Rigid ball-polyhedra in Euclidean 3-space

A ball-polyhedron is the intersection with non-empty interior of finitely many (closed) unit balls in Euclidean 3-space. One can represent the boundary of a ball-polyhedron as the union of vertices, edges, and faces defined in a rather natural way. A ball-polyhedron is called a simple ball-polyhedron if at every vertex exactly three edges meet. Moreover, a ball-polyhedron is called a standard ball-polyhedron if its vertex-edge-face structure is a lattice (with respect to containment). To each edge of a ball-polyhedron one can assign an inner dihedral angle and say that the given ball-polyhedron is locally rigid with respect to its inner dihedral angles if the vertex-edge-face structure of the ball-polyhedron and its inner dihedral angles determine the ball-polyhedron up to congruence locally. The main result of this paper is a Cauchy-type rigidity theorem for ball-polyhedra stating that any simple and standard ball-polyhedron is locally rigid with respect to its inner dihedral angles.Comment: 11 pages, 2 figure

On Form Factors in nested Bethe Ansatz systems

We investigate form factors of local operators in the multi-component Quantum Non-linear Schr\"odinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and we establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the "magnonic form factors", which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity) we obtain explicit solutions for the recursion relations.Comment: 34 pages, v2 (minor modifications

The role of temperature on the germination activity of leguminous crops exposed to saline conditions

Germination is an important starting point of plant life. Abiotic stresses during the germination stage in seeds can threaten the development process of a plant species. Abiotic factors such as temperature and salt concentration influence the germination process of various crop seeds, including leguminous species. The aim of this study is to determine the germination rate and seedling growth of leguminous cover crops under two different temperatures and four levels of salt stress. Alfalfa (Medicago sativa), red clover (Trifolium pratense), and chickpea (Cicer arietinum) were studied in this in vitro trial. The study results showed that the increase in sodium chloride (NaCl) concentration suppressed the growth of the germinated seedlings. At the same time, the increase in temperature reduced the germination rate of red clover and chickpea at higher salt concentrations. The data also showed a significant relationship between salt concentration and temperature on shoot and radicle growth in all three leguminous species. These data may benefit farmers and growers trying to cultivate these crops in unfavorable conditions

Agronomic benefits of long term trials

Long term trials have been established in favour of exploring and observing plant and soil interrelations on site. We may determine long term trials as live instruments providing ceteris paribus conditions in temporal sequences. This review is dealing with the introduction to major long term trials in the World and in Hungary. Giving a brief summary on plant nutritional research roots beginning with some data from Homer, and the fabulous initial willow tree experiment of van Helmont, as well as the basic inventions of physiological processes by von Liebig, Lawes and Boussingault. The most profound long term trials like Padova’s Orto Botanico, the Linné Garden of Uppsala and the Broadbalk of Rothamsted are presented in the lecture. Agronomic, educational and scientific benefits of the major Hungarian long term trials are also discussed from Westsik 1929 via Maronvásár and the National Plant Nutrition Trials (OMTK) founded in 1963. There is a list of experimental sites giving information on the most important recent long term trial locations and the activities

Nanographenes: Ultrastable, Switchable, and Bright Probes for Super-Resolution Microscopy

Super-resolution fluorescence microscopyh as enabled important breakthroughs in biology and materials science.Implementations such as single-molecule localization microscopy(SMLM) and minimal emission fluxes (MINFLUX) microscopyinthe localization mode exploit fluorophores that blink, i.e., switch on and off,stochastically.Here, weintroducenanographenes,namelylargepolycyclicaromatic hydrocarbons that can also be regarded as atomically precise graphene quantum dots,asanew class of fluorophores for super-resolution fluorescence microscopy. Nanographenes exhibit outstanding photophysical properties:intrinsic blinking even in air,excellent fluorescence recovery,and stability over several months.Asaproof of concept for super-resolution applications,weuse nanographenes in SMLM to generate 3D super-resolution images of silica nanocracks.O ur findings open the door for the widespread application of nanographenes in super-resolution fluorescence microscopy

Order of current variance and diffusivity in the rate one totally asymmetric zero range process

We prove that the variance of the current across a characteristic is of order t^{2/3} in a stationary constant rate totally asymmetric zero range process, and that the diffusivity has order t^{1/3}. This is a step towards proving universality of this scaling behavior in the class of one-dimensional interacting systems with one conserved quantity and concave hydrodynamic flux. The proof proceeds via couplings to show the corresponding moment bounds for a second class particle. We build on the methods developed by Balazs-Seppalainen for asymmetric simple exclusion. However, some modifications were needed to handle the larger state space. Our results translate into t^{2/3}-order of variance of the tagged particle on the characteristics of totally asymmetric simple exclusion.Comment: 23 pages; some minor typos correcte