March 1997 arXiv papers — page 14

Erik Koelink, René F. Swarttouw

For the Bessel function \begin{equation} \label{bessel} J_ν(z) = \sum\limits_{k=0}^{\infty} \frac{(-1)^k \left( \frac{z}{2} \right)^{ν+2k}}{k! Γ(ν+1+k)} \end{equation} there exist several $q$-analogues. The oldest $q$-analogues of the Bessel function were introduced by F. H. Jackson at the beginning of this century, see M. E. H. Ismail \cite{Is1} for the app

Hans J. Haubold

The physical principles and the mathematical structure involved in deriving an analytical representation of the internal structure of the sun are discussed. For a two-parameter family of a non-linear matter density distribution, the run of mass, pressure, temperature, and luminosity throughout the sun are expressed in terms of Gauss' hypergeometric funct

Murat Gunaydin

The realizations of the exceptional non-linear (quadratically generated, or W-type) N=8 and N=7 superconformal algebras with Spin(7) and G_2 affine symmetry currents are reviewed. Both the N=8 and N=7 algebras admit unitary realizations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G_2, with the central charges c=26/5 and c=5, respect

Herbert Nachbagauer

Starting from the von Neumann equation, we construct the quantum evolution equation for the effective action for systems in mixed states. This allows us to find the hierarchy of equations which describe the time evolution of equal time correlators. The method is applied explicitly to a scalar theory with quartic self-interaction.

Norbert Dragon, Tobias Hurth, Peter van Nieuwenhuizen

The Stueckelberg model for massive vector fields is cast into a BRS invariant, polynomial form. Its symmetry algebra simplifies to an abelian gauge symmetry which is sufficient to decouple the negative norm states. The propagators fall off like $1/k^2$ and the Lagrangean is polynomial but it is not powercounting renormalizable due to derivative couplings.

Yongseok Oh, Byung-Yoon Park

We improve the bound state approach of the Skyrme model applied to the heavy baryons by adopting a static heavy meson picture where the soliton moves around the fixed heavy meson. This allows to take into account the center of mass corrections in a more consistent way. The bound state masses so obtained are comparable to the experimentally observed $Λ_c$ and

V. Bernard, N. Kaiser, Ulf-G. Meißner

Single pion production off nucleons is studied in the framework of relativistic baryon chiral perturbation theory at tree level with the inclusion of the terms from the dimension two effective pion-nucleon Lagrangian. The five appearing low-energy constants are fixed from pion-nucleon scattering data. Despite the simplicity of the approach, most of the exist

Berthold Stech

The masses of quarks and leptons in units of $m_t$ are expressed in powers of $σ=\sqrt{m_c/m_t}$. The regularities found suggest specific mass matrices. They reproduce all masses and mixings in striking agreement with observation. A 90 degree relative phase angle between the off-diagonal elements of up and down quark matrices leads to a maximum magnitude for

D. Bruss, O. Nachtmann, P. Overmann

We propose to test the CP symmetry in the reactions Z -> mu+ mu- gamma and Z -> tau+ tau- gamma. The experimental analysis of angular correlations allows to determine a set of effective couplings: the electric and weak dipole moments of the muon and the tau lepton, and in particular chirality conserving 4-particle couplings, all of which can be induced by CP

J. Gluza, J. Maalampi, M. Raidal, M. Zralek

We study the single production of heavy neutrinos via the processes $e^-e^+ \to νN$ and $e^-γ\to W^- N$ at future linear colliders. As a base of our considerations we take a wide class of models, both with vanishing and non-vanishing left-handed Majorana neutrino mass matrix $m_L$. We perform a model independent analyses of the existing experimental data and

Adam K. Leibovich, Zoltan Ligeti, Iain W. Stewart, Mark B. Wise

Exclusive semileptonic B decays into $D_1$ and $D_2^*$ mesons are investigated including order $Λ_{QCD}/m_{c,b}$ corrections using the heavy quark effective theory. At zero recoil, the $Λ_{QCD}/m_{c,b}$ corrections can be written in terms of the leading Isgur-Wise function for these transitions, $τ$, and known meson mass splittings. We obtain an almost model

