bluuebunny/crossref_metadata_2025 huggingface dataset:
CORRELATION FUNCTIONS OF MULTISITE INTERACTION SPIN-S MODELS ON THE BETHE-LIKE LATTICES
Authors: GHULGHAZARYAN R. G.
Published: July 2002

Multisite interaction spin-S models in an external magnetic field are studied recursively on the Bethe-like lattices. The transfer-matrix method is extended to calculate exactly the two-spin correlation functions. The exact expressions for the correlation length and magnetic susceptibility are derived for spin-1/2 models. The singularity of the correlation length with critical index ν = 1 and the proportionality of magnetic susceptibility to correlation length in the second order phase transition region of spin-1/2 ferromagnetic models on the Bethe-like lattices are established analytically.
TOPOLOGICAL MODEL OF THE CHARGE AND MAGNETIC STRIPES IN LA2-XMEXCUO4 (ME = SR, BA, CA)
Authors: FIRSOV N. I. , NOVIKOV I. L. , KHUSNUTDINOV R. F. , KVASOV S. B.
Published: July 2002

In the paper the topological model of the charge ordering and magnetic ordering in La 2- x Me x CuO 4 is suggested. The model assumes that the spin polarons appear in the compound La 2 CuO 4 at the doping. The La substitution leads to the hole appearance in the p-band of the oxygen in CuO 4 unit. This carrier is in the medium of the magnetic moments of Cu ions and it interacts with this moments to form the spin polaron. At x>0.05 the polarons are mobile and they are arranged in the stripes at the temperature drop.
INFRARED EVIDENCE FOR THE COEXISTENCE OF FREE AND BOUND CHARGES IN Nd2-xCexCuO4 AND Bi2Sr2CuO6
Authors: LUPI S. , CALVANI P. , CAPIZZI M. , MASELLI P. , GIURA P. , ROY P.
Published: July 2002

Electron-doped Nd 2-x Ce x CuO 4 and hole-doped Bi 2 Sr 2 CuO 6 have been studied in the infrared to discriminate between the existing models of the optical conductivity σ(ω) in metallic cuprates. In Nd 2-x Ce x CuO 4 an absorption peak clearly visible in the insulating phase softens for increasing x and for decreasing temperature, until it reaches the far infrared (FIR peak) at the insulator-to-metal transition. In the superconducting phase it persists beside the free-carrier Drude absorption, as shown by fitting procedures, and disappears only in the overdoped normal metal. Direct evidence for the presence of the FIR peak in a metallic cuprate comes from the reflectivity of a Bi 2 Sr 2 CuO 6 film, measured down to 10 cm -1, where we could resolve the FIR peak from a normal Drude term as narrow as 35 cm -1 at low T. This observation provides direct evidence for the coexistence of free and "bound" charges in a superconducting cuprate.
ANISOTROPIC IN PLAIN Cu-O STRAIN AND THE STRIPE QUANTUM CRITICAL POINT IN YBa2Cu3O6+k
Authors: SANNA S. , MANCA P. , AGRESTINI S. , SAINI N. L. , BIANCONI A.
Published: July 2002

Anisotropic Cu-O strain has been measured and a relation between the superconducting critical temperature and the strain is studied in the YBa 2 Cu 3 O 6+ k (Y123). oxygen ordered YBa 2 Cu 3 O 6+ k phases. We show that the critical temperature scales both with the strain along the a axis (ε a ,) and along the b axis (ε b ). While undoped, the system is close to the critical strain, ε c ~ 0.043. The formation of chains with doping gives rise to a decrease of the ε b to take the system away from the critical point approaching the dynamical quantum stripe fluctuations (ε b <ε c ) and the ε a increases to approach the phase of superconducting stripes (ε a >ε c ).
QUANTUM MONTE CARLO METHODS FOR NUCLEI AT FINITE TEMPERATURE
Authors: ALHASSID Y.
Published: July 2002

We discuss finite temperature quantum Monte Carlo methods in the framework of the interacting nuclear shell model. The methods are based on a representation of the imaginary-time many-body propagator as a superposition of one-body propagators describing non-interacting fermions moving in fluctuating auxiliary fields. Fermionic Monte Carlo calculations have been limited by a "sign" problem. A practical solution in the nuclear case enables realistic calculations in much larger configuration spaces than can be solved by conventional methods. Good-sign interactions can be constructed for realistic estimates of certain nuclear properties. We present various applications of the methods for calculating collective properties and level densities.
THERMODYNAMICS AND PATH INTEGRALS FOR IDENTICAL PARTICLES: THE FORMALISM
Authors: BROSENS F. , LEMMENS L. F. , DEVREESE J. T.
Published: July 2002

A generalization of symmetrized density matrices in combination with the technique of generating functions allows to calculate the partition function and the static correlation functions of identical particles in a parabolic confining well with harmonic two-body interactions.
NEUTRON SCATTERING SIGNATURE OF d-DENSITY WAVE ORDER IN THE CUPRATES
Authors: CHAKRAVARTY SUDIP , KEE HAE-YOUNG , NAYAK CHETAN
Published: July 2002

An ordered d-density wave (DDW) state has been proposed as an explanation of the pseudogap phase in underdoped high-temperature superconductors. The staggered currents associated with this order have signatures which are qualitatively different from those of ordered spins. We apply the order parameter theory to an orthorhombic bilayer system and show that the expected magnitude as well as the momentum, energy, and polarization dependence of the consequent neutron scattering is consistent with the findings of a recent experiment.
SPATIAL BEHAVIOR OF EXCITON-POLARITON MASSES IN A LAYERED CRYSTAL BiI3
Authors: SHIRASAKA Y. , MINO H. , KAWAI T. , AKAI I. , KARASAWA T.
Published: July 2002

