bluuebunny/crossref_metadata_2025 huggingface dataset:
HOW TO COMPUTE GREEN'S FUNCTIONS FOR ENTIRE MASS TRAJECTORIES WITHIN KRYLOV SOLVERS
Authors: GLÄSSNER UWE , GÜSKEN STEPHAN , LIPPERT THOMAS , RITZENHÖFER GERO , SCHILLING KLAUS , FROMMER ANDREAS
Published: October 2004

The availability of efficient Krylov subspace solvers plays a vital role in the solution of a variety of numerical problems in computational science. Here we consider lattice field theory. We present a new general numerical method to compute many Green's functions for complex non-singular matrices within one iteration process. Our procedure applies to matrices of structure A = D − m, with m proportional to the unit matrix, and can be integrated within any Krylov subspace solver. We can compute the derivatives x(n) of the solution vector x with respect to the parameter m and construct the Taylor expansion of x around m. We demonstrate the advantages of our method using a minimal residual solver. Here the procedure requires one intermediate vector for each Green's function to compute. As real-life example, we determine a mass trajectory of the Wilson fermion matrix for lattice QCD. Here we find that we can obtain Green's functions at all masses ≥ m at the price of one inversion at mass m.
STUDY OF A RELATIVISTIC QUANTUM HARMONIC OSCILLATOR BY THE METHOD OF STATE-DEPENDENT DIAGONALIZATION
Authors: LEE H. C. , LIU K. L. , LO C. F.
Published: October 2004

We apply the method of State-dependent Diagonalization to study the eigenstates of the relativistic quantum harmonic oscillator in the low relativistic limit. The relativistic corrections of the energy eigenvalues of the quantum harmonic oscillator are evaluated for different values of the relativistic parameter α ≡ ħω0 / m0c2. Unlike the conventional exact diagonalization, this new method is shown to be very efficient for evaluating the energy eigenvalues and eigenfunctions. We have also found that for non-zero α the eigenfunctions of the system become more localized in space and that the ground state of the SHO (i.e., the α = 0 case) turns into a squeezed state. Furthermore, since our system is a special case of the quantum harmonic oscillator with a velocity-dependent anharmonic potential, this new approach should be very useful for investigating the cases with more complicated velocity-dependent anharmonic potentials.
CLUSTER CONCEPT DYNAMICS LEADING TO CREATIVE IDEAS WITHOUT CRITICAL SLOWING DOWN
Authors: GOLDENBERG Y. , SOLOMON S. , MAZURSKY D.
Published: October 2004

We present algorithmic procedures for generating systematically ideas and solutions to problems which are perceived as creative.

Our method consists of identifying and characterizing the most creative ideas among a vast pool. We show that they fall within a few large classes (archetypes) which share the same conceptual structure (Macros). We prescribe well defined abstract algorithms which can act deterministically on arbitrary given objects. Each algorithm generates ideas with the same conceptual structure characteristic to one of the Macros. The resulting new ideas turn out to be perceived as highly creative.

We support our claims by experiments in which senior advertising professionals graded advertisement ideas produced by our method according to their creativity. The marks (grade 4.6±0.2 on a 1–7 scale) obtained by laymen applying our algorithms (after being instructed for only two hours) were significantly better than the marks obtained by advertising professionals using standard methods (grade 3.6±0.2)).

The method, which is currently taught in USA, Europe, and Israel and used by advertising agencies in Britain and Israel has received formal international recognition.
CLASSICAL RATE OF UNIMOLECULAR ISOMERIZATION OF CYCLOBUTANONE
Authors: ZHAO MEISHAN
Published: October 2004

This paper presents calculations of the rate constant for the unimolecular isomerization of cyclobutanone using the theory of Gray and Rice as extended by Zhao and Rice. Such calculations are also carried out from classical trajectory and from local Lyapunov function analysis. The results of the calculations as a function of energy are compared, and the agreement is found to be uniformly good. The present approach is considered as a computationally feasible alternative to Davis' turnstile approach to the calculations of intramolecular energy transfer.
TWO-PHASE FLUID SUBJECTED TO TERRESTRIAL OR SPACE CONDITIONS: A LATTICE BOLTZMANN STUDY
Authors: SOFONEA VICTOR
Published: October 2004

A lattice Boltzmann model for two-phase fluids is used to find the equilibrium distribution of density and pressure across a vertical column under the action of terrestrial gravitational field. At low temperatures and without surface tension, the density distribution has a discontinuity point due to phase separation, while the pressure is always continuous. At temperatures far above the critical point, the fluid column behaves as an ideal gas and the well-known barometric formula is recovered. When surface tension is considered, this model gives also the correct behavior of a Van der Waals fluid placed in a tank subjected to terrestrial or space conditions in both cases, when the tank walls are wetted or not by the fluid.
SEX AND SELF-ORGANIZATION ON RUGGED LANDSCAPES
Authors: FINJORD JAN
Published: October 2004

The two-parent reproduction model of Derrida and Peliti is simulated on a rugged fitness landscape. Fixed fitness values for each possible genotype are assigned randomly, with all fit individuals having the same probability of reproduction. The previously observed transition to a self-organized state of the population with less recombinational load, implies an abrupt change of genetic overlap distributions, showing up characteristics of a phase transition. A crossover variant of the model has a smoother transition to the adapted regime, with a residual collective adaptation for small values of the threshold in fitness. When a geographical constraint (shortest possible distance) on pairwise reproduction in a population arranged one-dimensionally is imposed, a poised state results, suggestive of self-organized criticality.
DYNAMICS AND STRONG SIZE EFFECTS OF A BOOTSTRAP PERCOLATION PROBLEM
Authors: STAUFFER DIETRICH , DE ARCANGELIS LUCILLA
Published: October 2004