C. R. Allton, L. Conti, M. Crisafulli, L. Giusti

We present a high statistics study of the D- and B-meson decay constants. The results were obtained by using the Clover and Wilson lattice actions at two different values of the lattice spacing $a$, corresponding to $β=6.0$ and 6.2. After a careful analysis of the systematic errors present in the extraction of the physical results, by assuming quite conserva

H. Hanai

The polarization of tau leptons in the reaction e+ e- --> tau+ tau- has been measured using a e+e- collider, TRISTAN, at the center-of-mass energy of 58 GeV. From the kinematical distributions of daughter particles in tau --> e nu nu-bar, mu nu nu-bar, rho nu or pi(K) nu decays, the average polarization of tau- and its forward-backward asymmetry have been ev

John W. Barrett

Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be optimised to meet certain mathematical criteria, which ensure that the experiment has maximal sensitivity. Using this id

Michael A. Rudkovski

In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular, for two copies of the same group, the twisted product of group by itself through the action of inner automorphisms is a

E. A. Jagla

Transport properties of the vortex lattice in high temperature superconductors are studied using numerical simulations in the case in which the non-local interactions between vortex lines are dismissed. The results obtained for the longitudinal and transverse resistivities in the presence of quenched disorder are compared with the results of experimental mea

I. M. Suslov

The density of states for the Schroedinger equation with a Gaussian random potential is calculated in a space of dimension d=4-epsilon in the entire energy range including the vicinity of a mobility edge. Leading terms in 1/epsilon are taken into account for N \sim 1 (N is an order of perturbation theory) while all powers of 1/epsilon are essential for N>>1

R. I. Eglitis, A. V. Postnikov, G. Borstel

In extension of our previous study of KNbO_3 by the semiempirical Hartree-Fock method we present parameterization and total-energy results for non-ferroelectric KTaO_3 as a pure crystal (concentrating on the frozen phonon calculations) and that with Li impurities. The magnitudes of off-center Li displacements and the relaxation energies related to re-orienta

D. S. Geoghegan, A. Huetten, K. -H. Mueller, L. Schultz

A minimum in resistivity as a function of temperature for an as-quenched Au80Co20 ribbon prepared by melt-spinning using a wheel surface speed of 20 m s^{-1} is found at 25 K. No resistivity minimum is found for an as-quenched ribbon using a wheel surface speed of 60 m s^{-1}, however, upon heat treatment of this ribbon a resistivity minimum is recovered. Th

Daniel S. Fisher, Karin Dahmen, Sharad Ramanathan, Yehuda Ben-Zion

Simple models for ruptures along a heterogeneous earthquake fault zone are studied, focussing on the interplay between the roles of disorder and dynamical effects. A class of models are found to operate naturally at a critical point whose properties yield power law scaling of earthquake statistics. Various dynamical effects can change the behavior to a distr

A. A. Tsvetkov, J. Schuetzmann, D. van der Marel

We report on infrared reflectivity measurements of the $ab$-plane response of superconducting Bi$_2$Sr$_2$CuO$_6$ single crystals. The frequency dependent conductivity has a maximum near 700 cm$^{-1}$ at room temperature, which shifts to lower frequency and merges with a Drude-peak below 100 K. We attribute the unusual behaviour of the mid-infrared conductiv

Vincenzo Fiorentini, C. M. Carbonaro

We point out that contrary to a recent suggestion by Boero et al. (PRL 78, 887 (1997)) the +1 charge state of the oxygen vacancy in alpha-quartz cannot be invoked as a candidate E' center in alpha-quartz and silica.

Alex Hansen, E. H. Hauge, Joakim Hove, Frank A. Maao

We review some elementary aspects of the critical properties of the series of metal-insulator transitions that constitute the integer quantum Hall effect. Numerical work has proven essential in charting out this phenomenon. Without being complete, we review network models that seem to capture the essentials of this critical phenomenon.

