Cyclic projectors and separation theorems in idempotent convex geometry

Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold cartesian product of the max-plus semiring it is known that one can separate a vector from a closed subsemimodule that does not contain it. We establish here a more general separation theorem, which applies to any finite collection of closed semimodules with a trivial intersection. In order to prove this theorem, we investigate the spectral properties of certain nonlinear operators called here idempotent cyclic projectors. These are idempotent analogues of the cyclic nearest-point projections known in convex analysis. The spectrum of idempotent cyclic projectors is characterized in terms of a suitable extension of Hilbert's projective metric. We deduce as a corollary of our main results the idempotent analogue of Helly's theorem.Comment: 20 pages, 1 figur

Observation of Non-Exponential Orbital Electron Capture Decays of Hydrogen-Like 140^{140}Pr and 142^{142}Pm Ions

We report on time-modulated two-body weak decays observed in the orbital electron capture of hydrogen-like $^{140}$Pr$^{59+}$ and $^{142}$Pm$^{60+}$ ions coasting in an ion storage ring. Using non-destructive single ion, time-resolved Schottky mass spectrometry we found that the expected exponential decay is modulated in time with a modulation period of about 7 seconds for both systems. Tentatively this observation is attributed to the coherent superposition of finite mass eigenstates of the electron neutrinos from the weak decay into a two-body final state.Comment: 12 pages, 5 figure

Structural Alterations of Monocytes in Systemic Lupus Erythematosus

© 2017, Springer Science+Business Media, LLC. Systemic lupus erythematosus (SLE) is an autoimmune disease in which the immune system mistakenly attacks multiple organs and tissues of the body. To elucidate the involvement of blood cells in the pathogenesis of SLE, we used transmission electron microscopy to study ultrastructure of monocytes isolated from the blood of SLE patients. We found that in the SLE patients, a substantial fraction of monocytes had abnormal morphology that corresponded to the structural signs of either necrosis or apoptosis. The number of altered monocytes in the SLE patients was significantly higher than in healthy subjects and related directly with the level of anti-dsDNA autoantibodies in the blood. Our results suggest that monocytes are involved in the pathogenesis of SLE and undergo adverse necrotic and/or apoptotic changes, likely induced by autoantibodies

The stock optimization of automated warehouse

Automated warehouses play an important role in the functioning of production. One of the tasks of managing the warehouse system is to select the optimal size of the stock that is stored in the warehouse. In real production systems, certain delays are possible and common in the arrival of the next batch of goods of volume Q. Therefore, in the general case, the process of their receipt is random. One can compensate the deviations from the delivery schedule by introducing a safety stock of qstr, which allows organizing of the stable operation of the entire system

Application of the RMF mass model to the r-process and the influence of mass uncertainties

A new mass table calculated by the relativistic mean field approach with the state-dependent BCS method for the pairing correlation is applied for the first time to study r-process nucleosynthesis. The solar r-process abundance is well reproduced within a waiting-point approximation approach. Using an exponential fitting procedure to find the required astrophysical conditions, the influence of mass uncertainty is investigated. R-process calculations using the FRDM, ETFSI-Q and HFB-13 mass tables have been used for that purpose. It is found that the nuclear physical uncertainty can significantly influence the deduced astrophysical conditions for the r-process site. In addition, the influence of the shell closure and shape transition have been examined in detail in the r-process simulations.Comment: to be published in Phys. Rev. C, 22 pages, 9 figure

Ferromagnetism in magnetically doped III-V semiconductors

The origin of ferromagnetism in semimagnetic III-V materials is discussed. The indirect exchange interaction caused by virtual electron excitations from magnetic impurity level in the bandgap to the valence band can explain ferromagnetism in GaAs(Mn) no matter samples are degenerated or not. Formation of ferromagnetic clusters and percolation picture of phase transition describes well all available experimental data and allows to predict the Mn-composition dependence of transition temperature in wurtzite (Ga,In,Al)N epitaxial layers.Comment: 4 pages with 3 figure

Semiring and semimodule issues in MV-algebras

In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing the introduction and study of a suitable corresponding class of semimodules, called MV-semimodules. We present several results addressed toward a semiring theory for MV-algebras. In particular we show a representation of MV-algebras as a subsemiring of the endomorphism semiring of a semilattice, the construction of the Grothendieck group of a semiring and its functorial nature, and the effect of Mundici categorical equivalence between MV-algebras and lattice-ordered Abelian groups with a distinguished strong order unit upon the relationship between MV-semimodules and semimodules over idempotent semifields.Comment: This version contains some corrections to some results at the end of Section

Essential Dynamics of DNA-Antibody Complexes

© 2016, Springer Science+Business Media New York.Antibodies against double-stranded DNA play an important role in the pathogenesis of autoimmune diseases. Structural analysis of antibody-DNA complexes contributes to our understanding of the role of DNA-containing immune complexes in human pathologies and may help in designing novel treatments. In this paper, we study dynamics of the full-atomic structure of the molecular complexes formed by an antibody Fab fragment with double-stranded DNA, containing or not containing a thymine dimer. Molecular dynamics simulations are used in conjunction with the Principle Component Analysis technique. We found that removing a covalent bond from the thymine dimer results in changes of the structural dynamics of the light and heavy chains of Fab as well as in the DNA strands. A significant increase in mobility of the Fab light chain was observed throughout the entire simulation runs with a higher amplitude of fluctuations at the interface with DNA. Essential dynamics analysis of simulation trajectories of the antibody-dsDNA complexes shows that fluctuations in the low-frequency eigenvectors are localized at the ends of the DNA sequences, suggesting that these bending motions are important for the DNA-antibody interactions