Rotational analysis of the 9613 Å band of CH3D

The 9613 Å band of CH₃D has been photographed under high resolution using a path length of 640 m and a pressure of 593 Torr. The band is parallel in type and a rotational analysis has been carried out. The principal molecular constants for the upper state are:

$\text{T}{}_0\text{= 10404.770 (15)}\text{cm}{}^{\mathrm{?1}}\text{,}\text{B}\text{= 3.68941 (48)}\text{cm}{}^{\mathrm{?1}}$

. A few small (<0.2 cm^?1) rotational perturbations have been found in the excited state levels with K′ = 0 to 4. No transitions have yet been identified to levels with K′ > 4.The possibility of using the 9613 Å band as a means of measuring the $\text{D}\text{H}$ ratio in planetary atmospheres is discussed.     

On the mass of the ss^- member of the 1^3D1 meson nonet

In the framework of Regge phenomenology and meson meson mixing, this paper estimates the mass of isoscalar state （ss^-） of the 1^3D1 meson nonet, and the results given by two different approaches are 1735.51 ± 59MeV and 1730.29 ±46.SMeV.     

Measurements of air and noble-gas broadening and shift coefficients of the methane R3 triplet of the 2ν3 band

By using a tunable diode laser spectrometer with one absorption White cell for low pressure and one photoacoustic cell for high pressure, line shape parameters of the R3 triplet of the 2ν₃ band of methane at 1.65 μm were measured. The absorption line was recorded by using the wavelength modulation spectroscopy technique with first harmonic detection. The broadening and shift coefficients were obtained by fitting the first harmonic absorption signal while varying the pressure of different perturbing gases: air and noble gases (helium, neon, argon, krypton and xenon). We present here the results for the R3 triplet. The observed shift and broadening coefficients behaviors are discussed. Received: 17 November 2000 / Revised version: 19 February 2001 / Published online: 27 April 2001     

Note on loss of regularity for solutions of the 3—D incompressible euler and related equations

One of the central problems in the mathematical theory of turbulence is that of breakdown of smooth (indefinitely differentiable) solutions to the equations of motion. In 1934 J. Leray advanced the idea that turbulence may be related to the spontaneous appearance of singularities in solutions of the 3—D incompressible Navier-Stokes equations. The problem is still open. We show in this report that breakdown of smooth solutions to the 3—D incompressible slightly viscous (i.e. corresponding to high Reynolds numbers, or highly turbulent) Navier-Stokes equations cannot occur without breakdown in the corresponding solution of the incompressible Euler (ideal fluid) equation. We prove then that solutions of distorted Euler equations, which are equations closely related to the Euler equations for short term intervals, do breakdown.Sponsored by the United States Army under Contract No. DAAG29-80-C-0041, and partially supported by the National Science Foundation under Grant No. MCS-82-01599     

Development and Application of the 2D Relativistic Fokker-Planck Package

The Fokker Planck package which without the relativity effect has been developed in 2002. The package with relativity effect, which induced from Italy, is now developed. It conrains relativity effect, and is bounce averaged. It can deal with such as the trapping effect, wave heating, neutral beam injecting, and particle losses. It is very useful for our HL-2A experimental results analysis.     

Determination of the reaction-matrix elements of the D(d,n)3He and D(d,p)3H reactions forE d ≤500 keV

All available data of the mirror fusion reactions D(d, n)³He and D(d, p)³H have been subjected to a new analysis in order to extract the matrix elements of all 16 transitions necessary for inclusion of alll2 waves. Their energy dependence was assumed to be governed solely by Coulomb penetrabilities. The Levenberg-Marquardt algorithm was used to fit all experimental data. The experimental data are reproduced satisfactorily. The results compare well with anR-matrix analysis and with refined resonating group calculations. No suppression of quintet entrance-state transitions and therefore no neutron suppression in polarized fusion can be derived from this analysis.This work was funded by the German Federal Ministers for Research and Technology (BMFT) under the contract numbers 06-OK-153 and 06-OK-272     

Analysis of the Vibrational-Rotational Structure of 2ν1, ν1 + ν3, and 2ν3 Bands of the D2Se Molecule

The absorption spectrum of the D₂Se molecule in the region of 2₁, ₁ + ₃, and 2₃ absorption bands is registered with a high-resolution Fourier spectrometer and is studied theoretically for a Hamiltonian model with allowance for resonant interactions among (200), (101), and (002) vibrational states.     

Implications of unitarity and analyticity for the Dπ form factors

We consider the vector and scalar form factors of the charm-changing current responsible for the semileptonic decay D → πlν. Using as input dispersion relations and unitarity for the moments of suitable heavy-light correlators evaluated with Operator Product Expansions, including O(α _s ²) terms in perturbative QCD, we constrain the shape parameters of the form factors and find exclusion regions for zeros on the real axis and in the complex plane. For the scalar form factor, a low-energy theorem and phase information on the unitarity cut are also implemented to further constrain the shape parameters. We finally propose new analytic expressions for the Dπ form factors, derive constraints on the relevant coefficients from unitarity and analyticity, and briefly discuss the usefulness of the new parametrizations for describing semileptonic data.     