D. A. Head, G. J. Rodgers

We introduce a one-dimensional sandpile model with $N$ different particle types and an infinitesimal driving rate. The parameters for the model are the N^2 critical slopes for one type of particle on top of another. The model is trivial when N=1, but for N=2 we observe four broad classes of sandpile structure in different regions of the parameter space. We d

Juan M. Lopez, Miguel A. Rodriguez, Rodolfo Cuerno

In this paper we study kinetically rough surfaces which display anomalous scaling in their local properties such as roughness, or height-height correlation function. By studying the power spectrum of the surface and its relation to the height-height correlation, we distinguish two independent causes for anomalous scaling. One is super-roughening (global roug

Olivier Tribel, Jean Pierre Boon

We consider lattice gas automata where the lack of semi-detailed balance results from node occupation redistribution ruled by distant configurations; such models with nonlocal interactions are interesting because they exhibit non-ideal gas properties and can undergo phase transitions. For this class of automata, mean-field theory provides a correct evaluatio

P. A. Sreeram, Suresh G. Mishra

We study the existence of ferromagnetism in one dimensional Hubbard Model with on site interaction and nearest and next nearest neighbor hopping. Using the Hubbard I approximation, a self consistent equation for $<n_σ>$, the particle density with spin $σ$ is obtained. We find that ferromagnetism exists over a wide range of values of the next nearest neighbor

C. Reichhardt, C. J. Olson, Franco Nori

We present results from extensive simulations of driven vortex lattices interacting with periodic arrays of pinning sites. Changing an applied driving force produces a rich variety of novel dynamical plastic flow phases which are very distinct from those observed in systems with random pinning arrays. Signatures of the transition between these different dyna

Jun-ichi Inoue, Hidetoshi Nishimori, Yoshiyuki Kabashima

We study the generalization ability of a simple perceptron which learns unlearnable rules. The rules are presented by a teacher perceptron with a non-monotonic transfer function. The student is trained in the on-line mode. The asymptotic behaviour of the generalization error is estimated under various conditions. Several learning strategies are proposed and

Jun-ichi Inoue, Hidetoshi Nishimori

We study the on-line AdaTron learning of linearly non-separable rules by a simple perceptron. Training examples are provided by a perceptron with a non-monotonic transfer function which reduces to the usual monotonic relation in a certain limit. We find that, although the on-line AdaTron learning is a powerful algorithm for the learnable rule, it does not gi

Henning Schomerus

In semiclassical studies of systems with mixed phase space, the neighbourhood of bifurcations of co-dimension two is felt strongly even though such bifurcations are ungeneric in classical mechanics. We discuss a scenario which reveals this fact and derive the correct semiclassical contribution of the bifurcating orbits to the trace of the unitary time evolut

Smita Mathur, Sunita Nair

PKS1830-211 is an unusually radio-loud gravitationally lensed quasar. In the radio, the system appears as two compact, dominant features surrounded by relatively extended radio emission which forms an Einstein Ring. As the line of sight to it passes close to our Galactic center, PKS1830-211 has not been detected in wave-bands other than the radio and X-ray s

A. Huss, B. Jain, M. Steinmetz

The formation of galaxy clusters in hierarchically clustering universes is investigated by means of high resolution N-body simulations. The simulations are performed using a newly developed multi-mass scheme which combines a PM code with a high resolution N-body code. Numerical effects due to time stepping and gravitational softening are investigated as well

Karen M. Leighly, Paul T. O&#39;Brien, Rick Edelson, Ian M. George

We present the data and preliminary analysis for a series of 90 ROSAT HRI and two ASCA observations of the broad-line radio galaxy 3C 390.3. These data were obtained during the period 1995 January 2 to 1995 October 6 as part of an intensive multiwavelength monitoring campaign. The soft X-ray flux in the ROSAT band varied by nearly a factor of four during the

Hans Böhringer, Doris M. Neumann, Sabine Schindler, John Huchra

The measurement of precise galaxy distances by Cepheid observations out to the distance of the Virgo cluster is important for the determination of the Hubble constant ($H_0$). The Virgo cluster is thereby often used as an important stepping stone. The first HST measurement of the distance of a Virgo galaxy (M100) using Cepheid variables provided a value for

K. M. Leighly, Paul T. O&#39;Brien

We present analysis of the light curve from the ROSAT HRI monitoring observations of the broad-line radio galaxy 3C 390.3. Observed every three days for about 9 months, this is the first well sampled X-ray light curve on these time scales. The flares and quiescent periods in the light curve suggest that the variability is nonlinear, and a statistical test yi

P. Jablonka

We discuss the integrated properties of the stellar population in bulges along the Hubble sequence and new HST data for individual stars in the bulge of M31.