We confirm the results of Chaves and collaborators of very large size effects in the case when a site on the triangular lattice is permanently emptied if it has less than three occupied neighbors. We also show that the relaxation time peaks at an initial concentration different from the percolation threshold.
SPONTANEOUS SCALING EMERGENCE IN GENERIC STOCHASTIC SYSTEMS
Authors: SOLOMON SORIN , LEVY MOSHE
Published: October 2004

We extend a generic class of systems which have previously been shown to spontaneously develop scaling (power law) distributions of their elementary degrees of freedom.

While the previous systems were linear and exploded exponentially for certain parameter ranges, the new systems fulfill nonlinear time evolution equations similar to the ones encountered in Spontaneous Symmetry Breaking (SSB) dynamics and evolve spontaneously towards "fixed trajectories" indexed by the average value of their degrees of freedom (which corresponds to the SSB order parameter). The "fixed trajectories" dynamics evolves on the edge between explosion and collapse/extinction.

The systems present power laws with exponents which in a wide range (α < –2.) are universally determined by the ratio between the minimal and the average values of the degrees of freedom. The time fluctuations are governed by Levy distributions of corresponding power. For exponents α > −2 there is no "thermodynamic limit" and the fluctuations are dominated by a few, largest degrees of freedom which leads to macroscopic fluctuations, chaos, and bursts/intermittency.
FLIPPING OF MAGNETIZATION IN ISING MODELS AT Tc
Authors: STAUFFER DIETRICH
Published: October 2004

The two-dimensional simulations of Majumdar, Bray, Cornell, and Sire are confirmed and generalized to three to five dimensions. They agree with their epsilon expansion.
RECURSIVE ALGORITHM FOR THE GENERATION OF RELATIVISTIC KINEMATICS FOR COLLISIONS AND DECAYS WITH REGULARIZATIONS OF SHARP PEAKS
Authors: ILYIN V. A. , KOVALENKO D. N. , PUKHOV A. E.
Published: October 2004

We describe an algorithm for the generation of relativistic kinematics for collision and decay processes with multiparticle final states. In the framework of this algorithm it is possible to generate different kinematics covering most of practically interesting cases. One gets a possibility to introduce different sets of integration variables. As a result different sets of kinematical singularities can be regularized. To smooth sharp peaks some regularization formulas and procedures are used covering most typical cases. The algorithm is realized in the package CompHEP created for automatic calculations of collision and decay processes.
TRANSFER-MATRIX METHOD FOR HARD-SQUARE LATTICE GAS
Authors: TODO SYNGE , SUZUKI MASUO
Published: October 2004

An improved sparse-matrix factorization technique for the transfer matrix of the hard-square lattice gas is proposed to perform exact diagonalization up to the strip width N = 34. The critical point, critical free-energy density, and universal parameters are determined accurately. The eigenvalue spectrum of the transfer matrix is also precisely investigated at the critical point for different boundary conditions.
AN EIGHTH-ORDER METHOD WITH MINIMAL PHASE-LAG FOR ACCURATE COMPUTATIONS FOR THE ELASTIC SCATTERING PHASE-SHIFT PROBLEM
Authors: SIMOS T. E.
Published: October 2004

A new hybrid eighth-algebraic-order two-step method with phase-lag of order ten is developed for computing elastic scattering phase shifts of the one-dimensional Schrödinger equation. Based on this new method and on the method developed recently by Simos we obtain a new variable-step procedure for the numerical integration of the Schrödinger equation. Numerical results obtained for the integration of the phase shift problem for the well known case of the Lenard–Jones potential show that this new method is better than other finite difference methods.
SIMULATION OF A MULTICRITICAL FCC ISING ANTIFERROMAGNET
Authors: RENNÉ D.
Published: October 2004

Inspired by the work by Kämmerer, Dünweg, Binder, and d'Onorio de Meo we investigated the spin-[Formula: see text] Ising antiferromagnet on a fcc lattice in a homogeneous external magnetic field H with uniform nearest-neighbor interaction J by Monte Carlo simulations. In order to answer the open question whether this system exhibits a triple point or a multicritical point for positive H, we mainly studied lattices with 4 · 323 and 4 · 723 spins. We found a multicritical point at (Hc, kBTc) = (3.49 ± 0.02, 1.02 ± 0.01) J in the thermodynamic limit.
CELLULAR AUTOMATA MODELS OF RING DYNAMICS
Authors: GRAVNER JANKO
Published: October 2004

This paper describes three models arising from the theory of excitable media, whose primary visual feature are expanding rings of excitation. Rigorous mathematical results and experimental/computational issues are both addressed. We start with the much-studied Greenberg–Hastings model (GHM) in which the rings are very short-lived, but they do have a transient percolation property. By contrast, in the model we call annihilating nested rings (ANR), excitation centers only gradually lose strength, i.e., each time they become inactive (and then stay so forever) with a fixed probability; we show how the long-term global connectivity properties of the set of excited sites undergo a phase transition. Second part of the paper is devoted to digital boiling (DB) in which new rings spontaneously appear at rested sites with a positive probability. We focus on such (related) issues as convergence to equilibrium, equilibrium excitation level and success of the basic coupling.
SUMMATION OF LOGARITHMIC INTERACTIONS IN PERIODIC MEDIA
Authors: GRØNBECH-JENSEN NIELS
Published: October 2004

