Absence of continuous symmetry breaking in a one-dimensional n−2 model

For a one-dimensional array ofS ^N–1 spins (N 2) with isotropic pair interactions (and more general systems) with J(j–i) obeying sup_n[n^–1 ₁ ⁿ j ²|J(j)|]<, we prove that every equilibrium state is invariant under the natural action ofSO(N). In particular, there is no long-range order of the conventional type. Included is the caseJ(n)=n ^–2.Research partially supported by U.S.N.S.F. Grant No. MCS-78-01885.S. Fairchild Scholar at Caltech. On leave from Departments of Mathematics and Physics, Princeton University, Princeton, New Jersey 08544.     

O(N) vector model with twisted boundary conditions

Prompted by a recent article of Chakravarty, we reexamine theO(N) vector model with twisted boundary conditions ind dimensions in the various frameworks of the =d–2 expansion, the =4–d expansion, and the large-N expansion. These continuum models describe the physics below the critical temperatureT _c and nearT _c of a latticeO(N) spin model. We determine the effect of the twisting on finite-size scaling functions, for various geometries.On leave from G. Nadjakov Institute of Solid State Physics, 1784 Sofia, Bulgaria.     

Excess molar volumes, viscosities, and refractive indices for binary and ternary mixtures of {cyclohexanone (1) + N,N-dimethylacetamide (2) + N,N-diethylethanolamine (3)} at (298.15, 308.15, and 318.15) K

Densities ρ, viscosities η, and refractive indices n_D, of the binary and ternary mixtures formed by cyclohexanone + N,N-dimethylacetamide + N,N-diethylethanolamine were measured at (298.15, 308.15, and 318.15) K for the liquid region and at ambient pressure for the whole composition ranges. The excess molar volumes V_m^E, viscosity deviations Δη, and refractive index deviations Δn_D, were calculated from experimental densities and refractive indices. The excess molar volumes are positive over the mole fraction range for binary mixtures of cyclohexanone(1) + N,N-dimethylacetamide (2) and N,N-dimethylactamide (2) + N,N-diethylethanolamine (3) and increase with increasing temperatures from (298.15 to 318.15) K. The excess molar volumes of cyclohexanone (1) + N,N-diethylethanolamine (3) are S-shaped dependence on composition with negative values in the N,N-diethylethanolamine rich-region and positive values at the opposite extreme and increase with increasing temperatures from (298.15 to 318.15) K. The excess molar volumes are positive over the whole mole fraction ranges for the ternary mixtures at all temperatures. Viscosity deviations are negative over the mole fraction range for all binary and ternary mixtures and decrease with increasing temperatures from (298.15 to 318.15) K. Refractive index deviations are negative over the mole fraction range for all binary and ternary mixtures and increase with increasing temperatures from (298.15 to 318.15) K. The experimental data of constitute were correlated as a function of the mole fraction by using the Redlich–Kister equation for binary and , Cibulka, Jasinski and Malanowski , Singe et al., Pintos et al., Calvo et al., Kohler, and Jacob–Fitzner for ternary mixture, respectively. McAllister^'s three body, Hind, and Nissan–Grunberg models were used for correlating the kinematic and dynamic viscosity of binary mixtures. The experimental data of the constitute binaries are analyzed to discuss the nature and strength of intermolecular interactions in these mixtures.     

Wess–Zumino Currents on S3 × R Spacetime

Based on the group theory powerful techniques, as a rigorous tool for treating fields on S ³ × R spacetime, which is the manifold of SU(2), we put the supersymmetric Wess–Zumino model on the S ³ × R background. After deriving the system of Klein–Gordon–Dirac-type equations, for the scalar and Majorana fields, we get in the corresponding current, besides the supercurrent, an additional term due to the coupling of spin to gravity. Finally, considerations on the solutions of the fields equations are made, pointing out significant differences from the Minkowskian case.     