A. Lazarian, W. G. Roberge

The recent detection of interstellar polarization in the solid CO feature near 4.67 micron shows that CO-mantled grains can be aligned in cold molecular clouds. These observations conflict with a theory of grain alignment which attributes the polarization in molecular clouds to the effects of cosmic rays: according to this theory, oblate spheroidal grains wi

B. de Carlos, J. R. Espinosa

Thermal two-loop QCD corrections associated with light stops have a dramatic effect on the strength of the MSSM electroweak phase transition, making it more strongly first order as required for the viability of electroweak baryogenesis. We perform a perturbative analysis of the transition strength in this model, including these important contributions, exten

S. Ambrosanio, Graham D. Kribs, Stephen P. Martin

We consider a general class of models with gauge-mediated supersymmetry breaking in which the gravitino is the lightest supersymmetric particle. Several qualitatively different scenarios arise for the phenomenology of such models, depending on which superpartner(s) decay dominantly to the gravitino. At LEP2, neutralino pair production and slepton pair produc

Duane A. Dicus, Wayne W. Repko

The cross sections for the processes γν--> γγν, γγ-->γν\barν and ν\barν -->γγγare calculated with the aid of an effective Lagrangian derived from the Standard model. These cross sections are shown to be much larger than the elastic cross section σ(γν--> γν) for photon energies $ω> 1$ keV. Possible astrophysical implications are discussed.

Andrei Linde, Antonio Riotto

We propose a simple realization of hybrid inflation in supergravity, which does not require any unnaturally small parameters. Inflation in this scenario is relatively short, and inflationary density perturbations fall down on large scales, which corresponds to a blue spectrum with n > 1. Superheavy strings which are formed after inflation in this scenario pr

N. Khviengia, Z. Khviengia, H. Lu, C. N. Pope

We make a proposal for a bosonic field theory in twelve dimensions that admits the bosonic sector of eleven-dimensional supergravity as a consistent truncation. It can also be consistently truncated to a ten-dimensional Lagrangian that contains all the BPS p-brane solitons of the type IIB theory. The mechanism allowing the consistent truncation in the latter

Dimitri Polyakov

The paper discusses the connection between S-duality and string-theoretic picture-changing formalism. The singular limit of the picture-changing transformation at zero momentum leads to the presence of the topological 5-form charge in the type IIB superalgebra which is attributed to the M5-brane. The topological charge defines the boundary D-brane state, whi

Yu Shi

For spontaneous breaking of global or gauge symmetry, it is superfluous to assume that the vacuum expectation value of the scalar field manifesting the symmetry is nonvanishing. The vacuum with spontaneous symmetry breaking simply corresponds to nonzero number of particles of one or more components of the real scalar field.

Horia C. Pop

A classical theorem of Scheunert on $G$-color Lie algebras, asserts in the case of finitely generated abelian groups, one can twist the algebra structure and the commutation bicharacter on $G$ by a 2-cocycle twist to a super-Lie $G$ graded, algebra. In this paper we show that this can be done for an arbitrary group.

Jörg Brendle, Benedikt Loewe

We give characterizations for the (in ZFC unprovable) sentences ``Every $\Sb{1}{2}$--set is measurable&#34; and ``Every $\Db{1}{2}$--set is measurable&#34; for various notions of measurability derived from well--known forcing partial orderings.

