Maximal amplitudes of hyperelliptic solutions of the derivative nonlinear Schrödinger equation

A simple formula is proven for an upper bound for amplitudes of hyperelliptic (finite-gap or N-phase) solutions of the derivative nonlinear Schrödinger equation. The upper bound is sharp, viz, it is attained for some initial conditions. The method used to prove the upper bound is the same method, with necessary modifications, used to prove the corresponding bound for solutions of the focusing NLS equation (Wright OC, III. Sharp upper bound for amplitudes of hyperelliptic solutions of the focusing nonlinear Schrödinger equation. Nonlinearity. 2019;32:1929-1966).     

Mean Amplitudes of Vibration for Some Linear Gold(I) Complexes

Recently, Braunstein and Clark¹ described the synthesis and vibrational spectra of complexes containing the AuCl₂, AuBr² and AuI₂ ions. In order to obtain a deeper insight into the vibrational properties of these anions it seems interesting to calculate, using the available spectroscopic data, values for the mean amplitudes of vibration and some related quantities.     

Harmonic Force Fields and Mean Amplitudes for Aluminum Triiodide Dimer and Monomer

Harmonic force fields for AlI₃ (in-plane) and Al₂I₆ are developed from incomplete experimental assignments of vibrational frequencies and comparison with related molecules analysed previously. The missing frequencies are predicted from the calculations. Mean amplitudes of vibration are calculated.     

Harmonic Force Fields and Mean Amplitudes for Aluminum Trifluoride Monomer and Dimber

Recently, in this Journal, J. D. Macomber¹ has inquired into the mechanisms by which a signal is produced in a crossed-coil NMR spectrometer, His reflections led him to question the conventional explanation and to propose in its place a novel and more subtle one. The claim is made that the crossed-coil instrument is unique in its performance of a special form of emission spectroscopy-the detection of coherent spontaneous radiation (superradiance).² It is important to question fundamentals; however, we must disagree with the author's conclusions.     

Scattering amplitudes from multivariate polynomial division

We show that the evaluation of scattering amplitudes can be formulated as a problem of multivariate polynomial division, with the components of the integration-momenta as indeterminates. We present a recurrence relation which, independently of the number of loops, leads to the multi-particle pole decomposition of the integrands of the scattering amplitudes. The recursive algorithm is based on the weak Nullstellensatz theorem and on the division modulo the Gröbner basis associated to all possible multi-particle cuts. We apply it to dimensionally regulated one-loop amplitudes, recovering the well-known integrand-decomposition formula. Finally, we focus on the maximum-cut, defined as a system of on-shell conditions constraining the components of all the integration-momenta. By means of the Finiteness Theorem and of the Shape Lemma, we prove that the residue at the maximum-cut is parametrized by a number of coefficients equal to the number of solutions of the cut itself.     

Improved Light-Cone QCD Sum Rule Analysis of Rare Decays Λ_b → Λ_γ and Λ_b → Λl~+ l~-

We present a systematic light-cone QCD sum rule study of the exclusive rare radiative decay Λ b →Λγ and rare semileptonic decay Λ b →Λl + l within the framework of the standard model. Although some light-cone sum rule (LCSR) studies on these rare processes can be found in different literatures, it is necessary to reanalyze them systematically for the reason that either the baryonic distribution amplitudes are improved or different interpolating currents for the Λ b baryon may lead to quite different results. In addition, the rare process Λ b →Λγ has not yet been analyzed by LCSR with the Ioffe-type current. Taking all these reasons into account, we perform LCSR calculations of both the processes with two types of interpolating currents. Our calculations show that the choice of the interpolating current for the Λ b baryon can affect the predictions significantly, especially for the rare radiative decay process.     

Mittlere Schwingungsamplituden von XeOF 5 −

Mean amplitudes of vibration for the XeOF ₅ ^– anion have been calculated from knownRaman data in a wide temperature range. The results are briefly discussed and some comparisons with otherZXY ₅ species, as well as with related xenon compounds are made.

     

Relationship Between 1H-1H and 19F-19F Inter-Ring Coupling Constants in Fused Aza-Aromatic Systems

A complete analysis of the proton magnetic resonance spectra of quinoline¹ and isoquinoline^2,3 allowed to obtain signs and accurate magnitudes of the ¹H-¹H inter-ring coupling constants (HIRC). Since corresponding ¹⁹F-¹⁹F inter-ring coupling constants (FIRC) in perfluoro-quinoline⁴ and -isoquinoline⁵ are available it was worthwhile to consider whether a correlation could be established between HIRC and FIRC. A correlation of this kind would be of obvious interest to a better understanding of the transmission mechanism of long-range ¹⁹F-¹⁹F couplings.     

Is there a hadron spin-flip contribution to the Coulomb-hadron interference at small momentum transfer and high energies?

The analysing power A_N is examined in the range of the Coulomb-hadron interference on the basis of the experimental data from p_L = 6 GeV/c up to 200 GeV/c taking account of a phenomenological analysis at p_L = 6 GeV/c and a dynamic high-energy spin model. The results are compared with the new RHIC data at p_L = 100 GeV/c. The new experimental data obtained at RHIC indicate small contributions of the hadron spin-flip amplitude.