We present a set of expressions for evaluating energies and forces between particles interacting logarithmically in a finite two-dimensional system with periodic boundary conditions. The formalism can be used for fast and accurate, dynamical or Monte Carlo, simulations of interacting line charges or interactions between point and line charges. The expressions are shown to converge to usual computer accuracy (~10–16) by adding only few terms in a single sum of standard trigonometric functions.
INDIVIDUAL ADAPTATION IN A PATH-BASED SIMULATION OF THE FREEWAY NETWORK OF NORTHRHINE–WESTFALIA
Authors: NAGEL KAI
Published: October 2004

Traffic simulations are made more realistic by giving individual drivers intentions, i.e., an idea of where they want to go. One possible implementation of this idea is to give each driver an exact pre-computed path, that is, a sequence of roads this driver wants to follow. This paper shows, in a realistic road network, how repeated simulations can be used so that drivers can explore different paths, and how macroscopic quantities such as locations of jams or network throughput change as a result of this.
ISING KINETICS WITH HUNDRED GIGA-SITES
Authors: STAUFFER DIETRICH , KNECHT RENATE
Published: October 2004

From presumed world-record simulations up to 48003 and 1125 and from the Ito algorithm applied to smaller 3D lattices we obtain the dynamical critical exponent z near 2.05 in three dimensions and J/kBTc = 0.11391 in five.
EXTINCTION OF SMALL POPULATIONS IN THE BIT-STRING MODEL OF BIOLOGICAL AGEING
Authors: PÁL KÁROLY F.
Published: October 2004

In the framework of the bit-string model of biological ageing we show that the survival chance of a small population in an environment of limited carrying capacity grows exponentially with the size of the habitat. Extinction is usually preceded by a gradual decline of the genetic condition of the population. With death due to senescence coming earlier, the typical population size shrinks, and at some stage the population dies out due to the fluctuations.
ON THE PERIODS OF THE ${\tt ranshi}$ RANDOM NUMBER GENERATOR
Authors: GUTBROD F.
Published: October 2004

The stochastic properties of the pseudo-random number generator [Formula: see text] are discussed, with emphasis on the average period. Within a factor 2 this turns out to be the root of the maximally possible period. The actual set of periods depends on minor details of the algorithm, and the system settles down in one of only a few different cycles. These features are in perfect agreement with absolute random motion in phase space, to the extent allowed by deterministic dynamics.
FOUR-VARIABLE LINK-INVARIANTS FOR THICKENED SURFACES
Authors: COTTA-RAMUSINO PAOLO , RINALDI MAURIZIO
Published: October 2004

For a given two-dimensional compact oriented surface Σ with boundary, we define invariants with 4 variables for links in Σ×[0, 1]. These invariants restrict to the two-variable HOMFLY polynomials when Σ=D2. Some comments are made about the action of the mapping class group of Σ on these invariants.
Integrating a weight system of order n to an invariant of (n−1)-singular knots
Authors: DOMERGUE MICHEL , DONATO PAUL
Published: October 2004

Starting from a Weight-System denoted by P and defined on the n-Chord-Diagrams with values in an arbitrary Q–module, we give an explicit combinatorial formula for an invariant of (n–1)-singular knots which has P as its derivative. The formula is defined for regular knot projections. Its invariance under singular Reidemeister moves is then proved.
ON CANONICAL GENUS AND FREE GENUS OF KNOT
Authors: KOBAYASHI MASAKO , KOBAYASHI TSUYOSHI
Published: October 2004

We show that the differences between canonical genus and free genus, and differences between free genus and usual genus of a knot can be arbitrarily large.
KNOTS WITH UNKNOTTING NUMBER ONE AND GENERALISED CASSON INVARIANT
Authors: LINES DANIEL
Published: October 2004

We extend the classical notion of unknotting operation to include operations on rational tangles. We recall the “classical” conditions (on the signature, linking form etc.) for a knot to have integral (respectively rational) unknotting number one. We show that the generalised Casson invariant of the twofold branched cover of the knot gives a further necessary condition. We apply these results to some Montesinos knots and to knots with less than nine crossings.
FINITE-DEGREE LINK INVARIANTS AND CONNECTIVITY
Authors: SAWIN STEVE
Published: October 2004

Finite-degree invariants of links are defined following [Sta92] and Kontsevich’s integral is shown to generalize to this situation. The notion of connectivity is introduced, and finite-degree invariants are shown to decompose into a finite sum of invariants of finite degree and connectivity. Given an invariant of finite connectivity, a polynomial invariant of finite connectivity is given encoding its value of the invariant on cabled links. Invariants of finite degree and connectivity are constructed from the linking matrix and shown to classify finite-degree invariants of large connectivity.
TANGLE EQUATIONS
Authors: ERNST C.
Published: October 2004

We are given fixed rational tangles P and R and knots or links K1 and K2. Let O be a tangle such that N(O+P)=K1and N(O+R)=K2, where N is the numerator construction on the tangles O+P and O+R, respectively. N(O+P)=K1and N(O+R)=K1 form two equations, in which O is treated as a variable and P, R, K1and K2 are kept fixed. The number and types of solutions for O in the cases where K1and K2 are 4-plats or Montesinos knots are discussed.
TUNNELS OF 2-BRIDGE LINKS
Authors: KUHN MARTIN
Published: October 2004

