The unsatisfiability threshold revisited

The problem of determining the unsatisfiability threshold for random 3-SAT formulas consists in determining the clause to variable ratio that marks the experimentally observed abrupt change from almost surely satisfiable formulas to almost surely unsatisfiable. Up to now, there have been rigorously established increasingly better lower and upper bounds to the actual threshold value. In this paper, we consider the problem of bounding the threshold value from above using methods that, we believe, are of interest on their own right. More specifically, we show how the method of local maximum satisfying truth assignments can be combined with results for the occupancy problem in schemes of random allocation of balls into bins in order to achieve an upper bound for the unsatisfiability threshold less than 4.571. In order to obtain this value, we establish a bound on the q-binomial coefficients (a generalization of the binomial coefficients). No such bound was previously known, despite the extensive literature on q-binomial coefficients. Finally, to prove our result we had to establish certain relations among the conditional probabilities of an event in various probabilistic models for random formulas. It turned out that these relations were considerably harder to prove than the corresponding ones for unconditional probabilities, which were previously known.     

Creation of entangled states of excitons in coupled quantum dots

We present two methods for the creation of two-particle entangled states of excitons in a coupled quantum dot system. The system contains two identical quantum dots that are coupled by an inter-dot hopping process. The manipulation of the system is succeeded by proper application of an external laser field.     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

1.2 Anorganische analyse

Ohne Zusammenfassung     

Isobar separation at FRS-ESR – a development towards pure isomeric stored beams

One important goal of the ILIMA project at FAIR is the study of masses and decay properties of relativistic isomeric beams stored and cooled in the planned storage-ring complex. A new scheme is described, where a storage-cooler ring is used for high-resolution mass separation. Experimental results on the separation of the isobaric pair ¹⁴⁰Pr-¹⁴⁰Ce are presented. P. Beller, deceased.     

L1-optimal estimates for a regression type function in R

Let X₁, X₂, …, X_n be random vectors that take values in a compact set in R^d, d ≥ 1. Let Y₁, Y₂, …, Y_n be random variables (“the responses”) which conditionally on X₁ = x₁, …, X_n = x_n are independent with densities f(y | x_i, θ(x_i)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θ_q,d of real valued functions, an optimal L₁-consistent estimator of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θ_q,d.     

On-line nuclear orientation study of184Au

The¹⁸⁴Au→¹⁸⁴Pt decay, studied on-line with the UNISOR facility at HHIRF, is discussed. Gamma-ray and conversion-electron spectroscopy of¹⁸⁴Pt as well as on-line nuclear orientation measurements of¹⁸⁴Au were done. A new low-lying level scheme of¹⁸⁴Pt is proposed. Two coexisting bands with different deformations and their respective γ-vibrational bands are established. Internal conversion coefficients for interband transitions between states with the same spin are extracted from the spectroscopy measurements. The relative E0 contents of the transitions are determined by combining internal conversion coefficients with E2/M1 mixing ratios deduced from gamma-ray anisotropies measured from oriented nuclei.     

Coercivity analysis in R17Fe83−χBχ magnets

We studied the coercivity in magnets of composition R₁₇Fe_83−χB_χ (R = Nd, Pr and χ = 8, 30), using measurements of the coercive field H_c, its angular dependence, and the magnetic viscosity coefficient S_v, for temperatures between 4.2 and 500 K. The results are discussed in relation to a model which does not specifically consider the detailed mechanisms involved in magnetization reversal, but which provides information about the magnetic properties in the activation volume v where magnetization reversal is initiated. It is concluded that the ordering temperature in v tends to be slightly smaller than in the bulk and that the room temperature anisotropy in v is not strongly reduced with respect to the bulk value. Finally, a direct evaluation of the dipolar interactions is in good agreement with results obtained from H_c(T).     

Assignments of methanol laser lines by frequency measurements and Fourier transform spectroscopy

We have measured the frequencies of four CH₃OH far-infrared laser lines that were previously known only by wavelength measurement. Two of these lines turned out to be doublets, bringing the total number of measured lines to six. We can now confirm the assignments of five of them and definitely disprove the assignments proposed for the sixth.In particular we confirm the assignments for the four strong laser lines at 205 and 208 µm pumped by the 9-P(34) CO₂ laser line. These lines share a common upper level in the first excited CO-stretch state, and terminate in the upper and lower levels of a hybrid state with J=5. Heterodyne frequency measurements and conventional microwave spectroscopy show that both lines are split into two components approximately 3.5 MHz apart. The origin of this further splitting is interpreted as a perturbed K-splitting.Work supported by Consiglio Nazionale delle Ricerche -Italia     

Taylor-Galerkin algorithms for viscoelastic flow: Application to a model problem

Coupled and decoupled Taylor-Galerkin algorithms are considered for viscoelastic flow and a model problem—transient startup Poiseuille flow in a channel under a fixed pressure gradient. All algorithms reproduce the steady-state solutions and are stable at high elasticity numbers (E). For a fixed mesh, the coupled and decoupled versions (TGC and TGD) give exceptional time-accuracy at low elasticity numbers [to within O(1%) at E = 1] and reasonable accuracy at high elasticity numbers [to within O(10%) at E = 10, 100]. By definition, the decoupled false-transient scheme (TGF), which uses different time scales for velocity and stress time stepping, provides a poor transient history. Where the main requirement is to compute a steady-state algorithm efficiency is crucial. The TGF scheme attains a steady state between six to eight times faster than does the TGC scheme, and the latter is over twice as fast as the TGD form. © 1994 John Wiley & Sons, Inc.