Poisson limit theorems for the Robinson-Schensted correspondence and for the multi-line Hammersley process

We consider Robinson-Schensted-Knuth algorithm applied to a random input and study the growth of the bottom rows of the corresponding Young diagrams. We prove multidimensional Poisson limit theorem for the resulting Plancherel growth process. In this way we extend the result of Aldous and Diaconis to more than just one row. This result can be interpreted as convergence of the multi-line Hammersley process to its stationary distribution which is given by a collection of independent Poisson point processes.Comment: version 2: 41 pages, the proofs are now more detaile

Deformed Galilei symmetry

A particular deformation of central extended Galilei group is considered. It is shown that the deformation influences the rules of constructing the composed systems while one particle states remain basically unaffected. In particular the mass appeared to be non additive.Comment: 14 pages LaTeX2e fil

Limit shapes of evacuation and jeu de taquin paths in random square tableaux

We consider large random square Young tableaux and look for typical (in the sense of probability) jeu de taquin paths and evacuation paths in the asymptotic setting. We show that the probability distribution of such paths converges to a random meridian connecting the opposite corners of the square.Comment: 12 pages. Extended abstract of FPSAC 2020 conference. A full version of this extended abstract will be available soon as a separate pape

Chiral fermions, massless particles and Poincare covariance

The coadjoint orbit method is applied to the construction of Hamiltonian dynamics of massless particles of arbitrary helicity. The unusual transformation properties of canonical variables are interpreted in terms of nonlinear realizations of Poincare group. The action principle is formulated in terms of new space–time variables with standard transformation properties.Piotr Kosi´nski gratefully acknowledges fruitful discussion and kind correspondence with P.Horvathy and J.Lukierski.The re-search was supported by the grant of National Science Centrenum-ber DEC-2013/09/B/ST2/02205

Depurification by Lorentz boosts

We consider a particle of half-integer spin which is nonrelativistic in the rest frame. Assuming the particle is completely polarized along third axis we calculate the Bloch vector as seen by a moving observer. The result for its length is expressed in terms of dispersion of some vector operator linear in momentum. The relation with the localization properties is discussed.Comment: 5 page

Crystal structure of sparteinium tetrachlorocuprate monohydrate‑packing polymorph

A new polymorph of sparteinium tetrachlorocuprate monohydrate [(C15H28N2)CuCl4·H2O] is reported. The structure of the analyzed crystal was solved in the orthorhombic P212121 space group with the following unit cell parameters at 295 K: a = 9.7722(2) Å; b = 13.4582(3) Å; c = 15.1582(3) Å. The various types of hydrogen bonding interactions existing in the crystal structure of this salt were compared with the data of the previously reported polymorph. XRPD measurement proved that our salt consists of a pure phase of the new polymorph. Cooling down the salt to ca. 230 K caused its color to change from orange-brown to yellow. DSC experiments revealed that during the cooling an endothermic process takes place corresponding to the mentioned color change of the salt

A note on the action-angle variables for the rational Calogero-Moser system

A relationship between the action-angle variables and the canonical transformation relating the rational Calogero-Moser system to the free one is discussed.Comment: 6 pages, LaTeX. Acknowledgments are slightly altere

Ethylene glycol ethers induce oxidative stress in the rat brain

Ethylene glycol ethers (EGEs) are components of many industrial and household products. Their hemolytic and gonadotoxic effects are relatively well known while their potential adverse effects on the central nervous system have not yet been clearly demonstrated. The aim of the present study was to examine the effects of 4-week administration of 2-buthoxyethanol (BE), 2-phenoxyethanol (PHE) and 2-ethoxyethanol (EE) on the total antioxidant capacity, activity of some antioxidant enzymes, such as the superoxide dismutase (SOD), catalase, glutathione peroxidase (GPX) and glutathione reductase and lipid peroxidation in the frontal cortex and hippocampus in the rat. These studies showed that BE and PHE decreased the total antioxidant activity, SOD and GPX activity, while increased lipid peroxidation in the frontal cortex. Like in the frontal cortex, also in the hippocampus BE and PHE attenuated the total antioxidant activity, however, lipid peroxidation was increased only in animals which received BE while reduction in GPX activity was present in rats administered PHE. The obtained data indicated that 4-week administration of BE and PHE, but not EE, reduced the total antioxidant activity and enhanced lipid peroxidation in the brain. In the frontal cortex, adverse effects of PHE and BE on lipid peroxidation probably depended on reduction in SOD and GPX activity, however, in the hippocampus the changes in the total antioxidant activity and lipid peroxidation were not connected with reduction of the investigated antioxidant enzyme activity

The Carbon Footprint Methodology in CFOOD Project

In the paper, the research on the process of optimizing the carbon footprint to obtain the low-carbon products is presented. The optimization process and limits were analyzed based on the CFOOD project co-financed by the Polish Research and Development Agency. In the article, the carbon footprint (CF) testing methods with particular emphasis on product life cycle assessment (LCA) are discussed. The main problem is that the energy received from the energy-meters per the production stage is not directly represented in the raw data set obtained from the factory because many production line machines are connected to a single measurement point. In the paper, we show that in some energy-demanding production stages connected with cooling processes the energy used for the same stage and similar production can differ even 25-40%. That is why the energy optimization in the production can be very demandin

Changes in spino-pelvic alignment after surgical treatment of isthmic spondylolisthesis

Background and purpose To analyze the changes in spino-pelvic parameters after surgical treatment of lumbar isthmic spondylolisthesis. Materials and methods Sixty patients recruited from a group of consecutive series of 128 cases with isthmic spondylolisthesis operated on between 2002 and 2012 in the Department of Neurosurgery, Tarnow, Poland. All patients were operated on by the same surgeon (the first author). Spino-pelvic parameters: PI, SS, PT, LSA, and LL were measured manually on standing lateral view radiograms. Patients were divided according to Spinal Deformity Study Group classification which we modified for means of analysis: (A) low-grade group: subgroups with balanced pelvis and unbalanced pelvis (instead of normal and high PI subgroups), (B) high-grade group: subgroups with balanced and unbalanced pelvis. Results Twenty-nine patients had unbalanced pelvis before the operation. In 10 of them (34%), the procedure resulted in full correction of pelvis position meaning that they achieved balanced pelvis after the surgery. There were 6 patients with low-grade slip who had balanced pelvis preoperatively but showed unbalanced pelvis after the surgery but this loss of balanced pelvis did not affect the clinical outcome which overall was good among them. Patients with unbalanced pelvis presented changes towards restoration of spino-sacro-pelvic anatomy postoperatively: PT decreased while SS increased, although these changes were not statistically significant. Conclusion Further studies are needed to confirm whether surgical correction of spino-pelvic parameters results in better clinical outcome in patients with isthmic spondylolisthesis