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We present a derivation of the numerical phenomenon that differences between the Riemann zeta function's nontrivial zeros tend to avoid being equal to the imaginary parts of the zeros themselves, a property called statistical "repulsion" between the zeros and their differences. Our derivation relies on the statistical properties of the prime zeta function, whose singularity structure specifies the positions of the Riemann zeros. We show that the prime zeta function on the critical line is asymptotically normally distributed with a covariance function that is closely approximated by the logarithm of the Riemann zeta function's magnitude on the 1-line. This creates notable negative covariance at separations approximately equal to the imaginary parts of the Riemann zeros. This covariance function and the singularity structure of the prime zeta function combine to create a conditional statistical bias at the locations of the Riemann zeros that predicts the zero-difference repulsion effect. Our method readily generalizes to describe similar effects in the zeros of related L-functions., Comment: Fixed more typos and minor corrections

Direct Statistical Simulation (DSS) solves the equations of motion for the statistics of turbulent flows in place of the traditional route of accumulating statistics by Direct Numerical Simulation (DNS). That low-order statistics usually evolve slowly compared with instantaneous dynamics is one important advantage of DSS. Depending on the symmetry of the problem and the choice of averaging operation, however, DSS is usually more expensive computationally than DNS because even low order statistics typically have higher dimension than the underlying fields. Here we show that it is possible to go much further by using Proper Orthogonal Decomposition (POD) to address the "curse of dimensionality." We apply POD directly to DSS in the form of expansions in the equal-time cumulants to second order (CE2). We explore two averaging operations (zonal and ensemble) and test the approach on two idealized barotropic models on a rotating sphere (a jet that relaxes deterministically towards an unstable profile, and a stochastically-driven flow that spontaneously organizes into jets). Order-of-magnitude savings in computational cost are obtained in the reduced basis, potentially enabling access to parameter regimes beyond the reach of DNS., Comment: 17 pages and 11 figures. Corrections, improved figures, and new section on "Continuation in Parameter Space."

We investigate the Fokker-Planck description of the equal-time statistics of the three-dimensional Lorenz-63 attractor with additive white noise. The invariant measure is found by computing the zero (or null) mode of the linear Fokker-Planck operator as a problem of sparse linear algebra. Two variants are studied: A self-adjoint construction of the linear operator, and the replacement of diffusion with hyperdiffusion. We also access the low-order statistics of the system by a perturbative expansion in equal-time cumulants. Comparison is made to statistics obtained by the standard approach of accumulation via direct numerical simulation. Theoretical and computational aspects of the Fokker-Planck and cumulant expansion methods are discussed., Comment: 13 pages, 6 figures. A typo corrected and larger axes numbers. To appear in Physical Review E

This marketing research project was undertaken to provide the International Institute of the University of Dallas with information regarding the career perception of foreign language majors for its use in recruitment for the International Management Program. Students from Arkansas, Louisiana, Oklahoma, and Texas were included in the study. Primary data were collected by mailing 590 questionnaires to Foreign Language Department Chairmen for distribution to foreign language majors. A total of 249 replies were received, representing a return rate of 45.4 percent. Secondary data were collected from various government, language association, and career placement association publications. The following were among the conclusions drawn from the data: (1) The potential market of foreign language majors for recruitment into an International Management Program is predominantly female, 78 percent versus 22 percent male. (2) More than 80 percent of the respondents indicated that career objective was an important consideration in the decision to pursue a foreign language major. (3) Female respondents appear to assign a higher preference to business (rank 4th) than do the male respondents (rank 5th). (4) Females perceive their chances for a business career to be less than their preference. (5) Males appear to prefer teaching, government, or graduate study. (6) Seventy-five percent of the respondents indicated some level of interest in an MBA program. (Author/KM)