Experimental tests for detecting spin polarization pick-up of single-electron19F-ions on emergence from magnetized iron

A new method to detect polarization pick-up by ions emerging from thin polarized ferromagnetic layers has been tested. The applied technique consists in the observation of attenuated-angular correlations and atomic spin precessions for single-electron ions recoiling through vacuum in weak transverse magnetic fields. The Coulomb-excited¹⁹F(5/2⁺) state at 197 keV was used as probe. The experimental concept is described and the expected effects are discussed using the perturbed angular correlation formalism for polarized hyperfine interactions.     

VUV generation by eighth-order nonlinearity in Hg vapour

Direct eighth-harmonic generation ( = 134.4 nm) of Nd-laser radiation has been studied experimentally in Hg vapour. An electric field produced by free electrons created by photoionization is shown to be reasonable for even-order harmonic generation in a centrosymmetric medium.     

Mixing properties of mim diodes in the infrared

Point contact MIM diodes of different materials have been tested as harmonic mixers at 29 THz and 88 THz. From the analysis of the I-V static characteristic quantitative informations have been obtained about the effectiveness of the diodes as high order mixers.     

Spanning tree formulas and chebyshev polynomials

The Kirchhoff Matrix Tree Theorem provides an efficient algorithm for determiningt(G), the number of spanning trees of any graphG, in terms of a determinant. However for many special classes of graphs, one can avoid the evaluation of a determinant, as there are simple, explicit formulas that give the value oft(G). In this work we show that many of these formulas can be simply derived from known properties of Chebyshev polynomials. This is demonstrated for wheels, fans, ladders, Moebius ladders, and squares of cycles. The method is then used to derive a new spanning tree formula for the complete prismR _n (m) =K _m ×C _n . It is shown that $$2^{\left( {\begin{array}{*{20}c} n \\ 2 \\ \end{array} } \right)\left( {1 - \frac{1}{{r - 1}} + o\left( 1 \right)} \right)} $$ whereT _n (x) is then ^th order Chebyshev polynomial of the first kind.     

Barium

Ohne Zusammenfassung     

A comparison of the stochastic theory of the crystal growth and the Stefan problem

The stochastic theory of the crystal growth is compared with the solution of the Stefan problem in the case of Sn solidification. It is shown that the stochastic theory gives the same results as the solution of the Stefan problem if kinetic processes at the solidification front are very rapid.     

Periodic solutions of quasilinear non-autonomous systems with impulses

The paper considers a system of differential equations with impulse perturbations at fixed moments in time of the form where x ? R ⁿ, ε is a small parameter, Sufficient conditions have been found for existence of the periodic solution of the given system in the critical and non-critical cases.     

Equivalence of functional-differential equations of neutral type and abstract Cauchy problems

Equivalence of functional-differential equations of neutral type to well-posed abstract Cauchy problems in the state spaces ⁿ }L ^p ,L ^p resp.C is investigated. The assumptions allow non-atomic difference operators.This work was supported by the Fonds zur Förderung der wissenschaftlichen Forschung (Austria) under Grant No. P4534.Work done by this author was done during a stay at the University of Graz from October 1981 till April 1984.     

Limiting Lagrangians: A primal approach

In this paper, we consider a convex program with either a finite or an infinite number of constraints and its formal Lagrangian dual. We show that either the primal program satisfies a general condition which implies there is no duality gap or that there is a nonzero vectord with the following properties: First, wheneverd is added to the objective function, where is a positive number not greater than one, the resulting program satisfies the general sufficient condition cited above for no duality gap. Second, the optimal value of this perturbed program is attained and tends to the optimal value of the original program as tends to zero. Third, the optimal solutions of the perturbed programs form a minimizing sequence of the original program. As a consequence of the above, we derive the limiting Lagrangian theory of Borwein, Duffin, and Jeroslow.The authors are indebted to an unknown referee who suggested the very short and elegant proofs of Lemma 2.3 and Theorem 2.3.This work was completed while the first author was a member of the College of Management, Georgia Institute of Technology, Atlanta, Georgia.