Upper bounds for the diameter and height of graphs of convex polyhedra

Let Δ(d, n) be the maximum diameter of the graph of ad-dimensional polyhedronP withn-facets. It was conjectured by Hirsch in 1957 that Δ(d, n) depends linearly onn andd. However, all known upper bounds for Δ(d, n) were exponential ind. We prove a quasi-polynomial bound Δ(d, n)≤n ^{2 logd+3}. LetP be ad-dimensional polyhedron withn facets, let ϕ be a linear objective function which is bounded onP and letv be a vertex ofP. We prove that in the graph ofP there exists a monotone path leading fromv to a vertex with maximal ϕ-value whose length is at most . This research was supported in part by a BSF grant, by a GIF grant, and by ONR-N00014-91-C0026.     

Phase transitions in the tantalum-hydrogen system observed by PAC

The perturbation felt by¹⁸¹Hf probes in a¹⁸¹HfTa lattice loaded with 30 at% hydrogen was observed by PAC as a function of temperature. Three different interactions were identified: 1) Ν_Q1=433 (6) MHz, η=0.45 2) Ν_Q2=142 (9) MHz, η=0.9, and 3) Ν_Q?0, σ=4–14 Μ^?1 which are attributed to the Β^?, ε^? and α-phase in TaH system, respectively.     

ZnO–SnO2 branch–stem nanowires based on a two-step process: Synthesis and sensing capability

ZnO–SnO₂ branch–stem nanostructures were realized on a basis of a two-step process. In step 1, SnO₂-stem nanowires were synthesized. In step 2, ZnO-branch nanowires were successfully grown on the SnO₂-stem nanowires through a simple evaporation technique. We have pre-deposited thin Au layers on the surface of SnO₂ nanowire stems and subsequently evaporated Zn powders on the nanowires. The ZnO branches, which sprouted from the SnO₂ stems, had diameters in a range of 30–35 nm. As-synthesized branches were of single crystalline hexagonal ZnO structures. Since the branch tips were comprised of Au-containing nanoparticles, the Au-catalyzed vapor–liquid–solid growth mechanism was more likely to control the growth process of the ZnO branches. To test a potential use of ZnO–SnO₂ branch–stem nanostructures in chemical gas sensors, their sensing performances with respect to NO₂ gas were investigated, showing the promising potential in chemical gas sensors.     

New asymptotic representations of the noncentral t-distribution

New asymptotic approximations of the noncentral t distribution are given a generalization of the Student's t distribution. Using new integral representations, we give new asymptotic expansions not only for large values of the noncentrality parameter but also for large values of the degrees of freedom parameter. In some cases, we accept more than one large parameter. These results are not only in terms of elementary functions, but also in terms of the complementary error function and the incomplete gamma function. A number of numerical tests demonstrate the performance of the asymptotic approximations.     

Quantum mechanics without the projection postulate

I show that the quantum state can be interpreted as defining a probability measure on a subalgebra of the algebra of projection operators that is not fixed (as in classical statistical mechanics) but changes with and appropriate boundary conditions, hence with the dynamics of the theory. This subalgebra, while not embeddable into a Boolean algebra, will always admit two-valued homomorphisms, which correspond to the different possible ways in which a set of determinate quantities (selected by and the boundary conditions) can have values. The probabilities defined by (via the Born rule) are probabilities over these two-valued homomorphisms or value assignments. So any universe of interacting systems, including those functioning as measuring instruments, can be modelled quantum mechanically without the projection postulate.     

Life prediction of thermally cracked railway wheels: Growth estimation of cracks with arbitrary shape

A computer program for railway wheel life prediction has been developed incorporating an elastoplastic calculation of both the residual stress field induced by shoe-braking and the superposed alternating rolling contact stresses. The possibilities of unstable propagation of surface cracks, crack arrest, fatigue propagation through a complex stress field and crack detention on reaching the threshold value have been accounted for. An approximate method for crack growth prediction is used providing bounds for instantaneous crack front position and estimations of crack shape within short computing times. Some examples of application for an UIC R7 wheel are presented.     

Antiferromagnetic Resonance in GdB<Subscript>6</Subscript>

The electron spin resonance has been measured for the first time both in the paramagnetic phase of the metallic GdB₆ antiferromagnet (T_N = 15.5K) and in the antiferromagnetic state (T < T_N). In the paramagnetic phase below T* ~ 70 K, the material is found to exhibit a pronounced increase in the resonance linewidth and a shift in the g-factor, which is proportional to the linewidth Δg(T) ~ ΔH(T). Such behavior is not characteristic of antiferromagnetic metals and seems to be due to the effects related to displacements of Gd³⁺ ions from the centrosymmetric positions in the boron cage. The transition to the antiferromagnetic phase is accompanied by an abrupt change in the position of resonance (from μ₀H₀ ≈ 1.9 T to μ₀H₀ ≈ 3.9 T at ν = 60 GHz), after which a smooth evolution of the spectrum occurs, resulting eventually in the formation of the spectrum consisting of four resonance lines. The magnetic field dependence of the frequency of the resonant modes ω₀(H₀) obtained in the range of 28–69 GHz is well interpreted within the model of ESR in an antiferromagnet with the easy anisotropy axis ω/γ = (H ₀ ² +2H_AH_E)^1/2, where H_E is the exchange field and H_A is the anisotropy field. This provides an estimate for the anisotropy field, H_A ≈ 800 Oe. This value can result from the dipole?dipole interaction related to the mutual displacement of Gd³⁺ ions, which occurs at the antiferromagnetic transition.