Neutral currents and neutrino identity

The possibility is considered that in the neutral current reactions ν+ target → ν′ + …, the final neutrino ν′ may be distinct from the initial neutrino ν. A test of neutrino identity is proposed based on the scattering of low energy (reactor) antineutrinos $\text{ν}{}_{\mathrm{e}}$ from an electron target.     

Neutrino-excitation of baryon resonances and single pion production

This is an attempt to describe all existing data on neutrino production of single pions in the resonance region up to W = 2 GeV in terms of the relativistic quark model of Feynman, Kislinger and Ravndal (FKR). We considered single pion production to be mediated by all interfering resonances below 2 GeV. A simple noninterfering, nonresonant background of isospin $\text{1}\text{2}$ was added. It improved agreement with experiment, particularly in the ratio of isospin amplitudes in charged current reactions, at the expense of one additional constant. All total cross sections, cross section ratios and W-distributions are well reproduced at low and high energies, with charged and neutral currents (supposing the Salam-Weinberg theory with sin²$\text{θ}{}_{\mathrm{w}}\text{≈}\text{1}\text{4}$ to be correct), and for neutrinos and antineutrinos, giving predictions where data are lacking. New predictions have been made for complex angular distributions in $\text{N}$π channels exhibiting strong interference between neighbouring resonances. These are sensitive (for 1.1 GeV ? W ? 1.5 GeV) to the sign of the Roper resonance P₁₁(1450) which is controversial in photoproduction experiments.     

Stabilisation of copper(II) tertiary-phosphine or -arsine complexes—II. Role of inductive effect and reaction conditions in stabilising copper(II)-arsine complexes of hybrid oxygen-arsenic ligands from o-R2AsC6H4CO2H

The characterization of the products of reactions between anhydrous/hydrated copper(II) acetate and the title acids having R = Me, C₆H₁₁, Ph and p-tolyl in different solvents and at different temperatures with the help of elemental analysis, TGA, DTA, room temperature magnetic susceptibility, IR, and UV-VIS and EPR spectral data reveal that a competition exists between the chelation of arsine to copper(II) on one side and the reduction of copper(II) to copper(I) and the subsequent chelation of the arsine to copper(I) and/or that of the arsine oxide to copper(II) on the other. This competition which is expected to be normally governed by the inductive effect of group R is disturbed by the change in reaction conditions leading to the conclusion that the reaction conditions rather than the inductive effect of the group R control the mode of reaction.     

Average inelasticity and average Q2 in deep-inelastic neutrino-nucleon interactions

We show that under the assumptions of scaling and the Callan-Gross relation, the average inelasticity of neutrino as well as antineutrino scattering from an isoscalar nucleon target is completely determined by the ratio of the total cross sections for these reactions. Bounds are obtained on the average (momentum-transfer)² in terms of this ratio. Constraints applicable to scattering from proton or neutron targets are derived.     

Difference sets in abelian groups ofp-rank two

Under a technical assumption that pertains to the so-called self-conjugacy, we prove: if an abelian groupG ofp-rank two,p a prime, admits a (nontrivial) (v, k, ) difference setD, then for each for some subgroupC _p ofG of orderp. Consequently,k(p=1), with equality only ifF=1/p D , whereD is the image ofD under the canonical homomorphism fromG ontoG/E (E being the unique elementary abelian subgroup ofG of orderp ²), is a (v/p ²,k/p, ) difference set inG/E. As applications, we establish the nonexistence of (i) (96, 20, 4) difference sets in ₄ x ₈ x ₃, (ii) (640, 72, 8) difference sets in ₈ x ₁₆ x ₅ and (iii) (320, 88, 24) difference sets in ₈ x ₈ x ₅. The first one fills a missing entry in Lander's table [6] and the other two in Kopilovich's table [5] (all with the answer no). We also point out the connection of the parameter sets in (i) above with the Turyn-type bounds [10] for the McFarland difference sets [9].Research partially supported by NSA Grant #904-92-H-3057 and by NSF Grant # NCR-9200265.     

Analysis of the nonlinear vibration of a two-mass–spring system with linear and nonlinear stiffness

An analytical approach is developed for areas of nonlinear science such as the nonlinear free vibration of a conservative, two-degree-of-freedom mass–spring system having linear and nonlinear stiffnesses. The main contribution of this research is twofold. First, it introduces the transformation of two nonlinear differential equations for a two-mass system using suitable intermediate variables into a single nonlinear differential equation and, more significantly, the treatment of a nonlinear differential system by linearization coupled with Newton’s method. Secondly, the major section is the solving of the governing nonlinear differential equation where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using a first-order variational approach. The aforementioned approach proposed by J.H. He, who actually developed the method, is exactly He’s variational method. This approach is an explicit method with high validity for resolving strong nonlinear oscillation system problems. Two examples of nonlinear two-degree-of-freedom mass–spring systems are analyzed, and verified with published results and exact solutions. The method can be easily extended to other nonlinear oscillations and so could be widely applicable in engineering and science.