Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

Effect of high hydrostatic pressure treatments on volatiles of berry purées

High hydrostatic pressure (HHP) technology, as a promising alternative of thermal-treatment and chemical preservatives, can be used to produce minimally processed foods. It has the advantage of affecting only non-covalent bonds of macromolecules in foods, and thus preserves nutritional components, taste, and flavour exceptionally well. However, HHP also influences enzymatic reactions of food. Although some of these changes are often beneficial, monitoring the potential effects of high pressure treatments — especially in the field of product and technology development — is essential. The aim of this study was to point out some parameters of high hydrostatic pressure technique (pressure, temperature, build-up time, holding time, number of cycles) that can substantially impact the sensory properties of treated products

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

The TQ equation of the 8 vertex model for complex elliptic roots of unity

We extend our studies of the TQ equation introduced by Baxter in his 1972 solution of the 8 vertex model with parameter $\eta$ given by $2L\eta=2m_1K+im_2K'$ from $m_2=0$ to the more general case of complex $\eta.$ We find that there are several different cases depending on the parity of $m_1$ and $m_2$.Comment: 30 pages, LATE

Robot Compatible Environment and Conditions

Service robot technology is progressing at a fast pace. Accurate robot-friendly indoor localization and harmonization of built environ-ment in alignment with digital, physical, and social environment becomes emphasized. This paper proposes the novel approach of Robot Compatible Environment (RCE) within the architectural space. Evolution of service robotics in connection with civil engineering and architecture is discussed, whereas optimum performance is to be achieved based on robots’ capabilities and spatial affordances. For ubiquitous and safe human-robot interaction, robots are to be integrated into the living environment. The aim of the research is to highlight solutions for various interconnected challenges within the built environment. Our goal is to reach findings on comparison of robotic and accessibility standards, synthesis of navigation, access to information and social acceptance. Checklists, recommendations, and design process are introduced within the RCE framework, proposing a holistic approach

Edwards-Wilkinson surface over a spherical substrate: 1/f1/f noise in the height fluctuations

We study the steady state fluctuations of an Edwards-Wilkinson type surface with the substrate taken to be a sphere. We show that the height fluctuations on circles at a given latitude has the effective action of a perfect Gaussian $1/f$ noise, just as in the case of fixed radius circles on an infinite planar substrate. The effective surface tension, which is the overall coefficient of the action, does not depend on the latitude angle of the circles.Comment: 6 page

Frictional coupling between sliding and spinning motion

We show that the friction force and torque, acting at a dry contact of two objects moving and rotating relative to each other, are inherently coupled. As a simple test system, a sliding and spinning disk on a horizontal flat surface is considered. We calculate, and also measure, how the disk is slowing down, and find that it always stops its sliding and spinning motion at the same moment. We discuss the impact of this coupling between friction force and torque on the physics of granular materials.Comment: 4 pages, 5 figures; submitte

Geodesic equations and algebro-geometric methods

For an investigation of the physical properties of gravitational fields the observation of massive test particles and light is very useful. The characteristic features of a given space-time may be decoded by studying the complete set of all possible geodesic motions. Such a thorough analysis can be accomplished most effectively by using analytical methods to solve the geodesic equation. In this contribution, the use of elliptic functions and their generalizations for solving the geodesic equation in a wide range of well known space-times, which are part of the general Pleba\'nski-Demia\'nski family of solutions, will be presented. In addition, the definition and calculation of observable effects like the perihelion shift will be presented and further applications of the presented methods will be outlined.Comment: 8 pages, no figures; based on presentation at the conference "Relativity and Gravitation: 100 Years after Einstein in Prague," Prague, 2012. Relativity and Gravitation, volume 157 of Springer Proceedings in Physics, p 91. Springer International Publishing, 201

On Further Generalization of the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon

A rigidity theorem that applies to smooth electrovac spacetimes which represent either (A) an asymptotically flat stationary black hole or (B) a cosmological spacetime with a compact Cauchy horizon ruled by closed null geodesics was given in a recent work \cite{frw}. Here we enlarge the framework of the corresponding investigations by allowing the presence of other type of matter fields. In the first part the matter fields are involved merely implicitly via the assumption that the dominant energy condition is satisfied. In the second part Einstein-Klein-Gordon (EKG), Einstein-[non-Abelian] Higgs (E[nA]H), Einstein-[Maxwell]-Yang-Mills-dilaton (E[M]YMd) and Einstein-Yang-Mills-Higgs (EYMH) systems are studied. The black hole event horizon or, respectively, the compact Cauchy horizon of the considered spacetimes is assumed to be a smooth non-degenerate null hypersurface. It is proven that there exists a Killing vector field in a one-sided neighborhood of the horizon in EKG, E[nA]H, E[M]YMd and EYMH spacetimes. This Killing vector field is normal to the horizon, moreover, the associated matter fields are also shown to be invariant with respect to it. The presented results provide generalizations of the rigidity theorems of Hawking (for case A) and of Moncrief and Isenberg (for case B) and, in turn, they strengthen the validity of both the black hole rigidity scenario and the strong cosmic censor conjecture of classical general relativity.Comment: 25 pages, LaTex, a shortened version, including a new proof for lemma 5.1, the additional case of Einstein-Yang-Mills-Higgs systems is also covered, to appear in Class. Quant. Gra