Spatial behavior of the stacking fault excitons (SFE's) excited heavily in a two-dimensional space at a stacking fault interface in BiI 3 has been studied. The SFE's whose center-of-mass motion is confined at the interface show more efficient spatial expansion for higher excitation densities. In order to get phase information of the high-density SFE masses, the degnerate four-wave-mixing (DFWM) measurements with two laser beams including space-resolved regime were performed. It was found that the increase in the dephasing due to exciton-exciton collision is suppressed above a certain density. In a space-resolved regime, it turned out that the high-density exciton mass excited at one laser spot propagates coherently to the other laser-spot propagates coherently to the other laser-spot site and induces nonlinear polarization resulting in momentum-selective emission of the DFWM lights. These result suggest the possibility of a coherent collective motion of the SFE masses in a new condensate of the high-density exciton-polaritons.
GENERALIZED SUPERSYMMETRIES AND COMPOSITE STRUCTURE IN M-THEORY
Authors: LUKIERSKI JERZY
Published: July 2002

We describe generalized D = 11 Poincaré and conformal supersymmetries. The corresponding generalization of twistor and supertwistor framework is outlined with OSp(1|64) superspinors describing BPS preons. The [Formula: see text] BPS states as composed out of n = 32 - k preons are introduced, and basic ideas concerning BPS preon dynamics is presented. The lecture is based on results obtained by J.A. de Azcarraga, I. Bandos, J.M. Izquierdo and the author.1
ELECTRON–ELECTRON INTERACTION, QUANTUM INTERFERENCE AND SPIN FLUCTUATION EFFECTS IN THE RESISTIVITY OF Fe-RICH Fe-Zr METALLIC GLASSES
Authors: BABU P. D. , KAUL S. N. , BARQUÍN L. FERNÁNDEZ , SAL J. C. GÓMEZ , KETTLER W. H. , ROSENBERG M.
Published: July 2002

Electrical resistivity (ρ) measurements have been performed in various temperature ranges on different batches of samples with nominal composition x = 0 and 1 in the amorphous alloy series Fe 90+x Zr 10-x. An elaborate data analysis brings out clearly the actual functional dependences of ρ on temperature (T) in different temperature ranges. The results of this analysis, when discussed in the light of existing theories, permit identification of the dominant mechanisms of electrical transport in different temperature regions as electron-diffuson (non-propagating longitudinal spin fluctuations) scattering for T≤10 K, enhanced electron–electron interaction (EEI) effects in the range 10 K ≤T≤25 K and quantum interference (QI) effects, electron–phonon (e–ph) as well as electron–spin fluctuations scattering in different temperature ranges above 25 K. EEI and QI contributions to ρ, in turn, yield fairly accurate values for the diffusion constant (that obey the Einstein relation) and the dephasing time. Out of the inelastic scattering processes such as e–ph scattering, spin–orbit scattering and spin–flip scattering that destroy phase coherence, e–ph scattering seems to be the most effective dephasing mechanism. Dephasing persists to temperatures well above the Curie point and Debye temperature in the amorphous alloys in question.
Fluctuation Effects and Anomalous Diamagnetism in YBCO124 and in Underdoped YBCO123 from Susceptibility and 63Cu Nuclear Relaxation
Authors: Carretta P. , Lascialfari A. , Rigamonti A. , Rosso A. , Varlamov A. A.
Published: July 2002

The effects of superconducting fluctuations on the diamagnetic susceptibility and on the dynamical spin susceptibility involved in 63 Cu NMR-NQR relaxation rate are investigated in oriented powders of underdoped YBCO123 and of YBCO124 and compared with the ones in optimally doped YBCO123. While in this latter compound the fluctuation diamagnetism is well described by an anisotropic Ginzburg–Landau (GL) functional, in underdoped YBCO123 an anomalous diamagnetism is observed, with a strong enhancement of the susceptibility, in a wide temperature range. The magnetization curves cannot be described by any GL anisotropic functional. Also in YBCO124 the fluctuation diamagnetism is hard to describe by GL-type approach, although the enhancement is not as marked as in underdoped YBCO123. In YBCO124, and in underdoped YBCO123, the temperature and field dependences of the 63 Cu relaxation rates W appear different from the ones in underdoped YBCO123. No field-induced decrease of W is observed, as it is expected in the case of a changeover from s to d of the orbital simmetry of the fluctuating pairs or when the character of the fluctuations is different from the GL one.
Superconducting Pairs in Clusters and in the Cu-O Plane
Authors: Cini Michele , Balzarotti Adalberto , Stefanucci Gianluca
Published: July 2002

Recently, by exact diagonalisation methods, we reported superconducting pairing and flux quantization in Cu-O Hubbard clusters of up to 21 atoms. The pairing is due to a configuration interaction mechanism driven by symmetry, and arises when the least bound holes have vanishing mutual repulsion ( W =0 pairs). The second-order, spin-flip interaction leads to a net attraction for the singlet and repulsion for the triplet. Here we show that electron bound pairs also exist and show similar flux quantization properties. Then, we extend the theory of pairing to the full plane and to all orders.
NMR Analysis of Molecular Motion of Polyurethane Fluid
Authors: Minagawa Keiji , Okamura Hirokazu , Masuda Seizo , Tanaka Masami
Published: July 2002

Urethane modified polyethers having hard-soft-hard structure were prepared as simple model compounds for homogeneous ER fluids. The NMR relaxation analysis was applied to these polyurethane ER fluids, and the molecular motions and interactions were studied with a series of the data of spin-lattice relaxation time T 1 and the spin-spin relaxation time T 2. Two hard-soft-hard urethanes, which showed opposite ER effects, were found to have similar relaxation behaviors under no electric field. The temperature dependence of T 1 indicated existence of significant intermolecular interaction and the concentration dependence of T 2 suggested that the molecular interaction mainly occurs at the polyether main-chain.
MODULATION STRUCTURE OF A FRUSTRATED SPIN LADDER
Authors: WANG YUPENG
Published: July 2002

