259 research outputs found
A Note on the Spectrum of Composition Operators on Spaces of Real Analytic Functions
[EN] In this paper the spectrum of composition operators on the space of real analytic functions is investigated. In some cases it is completely determined while in some other cases it is only estimated.The research of the authors was partially supported by MEC and FEDER Project MTM2013-43540-P and the work of of Bonet by the Grant GV Project Prometeo II/2013/013. The research of Domanski was supported by National Center of Science, Poland, Grant No. DEC-2013/10/A/ST1/00091.Bonet Solves, JA.; Domanski, P. (2017). A Note on the Spectrum of Composition Operators on Spaces of Real Analytic Functions. Complex Analysis and Operator Theory. 11(1):161-174. https://doi.org/10.1007/s11785-016-0589-5S161174111Belitskii, G., Lyubich, Y.: The Abel equation and total solvability of linear functional equations. Studia Math. 127, 81â97 (1998)Belitskii, G., Lyubich, Y.: The real analytic solutions of the Abel functional equation. Studia Math. 134, 135â141 (1999)Belitskii, G., Tkachenko, V.: One-Dimensional Functional Equations. Springer, Basel (2003)Belitskii, G., Tkachenko, V.: Functional equations in real analytic functions. Studia Math. 143, 153â174 (2000)Bonet, J., DomaĆski, P.: Power bounded composition operators on spaces of analytic functions. Collect. Math. 62, 69â83 (2011)Bonet, J., DomaĆski, P.: Hypercyclic composition operators on spaces of real analytic fucntions. Math. Proc. Cambridge Phil. Soc. 153, 489â503 (2012)Bonet, J., DomaĆski, P.: Abelâs functional equation and eigenvalues of composition operators on spaces of real analytic functions. Integr. Equ. Oper. Theor. 81, 455â482 (2015). doi: 10.1007/s00020-014-2175-4Cartan, H.: VariĂ©tĂ©s analytiques rĂ©elles et variĂ©tĂ©s analytiques complexes. Bull. Soc. Math. France 85, 77â99 (1957)DomaĆski, P.: Notes on real analytic functions and classical operators, Topics in Complex Analysis and Operator Theory (Winter School in Complex Analysis and Operator Theory, Valencia, February 2010), Contemporary Math. 561 (2012) 3â47. Amer. Math. Soc, Providence (2012)DomaĆski, P., GoliĆski, M., Langenbruch, M.: A note on composition operators on spaces of real analytic functions. Ann. Polon. Mat. 103, 209â216 (2012)DomaĆski, P., Langenbruch, M.: Composition operators on spaces of real analytic functions. Math. Nachr. 254â255, 68â86 (2003)DomaĆski, P., Langenbruch, M.: Coherent analytic sets and composition of real analytic functions. J. reine angew. Math. 582, 41â59 (2005)DomaĆski, P., Langenbruch, M.: Composition operators with closed image on spaces of real analytic functions. Bull. Lond. Math. Soc. 38, 636â646 (2006)DomaĆski, P., Vogt, D.: The space of real analytic functions has no basis. Studia Math. 142, 187â200 (2000)Hörmander, L.: An Introduction to Complex Analysis in Several Variables. North Holland, Amsterdam (1986)Meise, R., Vogt, D.: Introduction to Functional Analysis. Clarendon, Oxford (1997)Smajdor, W.: On the existence and uniqueness of analytic solutions of the functional equation Ï ( z ) = h ( z , Ï [ f ( z ) ] ) . Ann. Polon. Math. 19, 37â45 (1967
Thermodynamics and tunneling spectroscopy in the pseudogap regime of the boson fermion model
Motivated by the STM experimental data on Bi_2 Sr_2 CaCU_2 O_{8+x} which
indicate the tunneling conductance asymmetry sigma(-V) not equal sigma(V), we
report that such a behavior can be explained in terms of the boson fermion
model. It has been shown in the recent studies, based on various selfconsistent
techniques to capture the many-body effects, that the low energy spectrum of
the boson fermion model is featured by an appearance of the pseudogap at T^* >
T_c. We argue that the pseudogap structure has to exhibit a particle-hole
asymmetry. This asymmetry may eventually depend on the boson concentration.Comment: 4 pages, 2 figures. submitted to Physica
Flow equation approach to the linear response theory of superconductors
We apply the flow equation method for studying the current-current response
function of electron systems with the pairing instability. To illustrate the
specific scheme in which the flow equation procedure determines the
two-particle Green's functions we reproduce the standard response kernel of the
BCS superconductor. We next generalize this non-perturbative treatment
considering the pairing field fluctuations. Our study indicates that the
