On Half Iterates of Functions Defined on Finite Sets

Four algorithms determining all functional square roots (half iterates) and seven algorithms finding one functional square root of any function f : X ! X defined on a finite set X, if these square roots exist, are presented herein. Time efficiency of these algorithms depending on the complexity of examined functions is compared and justification of correctness is given. Moreover, theorems which make finding half iterates possible in some cases or facilitate this task are formulated

The Structure Of Functional Graphs For Functions From A Finite Domain To Itself For Which A Half Iterate Exists

The notion of a replica of a nontrivial in-tree is defined. A result enabling to determine whether an in-tree is a replica of another in-tree employing an injective mapping between some subsets of sources of these in-trees is presented. There are given necessary and sufficient conditions for the existence of a functional square root of a function from a finite set to itself through presenting necessary and sufficient conditions for the existence of a square root of a component of the functional graph for the function and for the existence of a square root of the union of two components of the functional graph for the function containing cycles of the same length using the concept of the replica

Photodegradation of the H1H^{1} antihistaminic topical drugs emedastine, epinastine, and ketotifen and ROS tests for estimations of their potent phototoxicity

In this study, important H1 antihistaminic drugs, i.e., emedastine (EME), epinastine (EPI), and ketotifen (KET), were irradiated with UV/Vis light (300–800 nm) in solutions of different pH values. Next, they were analyzed by new high performance liquid chromatography (HPLC) methods, in order to estimate the percentage of degradation and respective kinetics. Subsequently, ultra-performance liquid chromatography tandem-mass spectrometry (UPLC-MS/MS) was used to identify their photodegradation products and to propose degradation pathways. In addition, the peroxidation of linoleic acid and generation of singlet oxygen (SO) and superoxide anion (SA) were examined, together with the molar extinction coeffcient (MEC) evaluation, to estimate their phototoxic risk. The photodegradation of all EME, EPI, and KET followed pseudo first-order kinetics. At pH values of 7.0 and 10.0, EPI was shown to be rather stable. However, its photostability was lower at pH 3.0. EME was shown to be photolabile in the whole range of pH values. In turn, KET was shown to be moderately labile at pH 3.0 and 7.0. However, it degraded completely in the buffer of pH 10.0. As a result, several photodegradation products were separated and identified using the UPLC-MS/MS method. Finally, our ROS assays showed a potent phototoxic risk in the following drug order: EPI < EME < KET. All of these results may be helpful for manufacturing, storing, and applying these substantial drugs, especially in their ocular formulations

The Boost of Toluene Capture in UiO-66 Triggered by Structural Defects or Air Humidity

This work aimed to investigate the adsorption of toluene in UiO-66 materials. Toluene is a volatile, aromatic organic molecule that is recognized as the main component of VOCs. These compounds are harmful to the environment as well as to living organisms. One of the materials that allows the capture of toluene is the UiO-66. A satisfactory representation of the calculated isotherm steep front and sorption capacity compared to the experiment was obtained by reducing the force field σ parameter by 5% and increasing ϵ by 5%. Average occupation profiles, which are projections of the positions of molecules during pressure increase, as well as RDFs, which are designed to determine the distance of the center of mass of the toluene molecule from organic linkers and metal clusters, respectively, made it possible to explain the mechanism of toluene adsorption on the UiO-66 material.</p

Carbon dioxide capture enhanced by pre-adsorption of water and methanol in UiO-66

The rapidly rising level of carbon dioxide in the atmosphere resulting from human activity is one of the greatest environmental problems facing our civilization today. Most technologies are not yet sufficiently developed to move existing infrastructure to cleaner alternatives. Therefore, techniques for capturing carbon dioxide from emission sources may play a key role at the moment. The structure of the UiO‐66 material not only meets the requirement of high stability in contact with water vapor but through the water pre‐adsorbed in the pores, the selectivity of carbon dioxide adsorption is increased. We successfully applied the recently developed methodology for water adsorption modelling. It allowed to elucidate the influence of water on CO(2) adsorption and study the mechanism of this effect. We showed that water is adsorbed in octahedral cage and stands for promotor for CO(2) adsorption in less favorable space than tetrahedral cages. Water plays a role of a mediator of adsorption, what is a general idea of improving affinity of adsorbate. On the basis of pre‐adsorption of methanol as another polar solvent, we have shown that the adsorption sites play a key role here, and not, as previously thought, only the interaction between the solvent and quadrupole carbon dioxide. Overall, we explained the mechanism of increased CO(2) adsorption in the presence of water and methanol, as polar solvents, in the UiO‐66 pores for a potential post‐combustion carbon dioxide capture application