Andrzej Z. Gorski, Jacek Szmigielski

Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$ to be self-adjoint and skew self-adjoint or whether they have to be viewed as creation and annihilation operators. The

Bruno G. Carneiro da Cunha, P. Teotonio-Sobrinho

We study a class of lattice field theories in two dimensions that includes gauge theories. Given a two dimensional orientable surface of genus $g$, the partition function $Z$ is defined for a triangulation consisting of $n$ triangles of area $ε$. The reason these models are called quasi-topological is that $Z$ depends on $g$, $n$ and $ε$ but not on the detai

R. Harr, C. Liapis, P. Karchin, C. Biino

Using a silicon vertex detector, we measure the charged particle pseudorapidity distribution over the range 1.5 to 5.5 using data collected from PbarP collisions at root s = 630 GeV. With a data sample of 3 million events, we deduce a result with an overall normalization uncertainty of 5%, and typical bin to bin errors of a few percent. We compare our result

Marc Mars, Roustam M. Zalaletdinov

The definition of the covariant space-time averaging scheme for the objects (tensors, geometric objects, etc.) on differentiable metric manifolds with a volume n-form, which has been proposed for the formulation of macroscopic gravity, is analyzed. An overview of the space-time averaging procedure in Minkowski spacetime is given and comparison between this a

M. Ferconi, G. Vignale

We present a density-functional theory (DFT) approach to the study of the phase diagram of the maximum density droplet (MDD) in two-dimensional quantum dots in a magnetic field. Within the lowest Landau level (LLL) approximation, analytical expressions are derived for the values of the parameters $N$ (number of electrons) and $B$ (magnetic field) at which th

Shiwei Zhang, J. Carlson, J. E. Gubernatis

We present the results of a quantum Monte Carlo study of the extended $s$ and the $d_{x^2-y^2}$ pairing correlation functions for the two-dimensional Hubbard model, computed with the constrained-path method. For small lattice sizes and weak interactions, we find that the $d_{x^2-y^2}$ pairing correlations are stronger than the extended $s$ pairing correlatio

J. M. G. Vilar, J. M. Rubí

We present a class of systems for which the signal-to-noise ratio as a function of the noise level may display a multiplicity of maxima. This phenomenon, referred to as stochastic multiresonance, indicates the possibility that periodic signals may be enhanced at multiple values of the noise level, instead of at a single value which has occurred in systems co

J. M. G. Vilar, J. M. Rubí

We analyze the consequences that the choice of the output of the system has in the efficiency of signal detection. It is shown that the signal and the signal-to-noise ratio (SNR), used to characterize the phenomenon of stochastic resonance, strongly depend on the form of the output. In particular, the SNR may be enhanced for an adequate output.

Sergei Skorik

We derive an exact expression for the Kubo conductunce in the Quantum Hall device with the point-like intra-edge backscattering. This involves the calculation of current-current correlator exactly, which we perform using form-factor method. In brief, the full set of intermediate states is inserted in the correlator, and for each term the closed mathematical

V. Yu. Irkhin, A. A. Katanin

The nonlinear sigma-model and its generalization on N-component spins, the O(N) model, are considered to describe thermodynamics of a quantum quasi-two-dimensional (quasi-2D) Heisenberg antiferromagnet. A comparison with standard spin-wave approaches is performed. The sublattice magnetization, Neel temperature and spin correlation function are calculated to

Parongama Sen

We investigate the number of red sites on the elastic and real backbone when right at the percolation threshold a spanning cluster exists between two sites at opposite faces of the lattice and found that it scales in the same way as in the case of percolation between two plates. We also find out that the number of common red sites scales similarly for both k

V. Yu. Irkhin, A. A. Katanin, M. I. Katsnelson

Critical exponents in the CP^{N-1} model, which describes localized-moment ferro- and antiferromagnets (N=2 in the Heisenberg model), are calculated from two-particle Green&#39;s functions to first order in 1/N. For d=2+εthe results agree with earlier renormalization group calculations. For d=3 the leading 1/N-corrections turn out to be very large at N=2. Fo

V. Yu. Irkhin, A. A. Katanin, M. I. Katsnelson

The self-consistent spin-wave theory is applied to investigate the magnetization distribution around the impurity in isotropic and easy-axis two-dimensional ferro- and antiferromagents. The temperature dependences of host magnetization disturbance and impurity magnetization are calculated. The short-range order in the isotropic case is investigated. Importan

Yu Shi

Yang&#39;s $η$ pairing operator is generalized to explore off-diagonal long-range order in the Hubbard bilayer with an arbitrary chemical potential. With this operator and a constraint condition on annihilation and creation operators, we construct explicitly eigenstates which possess simultaneously three kinds of off-diagonal long-range order, i.e., the intr

Chien-Jung Huang, C. J. Umrigar, M. P. Nightingale

Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a Jastrow factor. In this paper we study the importance of including high-order, nucleus-three-electron correlations in the Jastrow factor. An efficient algorithm based

Adam Burrows

There has been a new infusion of ideas in the study of the mechanism and early character of core--collapse supernovae. However, despite recent conceptual and computational progress, fundamental questions remain. Some are summarize herein.