We study a two-leg spin-1/2 ladder with isotropic exchanges and biquadratic interactions in the basic plaquettes. It is shown that for the extremely frustrated case, the system exhibits a self-organized phase separation. In some parameter regions, the singlet rungs form a Wigner-like lattice in the triplet-rung host. There are three types of elementary excitations in this modulation phase, i.e. the spinons in a triplet domain, the broken singlet rungs and the deformation of the Wigner-like lattice. The flux phase induced by an external magnetic field in the rung-dimerized phase is also discussed.
ELECTRONIC PAIRING AND VARIATION IN THE NORMAL STATE OF METAL
Authors: ZHANG LIYUAN , HAN QIANG
Published: July 2002

Reviewing the situation of the experimental studies of the normal state in high-Tc super-conductors (HTS), we have put forward nine points to be necessarily considered in any theory of the normal state in HTS. It is argued that the two-dimension two-subsystem model is at least qualitatively consistent with all these nine points. On the basis of these arguments, the problem of the electronic pairing and variation in the normal state of metal has been discussed. We have put forward three variation of metals, i.e. the conventional metal (Fermi liquid), near conventional metal and the metal with the markedly pseudogapped metallic behaviour which may be a marginal Fermi liquid.
UPDATE ON THE NUMEROUS NOVEL CONSEQUENCES OF THE MIDGAP STATES IN UNCONVENTIONAL HIGH-Tc SUPERCONDUCTORS
Authors: HU CHIA-REN
Published: July 2002

An update of a previous review on the many effects and novel consequences of the midgap states predicted to exist in d-wave superconductors is given. Four works done by the author and his collaborators are reviewed with a bit more details, but many works done by other researchers since the previous review are also included. These predictions, if not proven later to require modifications due to additional considerations, can help settle unequivocally the d-wave nature of pairing in high-Tc superconductors.
TWO-SITE POLARON PROBLEM: A PERTURBATION APPROACH WITH VARIATIONAL BASIS STATES
Authors: DAS A. N. , CHATTERJEE JAYITA
Published: July 2002

A convergent perturbation method using modified Lang Firsov transformation is developed for a two-site single-polaron system. The method is applicable for the entire range of the electron–phonon coupling strength from the antiadiabatic limit to the intermediate region of hopping. The single-electron energies, oscillator wavefunctions and correlation functions, calculated using this method, are in good agreement with the exact results.
EXISTENCE OF A PHOTONIC BAND GAP AND UNDERLYING PHYSICAL PROCESSES
Authors: JOHRI G. K. , TIWARI AKHILESH , SAXENA SAUMYA , JOHRI MANOJ
Published: July 2002

Mechanisms of the overlapping of gaps due to a refractive index difference minimum and Anderson localization for photonic band gap (PBG) have been used and they give a refractive index contrast difference of less than two percent for X-, L-, and W-points of the Brillouin zone for the pseudogap. Another physical process for the existence of PBG is the use of scattering strength (ε r ≥ 1) for fcc lattice structure. We have found refractive index contrast in the range 2.41–14.21 for the existence of the complete photonic band gap for bound photons (ε r ≥ 1). The lowest limit to yield a gap is 2.41 for valence photons (ε r = 1) at volume filling fraction 85.5% for spherical air atoms and at 14.5% for dielectric spheres. This work is reported for the first time and it is useful for maintaining connectivity and for easier fabrication of photonic crystals.
ATOMIC LAYER EPITAXY BY ISOTHERMAL CLOSED SPACE SUBLIMATION
Authors: de MELO O. , PURÓN E. , SÁNCHEZ M. , LARRAMENDI E. , HERNÁNDEZ L. C , TOBEÑAS S. , TAMURA M. , CRUZ-GANDARILLA F. , HESIQUIO GARDUÑO M.
Published: July 2002

Atomic Layer Epitaxy growth of optoelectronic semiconductors ZnTe, CdTe and CdxZn1-x Te and CdSe films is achieved by using a novel isothermal closed space sublimation system. The quality of the films and the Atomic Layer Epitaxy regime was confirmed by X-Rays and electron diffraction, Transmission Electron Microscope observations and composition measurement of the ternary CdxZn1-x Te alloys. The difference in vapor pressures between the elemental source and the growing surface is the driven force for the growth; this difference being zeroed once the surface is completely. ZnTe growth is regulated at 1 ML/cycle while CdTe is regulated at 0.5 ML/cycle.
A NEW COMBUSTION SYNTHESIS TECHNIQUE FOR RARE EARTH-DOPED III-NITRIDE LUMINESCENT POWDERS
Authors: RAMOS F. E. , GARCIA R. , HIRATA G. A. , BOSZE E. J. , MCKITTRICK J.
Published: July 2002