In the class of links with one unknotting tunnel the 2-bridge links are characterized by the property of consisting of two trivial components. The tunnels of 2-bridge links are classified.
DETECTING KNOT INVERTIBILITY
Authors: KUPERBERG GREG
Published: October 2004

We discuss the consequences of the possibility that Vassiliev invariants do not detect knot invertibility as well as the fact that quantum Lie group invariants are known not to do so. On the other hand, finite group invariants, such as the set of homomorphisms from the knot group to M11, can detect knot invertibility. For many natural classes of knot invariants, including Vassiliev invariants and quantum Lie group invariants, we can conclude that the invariants either distinguish all oriented knots, or there exist prime, unoriented knots which they do not distinguish.
DISTINGUISHING MUTANTS BY KNOT POLYNOMIALS
Authors: MORTON HUGH R. , CROMWELL PETER R.
Published: October 2004

We consider the problem of distinguishing mutant knots using invariants of their satellites. We show, by explicit calculation, that the Homfly polynomial of the 3-parallel (and hence the related quantum invariants) will distinguish some mutant pairs.

Having established a condition on the colouring module which forces a quantum invariant to agree on mutants, we explain several features of the difference between the Homfly polynomials of satellites constructed from mutants using more general patterns. We illustrate this by our calculations; from these we isolate some simple quantum invariants, and a framed Vassiliev invariant of type 11, which distinguish certain mutants, including the Conway and Kinoshita-Teresaka pair.
ALL LINS-MANDEL SPACES ARE BRANCHED CYCLIC COVERINGS OF S3
Authors: MULAZZANI MICHELE
Published: October 2004

In this paper we show that all Lins-Mandel spaces S (b, l, t, c) are branched cyclic coverings of the 3-sphere. When the space is a 3-manifold, the branching set of the covering is a two-bridge knot or link of type (l, t) and otherwise is a graph with two vertices joined by three edges (a θ-graph). In the latter case the singular set of the space is always composed by two points with homeomorphic links. The first homology groups of the Lins-Mandel manifolds are computed when t=1 and when the branching set is a knot of genus one. Furthermore the family of spaces has been extended in order to contain all branched cyclic coverings of two-bridge knots or links.
SPLITTING VERSUS UNLINKING
Authors: ADAMS COLIN C.
Published: October 2004

We will prove that there exists a link consisting of two components, each of which is individually unknotted, such that the link can be split with a single crossing change, however any such crossing change must knot one of the components.
Ribbon Abelian Categories as Modular Categories
Authors: Lyubashenko V.
Published: October 2004

A category N of labeled (oriented) trivalent graphs (nets) or ribbon graphs is extended by new generators called fusing, braiding, twist and switch with relations which can be called Moore-Seiberg relations. A functor to N is constructed from the category Surf of oriented surfaces with labeled boundary and their homeomorphisms. Given a (eventually non-semisimple) k-linear abelian ribbon braided category [Formula: see text] with some finiteness conditions we construct a functor from a central extension of N with the set of labels [Formula: see text] ObC to k-vector spaces. Composing the functors we get a modular functor from a central extension of Surfto k-vector spaces.
KNOTTED SOLID TORI DECOMPOSITIONS OF B3 AND S3
Authors: OH SEUNGSANG
Published: October 2004

We give several kinds of tilings of regular solids, B3 and S3, by knotted solid tori or handlebodies all of which are congruent and nontrivially linked. We also present higher dimensional tilings of Bp+3 by congruent regular neighborhoods of any p-spun knot.
ON THE ARF INVARIANT OF A PURELY PROPER LINK
Authors: TRALDI LORENZO
Published: October 2004

Let L be a link in S3, and suppose all the linking numbers in L are even. We observe that the Arf invariant of L is determined in several different ways by the sublinks containing no more than three components of L.
ON FINITE TYPE 3-MANIFOLD INVARIANTS I
Authors: GAROUFALIDIS STAVROS
Published: October 2004

Recently Ohtsuki [Oh2], motivated by the notion of finite type knot invariants, introduced the notion of finite type invariants for oriented, integral homology 3-spheres. In the present paper we propose another definition of finite type invariants of integral homology 3-spheres and give equivalent reformulations of our notion. We show that our invariants form a filtered commutative algebra. We compare the two induced filtrations on the vector space on the set of integral homology 3-spheres. As an observation, we discover a new set of restrictions that finite type invariants in the sense of Ohtsuki satisfy and give a set of axioms that characterize the Casson invariant. Finally, we pose a set of questions relating the finite type 3-manifold invariants with the (Vassiliev) knot invariants.
COVERINGS OF LINKS AND A GENERALIZATION OF RILEY’S CONJECTURE B
Authors: GONZÁLEZ-ACUÑA F. , RAMÍREZ ARTURO
Published: October 2004

Let k be a knot in S3, ψ: π1(S3–k)→Zα1 * Zα2 an epimorphism sending a meridian to an element of length 2 and ω: Zα1 * Zα2→Sσ a transitive representation into a symmetric group. Information is given (in Theorem B##) on the homologies of the unbranched and branched covers associated to ωψ which generalizes a conjecture of Riley. When k is a torus knot these homologies are actually computed.
AN OBSERVATION OF SURFACE BRAIDS VIA CHART DESCRIPTION
Authors: KAMADA S.
Published: October 2004