residual diamagnetic behavior detected above the transition temperature in the
cuprate superconductors can originate from the noncondensed preformed pairs.Comment: 12 pages, 4 figure
Unconventional particle-hole mixing in the systems with strong superconducting fluctuations
Development of the STM and ARPES spectroscopies enabled to reach the
resolution level sufficient for detecting the particle-hole entanglement in
superconducting materials. On a quantitative level one can characterize such
entanglement in terms of the, so called, Bogoliubov angle which determines to
what extent the particles and holes constitute the spatially or momentum
resolved excitation spectra. In classical superconductors, where the phase
transition is related to formation of the Cooper pairs almost simultaneously
accompanied by onset of their long-range phase coherence, the Bogoliubov angle
is slanted all the way up to the critical temperature Tc. In the high
temperature superconductors and in superfluid ultracold fermion atoms near the
Feshbach resonance the situation is different because of the preformed pairs
which exist above Tc albeit loosing coherence due to the strong quantum
fluctuations. We discuss a generic temperature dependence of the Bogoliubov
angle in such pseudogap state indicating a novel, non-BCS behavior. For
quantitative analysis we use a two-component model describing the pairs
coexisting with single fermions and study their mutual feedback effects by the
selfconsistent procedure originating from the renormalization group approach.Comment: 4 pages, 4 figure
Real space inhomogeneities in high temperature superconductors: the perspective of two-component model
The two-component model of high temperature superconductors in its real space
version has been solved using Bogoliubov-de Gennes equations. The disorder in
the electron and boson subsystem has been taken into account. It strongly
modifies the superconducting properties and leads to local variations of the
gap parameter and density of states. The assumption that the impurities mainly
modify boson energies offers natural explanation of the puzzling positive
correlation between the positions of impurities and the values of the order
parameter found in the scanning tunnelling microscopy experiments.Comment: 19 pages, IOPP style include
Effect of disorder on superconductivity in the boson-fermion model
We study how a randomness of either boson or fermion site energies affects
the superconducting phase of the boson fermion model. We find that, contrary to
what is expected for s-wave superconductors, the non-magnetic disorder is
detrimental to the s-wave superconductivity. However, depending in which
subsystem the disorder is located, we can observe different channels being
affected. Weak disorder of the fermion subsystem is responsible mainly for
renormalization of the single particle density of states while disorder in the
boson subsystem directly leads to fluctuation of the strength of the effective
pairing between fermions.Comment: 7 pages, 6 figures. Physical Review B (accepted for publication
Atomistic mechanism of transmembrane helix association
Transmembrane helix association is a fundamental step in the folding of helical membrane proteins. The prototypical example of this association is formation of the glycophorin dimer. While its structure and stability have been well-characterized experimentally, the detailed assembly mechanism is harder to obtain. Here, we use all-atom simulations within phospholipid membrane to study glycophorin association. We find that initial association results in the formation of a non-native intermediate, separated by a significant free energy barrier from the dimer with a native binding interface. We have used transition-path sampling to determine the association mechanism. We find that the mechanism of the initial bimolecular association to form the intermediate state can be mediated by many possible contacts, but seems to be particularly favoured by formation of non-native contacts between the C-termini of the two helices. On the other hand, the contacts which are key to determining progression from the intermediate to the native state are those which define the native binding interface, reminiscent of the role played by native contacts in determining folding of globular proteins. As a check on the simulations, we have computed association and dissociation rates from the transition-path sampling. We obtain results in reasonable accord with available experimental data, after correcting for differences in native state stability. Our results yield an atomistic description of the mechanism for a simple prototype of helical membrane protein folding