Semiempirical investigation of perturbations of the g factors of electronic-vibrational-rotational levels of hydrogen: III. The r 3Π g − and s 3Δ g − states of the H2 and D2 molecules

The g factors of rovibrational levels of the (4d)r ³Π _g ^? and (4d)s ³Δ _g ^? states of the H₂ and D₂ molecules have been obtained for the first time. These values were found within the nonadiabatic model taking into account the interaction of the 4dπ³Π_g and 4dδ³Δ_g states in the pure precession approximation using semiempirical values of the expansion coefficients of the wave function in an adiabatic basis, which was obtained for the first time for the states of the triplet 4d complex of terms of the hydrogen molecules, and the results of numerical calculation of the overlap integrals of the vibrational wave functions of these states. It is established that the interference effects of the interaction between the 4dπ³Π _g ^? and 4dδ³Δ _g ^? states lead to significant (up to 7 times for the r ³Π _g ^? state of the H₂ and D₂ molecules and 70 and 8 times for the s ³Δ _g ^? state of the H₂ and D₂ molecules, respectively) differences between the nonadiabatic values of the g factors and the corresponding adiabatic values. It is found that the perturbed values of the g factors are much closer to the values corresponding to the case of Hund’s d coupling of angular momenta than to the values corresponding to the b coupling. It is established that the perturbations of the g factors of rovibrational levels of the states of the 4d complex of terms are much greater (up to 2 times for the ³Π _g ^? states and 350 times for the ³Δ _g ^? states) than the perturbations of the same characteristics for the 3d complex of terms of the hydrogen molecule with the same vibrational and rotational quantum numbers.     

Mathematical structure of the three-dimensional（3D） Ising model

An overview of the mathematical structure of the three-dimensional(3D) Ising model is given from the points of view of topology,algebra,and geometry.By analyzing the relationships among transfer matrices of the 3D Ising model,Reidemeister moves in the knot theory,Yang-Baxter and tetrahedron equations,the following facts are illustrated for the 3D Ising model.1) The complex quaternion basis constructed for the 3D Ising model naturally represents the rotation in a(3+1)-dimensional space-time as a relativistic quantum statistical mechanics model,which is consistent with the 4-fold integrand of the partition function obtained by taking the time average.2) A unitary transformation with a matrix that is a spin representation in 2 n·l·o-space corresponds to a rotation in 2n·l·o-space,which serves to smooth all the crossings in the transfer matrices and contributes the non-trivial topological part of the partition function of the 3D Ising model.3) A tetrahedron relationship would ensure the commutativity of the transfer matrices and the integrability of the 3D Ising model,and its existence is guaranteed by the Jordan algebra and the Jordan-von Neumann-Wigner procedures.4) The unitary transformation for smoothing the crossings in the transfer matrices changes the wave functions by complex phases φx,φy,and φz.The relationship with quantum field and gauge theories and the physical significance of the weight factors are discussed in detail.The conjectured exact solution is compared with numerical results,and the singularities at/near infinite temperature are inspected.The analyticity in β=1/(kBT) of both the hard-core and the Ising models has been proved only for β0,not for β=0.Thus the high-temperature series cannot serve as a standard for judging a putative exact solution of the 3D Ising model.     

Thermodynamics of the 3D Hubbard model on approaching the Néel transition

We study the thermodynamic properties of the 3D Hubbard model for temperatures down to the Néel temperature by using cluster dynamical mean-field theory. In particular, we calculate the energy, entropy, density, double occupancy, and nearest-neighbor spin correlations as a function of chemical potential, temperature, and repulsion strength. To make contact with cold-gas experiments, we also compute properties of the system subject to an external trap in the local density approximation. We find that an entropy per particle S/N ≈ 0.65(6) at U/t = 8 is sufficient to achieve a Néel state in the center of the trap, substantially higher than the entropy required in a homogeneous system. Precursors to antiferromagnetism can clearly be observed in nearest-neighbor spin correlators.     

Close-range optical measurement of aircraft's 3D attitude and accuracy evaluation

A new screen-spot imaging method based on optical measurement is proposed,which is applicable to the close-range measurement of aircraft's three-dimensional (3D) attitude parameters.Laser tracker is used to finish the global calibrations of the high-speed cameras and the fixed screens on test site,as well as to establish media-coordinate-frames among various coordinate systems.The laser cooperation object mounted on the aircraft surface projects laser beams on the screens and the high-speed cameras syn- chronously record the light-spots' position changing with aircraft attitude.The recorded image sequences are used to compute the aircraft attitude parameters.Based on the matrix analysis,the error sources of the measurement accuracy are analyzed,and the maximum relative error of this mathematical model is estimated.The experimental result shows that this method effectively makes the change of aircraft position distinguishable,and the error of this method is no more than 3′while the rotation angles of three axes are within a certain range.     

