Properties of Quantum Languages

The class of quantum languages Q() over an alphabet is the class of languages accepted by quantum automata. We study properties of Q() and compare Q() with the class of regular languages R(). It is shown that Q() is closed under union, intersection, and reversal but is not closed under complementation, concatenation, or Kleene star. It is also shown that Q() and R() are incomparable. Finally, we prove that L Q() if and only if L admits a transition amplitude function satisfying a certain property and a similar characterization is given for R().     

Four-wave mixing in CO via the C 1Σ+ (υ′=0) state

Coherent vacuum ultraviolet (VUV) radiation was generated by four-wave difference frequency mixing (_VUV=2₁–₂) of pulsed dye laser radiation in carbon monoxide (CO). The frequency ₁ was tuned to the C ¹⁺(=0)X ¹⁺(=0) two-photon transition, while the dye laser frequency ₂ was scaned around 17650 cm^–1 which corresponds to the A ¹(=7)«C ¹⁺(=0) transition energy. The VUV intensity was found to be strongly wavelength dependent. The analysis of the spectrum revealed (i) that the VUV intensity was enhanced by the rotational levels of the A ¹(=7) state and (ii) that the off-resonance excitation in the C ¹⁺(=0)X ¹⁺(=0) two-photon transition greatly contributed to the present four-wave mixing process. The effects of pumping laser detuning, saturation and foreign gases are briefly discussed.     

Mathematical properties of the vacuum polarization function

This paper is an investigation of certain mathematical properties of the vacuum polarization function (s). We show that (s) is a Herglotz function, has no complex zeroes, and belongs to the class of functions called typically real. In addition, we obtain upper bounds on the higher derivatives of (s), at s=0, given that we know the value of the first derivative at that point.Research supported in part by NASA Grant NSG-8035     

Homoclinic orbits on compact hypersufaces in 293-1293-1293-1, of restricted contact type

Consider a smooth Hamiltonian system in ^2N , , the energy surface ={x/H(x)=H(0)} being compact, and 0 being a hyperbolic equilibrium. We assume, moreover, that {0} is of restricted contact type. These conditions are symplectically invariant. By a variational method, we prove the existence of an orbit homoclinic, i.e. non-constant and doubly asymptotic, to 0.     

Two-dimensional quenching lifetime measurement of OH:A 2 Σ +(υ′ = 1) and NO:A 2 Σ(υ′ = 0) in atmospheric-pressure flames

Planar laser-induced fluorescence is currently widely applied to research on combustion. However, conventional approaches for semi-quantitative measurement could not provide the satisfactory solution and the problem due to collisional quenching remains to be solved. This paper describes the two-dimensional (2D) quenching-time-constant measurement of OH:A ^{2 +}( = 1) and NO:A ² ( = 0) in flame cross sections at atmospheric pressure. These measurements involve 1–2 ns decay time of the excited state using a high-speed image intensifier and a tunable laser with a pulse duration of 3 ns at FWHM. The correlation factors of the exponential fits for the fluorescence decays after the laser pulse were larger than 0.999 in all experiments presented in this study. Furthermore, the measured Stern-Volmer plots of the quenching rate at 1.0, 1/2, 1/3, and 1/4 atm pressure using the same experimental apparatus was confirmed to have a linear relationship for both OH and NO, showing that the 2D decay-time measurements of 1–2 ns have been successful. For NO:A ² ( = 0), the obtained quenching rates inside the inner cone and in the outer flame in the NO-seeded methane-air Bunsen flame were 8.7 × 10⁸ and 7.8 × 10⁸ s^–1, respectively, and for OH:A ² ( = 1), the obtained quenching rate mapping in the outer flame was around 5.6 × 10⁸ s^–1 in the methane-air flame.     