A surface braid is a generalization of classical braids, which is related to classical and 2-dimensional knot theory. It is described by a diagram on a 2-disk called a chart. We prove that surface braids are in one-to-one correspondence to such diagrams modulo some elementary moves. It helps us to handle surface braids. As an application we calculate the Grothendieck group of the semi-group of surface braids. A theorem on symmetric equivalence for the braid group is also given.
POLYNOMIAL INVARIANTS OF PERIODIC KNOTS
Authors: YOKOTA YOSHIYUKI
Published: October 2004

We give a new criterion for the periodicity of knots combining the skein and Kauffman polynomials which extends the old results using the polynomials individually.
TWO-DIMENSIONAL TOPOLOGICAL QUANTUM FIELD THEORIES AND FROBENIUS ALGEBRAS
Authors: ABRAMS LOWELL
Published: October 2004

We characterize Frobenius algebras A as algebras having a comultiplication which is a map of A-modules. This characterization allows a simple demonstration of the compatibility of Frobenius algebra structure with direct sums. We then classify the indecomposable Frobenius algebras as being either “annihilator algebras” — algebras whose socle is a principal ideal — or field extensions. The relationship between two-dimensional topological quantum field theories and Frobenius algebras is then formulated as an equivalence of categories. The proof hinges on our new characterization of Frobenius algebras.

These results together provide a classification of the indecomposable two-dimensional topological quantum field theories.
BRAIDS AND MOVIES
Authors: CARTER J. SCOTT , SAITO MASAHICO
Published: October 2004

Knotted surfaces in 4-space are described by sequences of classical braids. We provide a finite set of moves to such sequences of classical braid words such that two sequences represent the same knotting if and only if they are related by a sequence of moves in this set.
REMARKS ON THE A-POLYNOMIAL OF A KNOT
Authors: COOPER D. , LONG D.D.
Published: October 2004

This paper reviews the two variable polynomial invariant of knots defined using representations of the fundamental group of the knot complement into [Formula: see text]. The slopes of the sides of the Newton polygon of this polynomial are boundary slopes of incompressible surfaces in the knot complement. The polynomial also contains information about which surgeries are cyclic, and about the shape of the cusp when the knot is hyperbolic. We prove that at least some mutants have the same polynomial, and that most untwisted doubles have non-trivial polynomial. We include several open questions.
BRAID GROUP REPRESENTATIONS ASSOCIATED WITH ${\mathfrak{sl}}_m$
Authors: LAWRENCE RUTH J.
Published: October 2004

It has been seen elsewhere how elementary topology may be used to construct representations of the Iwahori-Hecke algebra associated with two-row Young diagrams, and how these constructions are related to the production of the same representations from the monodromy of n-point correlation functions in the work of Tsuchiya & Kanie and to the construction of the one-variable Jones polynomial. This paper investigates the extension of these results to representations associated with arbitrary multi-row Young diagrams and a functorial description of the two-variable Jones polynomial of links in S3.
CASSON-GORDON INVARIANTS OF GENUS ONE KNOTS AND CONCORDANCE TO REVERSES
Authors: NAIK SWATEE
Published: October 2004

For genus one knots the Casson-Gordon invariant τ is expressed in terms of the classical signatures, generalizing an earlier result of P. Gilmer. As an application it is shown that the pretzel knots K(3, –5, 7) and K(3, –5, 17) are not concordant to their reverses.
THE RESHETIKHIN-TURAEV REPRESENTATION OF THE MAPPING CLASS GROUP AT THE SIXTH ROOT OF UNITY
Authors: WRIGHT GRETCHEN
Published: October 2004

The quantum group construction of Reshetikhin and Turaev provides representations of the mapping class group, indexed by an integer parameter r. This paper presents computations of these representations when r=6, and analyzes their relationship to other topological invariants. It is shown that in genus 2, the representation splits into two summands. The first summand factors through the mapping class group action on the first homology of the surface with Z/3Z coefficients, while the second summand can be analyzed via its restriction to the subgroup of the mapping class group which is normally generated by the sixth power of a Dehn twist on a nonseparating curve. This analysis reveals a connection to the homology intersection pairing on the surface, and also yields information about the kernel and image of the representation. It is also shown that the representation yields a family of 2-dimensional nonabelian representations of the Torelli group.

This paper continues the program established by the author in [Wr] to relate the Reshetikhin-Turaev representations at specific roots of unity to classical invariants.
INVARIANT POLYNOMIAL OF FRAMED KNOTS IN THE SOLID TORUS AND ITS APPLICATION TO WAVE FRONTS AND LEGENDRIAN KNOTS
Authors: AICARDI FRANCESCA
Published: October 2004

An invariant polynomial s(t) is defined for framed knots in the solid torus. The coefficients are Vassiliev invariants of order one. An invariant polynomial A(t) of Legendrian curves is introduced and it is shown how to calculate it from their fronts. The coefficient of A(t) of the order n term is the restriction to the discriminant of the selftangencies with partial index n of the Arnold invariant J+ of wave fronts. The polynomial A(t) of a Legendrian curve is recovered from the polynomial s(t) of the Legendrian knot, provided with its natural contact framing.
FIXED-WRITHE ISOTOPIES AND THE TOPOLOGICAL CONSERVATION LAW FOR CLOSED, CIRCULAR DNA
Authors: MILLER DAVID , BENHAM CRAIG
Published: October 2004