W. B. Hubbard, T. Guillot, J. I. Lunine, A. Burrows

Electron-degenerate, pressure-ionized hydrogen (usually referred to as metallic hydrogen) is the principal constituent of brown dwarfs, the long-sought objects which lie in the mass range between the lowest-mass stars (about eighty times the mass of Jupiter) and the giant planets. The thermodynamics and transport properties of metallic hydrogen are important

B. Berg, J. Riedler

This paper deals with a situation of some importance for the analysis of experimental data via Neural Network (NN) or similar devices: Let $N$ data be given, such that $N=N_s+N_b$, where $N_s$ is the number of signals, $N_b$ the number of background events, both unknown. Assume that a NN has been trained, such that it will tag signals with efficiency $F_s$,

Daniel P. Arovas, Yuli Lyanda-Geller

Angular momentum $J=3/2$ holes in semiconductor heterostructures are showed to accumulate nonabelian geometric phases as a consequence of their motion. We provide a general framework for analyzing such a system and compute conductance oscillations for a simple ring geometry. We also analyze a figure-8 geometry which captures intrinsically nonabelian interfer

L. A. Dickey

In field theories one often works with the functionals which are integrals of some densities. These densities are defined up to divergence terms (boundary terms). A Poisson bracket of two functionals is also a functional, i.e., an integral of a density. Suppose the divergence term in the density of the Poisson bracket be fixed so that it becomes a bilinear f

A. A. Davydov

This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a (non-abelian) c ohomological nature. Using this fact the maps from the sets of twistings to some cohomology groups (Hochsc

F. de Jong, H. Lenske

We present a calculation of nuclear matter which goes beyond the usual quasi-particle approximation in that it includes part of the off-shell dependence of the self-energy in the self-consistent solution of the single-particle spectrum. The spectral function is separated in contributions for energies above and below the chemical potential. For holes we appro

N. E. Mavromatos

I review recent work on the infrared structure of (2+1)-dimensional Abelian gauge theories and their application to condensed matter physics. In particular, within a large-N Schwinger-Dyson treatment, and including an `infrared momentum cut-off&#39;, I demonstrate the existence of a non-trivial infrared fixed point of the renormalization group. I connect thi

S. Groote, J. G. Körner, A. A. Pivovarov, K. Schilcher

We exploit the fact that within massless perturbative QCD the same Green&#39;s function determines the hadronic contribution to the $τ$ decay width and the moments of the $e^+e^-$ cross section. This allows one to obtain relations between physical observables in the two processes up to an unprecedented high order of perturbative QCD. A precision measurement

Yu. Levin

A new optical topology and signal readout strategy for a laser interferometer gravitational wave detector were proposed recently by Braginsky and Khalili . Their method is based on using a nonlinear medium inside a microwave oscillator to detect the gravitational-wave-induced spatial shift of the interferometer&#39;s standing optical wave. This paper propose

Ping Xu

The purpose of this paper is to establish an explicit correspondence between various geometric structures on a vector bundle with some well-known algebraic structures such as Gerstenhaber algebras and BV-algebras. Some applications are discussed. In particular, we found an explicit connection between the Koszul-Brylinski operator of a Poisson manifold and it

G. DeGiacomo, M. Lenzerini

Most modern formalisms used in Databases and Artificial Intelligence for describing an application domain are based on the notions of class (or concept) and relationship among classes. One interesting feature of such formalisms is the possibility of defining a class, i.e., providing a set of properties that precisely characterize the instances of the class.

Galina V. Lipunova

The pattern of variations in the intensity of magnetodipole losses is studied with the relativistic effect of magnetic-field dissipation during collapse into a black hole taken into account. A burst-type solution can be obtained both for a direct collapse and for the formation of a rapidly-rotating, self-gravitating object - a spinar - using a simple model.