Sigma-Boundary Statistics by Length and Number

This paper presents a rationale for comparative use of length fraction and number fraction statistics in grain boundary analysis from orientation maps generated by electron back-scatter diffraction (EBSD). The length and number fraction statistics for 3 ⁿ coincidence site lattice (CSL) boundaries were measured and compared. The length fraction of 3 boundaries was 0.48 whereas the number fraction was significantly less, 0.36. A simple model was generated to estimate both the length fraction and number fraction of annealing twins (a subset of 3). The model showed that the number fraction of twins is 0.68, 0.75, 0.79 and 0.82 of the length fraction for 1, 2, 3 and 4 twins-per-grain respectively. For the experimental data the number fraction was 0.76 of the length fraction, implying that there were on average two twins-per-grain. In contrast to the 3 case, the length fraction for 9 and 27 boundaries was less than the number fraction. There are more inaccuracies involved in obtaining the number fraction than in obtaining the length fraction from EBSD maps, therefore the length fraction should be recommended as the standard reporting method. However a knowledge of the distribution in the microstructure of 3 ⁿ segments is often crucial to the inquiry in addition to the length fraction.     

The Landau-Lifshitz equation,elliptic curves and the ward transform

The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters ₁, ₂, ₃ that live on an elliptic curve . The crucial role of the groupK ₂ × ₂ of translations by the half-periods of and its non-trivial central extension is brought out and an analogue of Birkhoff factorisation for -equivariant loops in is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over . Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC (S ¹).     

The C1 Σ +-B1-Σ + amplified spontaneous emission in CO

The first observation of the amplified spontaneous emission (ASE) from the RydbergC ^{1 +}( = 0) state of CO is reported. When theC ^{1 +}( = 0) state was populated through the two-photon excitation, infrared radiation near 2.0 m was ejected in forward as well as backward directions along the laser propagation. The assignment as theC ^{1 +}( = 0) B ^{1 +}( = 0) transition was confirmed. Several characteristics of ASE from theC ^{1 +}( = 0) state are presented.This work was supported by the Morino Foundation, a Grant-in-Aid (No. 07640697) and that on Priority-Area-Research Photoreaction Dynamics (No. 07228268) from the Ministry of Education, Science, Sports and Culture, Japan.     

Symplectic Structures on Moduli Spaces of Parabolic Higgs Bundles and Hilbert Scheme

Parabolic triples of the form (E_*,,) are considered, where (E_*,) is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle (E_*,) a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bundles is obtained. The pull back, by this map, of the symplectic form on the moduli space of stable parabolic Higgs bundles will be denoted by d. On the other hand, there is a map from the moduli space of stable parabolic triples to a Hilbert scheme Hilb(Z), where Z denotes the total space of the line bundle K_{X X}(S), that sends a triple (E_*,,) to the divisor defined by the section on the spectral curve corresponding to the parabolic Higgs bundle (E_*,). Using this map and a meromorphic one–form on Hilb(Z), a natural two–form on the moduli space of stable parabolic triples is constructed. It is shown here that this form coincides with the above mentioned form d.     

BΛF theory and flat spacetimes

We propose a reduced constrained Hamiltonian formalism for the exactly solubleBF theory of flat connections and closed two-forms over manifolds with topology ³ × (0,1). The reduced phase space variables are the holonomies of a flat connection for loops which form a basis of the first homotopy group ₁( ³), and elements of the second cohomology group of ³ with value in the Lie algebraL(G). WhenG=SO(3,1), and if the two-form can be expressed asB=ee, for some vierbein fielde, then the variables represent a flat spacetime. This is not always possible: We show that the solutions of the theory generally represent spacetimes with global torsion. We describe the dynamical evolution of spacetimes with and without global torsion, and classify the flat spacetimes which admit a locally homogeneous foliations, following thurston's classification of geometric structures.This research is supported in part by the National Science Foundation, Grant No. PHY 89-04035, by CONACyT Grant No. 400349-1714E (Mexico), and by the Association Générale pour la Coopération et le Développement (Belgium).     