This paper proves that the set of all smooth, closed space curves having the same knot type and writhe is path-connected.
KNOT-INEVITABLE PROJECTIONS OF PLANAR GRAPHS
Authors: TANIYAMA KOUKI , TSUKAMOTO TATSUYA
Published: October 2004

For each odd number n, we describe a regular projection of a planar graph such that every spatial graph obtained by giving it over/under information of crossing points contains a (2, n)-torus knot. We also show that for any spatial graph H, there is a regular projection of a (possibly nonplanar) graph such that every spatial graph obtained from it contains a subgraph that is ambient isotopic to H.
DECOHERENCE CAUSED BY TOPOLOGY IN A TIME-MACHINE SPACETIME
Authors: MENSKY MICHAEL B. , NOVIKOV IGOR D.
Published: October 2004

Nonrelativistic quantum theory of noninteracting particles in the spacetime containing a region with closed time-like curves (time-machine spacetime) is considered with the help of the path-integral technique. It is argued that, in certain conditions, a sort of superselection may exist for evolution of a particle in such a spacetime. All types of evolution are classified by the number n defined as the number of times the particle returns back to its past. It corresponds also to the topological class [Formula: see text] of trajectories of a particle. The evolutions corresponding to different values of n are noncoherent. The amplitudes corresponding to such evolutions may not be superposed. Instead of one evolution operator, as in the conventional (coherent) description, evolution of the particle is described by a family Un of partial evolution operators. This is done in analogy with the formalism of quantum theory of measurements, but with essential new features in the dischronal region (the region with closed time-like curves) of the time-machine spacetime. Partial evolution operators Un are equal to integrals Kn over the classes of paths [Formula: see text] if the evolution begins and ends in the chronal regions. If the evolution begins or/and ends in the dischronal region, the integral Kn over the class [Formula: see text] should be multiplied by a certain projector to give the partial evolution operator Un. Thus defined partial evolution operators possess the property of generalized unitarity ∑nUn†Un=1 and multiplicativity Um(t″, t′)Un(t′, t)=Um+n(t″, t). In the last equation however one of the numbers m or n (or both) must be equal to zero. Therefore, the part of evolution containing repeated returning backward in time cannot be factorized: all backward passages of the particle have to be considered as a single act, that cannot be presented as gradually, step by step, passing through “causal loops.” The (generalized) multiplicativity and unitarity take place for arbitrary time intervals including

(i) propagating in initial and final chronal regions (containing no time-like closed curves) or from the initial chronal region to the final one, and

(ii) propagating within the time machine (in the dischronal region), from the time machine to the final chronal region or from the initial chronal region to the time machine.
DIRAC FIELD IN A GRAVITATIONAL SHOCK WAVE BACKGROUND
Authors: SHAISULTANOV R.
Published: October 2004

We study the scattering of spin 1/2 fields in the gravitational shock-wave geometries. The S-matrix for this process is computed. The helicity flip of the spin 1/2 ultrarelativistic Dirac particle is discussed. An analogy with the quantum-electrodynamic case is pointed out.
DETECTABILITY OF GRAVITATIONAL WAVE BURSTS FROM A CLASS OF NEUTRON STAR STARQUAKE GRB MODELS
Authors: HORVATH J.E.
Published: October 2004

A large class of gamma-ray burst (GRB) models (overwhelming until recently) involve-the release of energy in a neutron star quake. Even though the extreme isotropy of the GRB sky established by the BATSE experiment has now shifted the interest to cosmological models, the former starquake scenarios are still attractive and may naturally produce a gravitational wave burst which carries most of the released energy. We discuss the prospects for detection of these high-frequency bursts by the forthcoming interferometers and spheroidal antennas, emphasizing the most recent results on the distribution and nature of the GRB sources. We find that, even if the overall picture is correct, the positive detection of GRB-associated gravitational wave bursts is unlikely and therefore these events will not be a prime target for the detectors.
SURFACE VIBRATIONS OF STRATIFIED NEUTRON STAR IN THE NEWTONIAN LIMIT OF GRAVITY
Authors: BASTRUKOV S.I.
Published: October 2004

From theoretical analysis of the radial distribution of bulk density in the neutron star interior it follows that a neutron star is a strongly stratified compact stellar object with a rather complicated layering structure: the density of outer layers (crust, neutron-rich nuclei, electrons) is much less than the density of the inner region of the stiff core (dense matter of superfluid neutrons, superconducting protons). Simplifying this picture we study the surface vibrations of a nonrotating neutron star in the model of a rigid-like inert core covered by the dynamical liquid-like layer; the effects of gravity are described in the Newtonian limit. The eigenfrequencies of surface pulsations are derived in the analytic form as a function of multipole degree of spheroidal configurations, densities and radii of the core and outer layer. The conclusions of the liquid layer model are compared with those for the Kelvin model of a heavy liquid drop to find out the difference in the eigenfrequencies of spheroidal vibrations corresponding to neutron stars with approximately uniform distribution of density and stars with stratified mass distribution.
TWO FAMILIES OF EXACT DISKS WITH A CENTRAL BLACK HOLE
Authors: LEMOS JOSÉ P.S. , LETELIER PATRICIO S.
Published: October 2004

