Measurement of local moment on Ce in CeRh3B2

We have employed the TDPAC technique to measure the paramagnetic enhancement factor of¹⁴⁰Ce in CeRh₃B₂ in the temperature range 300 K down to 115 K. Our measurements show that above T_c=115 K, the trend for(T) closely follows that for trivalent cerium.     

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.     

Lattice instability in Hf1-x Ta x V2 compounds

The temperature dependence of the electric quadrupole interaction frequency _l ^o , experienced by the¹⁸¹Ta probe occupying Hf site in the compounds Hf_1-xTa_xV₂ has been measured for x=0.06, 0.10 and 0.20 in the temperature region between 8.5 K to 296 K. The measurements show lattice transformation in all the three compounds below 120 K.     

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.     

Nucleon-nucleon forces in a nonrelativistic quark model

Conclusion We have considered allNN-partial waves simultaneously. The central part of the one gluon exchange is always repulsive, the tensor part can be neglected and the spin-orbit part is too weak for this choice of parameters. An additional colourless V^MEP potential allows us to reproduce the experimental data. However, this potential cannot be related to a long range one-pion exchange potential.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

Pionic decay of hypernuclei

The mass number dependence of the total pionic decay rate of hypernuclei is evaluated under the closure approximation by using DDHF single-particle wave functions and taking into account the pion distortion and absorption. The effect ofNN andN correlations are then incorporated and found to give a drastic enhancement especially in heavy hypernuclei. More detailed features are discussed for partial and total decay rates of typical light hypernuclei.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.     

On subharmonic functions dominated by certain functions

Given two kinds of functionsf(X) andh(y) defined on them-dimensional Euclidean spaceR ^m (m≧1) and the set of positive real numbers respectively, we give an estimation of growth of subharmonic functionsu(P) defined onR ^m+n (n≧1) such that $$u(P) \leqq f\left( X \right)h\left( {\left\| Y \right\|} \right)$$ for anyP=(X, Y),X ∈R ^m, Y ∈R ⁿ, where ‖Y ‖ denotes the usual norm ofY. Using an obtained result, we give a sharpened form of an ordinary Phragmén-Lindelöf theorem with respect to the generalized cylinderD ×R ⁿ, with a bounded domainD inR ^m.     

The uniqueness of the adjoint operation I

Let H be a complex, infinite-dimensional Hilbert space. Let B(H) denote the set of bounded linear operators on H. This paper contains a nonlinear characterization of the adjoint operation on B(H). The statement of this result is:THEOREM:Let h: B(H) B(H)be a function such that h(I)0.Then h(ST)=h(T)h(S)and h(S)S0for all elements Sand Tof B(H)if and only if h(S)=S^* for all S B(H).