A new low temperature method to produce ( (RE)xGa1-x)2O3(1≥x≥0 and RE=Eu, Yb, Pr and Tm) powders with high purity, high chemical homogeneity and improved crystallinity has been developed. This procedure produces finely divided powders through an exothermic reaction between the precursors. The process starts with aqueous solutions of RE(NO3)3 and Ga(NO3)3 as the precursors and hydrazine as the (non-carbonaceous) fuel. The combustion reaction occurs when heating the precursors between 150 and 200°C in a closed vessel filled with an inert gas (Ar), which yields (RExGa1-x)2O3 directly. The preparation of RE-doped Ga2O3 powders was using a new combustion synthesis technique (Hydrazine / metal nitrate method). The preparation of Eu-doped GaN was using the ammonium hexafluoro-metal method. The powders were crystalline and high-purity as determined by XPS, EDS, SEM and XRD measurements.
THE HOT CARRIER TEMPERATURE AND THE IMPURITY BAND IN KANE'S THEORY FOR HEAVILY DOPED SEMICONDUCTOR PHOTOLUMINESCENCE ANALYSIS
Authors: FONTHAL G. , TOBÓN L. E. , QUINTERO J. , PIRAQUIVE N. , ARIZA-CALDERÓN H.
Published: July 2002

We analyzed the photoluminescence (PL) spectra on heavily doped GaAs:Sn samples by Kane's theory including a Lorentzian, a Gaussian and the hot carrier temperature. The band gap, the Fermi level, and the Urbach tail were the fitting parameters. Good results were obtained when the theoretical and experimental values were compared for the three parameters. The Urbach energy magnitude and the topological disorder parameter increased when the impurity concentration augment. The average phononic participation was very close with the tabulated values. New information about a shoulder in the high energy side was obtained, too.
STRUCTURAL AND TRANSPORT PROPERTIES OF La0.5Ca0.5-xBaxMnO3(0 ≤ x ≤ 0.5)
Authors: JIANG Y. , YUAN S. L.
Published: July 2002

We have experimentally investigated the effects of Ca 2+ site substitution by bigger Ba 2+ ions in charge ordered La 0.5 Ca 0.5 MnO 3 on structural and transport properties. The results show that the samples with lower Ba-doping (x < 0.3) are of orthorhombic structure. Along with the increasing of Ba content, hexagonal phase BaMnO 3 appears, indicating the two phases in the samples with x ≥ 0.3. The biphasic structure greatly affects the behaviors of resistivity and magnetoresistance of La 0.5 Ca 0.5-x Ba x MnO 3.
MAGNETIC SUSCEPTIBILITY OF THE RELATIVISTIC BOSON GAS
Authors: HOMORODEAN LAUREAN
Published: July 2002

We present the temperature dependences of the magnetic susceptibilities for degenerate (below the Bose–Einstein-condensation temperature) and nondegenerate ideal gases of relativistic charged spinless bosons. The nonrelativistic limits of these laws are also discussed. A comparison with the relativistic electron gas is made.
THE EXACT EVALUATION OF THE RESPONSE FUNCTION FOR WAVE PROPAGATION IN RANDOM MEDIA: A FUNCTIONAL INTEGRAL APPROACH
Authors: BOTELHO LUIZ C. L.
Published: July 2002

We deduce exactly, in a functional integral approach, the Green response-function for the wave equation subject to an external white noise.
THE SPINLESS FALICOV–KIMBALL MODEL AWAY FROM HALF-FILLING
Authors: GÁL ŠTEFAN
Published: July 2002

The one-dimensional spinless Falicov–Kimball (FKM) model is studied in the strong coupling limit away from half-filling. The small-cluster exact-diagonalization calculations are employed to obtain valence transitions in the ground state and for finite temperatures. It is found that in the ground state, the model describes continuous valence transitions for small band-fillings and both continuous and discontinuous transitions near half-filling. At finite temperatures, only continuous valence transitions are obtained. The valence is integer at low temperatures for small band-fillings and in other cases, it takes only intermediate values.
STRUCTURAL ATTRIBUTE FEATURE CODE REPRESENTATION AND RECOGNITION OF MULTIFONT PRINTED CHINESE CHARACTERS
Authors: LIN ZHEN YONG , LIU PING
Published: July 2002

In this paper, a new structural representation and fuzzy matching scheme are proposed for multifont printed Chinese character recognition. A Chinese character is decomposed into eight stroke types. A complete structural attribute feature codes among different types of strokes are defined and extracted, which consist of weak and strong primary codes and secondary codes. Weak and strong primary feature codes depict the global and local spatial relationships among different types of strokes respectively, and they are used for a detailed match. A fuzzy matching scheme is used for detailed match between an input character and candidate characters. An experiment on 3755 Chinese characters used daily in multifonts and multisizes shows that our method is robust and can achieve high recognition accuracy.
THE LOCAL ACTIVITY CRITERIA FOR "DIFFERENCE-EQUATION" CNN
Authors: SBITNEV VALERY I. , YANG TAO , CHUA LEON O.
Published: July 2002

In this paper we use an exponential conformal mapping and a z-transform to "translate" the local activity criteria for continuous-time reaction–diffusion cellular nonlinear networks (CNN) to those for difference-equation CNNs. A difference-equation CNN is modeled by a set of difference equations with a constant sampling interval δt>0. Since a difference-equation CNN tends to a continuous-time CNN when δt→0, we can view the Laplace transform of a continuous-time CNN as the limit of the conformal-mapping z-transform of a corresponding difference-equation CNN. Based on the relation between Laplace transform and our conformal-mapping z-transform, we extend the local activity criteria from a continuous-time CNN to a difference-equation CNN. We have proved the rather surprising result that the class of all reaction–diffusion difference-equation CNNs with two state variables and one diffusion coefficient is locally active everywhere, i.e. its local passive region is empty. In particular, as δt→0, the local-passive region of a continuous-time CNN cell transforms into the "edge-of-chaos" region of a corresponding difference-equation CNN cell with δt>0. Remarkably, as δt→0 the locally active edge-of-chaos region degenerates into a locally passive region as the difference equation tends to a differential equation. These results highlight a fundamental difference between the qualitative properties of systems of nonlinear differential- and difference-equations.
SPATIAL AND TEMPORAL NOISE SPECTRA OF SPATIALLY EXTENDED SYSTEMS WITH ORDER–DISORDER PHASE TRANSITIONS
Authors: STALIUNAS K.
Published: July 2002