The gravitational field of a configuration formed by a static disk and a Schwarzschild black hole is analysed for two families of disks. The matter of the disks is made of counter-rotating particles with as many particles rotating to one side as to the other, in such a way that the net angular momentum is zero and the disk is static. The first family consists of peculiar disks, in the sense that they are generated by two opposite dipoles. The particles of the disk have no pressure or centrifugal support. However, when there is a central black hole, centrifugal balance in the form of counter-rotation appears. The second family is a one parameter family of self-similar disks which includes at one end a Newtonian disk, and at the other a topological defect of spacetime. The presence of the black hole impresses more rotational velocity to the particles. These two families are of infinite extent. Some interesting physical effects are studied.
THE DETECTION OF GRAVITATIONAL WAVES
Authors: JU L. , BLAIR D.G.
Published: October 2004

This paper reviews the field of gravitational wave detection. The characteristics of gravitational waves and the possible sources of detectable waves are discussed. This includes a discussion of a new source, the stochastic background of cosmological gravitational waves from supernovae during the epoch of galaxy formation. Methods of using both resonant mass antennas and laser interferometer detectors are reviewed. Noise sources that limit detector sensitivity are summarised, while new methods, and new materials which can simplify and improve detector performance are described.
BARYONIC DARK CLUSTERS IN GALACTIC HALOS
Authors: PAOLIS F. DE , INGROSSO G. , JETZER PH. , RONCADELLI M.
Published: October 2004

Besides MACHOs (Massive Astrophysical Compact Halo Objects) discovered by microlensing, cold molecular clouds (mainly of H 2) may well contribute substantially to the galactic halo dark matter. We describe a model for the formation and evolution of proto globular clusters towards either globular clusters or dark clusters of MACHOs and molecular clouds, depending on the distance from the galactic centre. Moreover, we discuss various methods to test this scenario, which rely upon observations in several bands of the electromagnetic spectrum. In particular, we estimate the γ-ray flux arising from halo molecular clouds through the interaction with high-energy cosmic-ray protons. Molecular clouds can also be detected via the absorption lines they would produce in the spectrum of stars located in the Large Magellanic Cloud and via the anisotropy they would introduce in the Cosmic Background Radiation when looking at the halo of M31 galaxy. Finally, we address the possibility of discovering MACHOs by infrared searches.
THREE-DIMENSIONAL BILLIARDS WITH TIME MACHINE
Authors: MENSKY MICHAEL B. , NOVIKOV IGOR D.
Published: October 2004

Self-collision of a nonrelativistic classical point-like body, or particle, in the spacetime containing closed time-like curves (time-machine spacetime) is considered. A point-like body (particle) is an idealization of a small ideal elastic billiard ball. The known model of a time machine is used containing a wormhole leading to the past. If the body enters one of the mouths of the wormhole, it emerges from another mouth in an earlier time so that both the particle and its “incarnation” coexist during some time and may collide. Such self-collisions are considered in the case when the size of the body is much less than the radius of the mouth, and the latter is much less than the distance between the mouths. Three-dimensional configurations of trajectories with a self-collision are presented. Their dynamics is investigated in detail. Configurations corresponding to multiple wormhole traversals are discussed. It is shown that, for each world line describing self-collision of a particle, dynamically equivalent configurations exist in which the particle collides not with itself but with an identical particle having a closed trajectory (Jinnee of Time Machine).
ON THE HORIZON HYPOTHESIS IN QUANTUM COSMOLOGY
Authors: POLLOCK M.D.
Published: October 2004

The mini-superspace approximation in quantum cosmology, whereby the space—time is restricted to the Friedmann form ds2=dt2−a2(t)dx2, requires the integrated three-space ∫d3x to be finite, in order that the operator replacements p→−iħ∂/∂q are well defined for the canonically conjugate momenta and coordinates (p, q). We have previously agued that this procedure can be made exact by cutting off the physical space at the causal horizon, so that ∫d3x=1 and a(t0)=(4π/3)1/3ξ−1(t0), where ξ≡d(ln a)/dt is the Hubble parameter and t0 is the present time, assuming dx2 to be flat. A corollary of this horizon hypothesis is that all quantum field theoretical integrals are similarly cut off. It is pointed out that the analysis by Jing and Fang of the two-year results for the COBE DMR observations of the quadrupole anisotropy of the cosmic microwave background radiation substantiates this idea (although the alternative explanation, that there are smaller density fluctuations at larger scales, is not ruled out). Also, the cosmological Schrödinger equation (Wheeler-DeWitt equation) for the wave function of the Universe Ψ, obtained from the heterotic superstring theory of Gross et al., is shown to be separable only when the physical space is isotropic and conformally flat, and in the approximation that quartic and higher-order terms in ξ are ignorable, and the solution is then expressed in terms of parabolic cylinder functions (Weber-Hermite functions). Finally, the occurrence of large density fluctuations via the indeterminacy relation ΔπξΔξ~ħ is further discussed.
JEANS MASS OF NEWTONIAN BOSE CLOUDS
Authors: MEMBRADO M. , AGUERRI J.A.L.
Published: October 2004

The gravitational instability of free and dilute Newtonian boson clouds has been examined. For collisionless Newtonian boson clouds with a uniform unperturbated Bose gas density, it is deduced that the gravitational instability will never give rise to the formation of boson stars, but only black holes; however if the unperturbated density, in the neighbourhood of the perturbation, has a scale length equal to or smaller than the perturbation wavelength, the formation of free Newtonian boson stars could also be possible. For dilute Newtonian boson clouds it is shown that the gravitational instability can lead the cloud to condense into boson stars of different masses but identical radii, in agreement with studies about equilibrium configurations of dilute Newtonian boson stars. The galactic distribution of these Newtonian boson stars, and hence, the average distance among them is also discussed.
THE TUNNELING, THE SECOND ORDER RELATIVISTIC PHASE TRANSITIONS AND PROBLEM OF THE MACROSCOPIC UNIVERSE ORIGIN
Authors: BURDYUZHA V.V. , PONOMAREV Yu.N. , LALAKULICH O.D. , VERESHKOV G.M.
Published: October 2004