Measurement of the exclusive D(p,e+e−)3He and D(p, γ)3He reactions at 98 and 176 MeV

A high resolution magnetic pair spectrometer for medium energy photons has been used for studies of the exclusive (p, e⁺e⁻) and (p, γ) reactions on deuterium at 98 and 176 MeV. The (p, e⁺e⁻) cross sections, obtained at 40° and 80°, are compared with the corresponding data for the (p, γ) reaction measured with the same apparatus. At small virtual photon masses the (p, e⁺e⁻) cross sections show significant enhancement over what is expected from model calculations, a behaviour which has earlier been observed also for the ¹¹B(p, e⁺e⁻)¹²C reaction.     

Temperature dependence of nitrogen and oxygen broadening of the 16O3 ν 3 band

High-resolution Fourier transform absorption spectra of ozone broadened by N₂ and O₂ have been recorded at room temperature and at 225 K. Nitrogen- and oxygen-broadened half-widths and their temperature dependence for respectively 160 ro-vibrational transitions on the ¹⁶O₃ ν ₃ band with a wide range of rotational quantum numbers J (2–48) and K_a (0–8) have been determined.     

Jordanian twist quantization of D=4 Lorentz and Poincaré algebras and D=3 contraction limit

We describe in detail the two-parameter nonstandard quantum deformation of the D=4 Lorentz algebra , linked with a Jordanian deformation of . Using the twist quantization technique we obtain the explicit formulae for the deformed co-products and antipodes. Further extending the considered deformation to the D=4 Poincaré algebra we obtain a new Hopf-algebraic deformation of four-dimensional relativistic symmetries with a dimensionless deformation parameter. Finally, we interpret as the D=3 de Sitter algebra and calculate the contraction limit (R is the de Sitter radius) providing an explicit Hopf algebra structure for the quantum deformation of the D=3 Poincaré algebra (with mass-like deformation parameters), which is the two-parameter light-cone κ-deformation of the D=3 Poincaré symmetry.     

First-principles study of the （001） surface of cubic PbHfO3 and BaHfO3

Using first-principles techniques,we investigate the(001) surfaces of cubic PbHfO3(PHO) and BaHfO3(BHO) terminated with both AO(A=Pb and Ba) and HfO2.Surface structure,partial density of states,band structure,and surface energy are obtained.The BaO surface is found to be similar to its counterpart in BHO.For the HfO2-terminated surface of cubic PHO,the largest relaxation appears on the second-layer atoms but not on the first-layer ones.The analysis of the structure relaxation parameters reveals that the rumpling of the(001) surface for PHO is stronger than that for BHO.The surface thermodynamic stability is explored,and it is found that both the PbO-and the BaO-terminated surfaces are more stable than the HfO2-terminated surfaces for PHO and BHO,respectively.The surface energy calculations show that the(001) surface of PHO is more easily constructed than that of BHO.     

Influence of the reagent vibration on the stereo-dynamics of the reactions D^- ＋ H2 and H^- ＋ D2

Employing the quasi-classical trajectory method and the potential energy surface of Panda and Sathyamurhy [Panda A N and Sathyamurthy N 2004 J.Chem.Phys.121 9343],the effect of the reagent vibration on vector correlation of the ion-molecule reactions D～-+H₂ and H～-+D₂ is studied at a collision energy of 35.7 kcal/mol.Four generalized polarization-dependent differential cross sections （2π/σ）（dσ 00 /dωt）,（2π/σ）（dσ 20 /dωt）,（2π/σ）（dσ 22+ /dωt）,and （2π/σ）（dσ 21 /dωt） are presented in the centre-of-mass reference frame,separately.At the same time,the effects on the product angular distributions P （θr）,P （φr） and P （θr,φr） of the title reactions are also analysed.The calculated results show that the scattering tendencies of the product HD,the alignment and the orientation of j sensitively depend on reagent molecule vibration.     

Assignments of the 13C NMR Spectra of Enhydrin and 2′,3′-Dehydromelnerin A and the Molecular Structure of Enhydrin

Abstract

Two melampolide-type sesquiterpene lactones, enhydrin and 2,′ 3′-dehydromelnerin A, were isolated from a Louisiana population of Polymnia uvedalia. Their ¹³C NMR spectra were assigned using ¹³C-¹H correlation, DEPT and COLOC experiments. The molecular structure of enhydrin was established by single crystal X-ray diffraction.