Productivity Divergence across Kansas Farms

This study used 30 years of continuous data for 135 farms in Kansas to explore changes in productivity using Malmquist productivity indices (MPI). The indices were used to determine whether there was productivity convergence or divergence in Kansas farms. The results showed there was significant divergence among the farms. The average annual productivity growth was 0.50 percent; the top farms based on MPI were larger in terms of value of farm production, crop farm income, and livestock farm income and received a larger percentage of their income from oilseeds, feed grains, and swine than the other farms on average.convergence, divergence, productivity growth, Production Economics, Productivity Analysis,

Productivity Divergence Across Kansas Farms

This study used 30 years of continuous data for 135 farms in Kansas to explore changes in productivity using Malmquist productivity indices. The indices were used to determine whether there was productivity convergence or divergence in Kansas farms. The results showed that there was significant divergence among the farms and not a tendency for farms to catch-up to the same levels of productivity as the top farms in the sample. The average annual productivity growth over the sample period, 1979-2008, was 0.50 percent. The top farms based on MPI were larger in terms of value of farm production, crop farm income and livestock farm income and received a larger percentage of their income from oilseeds, feed grains, and swine than the other farms on average and relatively less of their income from small grains.Farm Management, Production Economics, Productivity Analysis,

Purification and electron cryomicroscopy of coronavirus particles.

Intact, enveloped coronavirus particles vary widely in size and contour, and are thus refractory to study by traditional structural means such as X-ray crystallography. Electron microscopy (EM) overcomes some problems associated with particle variability and has been an important tool for investigating coronavirus ultrastructure. However, EM sample preparation requires that the specimen be dried onto a carbon support film before imaging, collapsing internal particle structure in the case of coronaviruses. Moreover, conventional EM achieves image contrast by immersing the specimen briefly in heavy-metal-containing stain, which reveals some features while obscuring others. Electron cryomicroscopy (cryo-EM) instead employs a porous support film, to which the specimen is adsorbed and flash-frozen. Specimens preserved in vitreous ice over holes in the support film can then be imaged without additional staining. Cryo-EM, coupled with single-particle image analysis techniques, makes it possible to examine the size, structure and arrangement of coronavirus structural components in fully hydrated, native virions. Two virus purification procedures are described

Zeros of Random Orthogonal Polynomials

Let $\{f_j\}$ be a sequence of orthonormal polynomials where the orthogonality relation is satisfied on either the real line (OPRL) or on the unit circle (OPUC). We study zero distribution of random linear combinations of the form$$P_n(z)=\sum_{j=0}^n\eta_jf_j(z),$$where $\{\eta_j\}$ are random variables. We give quantitative estimates on the zeros accumulating on the unit circle for a wide class of random polynomials $P_n$. When the coefficients $\{\eta_j\}$ are independent identically distributed (i.i.d.) real-valued standard Gaussian, we give asymptotics for the expected number of zeros of various classes of random sums $P_n$ spanned by OPUC. For the case when the coefficients $\{\eta_j\}$ are i.i.d.~complex-valued standard Gaussian coefficients, we derive a formula for the expected number of zeros of $P_n$. The formula is then applied to give asymptotics of the expected number of zeros of $P_n$ when $\{f_j\}$ are from the Nevai class. We also compute the limiting value as $n\rightarrow \infty$ of the variance of the number of zeros of $P_n$ in annuli that do not contain the unit circle for the case when $\{\eta_j\}$ are i.i.d.~complex-valued standard Gaussian random variables, and $\{f_j\}$ are OPUC from the Nevai class. In the case of annuli that contain the unit circle, for a wide class of random variables $\{\eta_j\}$ and $\{f_j\}$ that are OPUC, we give quantitative results that show the variance of the number of zeros of $P_n$ scaled by $n^2$ tends to zero as $n$ tends to infinity. The work is concluded by providing formulas for the variance of the number of zeros of a random orthogonal power series, specifically when $\sum_{j=0}^{\infty}\eta_j f_j(z)$, with $\{\eta_j\}$ being i.i.d.~complex-valued standard Gaussian, and $\{f_j\}$ are OPUC from the Szeg\H{o} class