We propose that the Universe was created from “Nothing” with a relatively small number of particles and it very quick relaxed to a quasi-equilibrium state at the Planck parameters. The classic cosmological solution for this Universe, with the calculation of its ability to undergo the second order relativistic phase transition (RPT), has two branches divided by a gap. On one of these branches near to the “Nothing” state the second order RPT is not possible at the GUT scale. The other branch is thermodynamically unstable. The quantum process of tunneling between the cosmological solution branches and the kinetics of the second order RPT are investigated by numerical methods. Another quantum geometrodynamics process (bounce from singularity) is also taken into consideration. It is shown that the discussed phenomenon with the calculation of all RPTs from the GUT scale (1016 Gev) to the Salam-Weinberg scale (102 Gev) gives the new cosmological scenarios of the macroscopic Universe origin with the observable number of particles.
SCALAR FIELD COSMOLOGIES WITH VISCOUS FLUID
Authors: CHIMENTO LUIS P. , JAKUBI ALEJANDRO S.
Published: October 2004

We investigate cosmological models with a free scalar field and a viscous fluid. We find exact solutions for a linear and nonlinear viscosity pressure. Both yield singular and bouncing solutions. In the first regime, a de Sitter stage is asymptotically stable, while in the second case we find power-law evolutions for a vanishing cosmological constant.
THE TOPOLOGY OF THE COSMIC MICROWAVE BACKGROUND ANISOTROPY ON THE SCALE ~1°
Authors: NOVIKOV D.I. , JØRGENSEN H.E.
Published: October 2004

In this paper we develop the theory of clusterization of peaks in a Gaussian random field. We have obtained new mathematical results from this theory and the theory of percolation and have proposed a topological method of analysis of sky maps based on these results. We have simulated 10°×10° sky maps of the cosmic microwave background anisotropy expected from different cosmological models with 0.5°–1° resolution in order to demonstrate how this method can be used for detection of non-Gaussian noise in the maps and detection of the Doppler-peak in the spectrum of perturbation of ΔT/T.
ASTROPHYSICAL AND COSMOLOGICAL CONSTRAINTS ON A SCALE-DEPENDENT GRAVITATIONAL COUPLING
Authors: BERTOLAMI ORFEU , GARCÍA-BELLIDO JUAN
Published: October 2004

We study the phenomenological consequences of the recently proposed idea of a running gravitational coupling on macroscopic scales. When applied to the rotation curves of galaxies, we find that their flatness requires the presence of baryonic dark matter. Bounds on the variation of the gravitational coupling from primordial nucleosynthesis and the change of the period of binary pulsars are analysed. We also study constraints on the variations of G with scale from gravitational lensing and the cosmic virial theorem, as well as briefly discuss the implications of such a scenario for structure formation.
PROBING THE GRAVITATIONAL GEON
Authors: COOPERSTOCK F.I. , FARAONI V. , PERRY G.P.
Published: October 2004

The Brill-Hartle gravitational geon construct as a spherical shell of small amplitude, high frequency gravitational waves is reviewed and critically analyzed. The Regge-Wheeler formalism is used to represent the most general gravitational wave perturbations of the spherical background as a superposition of tensor spherical harmonics and an attempt is made to build a nonsingular solution to meet the requirements of a gravitational geon. The attempted constructs of gravitational and electromagnetic geons are contrasted. High-frequency waves are seen to be a necessary condition for the geon and the field equations are decomposed accordingly. It is shown that this leads to the impossibility of forming a spherical gravitational geon. The attempted constructs of gravitational and electromagnetic geons are constructed. The spherical shell in the proposed BrillHartle geon does not meet the regularity conditions required for a nonsingular source and hence cannot be regarded as an adequate geon construct. Since it is the high frequency attribute which is the essential cause of the geon nonviability, it is argued that a geon with less symmetry is an unlikely prospect. The broader implications of the result are discussed with particular reference to the problem of gravitational energy.
INCREASE OF HAWKING RADIATION FROM BLACK HOLES BY DIRAC MONOPOLES
Authors: GONCHAROV YU. P. , FIRSOVA N.E.
Published: October 2004

We study a mechanism of increasing Hawking radiation from a black hole by using the example of twisted topologically inequivalent configurations (TICs) of a complex scalar field on the Schwarzschild black hole. Physically this increase is tied with the natural presence of Dirac monopoles on black holes. We satisfy both analytical and numerical considerations and find that twisted TICs give the contribution of order 17% to the total luminosity (summed up over all the TICs) of a black hole.
ON THE COSMOLOGICAL CONSTANT PROBLEM
Authors: DATTA DHURJATI PRASAD
Published: October 2004

A simple quantum mechanical model of a closed interacting system is studied following the intrinsic time formalism developed recently, on the basis of the modified Born-Oppenheimer approximation. Apart from shedding further insights into the recent results on a possible nongravitating vacuum energy in the universe, the study also offers potentially interesting possibilities even in atomic/molecular physics.