On the nature of spin- and orbital-resolved Cu+−NOCu^{+}-NO charge transfer in the gas phase and at Cu(I) sites in zeolites

Electronic factors essential for NO activation by Cu(I) sites in zeolites are investigated within spin-resolved analysis of electron transfer channels (natural orbitals for chemical valence). NOCV analysis is performed for three DFT-opti- mized models of Cu(I)–NO site in ZSM-5: [CuNO] ? , (T1)CuNO, and (M7)CuNO. NO as a non-innocent, open- shell ligand reveals significant differences between inde- pendent deformation density components for a and b spins. Four distinct components are identified: (i) unpaired electron donation from NO p k * antibonding orbital to Cu s,d ; (ii) backdonation from copper d yz to p \ * antibonding orbital; (iii) donation from occupied p k and Cu d xz to bonding region, and (iv) donation from nitrogen lone-pair to Cu s,d . Channel (i), corresponding to one-electron bond, shows-up solely for spin majority and is effective only in the interaction of NO with naked Cu ? . Channel (ii) dominates for models b and c: it strongly activates NO bond by populating antibonding p * orbital and weakens the N–O bond in contrast to channel (i), depopulating the antibonding orbital and strengthening N–O bond. This picture perfectly agrees with IR experiment: interaction with naked Cu ? imposes small blue-shift of N stretching frequency while it becomes strongly red-shifted for Cu(I) site in ZSM-5 due to enhanced backdonation

Defect-induced tuning of polarity-dependent adsorption in hydrophobic–hydrophilic UiO-66

Structural defects in metal–organic frameworks can be exploited to tune material properties. In the case of UiO-66 material, they may change its nature from hydrophobic to hydrophilic and therefore affect the mechanism of adsorption of polar and non-polar molecules. In this work, we focused on understanding this mechanism during adsorption of molecules with different dipole moments, using the standard volumetric adsorption measurements, IR spectroscopy, DFT + D calculations, and Monte Carlo calculations. Average occupation profiles showed that polar and nonpolar molecules change their preferences for adsorption sites. Hence, defects in the structure can be used to tune the adsorption properties of the MOF as well as to control the position of the adsorbates within the micropores of UiO-66.</p

Model-based reconstruction and projections of soil moisture anomalies and crop losses in Poland

Evidence shows that soil moisture (SM) anomalies (deficits or excesses) are the key factor affecting crop yield in rain-fed agriculture. Over last decades, Poland has faced several major droughts and at least one major soil moisture excess event leading to severe crop losses. This study aims to simulate the multi-annual variability of SM anomalies in Poland, using a process-based SWAT model and to assess the effect of climate change on future extreme SM conditions, potentially affecting crop yields in Poland. A crop-specific indicator based on simulated daily soil moisture content for the critical development stages of investigated crops (winter cereals, spring cereals, potato and maize) was designed, evaluated for past conditions against empirical crop-weather indices (CWIs), and applied for studying future climate conditions. The study used an ensemble of nine bias-corrected EURO-CORDEX projections for two future horizons: 2021–2050 and 2071–2100 under two Representative Concentration Pathways: RCP4.5 and 8.5. Historical simulation results showed that SWAT was capable of capturing major SM deficit and excess episodes for different crops in Poland. For spring cereals, potato and maize, despite a large model spread, projections generally showed increase of severity of soil moisture deficits, as well as of total area affected by them. Ensemble median fraction of land with extreme soil moisture deficits, occupied by each of these crops, is projected to at least double in size. The signals of change in soil moisture excesses for potato and maize were more dependent on selection of RCP and future horizon. © 2020, The Author(s)

Studia z Dziejów Państwa i Prawa Polskiego T. XXI Badania nad rozwojem instytucji politycznych i prawnych

Tytuł finansowany przez: Krakowską Akademię im. Andrzeja Frycza Modrzewskiego, Uniwersytet im. Marii Curie-Skłodowskiej w Lublinie, Uniwersytet Gdański, Uniwersytet Warszawsk