The impact of health on professionally active people's incomes in Poland. Microeconometric analysis
The outcome of the research confirms the occurrence of positive interaction between professionally active people's incomes and the self-assessed state of health. People declaring a bad state of health have incomes by 20% on average lower than people who enjoy good health (assuming that the remaining characteristics of the surveyed person are the same). In case of men, the impact of health state on incomes is slightly greater than in case of women.Wyniki badaĆ potwierdzajÄ
istnienie pozytywnej zaleĆŒnoĆci dochodĂłw osĂłb aktywnych zawodowo od stanu zdrowia mierzonego jego samoocenÄ
. Osoby deklarujÄ
ce zĆy stan zdrowia osiÄ
gajÄ
dochody przeciÄtnie o 20% niĆŒsze niĆŒ osoby, ktĂłre cieszÄ
siÄ dobrym stanem zdrowia (przy zaĆoĆŒeniu, ĆŒe pozostaĆe charakterystyki badanej osoby sÄ
takie same). W przypadku mÄĆŒczyzn zaleĆŒnoĆÄ dochodĂłw od stanu zdrowia jest nieznacznie silniejsza niĆŒ w przypadku kobiet
The incidence of healthcare-associated infections, their clinical forms, and microbiological agents in intensive care units in southern Poland in a multicentre study from 2016 to 2019
Introduction. Healthcare-associated infections (HAIs) are a serious problem of modern medicine. Patients hospitalized in intensive care units (ICUs) develop HAI significantly more often than patients in other hospital units. Materials and Methods. Analysis involved HAIs from three ICUs in southern Poland. The study was conducted in 2016â2019 on the basis of methodology recommended by the Healthcare-Associated Infections Surveillance Network (HAI-Net) and European Centre for Disease Prevention and Control (ECDC). The objective was to analyse HAIs, their clinical forms, and microbiological agents. Results. The study included 3028 patients hospitalized for 26,558 person-days (pds) in ICU. A total of 540 HAIs were detected; incidence per 100 hospitalizations was 17.8%, incidence density per 1000 pds was 20.3. The mortality of patients with HAI was 16%, and in Clostridioidesdifficile infection (CDI), the mortality was 28%. The most common clinical form of HAI was bloodstream infection (BSI): 209 cases (incidence rate 6.9%), followed by pneumonia (PN): 131 (incidence rate 4.3%), and urinary tract infection (UTI): 110 cases (incidence rate 3.6%). The most frequently isolated bacteria were Klebsiella pneumoniae 16.4%, Acinetobacter baumannii 14.4%, Staphylococcus aureus 11.8%, and Escherichia coli 11.4%. Conclusions. A two-fold higher incidence rate of BSI was detected compared to the average incidence in European countries. BSI of unknown source (BSI-UNK) was predominant. K. pneumoniae and A. baumannii bacteria were the most often isolated microorganisms causing HAI. Infection control based on incidence rate for each type of infection is necessary in ICU to assess the epidemiological situation
Multiple lipid binding sites determine the affinity of PH domains for phosphoinositide-containing membranes
Association of peripheral proteins with lipid bilayers regulates membrane signaling and dynamics. Pleckstrin homology (PH) domains bind to phosphatidylinositol phosphate (PIP) molecules in membranes. The effects of local PIP enrichment on the interaction of PH domains with membranes is unclear. Molecular dynamics simulations allow estimation of the binding energy of GRP1 PH domain to PIP3-containing membranes. The free energy of interaction of the PH domain with more than two PIP3 molecules is comparable to experimental values, suggesting that PH domain binding involves local clustering of PIP molecules within membranes. We describe a mechanism of PH binding proceeding via an encounter state to two bound states which differ in the orientation of the protein relative to the membrane, these orientations depending on the local PIP concentration. These results suggest that nanoscale clustering of PIP molecules can control the strength and orientation of PH domain interaction in a concentration-dependent manner
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