The noise power spectra of spatially extended dynamical systems are investigated, using as a model the Complex Ginzburg–Landau equation with a stochastic term. Analytical and numerical investigations show that the spatial spectra of the ordered state are similar to Bose–Einstein distribution, showing 1/k2 asymptotics in the long wavelength limit. The temporal noise spectra of the ordered state obtained are of 1/fα form, where α = 2 - D/2 with D the spatial dimension of the system.
ONE-DIMENSIONAL CELLULAR AUTOMATA WITH MEMORY: PATTERNS FROM A SINGLE SITE SEED
Authors: ALONSO-SANZ RAMÓN , MARTÍN MARGARITA
Published: July 2002

Standard Cellular Automata (CA) are ahistoric (memoryless): i.e. the new state of a cell depends on the neighborhood configuration only at the preceding time step. This article introduces an extension to the standard framework of CA by considering automata implementing memory capabilities. While the update rules of the CA remain the same, each site remembers a weighted mean of all its past states. The historic weighting is defined by a geometric series of coefficients based on a memory factor (α). The time evolution of one-dimensional CA with memory starting with a single live cell is studied. It is found that for α ≤ 0.5, the evolution corresponds to the standard (nonweighted) one, while for α > 0.5, there is a gradual decrease in the width of the evolving pattern, apart from discontinuities which sometimes may occur for certain rules and α values.
BIFURCATIONS IN RING ARRAYS OF PHASE-BISTABLE SYSTEMS
Authors: McNEIL KEN
Published: July 2002

This paper considers a system of identical parametric oscillators linearly coupled together in a ring geometry. The phase of the coupling is chosen so that the system takes on steady, rather than oscillatory, states, and this work focuses on the sequence of bifurcations from the zero steady state. Center manifold expressions are given for the forms of the solutions that emerge from these bifurcations, and full expressions are given for special cases. Secondary bifurcations are also briefly discussed.
IMPLEMENTING BACK-PROPAGATION- THROUGH-TIME LEARNING ALGORITHM USING CELLULAR NEURAL NETWORKS
Authors: YANG TAO , CHUA LEON O.
Published: July 2002

In a programmable (multistage) cellular neural network (CNN) structure, the CPU is a CNN universal chip which supports massively parallel computations on patterns and images, including videos. In this paper, we decompose the structure of a class of simultaneous recurrent networks (SRN) into a CNN program and run it on a von Neumann-like stored program CNN structure. To train the SRN, we map the back-propagation-through-time (BTT) learning algorithm into a sequence of CNN subroutines to achieve real-time performance via a CNN universal chip. By computing in parallel, the CNN universal chip can be programmed to implement in real time the BTT learning algorithm, which has a very high time complexity. An estimate of the time complexity of the BTT learning algorithm based on the CNN universal chip is presented. For small-scale problems, our simulation results show that a CNN implementation of the BTT learning algorithm for a two-dimensional SRN is at least 10,000 times faster than that based on state-of-the-art sequential workstations. For the few large-scale problems which we have so far simulated, the CNN implemented BTT learning algorithm maintained virtually the same time complexity with a learning time of a few seconds, while those implemented on state-of-the-art sequential workstations dramatically increased their time complexity, often requiring several days of running time. Several examples are presented to demonstrate how efficiently a CNN universal chip can speed up the learning algorithm for both off-line and on-line applications.
A GENERAL SMALL CANCELLATION THEORY
Authors: MCCAMMOND JONATHAN P.
Published: July 2002

In this article, a generalized version of small cancellation theory is developed which is applicable to specific types of high-dimensional simplicial complexes. The usual results on small cancellation groups are then shown to hold in this new setting with only slight modifications. For example, arbitrary dimensional versions of the Poincaré construction and the Cayley complex are described.
A NOTE ON LYAPUNOV TRANSFORMATION AND EXPONENTIAL DECAY IN LINEAR ODE SYSTEMS
Authors: AUZINGER W. , EDER A.
Published: July 2002

In this paper we consider a class of matrices A where all eigenvalues have negative real parts and are of a common magnitude O(1). Concerning the behavior of etA we provide a necessary and sufficient condition, via Lyapunov transformation, for an estimate of the form [Formula: see text] to be valid uniformly for t>0 with moderate-sized constants [Formula: see text] and [Formula: see text]. All relevant relations are quantitatively specified.
BEHAVIORAL DYNAMICS OF TWO INTERACTING HAWK–DOVE POPULATIONS
Authors: AUGER PIERRE , PARRA RAFAEL BRAVO DE LA , SÁNCHEZ EVA
Published: July 2002

We present a model of two interacting populations using two individual strategies, hawk and dove. Individuals encounter each other frequently and can change tactics several times in their life. Conflicts occur between individuals belonging to the same population and to different populations. The general model is based on the replicator equations which are used to describe the variations of the hawk proportions of the two populations. According to parameter values, namely the gain-, the intra- and inter-population costs, and the relative intra-population encounter rates, we classify the different phase portraits. We show that a decrease in the intra-population cost of a population provokes an increase in the hawk proportion in this population and of the dove proportion in the other population. An increase in the inter-population cost favors hawk strategy in the population which causes more injuries and dove strategy in the other. We also study the effects of the relative densities of the two populations on the stability of equilibria. In most cases, an increase in the relative density of a population leads to a decrease in hawk proportion in this population and of dove proportion in the other.
PROBABILISTIC ANALYSIS OF AN A POSTERIORI ERROR ESTIMATOR FOR FINITE ELEMENTS
Authors: DíEZ PEDRO , EGOZCUE JUAN JOSÉ
Published: July 2002