Search forN ϕ (1960) baryon

In the experiments at the SPHINX facility in the 70 GeV proton beam of the IHEP accelerator the diffractive production reactionsp+N[(1385)⁰ K ⁺] +N andp+N[(1385)⁰ K ⁺]+N+ (neutral particles) were studied. In the effective mass spectra of the [(1385)⁰ K ⁺] system in these processes there were no signals from the anomalously narrow baryon stateN (1960) which had been observed earlier in the measurement at the BIS-2 setup.SPHINX Collaboration (IHEP-ITEP)     

Geodesic Incompleteness in the ℂP 1 Model on a Compact Riemann Surface

It is proved that the moduli space of static solutions of the P ¹ model on spacetime ×, where is any compact Riemann surface, is geodesically incomplete with respect to the metric induced by the kinetic energy functional. The geodesic approximation predicts, therefore, that lumps can collapse and form singularities in finite time in these models.     

Observation of structural units at symmetric [001] tilt boundaries in SrTiO3

Incoherent Z-contrast imaging in the scanning transmission electron microscope allows atom column positions to be deduced directly from the experimental image, including locations where the column separation is less than the resolution limit. Maximum entropy analysis applied to the incoherent image locates the high-Z columns to an accuracy of ±0.2 Å. Oxygen coordination at the boundary plane can be deduced by high spatial resolution electron energy loss spectroscopy, and approximate column positions determined by simple bond-valence sum calculations. Observations of 25° (=85), 36° (=5) and 67° (=13) [001] symmetric tilt grain boundaries in SrTiO₃ bicrystals show that half columns are a ubiquitous feature of grain boundary structural units. The observed structural units can be combined to produce structural models for symmetric tilt boundaries over a 0–90° range. The =17 (410), =5 (310), and =5 (210) are found to be favored boundaries and the structures of all the other tilt boundaries are comprised of these units combined with =1 (100) and =1 (110) structural units. All the proposed boundary models show continuity of grain boundary structure over the entire misorientation range. The =17 (410) structural unit is asymmetric which induces microfacetting on all boundaries less than the =5, 36.87° misorientation.Work Supported by the U.S. Department of Energy under contract DE-Ac05-84OR21400.     

Measurement of the reaction γp → K0Σat photon energies up to 2.6 GeV⋆

The reaction p K⁰⁺ was measured in the photon energy range from threshold up to 2.6 GeV with the SAPHIR detector at the electron stretcher facility, ELSA, in Bonn. Results are presented on the reaction cross-section and the polarization of the ⁺ as a function of the kaon production angle in the centre-of-mass system, cos^c.m._K, and the photon energy. The cross-section is lower and varies less with photon energy and kaon production angle than that of p K⁺⁰. The ⁺ is polarized predominantly at cos^c.m._K 0. The data presented here are more precise than previous ones obtained with SAPHIR and extend the photon energy range to higher values. They are compared to isobar model calculations.     

Faceting of Σ3 and Σ9 Grain Boundaries in Copper

Faceting is a well documented phenomenon known both for surfaces and interfaces, particularly, grain boundaries (GBs). Faceting can be considered as a phase transition when the original surface or GB dissociates onto flat segments whose energy is less than that of the original surface or GB. For the investigation of GB faceting a cylindrical Cu bicrystal with an island grain was grown by the Bridgman technique. Grain 1 in this bicrystal is completely surrounded by grain 2. The dissociation 9 3 + 3 proceeds during the growth of the bicrystal. The twins appear instead of {111}₁/{115}₂ or (110)_9CSL facet. GB faceting was studied at 1293 K, 1073 K, and 873 K. The profiles of the GB thermal groove were analysed by atomic force microscopy. Wulff-Herring plots and GB phase diagrams have been constructed for the 3, 9 and 9 + 3 GBs. With increasing temperature the facets with low-density CSL-planes disappear in the GB shape. GB roughening phase transition can be responsible for this phenomenon.     