Solid-state NMR investigations of Si-29 and N-15 enriched silicon nitride

We compare ²⁹Si magic-angle spinning (MAS) nuclear magnetic resonance (NMR) spectra from the two modifications of silicon nitride, α-Si₃N₄ and β-Si₃N₄, with that of a fully (²⁹Si, ¹⁵N)-enriched sample ²⁹Si₃¹⁵N₄, as well as ¹⁵N NMR spectra of Si₃¹⁵N₄ (having ²⁹Si at natural abundance) and ²⁹Si₃¹⁵N₄. We show that the ¹⁵N NMR peak-widths from the latter are dominated by J(²⁹Si–¹⁵N) through-bond interactions, leading to significantly broader NMR signals compared to those of Si₃¹⁵N₄. By fitting calculated ²⁹Si NMR spectra to experimental ones, we obtained an estimated coupling constant J(²⁹Si–¹⁵N) of 20 Hz. We provide ²⁹Si spin-lattice (T₁) relaxation data for the ²⁹Si₃¹⁵N₄ sample and chemical shift anisotropy results for the ²⁹Si site of β-Si₃N₄. Various factors potentially contributing to the ²⁹Si and ¹⁵N NMR peak-widths of the various silicon nitride specimens are discussed. We also provide powder X-ray diffraction (XRD) and mass spectrometry data of the samples.     

In Vivo Detection of N-Coupled Protons in Rat Brain by ISIS Localization and Multiple-Quantum Editing

Three-dimensional image-selected in vivo spectroscopy (ISIS) was combined with phase-cycled ¹H–¹⁵N heteronuclear multiple-quantum coherence (HMQC) transfer NMR for localized selective observation of protons J-coupled to ¹⁵N in phantoms and in vivo. The ISIS–HMQC sequence, supplemented by jump–return water suppression, permitted localized selective observation of 2–5 μmol of [¹⁵N_indole]tryptophan, a precursor of the neurotransmitter serotonin, through the ¹⁵N-coupled proton in 20–40 min of acquisition in vitro at 4.7 T. In vivo, the amide proton of [5-¹⁵N]glutamine was selectively observed in the brain of spontaneously breathing ¹⁵NH₄⁺-infused rats, using a volume probe with homogeneous ¹H and ¹⁵N fields. Signal recovery after three-dimensional localization was 72–82% in phantoms and 59 ± 4% in vivo. The result demonstrates that localized selective observation of ¹⁵N-coupled protons, with complete cancellation of all other protons except water, can be achieved in spontaneously breathing animals by the ISIS–HMQC sequence. This sequence performs both volume selection and heteronuclear editing through an addition/subtraction scheme and predicts the highest intrinsic sensitivity for detection of ¹⁵N-coupled protons in the selected volume. The advantages and limitations of this method for in vivo application are compared to those of other localized editing techniques currently in use for non-exchanging protons.     

C, N CPMAS NMR and GIAO DFT calculations of stereoisomeric oxindole alkaloids from Cat's Claw (Uncaria tomentosa)

Oxindole alkaloids, isolated from the bark of Uncaria tomentosa [Willd. ex Schult.] Rubiaceae, are considered to be responsible for the biological activity of this herb. Five pentacyclic and two tetracyclic alkaloids were studied by solid-state NMR and theoretical GIAO DFT methods. The ¹³C and ¹⁵N CPMAS NMR spectra were recorded for mitraphylline, isomitraphylline, pteropodine (uncarine C), isopteropodine (uncarine E), speciophylline (uncarine D), rhynchophylline and isorhynchophylline. Theoretical GIAO DFT calculations of shielding constants provide arguments for identification of asymmetric centers and proper assignment of NMR spectra. These alkaloids are 7R/7S and 20R/20S stereoisomeric pairs. Based on the ¹³C CP MAS chemical shifts the 7S alkaloids (δ C3 70–71 ppm) can be easily and conveniently distinguished from 7R (δC3 74.5–74.9 ppm), also 20R (δC20 41.3–41.7 ppm) from the 20S (δC20 36.3–38.3 ppm). The epiallo-type isomer (3R, 20S) of speciophylline is characterized by a larger ¹⁵N MAS chemical shift of N4 (64.6 ppm) than the allo-type (3S, 20S) of isopteropodine (δN4 53.3 ppm). ¹⁵N MAS chemical shifts of N1–H in pentacyclic alkaloids are within 131.9–140.4 ppm.     