A residual type a posteriori error estimator for finite elements is analyzed using a new technique. In this case, the error estimate is the result of two consecutive projections of the exact error on two finite-dimensional subspaces. The analysis introduced in this paper is based on a probabilistic approach, that is, the idea is to assess the average value of the effectivity index (the ratio estimated error over exact error) by assuming the randomness of the exact error. The average value characterizes the mean behavior of the estimator and it is found to be related with some geometric properties of the subspaces. These geometric properties are obtained from the standard matrices of the linear systems arising in the formulation of the finite element method.
A KINETIC MODEL FOR DROPLET COALESCENCE IN DENSE SPRAYS
Authors: ROQUEJOFFRE JEAN-MICHEL , VILLEDIEU PHILIPPE
Published: July 2002

This paper is devoted to the matematical analysis of a kinetic equation describing the process of droplet coalescence in a spatially homogeneous spray. In the first part, existence of a positive measure valued solution is proved, under very general assumptions on the collision kernel. In the second part, mass conservation and momentum preservation, as well as uniqueness and continuous dependence is established, under some more restrictive — but physically reasonable — assumptions on the model. Lastly, the time-asymptotic behavior of the solution is studied.
OPTIMAL CONTROL OF A BIOREACTOR WITH MODAL SWITCHING
Authors: LENHART SUZANNE M. , SEIDMAN THOMAS I. , YONG JIONGMIN
Published: July 2002

We consider a model for bioremediation of a pollutant by bacteria in a well-stirred bioreactor. A key feature is the inclusion of dormancy for bacteria, which occurs when the critical nutrient level falls below a critical threshold. This feature gives a discrete component to the system due to the change in dynamics (governed by a system of ordinary differential equations between transitions) at switches to/from dormancy. After setting the problem in an appropriate state space, the control is the rate of injection of the critical nutrient and the functional to be minimized is the pollutant level at the final time and the amount of nutrient added. The existence of an optimal control and a discussion of the transitions between dormant and active states are given.
ASYMPTOTIC JUSTIFICATION OF THE TREATMENT OF A METALLOSTATIC PRESSURE TYPE BOUNDARY CONDITION IN AN ALUMINIUM CASTING
Authors: BARRAL P. , QUINTELA P.
Published: July 2002

We present an asymptotic analysis to justify the treatment of a metallostatic pressure type boundary condition on a thermal free boundary arising from the thermomechanical modelling of aluminium alloy castings. The problem is solved by means of a fictitious domain method. Using the Saint-Venant's principle we shall justify that for a suitable choice of the Lamé coefficients in the fictitious domain, the solution obtained with this methodology approaches the initial problem solution "far" from the free boundary.
ANALYSIS OF SOME SHALLOW WATER PROBLEMS WITH RIGID-LID HYPOTHESIS
Authors: DI MARTINO B. , GIACOMONI C. , ORENGA P.
Published: July 2002

We present in this paper the analysis and the comparison of two two-dimensional geophysical flow problems using a rigid-lid approximation (i.e. we do not take into account the variation of surface elevation ζ). A first rigid-lid shallow water model (noted SWRL) is obtained by neglecting the variation of the surface in a weak formulation of a usual viscous shallow water model in depth-mean velocity formulation (noted SWFS for shallow water with free surface). We establish some existence results for this model and we propose a numerical resolution method. The second model we consider is an adaptation of the lake equations proposed by Levermore, Oliver and Titi,4 in which we take into account the viscous effects, in order to compare the two approaches. For the numerical resolution, we apply the curl operator on these equations and we propose a numerical algorithm to solve this problem, that we note SWLV (shallow water for the lake with viscosity). We present finally some comparative results in an idealized configuration between the SWRL, SWLV and SWFS models (in the case where the rigid-lid approximation seems to be reasonable).
NONCONFORMING ROTATED ${\mathcal Q}_1$ ELEMENT FOR REISSNER–MINDLIN PLATE
Authors: MING PINGBING , SHI ZHONG-CI
Published: July 2002

A new locking-free low order nonconforming rectangular finite element for the Reissner–Mindlin plate is presented. It consists of the nonconforming rotated [Formula: see text] element for one of the rotation components and the conforming [Formula: see text] element for the other component together with the conforming [Formula: see text] for the deflection. This element gives optimal error bounds for all variables uniform in the plate thickness t with respect to the energy norm as well as the L2-norm. Moreover, we have derived another nonconforming rectangular element with optimal error bounds uniform in t provided [Formula: see text].
ON THE ROBIN PROBLEM IN CLASSICAL POTENTIAL THEORY
Authors: RUSSO REMIGIO , TARTAGLIONE ALFONSINA
Published: July 2002

We give a technique to determine the analytical expression of the density of the logarithmic potential which assumes a constant value at the boundary of a smooth and simply connected plane domain.
ON KORN'S INEQUALITIES IN CURVILINEAR COORDINATES
Authors: CIARLET PHILIPPE G. , MARDARE SORIN
Published: July 2002

We show how the inequality of Korn's type on a surface can be established as a corollary to the three-dimensional Korn inequality in curvilinear coordinates. The proof relies in particular on a careful study of the linearized Kirchhoff–Love displacement fields inside a "shell-like" body.
A NOTE ON THE PROPAGATION OF BOUNDARY INDUCED DISCONTINUITIES IN KINETIC THEORY
Authors: AOKI KAZUO , BARDOS CLAUDE , DOGBE CHRISTIAN , GOLSE FRANÇOIS
Published: July 2002