Gas‐Kinetic Temperature of Planar High‐Frequency Capacitive Discharge Plasma in N2/CO2/He Gas Mixtures

Using methods of emission spectroscopy, we have determined the gaskinetic temperature fields of planar highfrequency capacitive discharge plasma in N₂/CO₂/He gas mixtures depending on the excitation frequency, discharge current, pressure, and chemical composition of the mixture. It is shown that the dominant contribution to the neutral component heating in the center of the discharge chamber is made by the processes of V–T relaxation of vibrationally excited molecules N₂(X ¹, V) and CO₂(X ¹, V), whereas in the zones near the electrodes an important role in the heating is played, along with the V–T relaxation of the N₂(X ¹, V) and CO₂(X ¹, V) molecules, by the processes of deactivation of the metastable states A ³ of the N₂ molecule.     

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. II. Molecular dynamics estimates of the friction coefficient

The friction coefficient exerted by a hard-sphere fluid on an infinitely massive Brownian sphere is calculated for several size ratios , where and are the diameters of the Brownian and fluid spheres, respectively. The exact microscopic expression derived in part I of this work from kinetic theory is transformed and shown to be proportional to the time integral of the autocorrelation function of the momentum transferred from the fluid to the Brownian sphere during instantaneous collisions. Three different methods are described to extract the friction coefficient from molecular dynamics simulations carried out onfinite systems. The three independent methods lead to estimates of which agree within statisticalerrors (typically 5%). The results are compared to the predictions of Enskog theory and of the hydrodynamic Stokes law. The former breaks down as the size ratio and/or the packing fraction of the fluid increase. Somewhat surprisingly, Stokes' law is found to hold withstick boundary conditions, in the range 1/4.5 explored in the present simulations, with a hydrodynamic diameterd=. The analysis of the moleuclar dynamics data on the basis of Stokes' law withslip boundary conditions is less conclusive, although the right trend is found as / increases.     

NaK 22Σ+ → 11Σ+ band optically pumped laser near 1.02 μm

Optically pumped laser emission has been observed on the NaK 2(A)¹⁺ 1(X)¹⁺ electronic state transition. The emission occurs between 1.015 and 1.035 m when a sodium-potassium heat-pipe oven is pumped with 695–745 nm pulsed dye laser radiation. The laser emission occurs on many ro-vibrational transitions without the use of cavity mirrors. However, the addition of a simple cavity increases both the number of observed lasing transitions and the amplitude of the emission on each line. We report our results for the dependence of the emission intensity on pump laser power, oven temperature, and buffer gas pressure.     

Light Σ hypernuclei and Σ− atoms

The structures of ⁴ He and ⁷ Li are investigated within the frame of the [³H + ⁺] + + [³He + ^o] model and the microscopic cluster model +2N+, respectively. The different binding mechanism between ⁴ He and ⁷ Li is emphasized together with a brief discussion on the ⁴ Be hypernucleus. It is clarified that the ⁴ He hypernucleus is bound due to the cooperative contribution from the and terms of -N interaction, while the ⁷ Li hypernucleus is bound mainly due to the term of -N interaction. The combined analysis of ^– atoms and ⁴ He hypernucleus is shown to be useful to reveal the characteristic differences among the model D, model F and soft core versions of the Nijmegen OBE potentials.The authors would like to express their sincere thanks to J. ofka, O. Richter, M. Sotona, L. Majling, A. Cieply and other colleagues in Nuclear Physics Institute (e/Prague), and H. Band, Y. Yamamoto and T. Motoba, for collaboration and useful discussions. We dedicate this article to the memory of the excellent activities of the late Prof. Jan ofka.     

On kaonic deuterium. Quantum field-theoretic and relativistic covariant approach

We study kaonic deuterium, the bound K^-d state A_{K d}. Within a quantum field-theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K^-d scattering for arbitrary relative momenta. Near threshold our formula reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering near threshold is defined by the resonances (1405), (1750) and a smooth elastic background, and the inelastic channels K^-d NY and K^-d NY, where Y = ^±,^{0} and ^{0}, where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K^-d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays A_Kd NY and experimental data on the rates of the NY pair production in the reactions K^-d NY. We obtain _{1s} = (630±100)eV. For the shift of the energy level of the ground state of kaonic deuterium we predict _{1s} = (325±60)eV.