On the number of invariant measures for higher-dimensional chaotic transformations

LetS be a bounded region inR ^N and letP={S _l } _i=1 ^m be a partition ofS into a finite number of closed subsets having piecewiseC ² boundaries of finite (N–1)-dimensional measure. Let :SS be piecewiseC ² onP and expanding in the sense that there exists 0<<1 such that for anyi=1,2,...,m, DT _i ^–1<, whereDT _i ^–1 is the derivative matrix ofT _i ^–1 and · is the Euclidean matrix norm. We prove that for some classes of such mappings, for example, Jabtonski transformations or convexity-preserving transformations, the number of crossing points constitutes a bound for the number of ergodic absolutely continuous -invariant measures. We give examples showing that in general the simple bound of one-dimensional dynamics cannot be generalized to higher dimensions. In fact, we show that it is possible to construct piecewise expandingC ² transformations on a fixed partition with a finite number of elements but which have an arbitrarily large number of ergodic, absolutely continuous invariant measures.     

One- and two-dimensional C–H/N–H dipolar correlation experiments under fast magic-angle spinning for determining the peptide dihedral angle φ

A recently proposed ¹³C–¹H recoupling sequence operative under fast magic-angle spinning (MAS) [K. Takegoshi, T. Terao, Solid State Nucl. Magn. Reson. 13 (1999) 203–212.] is applied to observe ¹³C–¹H and ¹⁵N–¹H dipolar powder patterns in the ¹H–¹⁵N–¹³C–¹H system of a peptide bond. Both patterns are correlated by ¹⁵N-to-¹³C cross polarization to observe one- or two-dimensional (1D or 2D) correlation spectra, which can be simulated by using a simple analytical expression to determine the H–N–C–H dihedral angle. The 1D and 2D experiments were applied to N-acetyl[1,2-¹³C,¹⁵N] -valine, and the peptide φ angle was determined with high precision by the 2D experiment to be ±155.0°±1.2°. The positive one is in good agreement with the X-ray value of 154°±5°. The 1D experiment provided the value of φ=±156.0°±0.8°.     

Electro-Strong Interaction and High Q 2 Events at HERA

A previously proposed unified field theory of electro-strong interactions requires two scales of length within hadrons, 10^–15 and 10^–18 m respectively, and the onset of new phenomena at the shorter scale. Studies at the HERA electron–proton collider at the shorter scale have revealed a possible excess of high-transverse momentum events, as expected, with Q ² 30,000 (GeV/c²). The collider is currently being upgraded. This will permit a clearer test to be carried out.     

Upper limits for lepton-flavor violation from the exotic μ− ν e− conversion

The transition matrix elements for coherent and incoherent channels of the neutrinoless ^– e^– conversion are investigated. The results refer to the ²⁷Al nucleus which has recently been chosen as a target in the MECO experiment at Brookhaven aiming to search for -e conversion events with a sensitivity 10^-17. These results are compared to those obtained previously for ⁴⁸Ti and ²⁰⁸Pb targets. We focus on the contributions to the branching ratio e^– originating from scalar, vector and axial vector interactions resulting in conventional extentions of the standard model and minimal supersymmetric models with and without -parity violation. With our calculations we extract very severe constraints for the flavor violation parameters.     

Finite-size effects in a field-theoretic model with long-range exchange interaction

We present a systematic approach to the calculation of finite-size (FS) effects for anO(n) field-theoretic model with both short-range (SR) and long-range (LR) exchange interactions. The LR exchange interaction decays at large distances as 1/r ^d+2–2,0⁺,0⁺. Renormalization group calculations ind=d _u – are performed for a system with a fully finite (block) geometry under periodic boundary conditions. We calculate the FS shift of the critical temperature and the FS renormalized coupling constant of the model to one-loop order. The universal scaling variable is obtained and the FS scaling hypothesis is verified.     

3D 1H-13C-14N correlation solid-state NMR spectrum

Nitrogen-14 (spin I = 1) has always been a nucleus difficult to observe in solid-state NMR and until recently its observation was restricted to one-dimensional (1D) spectra. We present here the first 3D ¹H–¹³C–¹⁴N NMR correlation spectrum. This spectrum was acquired on a test sample l-histidine·HCl·H₂O using a recently developed technique, which consists in indirectly observing ¹⁴N nuclei via dipolar recoupling with an HMQC-type experiment.     

