Theory of surface spin-exchange recombination of spin-polarized hydrogen

Calculations of the two-atom surface recombination rate for spinpolarized atomic hydrogen are carried out. Both the plane-wave Born approximation (PWBA) and the -dimensional distorted-wave model are employed. The field dependence forB=4 to 10 Tesla, and the temperature dependence for 0.2<T<1 K are examined for systems initially consisting of equal numbers ofa- andb-state atoms. The rates are analyzed with respect to para- and ortho-H₂ production, and to recombination to various vibrational and rotational states of H₂. The PWBA gives reasonable agreement with experiment with respect to the field-dependence and ortho-para production, but predicts an overall rate a factor of 40 above experiment. The -dimensional model underestimates the rate by a factor of 10³ and yields poorer agreement with experiment than the PWBA for the field-dependence and ortho-para production ratio. These results point out the need for a proper many-body treatment.     

Inclusive\bar K^{0*} (892) andK 0*(892) production on silicon by 200 GeVK − andπ −

The production of the neutralK ^? (892) resonances by 200 GeVK ^? andπ ^? has been studied over the kinematic range 0.0<x _f<1.0 andp _t ² <5.0 GeV². Longitudinal and transverse momentum distributions are presented. In addition the decay angular distributions inK ^? fragmentation to \(\bar K^{0*} \) have been investigated.     

Weak boson plus jet production in 2nd-order QCD

We calculate cross sections for the production ofW ⁺ andZ bosons in association with 1 and 2 jets at \(p\bar p\) collider energies. The expected rates for these processes in second-order QCD are presented as a function of the cuts on the transverse momenta of the jets and are compared with jet rates measured by UA1.     

Fe2P2O7 and Fe2P4O12 studied between 5–800 K

Mössbauer spectra of triclinic Fe₂P₂O₇ indicate the existence of two crystallographic metal positions in the structure. In the paramagnetic region the two Mössbauer doublets are closely overlapping. The magnetic transition takes place at ≈ 21 K and the saturated fields are around 12 tesla for the two positions. In monoclinic Fe₂P₄O₁₂ the two octahedrally coordinated metal positions give quite different quadrupole splittings (1.5 and 3 mm/s at room temperature) and hyperfine field values (42 and 12.5 Tesla at 5 K). The transition temperature is at ≈ 18.5 K.     

Superdegenerate point in FCC phase diagram: CVM and Monte Carlo investigations

We investigate the topology of the phase diagram of binary alloys on the fee lattice with first-neighbor antiferromagnetic interactions around the superdegenerate point, where the L1₀ and L1₂ phases meet. We treat the system as a hard-constraint lattice gas, following a procedure previously described by Lebowitzet al. We perform cluster variation method calculations in theT0 limit and Monte Carlo simulations directly atT=0 K on the ground states of the superdegenerate point. We find that: (i) there is no disordered phase in the neighborhood of this point; (ii) a phase L for which two of the four cubic sublattices have the same average occupancy and each of the two others are different appears between L1₀ and L1₂; (iii) the transition L/L1₂ is of first order.     

Comparative cooperative game theory

Given two side-payment gamesv andw, both defined for the same finite player-setN, the following three welfare criteria are characterized in terms of the datav andw: (A) For everyy C(w) there existsx C(v) such thatyx; (A) For everyxC(v) there existsyC(w) such thatyx; and (B) There existyC(w) andxC(v) such thatyx. (HereC(v) denotes the core ofv.) Given two non-side-payment gamesv andw, sufficient conditions for the criteria (A) and (B) are established, by observing that an ordinal convex game has a large core.In memory of my teacher in Japan, Professor Ryuichi Watanabe, 1928–1986.     

Inverse Spectral Transform for the Nonlinear Evolution Equation Generating the Davey-Stewartson and Ishimori Equations

A 2 + 1-dimensional nonlinear differential equation integrable by the inverse-spectral-transform method with the quartet operator representation is proposed. This GL(2, C)-valued chiral-field-type equation is the generating (prototype) equation for the Davey-Stewartson and Ishimori equations. It coincides with the nonlinear equation for the Davey-Stewartson eigenfunction ψ_DS. The initial-value problem for this equation is solved by the techniques for the and the nonlocal Riemann-Hilbert problem. The classes of exact solutions with the functional parameters and exponential-rational solutions are constructed by the method. The static lump solution in the case α = i and the exponentially localized solution at α = i are found. Other similar examples of nonlinear integrable equations in 2 + 1 and 1 + 1 dimensions are discussed.     

Nonlinear stability and convergence of finite-difference methods for the “good” Boussinesq equation

Summary The good Boussinesq equationu _tt =–u _xxxx +u _xx +(u ²) _xx has recently been found to possess an interesting soliton-interaction mechanism. In this paper we study the nonlinear stability and the convergence of some simple finite-difference schemes for the numerical solution of problems involving the good Boussinesq equation. Numerical experimentas are also reported.     

Best constants for approximations of periodic functions by Fejér operators

We obtain the best estimate for approximations of continuous 2-periodic functions by Fejér summation operators. The estimate is expressed in terms of the moduli of continuity of functions to be approximated. In the class of functions satisfying Lipschitz condition, we obtain the best constant for the approximation by Fejer integral and summation operators.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 1, pp. 75–82, 1990.