On higher genus Weierstrass sigma-function

The goal of this paper is to propose a new way to generalize the Weierstrass sigma-function to higher genus Riemann surfaces. Our definition of the odd higher genus sigma-function is based on a generalization of the classical representation of the elliptic sigma-function via Jacobi theta-function. Namely, the odd higher genus sigma-function $\sigma_{\chi}(u)$ (for u\in \C^g) is defined as a product of the theta-function with odd half-integer characteristic $\beta^{\chi}$, associated with a spin line bundle $\chi$, an exponent of a certain bilinear form, the determinant of a period matrix and a power of the product of all even theta-constants which are non-vanishing on a given Riemann surface. We also define an even sigma-function corresponding to an arbitrary even spin structure. Even sigma-functions are constructed as a straightforward analog of a classical formula relating even and odd sigma-functions. In higher genus the even sigma-functions are well-defined on the moduli space of Riemann surfaces outside of a subspace defined by vanishing of the corresponding even theta-constant.Comment: to be published in Physica

Economic structure, productivity, and infrastructure quality in southern Mexico

There are large and sustained differences in the economic performance of sub-national regions in most countries. The authors examine the economic structure and productivity in Southern Mexico and compare it with the rest of the country. The authors use firm level data from Mexican manufacturing to test the relative importance of firm level characteristics (such as human capital and technology adoption) compared with external characteristics (such as infrastructure quality and regulatory environment) in explaining productivity differentials. The authors find that the economic structure of Southern Mexico is considerably different from the rest of the country, with the economic landscape dominated by micro enterprises and a relative specialization in low productivity activities. This, coupled with low skill levels and fewer skill upgrading opportunities, reduces the performance of Southern firms. Productivity differentials between Southern firms and others, however, only exist for micro enterprises. The econometric analysis shows that while employee training and technology adoption enhance productivity, access to markets by improving transport infrastructure that link urban areas also have important productivity effects.Labor Policies,Economic Theory&Research,Municipal Financial Management,Environmental Economics&Policies,Banks&Banking Reform,Environmental Economics&Policies,Economic Theory&Research,Banks&Banking Reform,Municipal Financial Management,Microfinance

Functional representation of the Volterra hierarchy

In this paper I study the functional representation of the Volterra hierarchy (VH). Using the Miwa's shifts I rewrite the infinite set of Volterra equations as one functional equation. This result is used to derive a formal solution of the associated linear problem, a generating function for the conservation laws and to obtain a new form of the Miura and Backlund transformations. I also discuss some relations between the VH and KP hierarchy.Comment: 17 pages, submitted to Journal of Nonlinear Mathematical Physic

Mitochondrial DNA and temperature tolerance in lager yeasts

A growing body of research suggests that the mitochondrial genome (mtDNA) is important for temperature adaptation. In the yeast genus Saccharomyces, species have diverged in temperature tolerance, driving their use in high- or low-temperature fermentations. Here, we experimentally test the role of mtDNA in temperature tolerance in synthetic and industrial hybrids (Saccharomyces cerevisiae × Saccharomyces eubayanus or Saccharomyces pastorianus), which cold-brew lager beer. We find that the relative temperature tolerances of hybrids correspond to the parent donating mtDNA, allowing us to modulate lager strain temperature preferences. The strong influence of mitotype on the temperature tolerance of otherwise identical hybrid strains provides support for the mitochondrial climactic adaptation hypothesis in yeasts and demonstrates how mitotype has influenced the world’s most commonly fermented beverage.This work was supported by the USDA National Institute of Food and Agriculture (Hatch project no. 1003258), the NSF (grant no. DEB-1253634), and in part by the DOE Great Lakes Bioenergy Research Center (DOE BER Office of Science; nos. DE-SC0018409 and DE-FC02-07ER64494). E.P.B. was supported by a Louis and Elsa Thomsen Wisconsin Distinguished Graduate Fellowship. C.T.H. is a Pew Scholar in the Biomedical Sciences and a Vilas Faculty Early Career Investigator, supported by the Pew Charitable Trusts and the Vilas Trust Estate. D.P. is a Marie Sklodowska-Curie fellow of the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 747775). J.C.F. was supported by the NIH (no. GM080669)Peer Reviewe