In this paper, we study, on a very simple kinetic model, the flow structure induced by a discontinuity of the boundary data. The model considered is a stationary one-speed transport equation posed in a half-plane; for simplicity, the boundary data consist of the number density of incoming particles. The propagation of singularities is studied with the velocity averaging method.11
NUMERICAL ANALYSIS OF A MINIMAX OPTIMAL CONTROL PROBLEM WITH AN ADDITIVE FINAL COST
Authors: ARAGONE LAURA S. , DI MARCO SILVIA C. , GONZÁLEZ ROBERTO L. V.
Published: July 2002

In this paper we deal with the numerical analysis of an optimal control problem of minimax type with finite horizon and final cost. To get numerical approximations we devise here a fully discrete scheme which enables us to compute an approximated solution. We prove that the fully discrete solution converges to the solution of the continuous problem and we also give the order of the convergence rate. Finally we present some numerical results.
MORTAR SPECTRAL ELEMENT METHODS FOR ELLIPTIC EQUATIONS WITH DISCONTINUOUS COEFFICIENTS
Authors: BERNARDI CHRISTINE , CHORFI NEJMEDDINE
Published: July 2002

We consider a second-order elliptic equation with piecewise continuous coefficients in a bounded two-dimensional domain. We propose a spectral element discretization of this problem which relies on the mortar domain decomposition technique. We prove optimal error estimates. Next, we compare several versions, conforming or not, of this discretization by means of numerical experiments.
WELL-POSEDNESS OF AN INITIAL BOUNDARY VALUE PROBLEM FROM LASER DYNAMICS
Authors: JOCHMANN F. , RECKE L.
Published: July 2002

In this paper a mathematical model, consisting of nonlinear first-order ordinary and partial differential equations with initial and boundary conditions, for the dynamical behavior of multisection DFB (distributed feedback) semiconductor lasers is investigated. We introduce a suitable weak formulation and prove existence, uniqueness and regularity properties of the solutions. The assumptions on the data are quite general, in particular, the physically relevant case of piecewise smooth, but discontinuous with respect to space and time coefficients in the equations and in the boundary conditions is included.
ON THE EXISTENCE OF WEAK SOLUTIONS TO THE STATIONARY SEMICONDUCTOR EQUATIONS: THE CURRENT DRIVEN CASE
Authors: NAUMANN J.
Published: July 2002

This paper is concerned with the stationary drift-diffusion equations of a semiconductor device where along a part of the device boundary the total current flux is prescribed. We introduce the weak formulation of this mixed boundary value problem and prove the existence of a weak solution.
ADAPTIVE FINITE ELEMENT METHODS FOR REACTIVE COMPRESSIBLE FLOW
Authors: SANDBOGE ROBERT
Published: July 2002

We extend the adaptive streamline diffusion finite element method for compressible flow in conservation variables using P1× P0 space–time elements to include chemical reactions. The adaptive error control is based on an a posteriori error estimate involving a stability factor, which is estimated numerically. We prove for a model problem that the stability factor is bounded by a moderate constant.
POST-SURGICAL PASSIVE RESPONSE OF LOCAL ENVIRONMENT TO PRIMARY TUMOR REMOVAL II: HETEROGENEOUS MODEL
Authors: BELLOMO CARRYN , ADAM JOHN A.
Published: July 2002

An earlier mathematical model is further developed to describe the post-surgical response of the local environment to the removal of a spherical tumor in an infinite heterogeneous domain. The primary tumor is postulated to be a source of growth inhibitor prior to its removal at t=0. Closed form analytic solutions are derived, and the resulting relaxation wave arriving from the disturbed (previously steady) state is studied. The model arises from clinical observations of metastatic inhibition by angiostatin, an angiogenesis inhibitor.
HÖLDER ESTIMATES FOR THE ELASTIC FAR-FIELD PATTERN WITH RESPECT TO THE BOUNDARY
Authors: MITREA DORINA , MITREA MARIUS
Published: July 2002

We prove that under a small perturbation (in the Euclidean metric) of the boundary of a Lipschitz domain there corresponds a small variation (in the uniform norm) of the elastic far-field pattern. The corresponding estimate is of Hölder type. This is done under the assumptions that the Lipschitz character of the perturbation is bounded and that the frequency of the elastic waves is either sufficiently small or has a strictly positive imaginary part.
A POSTERIORI ERROR ESTIMATORS FOR MIXED APPROXIMATIONS OF EIGENVALUE PROBLEMS
Authors: DURÁN RICARDO G. , GASTALDI LUCIA , PADRA CLAUDIO
Published: July 2002

In this paper we introduce and analyze an a posteriori error estimator for the approximation of the eigenvalues and eigenvectors of a second-order elliptic problem obtained by the mixed finite element method of Raviart–Thomas of the lowest order. We define an error estimator of the residual type which can be computed locally from the approximate eigenvector and prove that the estimator is equivalent to the norm of the error in the approximation of the eigenvector up to higher order terms. The constants involved in this equivalence depend on the corresponding eigenvalue but are independent of the mesh size, provided the meshes satisfy the usual minimum angle condition. Moreover, the square root of the error in the approximation of the eigenvalue is also bounded by a constant times the estimator.
MODELLING OF HIGH-DIMENSIONAL DIFFUSION STOCHASTIC PROCESS WITH NONLINEAR COEFFICIENTS FOR ENGINEERING APPLICATIONS — PART I: APPROXIMATIONS FOR EXPECTATION AND VARIANCE OF NONSTATIONARY PROCESS
Authors: MAMONTOV Y. V. , WILLANDER M. , LEWIN T.
Published: July 2002

