The Poincaré Map of Randomly Perturbed Periodic Motion

A system of autonomous differential equations with a stable limit cycle and perturbed by small white noise is analyzed in this work. In the vicinity of the limit cycle of the unperturbed deterministic system, we define, construct, and analyze the Poincaré map of the randomly perturbed periodic motion. We show that the time of the first exit from a small neighborhood of the fixed point of the map, which corresponds to the unperturbed periodic orbit, is well approximated by the geometric distribution. The parameter of the geometric distribution tends to zero together with the noise intensity. Therefore, our result can be interpreted as an estimate of the stability of periodic motion to random perturbations. In addition, we show that the geometric distribution of the first exit times translates into statistical properties of solutions of important differential equation models in applications. To this end, we demonstrate three distinct examples from mathematical neuroscience featuring complex oscillatory patterns characterized by the geometric distribution. We show that in each of these models the statistical properties of emerging oscillations are fully explained by the general properties of randomly perturbed periodic motions identified in this paper.     

High‐power HgGa2S4 optical parametric oscillator pumped at 1064 nm and operating at 100 Hz

The defect chalcopyrite crystal HgGa₂S₄ has been employed in a 1064‐nm pumped optical parametric oscillator operating at 100 Hz, to generate ∼5 ns long idler pulses near 4 µm with energies as high as 6.1 mJ and average power of 610 mW. At crystal dimensions comparable to those available for the commercial AgGaS₂ crystal, operation of the 1064‐nm pumped HgGa₂S₄ OPO is characterized by much lower pump threshold and higher conversion efficiency, with the most important consequence that such a device might become practical at pump levels sufficiently lower than the optical damage threshold.     

Subsurface Carbon: A General Feature of Noble Metals

Carbon moieties on late transition metals are regarded as poisoning agents in heterogeneous catalysis. Recent studies show the promoting catalytic role of subsurface C atoms in Pd surfaces and their existence in Ni and Pt surfaces. Here energetic and kinetic evidence obtained by accurate simulations on surface and nanoparticle models shows that such subsurface C species are a general issue to consider even in coinage noble‐metal systems. Subsurface C is the most stable situation in densely packed (111) surfaces of Cu and Ag, with sinking barriers low enough to be overcome at catalytic working temperatures. Low‐coordinated sites at nanoparticle edges and corners further stabilize them, even in Au, with negligible subsurface sinking barriers. The malleability of low‐coordinated sites is key in the subsurface C accommodation. The incorporation of C species decreases the electron density of the surrounding metal atoms, thus affecting their chemical and catalytic activity.     

Key Role of a-Top CO on Terrace Sites of Metallic Pd Clusters for CO Oxidation

Pd-based catalysts are the most widely used for CO oxidation because of their outstanding catalytic activity and thermal stability. However, fundamental understanding of the detailed catalytic processes occurring on Pd-based catalysts under realistic conditions is still lacking. In this study, we investigated CO oxidation on metallic Pd clusters supported on Al₂O₃ and SiO₂. High-angle annular dark-field scanning transmission electron microscopy revealed the formation of similar-sized Pd clusters on Al₂O₃ and SiO₂. In contrast, CO chemisorption analysis indicated a gradual change in the dispersion of Pd (from 0.79 to 0.2) on Pd/Al₂O₃ and a marginal change in the dispersion (from 0.4 to 0.24) on Pd/SiO₂ as the Pd loading increased from 0.27 to 5.5 wt %; these changes were attributed to differences in the metal-support interactions. Diffuse reflectance infrared Fourier-transform spectroscopy revealed that fewer a-top CO species were present in Pd supported on Al₂O₃ than those in Pd supported on SiO₂, which is related to the morphological differences in the metallic Pd clusters on these two supports. Despite the different dispersion profiles and surface characteristics of Pd, O₂ titration demonstrated that linearly bound CO (with an infrared signal at 2090 cm⁻¹) reacted first with oxygen in the case of CO-saturated Pd on Al₂O₃ and SiO₂, which suggests that a-top CO on the terrace site plays an important role in CO oxidation. The experimental observations were corroborated by periodic density functional calculations, which confirmed that CO oxidation on the (111) terrace sites is most plausible, both kinetically and thermodynamically, compared to that on the edge or corner sites. This study will deepen the fundamental understanding of the effect of Pd clusters on CO oxidation under reaction conditions.     