Effect of Soil Chemistry on Microbial Biodiversity and Functionality in Grassland and Tilled Soils

Microorganisms are excellent indicators of soil health, because of their rapid response to environmental change. Traditional microbiology is ineffective for the study of soil, as \u3c 1% of microorganisms are currently culturable (Torsvik et al., 1996). Nucleic acid based methods, however, allow rapid detection of organisms, or particular genes, directly from soil samples. This work investigated, using polymerase chain reaction (PCR)-based approaches, the relationship between key chemical properties and bacterial biodiversity in grassland and tilled soils, with particular emphasis on the abundance and diversity of ammonium oxidisers

Dirt Road Corrugations

WE CONSIDER FACTORS INFLUENCING the build-up of corrugations on dirt roads and the reactions of vehicles to them. We suggest that corrugations are (at least in part) a consequence of a natural tangential oscillation of the tread surface of the car lure that occurs when the vehicle is being driven or braked. Secondly, we suggest that the unpleasant vibration experienced by a vehicle passing over a corrugated road is the result of a beat produced by the difference of the frequency of oscillation of its own tyres and the frequency of the stimulation received by the vehicle due to passage over a corrugated road. We consider how this is affected by actions that the driver can take and conclude with some recommendations and observations of related effects

Benchmarking of 3D space charge codes using direct phase space measurements from photoemission high voltage DC gun

We present a comparison between space charge calculations and direct measurements of the transverse phase space for space charge dominated electron bunches after a high voltage photoemission DC gun followed by an emittance compensation solenoid magnet. The measurements were performed using a double-slit setup for a set of parameters such as charge per bunch and the solenoid current. The data is compared with detailed simulations using 3D space charge codes GPT and Parmela3D with initial particle distributions created from the measured transverse and temporal laser profiles. Beam brightness as a function of beam fraction is calculated for the measured phase space maps and found to approach the theoretical maximum set by the thermal energy and accelerating field at the photocathode.Comment: 11 pages, 23 figures. submitted to Phys Rev ST-A

Notes on Euclidean Wilson loops and Riemann Theta functions

The AdS/CFT correspondence relates Wilson loops in N=4 SYM theory to minimal area surfaces in AdS5 space. In this paper we consider the case of Euclidean flat Wilson loops which are related to minimal area surfaces in Euclidean AdS3 space. Using known mathematical results for such minimal area surfaces we describe an infinite parameter family of analytic solutions for closed Wilson loops. The solutions are given in terms of Riemann theta functions and the validity of the equations of motion is proven based on the trisecant identity. The world-sheet has the topology of a disk and the renormalized area is written as a finite, one-dimensional contour integral over the world-sheet boundary. An example is discussed in detail with plots of the corresponding surfaces. Further, for each Wilson loops we explicitly construct a one parameter family of deformations that preserve the area. The parameter is the so called spectral parameter. Finally, for genus three we find a map between these Wilson loops and closed curves inside the Riemann surface.Comment: 35 pages, 7 figures, pdflatex. V2: References added. Typos corrected. Some points clarifie

Superconductivity in ferromagnetic metals and in compounds without inversion centre

The symmetry properties and the general overview of the superconductivity theory in the itinerant ferromagnets and in materials without space parity are presented. The basic notions of unconventional superconductivity are introduced in broad context of multiband superconductivity which is inherent property of ferromagnetic metals or metals without centre of inversion.Comment: 38 pages, no figure

Noether Symmetry of the Hyperextended Scalar Tensor theory for the FLRW models

We study in which conditions the Hyperextended Scalar Tensor theory in an FLRW background admits a Noether symmetry and derive the vectors field generating it.Comment: 11 page