This work is devoted to diffusion stochastic processes (DSPs) with nonlinear coefficients in n-dimensional Euclidean space at high n (n is much greater than a few units). It deals with expectation and variance of a nonstationary process whereas our accompanying work deals with covariance and spectral density of a stationary process. Combined, analytical-numerical approach is a reasonable and perhaps the only way to treat high-dimensional DSPs in practice. Each of the above works develops the corresponding parts of the analytical basis for this combined treatment. The present work proposes approximate analytical expressions for the expectation and variance in the form of two ordinary differential equation (ODE) systems. They are derived within DSP theory without any techniques directly related to stochastic differential equations. Both ODE systems allow for space nonhomogeneities of the diffusion and damping matrixes and thereby do take nonlinearities of the DSP coefficients into account. Some related topics like invariant processes and the aspects of practical implementation of the above expressions are discussed as well. A proper attention is paid to formulation of some features important in applications of DSPs to the real-world problems. The results of this work can equally be used in various engineering fields.
MODELLING OF HIGH-DIMENSIONAL DIFFUSION STOCHASTIC PROCESS WITH NONLINEAR COEFFICIENTS FOR ENGINEERING APPLICATIONS — PART II: APPROXIMATIONS FOR COVARIANCE AND SPECTRAL DENSITY OF STATIONARY PROCESS
Authors: MAMONTOV Y. V. , WILLANDER M.
Published: July 2002

This work is devoted to diffusion stochastic processes (DSPs) with nonlinear coefficients in n-dimensional Euclidean space at high n (n is much greater than a few units). It deals with covariance and spectral density of a stationary process whereas our accompanying work deals with expectation and variance of a nonstationary process. Combined, analytical–numerical approach is a reasonable and perhaps the only way to treat high-dimensional DSPs in practice. Each of the above works develops the corresponding parts of the analytical basis for this combined treatment. The present work proposes approximate analytical expressions for the covariance in the efficient integral form. The integral formula is based on the obtained analytical results for the covariance, allows for nonlinearities of the drift function, and is derived within DSP theory. No techniques directly related to stochastic differential equations are involved. The approximate expression for the covariance is also applied to evaluate the approximation for the spectral density. Some aspects of practical implementation of these approximations are discussed. The results of this work can equally be used in various engineering fields.
ASYMPTOTIC STABILITY OF TRAVELING WAVES IN SOLID-PROPELLANT COMBUSTION UNDER THERMAL RADIATION
Authors: VERRI MAURIZIO
Published: July 2002

The steady burning stability of solid propellants under thermal radiation with volumetric absorption is investigated. The combustion model we are dealing with includes the classical assumptions of quasiplanarity of all spatial variations, quasisteadiness of the gas phase and surface reaction. However, the stability analysis requires neither assuming a specific pyrolysis law nor formulating a specific flame submodel as long as the surface mass production and heat feedback satisfy some general properties, which are indeed observed experimentally. The existence of a steady state (traveling wave) solution is proved, and a dispersion relationship for its asymptotic stability is derived by conveniently transforming the problem into an evolution equation in a Banach space. The fully opaque burning surface limit and the case of transparent burning surface with exponential volumetric absorption are examined in details. The resulting stability regions in a proper parameter space are given and, finally, existence and stability of bifurcating time-periodic solutions are discussed.
BOUNDARY REGULARITY RESULTS FOR MODELS OF ELASTO-PERFECT PLASTICITY
Authors: FREHSE JENS , MÁLEK JOSEF
Published: July 2002

We study the question of integrability for the gradient of the stress near the boundary for models of elasto-perfect plasticity and their approximations.
MAPS OF SURFACE GROUPS TO FINITE GROUPS WITH NO SIMPLE LOOPS IN THE KERNEL
Authors: LIVINGSTON CHARLES
Published: July 2002

Let Fg denote the closed orientable surface of genus g. What is the least order finite group, Gg, for which there is a homomorphism ψ:π1(Fg)→Gg so that nontrivial simple closed curve on Fg represents an element in Ker (ψ)? For the torus it is easily seen that G1=Z2×Z2 suffices. We prove here that G2 is a group of order 32 and that an upper bound for the order of Gg is given by g2g+1. The previously known upper bound was greater than 2g22g.
COMPUTING THE WRITHE OF A KNOT
Authors: CIMASONI DAVID
Published: July 2002

We study the variation of the Tait number of a closed space curve according to its different projections. The results are used to compute the writhe of a knot, leading to a closed formula in case of polygonal curves.
STABLE EQUIVALENCE OF KNOTS ON SURFACES AND VIRTUAL KNOT COBORDISMS
Authors: SCOTT CARTER J. , KAMADA SEIICHI , SAITO MASAHICO
Published: July 2002

We introduce an equivalence relation, called stable equivalence, on knot diagrams and closed generically immersed curves on surfaces. We give bijections between the set of abstract knots, the set of virtual knots, and the set of the stable equivalence classes of knot diagrams on surfaces. Using these bijections, we define concordance and link homology for virtual links. As an application, it is shown that Kauffman's example of a virtual knot diagram is not equivalent to a classical knot diagram.
TESTING NEWTONIAN GRAVITY AT ULTRA-SHORT DISTANCES
Authors: KRAUSE DENNIS E. , FISCHBACH EPHRAIM
Published: July 2002

The appearance of new fundamental forces and extra-dimensional modifications to gravity in extensions of the Standard Model has motivated considerable interest in testing Newtonian gravity at ultra-short distances (≲10-4 m ). New experiments which attempt to probe these distances will encounter formidable new obstacles, including large intermolecular forces, which could obscure weak new forces or small modifications to Newton's law of gravity. Here we will review the motivation for conducting such ultra-short distance gravity experiments, and discuss some of the new problems that may arise in future experiments. Finally, we suggest a schematic design for a null experiment which would address some of these problems using the "iso-electronic" effect.