Isotope Effects on theO,H Coupling Constant and theO–{H} Nuclear Overhauser Effect in Water

The NMR spectra of solutions of 30%¹⁷O-enriched H₂O and D₂O in nitromethane display the resonances of the three isotopomers H₂O, HDO, and D₂O. All¹⁷O,¹H and¹⁷O,²H coupling constants and the primary and secondary isotope effects onJ(¹⁷O,¹H) have been determined. The primary effect is −1.0 ± 0.2 Hz and the secondary effect is −0.07 ± 0.04 Hz. Using integrated intensities in the¹⁷O NMR spectra, the equilibrium constant for the reaction H₂O + D₂O 2HDO is found to be 3.68 ± 0.2 at 343 K. From the relative integrated intensities of proton-coupled and -decoupled spectra the¹⁷O–{¹H} NOE is estimated for the first time, resulting in values of 0.908 and 0.945 for H₂O and HDO, respectively. This means that dipole–dipole interactions contribute about 2.5% to the overall¹⁷O relaxation rate in H₂O dissolved in nitromethane.     

Correlation between P chemical shift tensor and local structure in lithium cyclohexaphosphates Li6P6O18·3H2O and Li6P6O18

To understand the surprising behavior between the variations of the P′–P–P″ angles and the correlated variations of the O′–P–O″ ones, two lithium cyclohexaphosphate compounds Li₆P₆O₁₈·3H₂O and Li₆P₆O₁₈ are studied by solid state nuclear magnetic resonance (NMR) spectroscopy. The two compounds exhibit the same [P₆O₁₈]⁶⁻ ring anions but with 3m or internal symmetry, respectively. Such symmetries induce local distortions that are exhibited by NMR spectroscopy. One-dimensional (1D) NMR gives information on structural sites of ⁷Li and ³¹P ions and the crystallographic non-equivalencies are observed. Nevertheless, in the anhydrous compound, X-ray diffraction and NMR results do not completely agree and some discrepancy exists between the number of sites observed with the first technique and the number of lines exhibited in the NMR spectra either for ⁷Li or ³¹P nuclei. This problem is elucidated by using 2D double quantum NMR spectroscopy coupled with theoretical considerations. We find that the ³¹P chemical shift tensor is dependent on the deviations of the O–P–O angles from those in the regular tetrahedron. Within the same empirical model, we suggest that the surprising behavior between the variations of the P′–P–P″ and the ones of the O′–P–O″ is related to the overall charge on the PO₄ group. We also find the positions of the isotropic lines for ⁷Li essentially depend on the site co-ordination of this nuclei.     

Deeply bound pionic states with the (Σ −,Λ) reaction

We study the reaction ^– +A + (A ^–) with the ^– bound in the nucleus, as a means of producing deeply bound pionic states in nuclei, so far unobserved. The reaction is similar to the (n, p) reaction but, because of the ^–, mass difference, it allows the reaction to occur with smaller momentum transfer, thus increasing the transition probability and reducing the effects of distortion. The ratios of signal to background are one to two orders of magnitude better than in the (n, p) reaction.We would like to thank C. Dover and G. Tamas who helped us to get a perspective of the present and future possibilities of this and other reactions.One of us, J. Nieves wishes to acknowledge a fellowship from the Ministerio de Educatión y Ciencia. This work is partially supported by the CICYT. All the calculations have been done in the Centro Informático de la Universidad de Valencia.     

IR Spectra of Derivatives of Immunotropic 8-Azasteroids

By the method of IR Fourier spectroscopy with the use of numerical differentiation of spectral line profiles we have studied the spectra of some structural and functional derivatives of immunotropic 8-azasteroids in the region of C=O and C=C bonds (1800–1400 cm^–1). We have established the dependence of vibration frequencies of the C=O and C=C groups on the size of the ring D, the presence of heteroatoms (O, S) in the ring D, transformations in the -acyl--aminovinylcarbonyl fragment and in its adjacent positions of the heterosteroid skeleton, and the composite character of the absorption bands that are due to the vibrations of the C=O and C=C groups. The role of the structural and stereoelectronic factors in the observed group frequencies of 8-azasteroids is discussed.