundles which are often used in the theory of induced representations of groups are shown to be a subclass of the class of the G-Hilbert bundles which are proposed in this paper.
Kinks and extensions
Authors: Finkelstein David , McCollum Gin
Published: March 2003

Kinks, homotopically nontrivial lightcone fields on R4, can be black holes without curvature singularities, satisfying the weak energy condition. Kinks and all other spherically symmetric stationary spacetimes on R4 with roots of g00 have incomplete geodesics which need extension. For simple roots the Kruskal extension method works and the topology around each root is that of the Kruskal manifold. For multiple roots another extension method is given, based on symmetry, and another topology.
Structural properties of the canonical U(3) Racah functions and the U(3) : U(2) projective functions
Authors: Louck J. D. , Lohe M. A. , Biedenharn L. C.
Published: March 2003

The class of U(3) Racah functions which are identically zero are determined from the canonical splitting of the multiplicity. These results imply the form of a special class of (projective) tensor operators. The function Gq associated with the ’’stretched’’ (maximal null space) Wigner operator is generalized and shown to be applicable in determining the denominator for the minimal null space operator.
Dynamic stability and thermodynamics in kinetic theory and fluid mechanics
Authors: Grmela Miroslav
Published: March 2003

The study of the relationship between thermodynamic and local dynamic stability that has been developed in the previous papers is further extended. The dynamical systems considered include the multicomponent fluid dynamics and the two component Enskog–Vlasov dynamics.
Long time behavior of solutions to the linearized two component Enskog–Vlasov kinetic equations
Authors: Grmela Miroslav
Published: March 2003

Fluid dynamics is obtained from the study of the long time behavior of solutions to the two component Enskog–Vlasov kinetic equations. Both thermodynamic and dynamic phenomenological coefficients of fluid mechanics are expressed in terms of the phenomenological quantities entering the Enskog–Vlasov-type kinetic equations.
General techniques for single and coupled quantum anharmonic oscillators
Authors: Halpern Francis R.
Published: March 2003

Matrix mechanic methods are used to find approximate equations and solutions for quantum anharmonic oscillator problems. A series of hypotheses are introduced that truncate and partially decouple the infinite set of coupled equations that specify the problem in the matrix mechanics formulation. The dependent variables or unknowns in these equations are the matrix elements of the coordinate and momentum operators. The independent variables are the matrix indices and coupling strengths. The equations themselves specify that the off diagonal matrix elements of the Hamiltonian and the commutators expressed in terms of the unknowns vanish and that the diagonal commutator matrix elements vanish except for canonical pairs in which case they are equal to −ih/. The truncation and decoupling hypotheses offer an orderly procedure for dealing approximately with the vast array of equations of the exact problems. Only the leading behavior of the coordinate and momentum operator matrix elements is found in terms of the matrix indices and coupling parameters. Although general techniques are presented to find the equations, the solutions discussed and the applications are brief extensions of problems that have already been treated.
Separation of variables in the Hamilton–Jacobi, Schrödinger, and related equations. II. Partial separation
Authors: Havas Peter
Published: March 2003

Sufficient conditions are given for coordinate systems in which the Hamilton–Jacobi equation and the Schrödinger and related equations are partially separable in n dimensions. For the first equation, the solution is assumed to be a sum of ν+τ functions of a single variable, and of μ[0⩽μ⩽ (n−ν−τ)/2] groups of other variables; for the other equations, products of such functions are assumed. These assumptions lead to ν+τ completely separated differential equations, of which ν are linear in the separation constants, and μ partially separated equations depending on the remaining n−ν−τ variables. The general forms of the various metric tensors gkl of the Riemannian spaces Vn as well as of the allowed potentials V corresponding to the different possible types of such equations are determined; they are identical for the Hamilton–Jacobi equation and for the other equations studied, except that for the latter some of the metrics are further restricted by a condition on their determinants. The results are established by methods similar to those used in Paper I of this series for complete separation, and include the results obtained there as special cases. In the course of determining the allowed forms of the gkl it is also established that there exist ν+τ+μ independent first integrals linear and quadratic in the momenta for the dynamical systems descrived by the Hamilton–Jacobi or the Schrödinger equation. The ν linear ones are homogeneous, and the τ+μ quadratic ones correspond to homogeneous quadratic integrals of the geodesics of the Vn. These results imply the existence of ν Killing vectors and of τ+μ Killing tensors of rank two for the Vn. Further polynomial integrals can be constructed; those integrals of degree r which are independent of the original ν+τ+μ integrals each correspond to an independent Killing tensor of rank r.
Similarity solution for viscous and thermal gas flow in a cone
Authors: Liron N. , Wilhelm H. E.
Published: March 2003

The nonlinear, partial differential equations describing the compressible flow of a viscous and heat conducting gas in a cone are reduced to two coupled, ordinary, nonlinear differential equations by means of a self-similar transformation. These are solved numerically for the velocity and temperature distributions in the cone. It is shown that for given flow numbers R, P, and M, laminar flows exist only up to a critical cone angle ϑ0.
Approximate representations of a local current algebra
Authors: Menikoff Ralph , Sharp David H.
Published: March 2003

An approximate method for dealing with nonrelativistic many-body quantum systems having short range interactions is developed using local currents. The scheme is based on determining approximate representations of subalgebras of the local currents. This mathematical framework is used to discuss several approximation schemes.
The Weyl tensor and shear-free perfect fluids
Authors: Glass E. N.
Published: March 2003

It is proved that a necessary and sufficient condition for a shear-free perfect fluid to be irrotational is that the Weyl tensor be pure electric type. For shear-free isentropic flow with unit tangent uα, we find the conservation law ∇α(n1/3iω uα) =0, where i is the relativistic specific enthalpy, n is the conserved particle number density, and ω is the vorticity scalar.
Ergodicity of quantum mechanical systems
Authors: Matsuno Koichiro
Published: March 2003

The ergodicity of pure quantum states is maintained in the space of orthonormal quantum states which diagonalizes an observable. The ergodicity of mixed quantum states, which is met in quantum statistical mechanics admitting an ensemble of many similar systems, is identical to the principle of equal a priori probabilities.
Retarded multipole fields and the inhomogeneous wave equation
Authors: Couch W. E. , Torrence R. J.
Published: March 2003

The inhomogeneous wave equation for a class of driving terms that arise in certain physical problems is analyzed by introducing a kind of ’’inner product’’ g with respect to which the 2l-pole solutions, ψl, of the homogeneous wave equation are an orthogonal basis. This allows the condition that δ, the Lth multipole part of the driving term, will give rise to a nonspreading solution to be expressed as g (ψL,r2δ) =0. The complete solution is found in terms of its spreading and nonspreading parts, and the backscattered radiation is calculated from the spreading part.
On the computation of the prolate spheroidal radial functions of the second kind
Authors: Sinha B. P. , MacPhie R. H.
Published: March 2003

The series expansion for the prolate spheroidal radial function of the second kind (or its derivative) is found to be slowly convergent when the eccentricity of the spheroid is large (a thin spheroid). To overcome this difficulty, a method is presented in which a small finite number of terms are summed in the conventional manner, and then the infinite remainder series is approximated by an integral of a continuous function. The validity of the method is confirmed by comparing the computed Wronskian with the theoretical. Satisfactory agreement (three to five significant figures) and a very substantial reduction in computation time are achieved.