Elliptic semiplanes and group divisible designs with orthogonal resolutions

In this paper we prove that there exists an elliptic semiplaneS(v, k, m) withk –m 2 if and only if there exists a group divisible design GDD _k ((k –m)(k – 1);k –m; 0, 1) withm pairwise orthogonal resolutions. As an example of this theorem, we construct an elliptic semiplaneW(45, 7, 3) and show thatW is isomorphic to the elliptic semiplaneS(45, 7, 3) given by R. D. Baker.     

Regular and Chaotic Solutions of Duffing's Equation for Large Forcing

This paper uses an analytical approximation to study the periodicand chaotic solutions of the forced—damped Duffing's equation.The forcing is of fixed frequency and is taken to be a multipleof cos t. The forcing amplitude is large and its reciprocalis used to construct a small parameter , which is used as anexpansion parameter in the approximation. The solutions aredetermined as functions of . The damping is linear and proportionalto the velocity; the constant of proportionality is held fixedin this study.     

Observables on hypergraphs

Observables on hypergraphs are described by event-valued measures. We first distinguish between finitely additive observables and countably additive ones. We then study the spectrum, compatibility, and functions of observables. Next a relationship between observables and certain functionals on the set of measures M(H) of a hypergraph H is established. We characterize hypergraphs for which every linear functional on M(H) is determined by an observable. We define the concept of an effect and show that observables are related to effect-valued measures. Finally, we define operational transformations from M(H) to itself and show that they can be described as a certain combination of effects.On leave from University of Berne, Institute of Mathematical Statistics, Sidlerstrasse 5, CH-3012 Berne, Switzerland.     

Study of diffusion creep accompanying superplastic deformation of the alloy ZhS6KP

The development of diffusion creep (DC) accompanying superplastic deformation (SPD) of the highly doped nickel alloy ZhS6KP is studied based on an investigation of the redistribution of dispersed intragrain deposits of the phase of Ni₃(Al, Ti). Deposit-free zones (DFZ) are formed in the alloy, held at the temperature of SPD and accompanying deformation at the grain boundaries. The contribution of DC to the deformation was determined from a comparative analysis of the width of the DFZ in the deformed and undeformed parts of the samples for different grain sizes and rates of DC taking into account diffusion accommodation. It was established that for the optimum rate of SPD the upper limit of the contribution of DC to deformation for 2-m grains does not exceed 11%. It is concluded, based on the distribution of DFZ, that the effect of DC accompanying SPD is determined by diffusion fluxes, associated with the local concentration of stress accompanying the development of grain-boundary slipping.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 40–45, June, 1986.In conclusion, we thank Yu. M. Mishin for a useful discussion of the results.     

Field dependent critical fluctuations aboveT g in the ESR line width of the spin glassAgMn

The ESR of the spin glassAgMn (2.7 and 9.6 at %) has been investigated below and aboveT _g(0.1T _g<T<5T _g) at various microwave frequencies. The analysis yields:1) No explicit frequency dependence but strong magnetic field effects, inherent with ESR-experiments.2) Part of the excess line width is identified as critical spin fluctuations, following a power law. However, because of the presence of the applied field, the reduced temperaturet is not a good scaling variable. We choose the non-linear susceptibility X _s divided byH ², which scales as the order parameter susceptibility. The experiment yieldsW _ex(X _s /H ²) ^p ,p=0.42. From this we deduce z3.     

Structural changes of Zr x Cu100-x metallic glasses investigated by low temperature specific heat measurements

Amorphous alloys of Zr _x Cu_100–x (55x72) quenched from the melt are investigated by low temperature specific heat measurements. The influence of concentrationx, temperature of the melt before the quenching process and heat treatment on the electronic density of states, the Debye temperature and the superconducting transition temperature is examined. The latter one is the most affected value by structural relaxation while the specific heat in the normal conducting region remains nearly unchanged.     

Mössbauer effect of iodine at pressures to 30 GPa

We report the first high pressure¹²⁹I Mössbauer measurements with elemental iodine at pressures to 30 GPa. A 20 mg/cm^{2 129}I₂ absorber was mounted in a diamond anvil cell with an effective diameter of 0.21 mm. The source used was Mg₃ ^129mTeO₆. Experiments were performed mainly at 4 K and the pressure was monitored by the ruby fluorescence method. With increasing pressure we observe a gradual decrease in ¦e²qQ¦ and an increase in IS and values of the low pressure, molecular phase; at 16 GPa a new phase (HP1) is detected characterized by a change in sign of e²qQ and a smaller value of ¦e²qQ¦, and a substantial increase in . At 24 GPa a new phase (HP2) is formed that is characterized by a smaller value of . In general the population of the molecular phase decreases from 1.0 near 15 GPa to a value of 0.4 at 30 GPa. The fraction of the high pressure phase (HP1 + HP2) increases at the expense of the molecular phase and that of the HP2 at the expense of the HP1 phase. These observations are discussed in relation to the onset of a metallic phase near 16 GPa and recent x-ray diffraction studies.Work performed under the auspices of the U.S. Department of Energy.     

Real-space renormalization group for two-dimensional quantum spin systems

A generalization of the Niemeijer and Van Leeuwen real-space renormalization group method for quantum lattice spin systems is presented. A proposed rotationally invariant transformation which preserves the symmetry of the spin space is applied to several quantum systems on a triangular lattice. For the spin-1/2XY-model in both first- and second-order cumulant expansions a nontrivial fixed point exists, giving in the best approximation a critical interactionK _XY ^c =0.453 and critical exponent =1.65. A method of the reduction of the generalized arbitrary spin anisotropic Heisenberg model to the spin-half model is presented.