Halogen–Aromatic π Interactions Modulate Inhibitor Residence Times

Prolonged drug residence times may result in longer‐lasting drug efficacy, improved pharmacodynamic properties, and “kinetic selectivity” over off‐targets with high drug dissociation rates. However, few strategies have been elaborated to rationally modulate drug residence time and thereby to integrate this key property into the drug development process. Herein, we show that the interaction between a halogen moiety on an inhibitor and an aromatic residue in the target protein can significantly increase inhibitor residence time. By using the interaction of the serine/threonine kinase haspin with 5‐iodotubercidin (5‐iTU) derivatives as a model for an archetypal active‐state (type I) kinase–inhibitor binding mode, we demonstrate that inhibitor residence times markedly increase with the size and polarizability of the halogen atom. The halogen–aromatic π interactions in the haspin–inhibitor complexes were characterized by means of kinetic, thermodynamic, and structural measurements along with binding‐energy calculations.     

Enhanced photocatalytic activity of thin TiO2 films dotted with ZnS nanoparticles

The effect of Ni loading on the catalytic activity of Ni/ZrO₂ catalyst for methane steam reforming was investigated. The sample containing 15 wt.% Ni exhibited the highest activity as well as stability at 600°C. An erratum to this article is available at .     

CO coordination at XNi4 clusters with impurities X = H, C, O. A density functional study

We report a computational investigation of CO adsorption on small nickel clusters that contain single impurity atoms H, C, or O. At bare Ni 4 and clusters with H or O impurity, the most stable coordination of the probe molecule is on top of a Ni atom which interacts with the impurity. The CNi 4 cluster is an exception where 3-fold coordination of CO was determined to be more stable than that on top, however, by 4 kJ/mol only. Our results suggest that the heteroatoms X (X = H, C, O) affect only weakly the reactivity of the cluster with respect to CO; the binding energy of CO in the most stable complexes (CO)XNi 4 increases at most by 10% compared to the value for bare Ni 4, 194 kJ/mol. The impurity induces a small decrease of the CO infrared frequency shift for on-top coordinated CO, compared to Ni 4, because of partial oxidation of the metal moiety. A notable difference is predicted for clusters that contain a C impurity because of the different preferred coordination mode which results in a strong CO frequency red shift of approximately 300 cm (-1). The calculated characteristic CO frequency shifts may be helpful in identifying experimentally clusters with impurity atoms.     

Kähler manifolds of quasi-constant holomorphic sectional curvatures

The Kähler manifolds of quasi-constant holomorphic sectional curvatures are introduced as Kähler manifolds with complex distribution of codimension two, whose holomorphic sectional curvature only depends on the corresponding point and the geometric angle, associated with the section. A curvature identity characterizing such manifolds is found. The biconformal group of transformations whose elements transform Kähler metrics into Kähler ones is introduced and biconformal tensor invariants are obtained. This makes it possible to classify the manifolds under consideration locally. The class of locally biconformal flat Kähler metrics is shown to be exactly the class of Kähler metrics whose potential function is only a function of the distance from the origin in ? ⁿ . Finally we show that any rotational even dimensional hypersurface carries locally a natural Kähler structure which is of quasi-constant holomorphic sectional curvatures.     

Anticancer Potencies of PtII‐ and PdII‐linked M2L4 Coordination Capsules with Improved Selectivity

Pt^II‐ and Pd^II‐linked M₂L₄ coordination capsules, providing a confined cavity encircled by polyaromatic frameworks, exhibit anticancer activities superior to cisplatin against two types of leukemic cells (HL‐60 and SKW‐3) and pronounced toxicity against cisplatin‐resistant cells (HL‐60/CDDP). Notably, the cytotoxic selectivities of the Pt^II and Pd^II capsules toward cancerous cells are up to 5.3‐fold higher than that of cisplatin, as estimated through the non‐malignant/malignant‐cells toxicity ratio employing normal kidney cells (HEK‐293). In addition, the anticancer activity of the coordination capsules can be easily altered upon encapsulation of organic guest molecules.     

Flexible Polymer–Organic Solar Cells Based on P3HT:PCBM Bulk Heterojunction Active Layer Constructed under Environmental Conditions

In this study, some crucial parameters were determined of flexible polymer–organic solar cells prepared from an active layer blend of poly(3-hexylthiophene) (P3HT) and the fullerene derivative [6,6]-phenyl-C₆₁-butyric acid methyl ester (PCBM) mixed in 1:1 mass ratio and deposited from chlorobenzene solution by spin-coating on poly(ethylene terephthalate) (PET)/ITO substrates. Additionally, the positive effect of an electron transport layer (ETL) prepared from zinc oxide nanoparticles (ZnO np) on flexible photovoltaic elements’ performance and stability was investigated. Test devices with above normal architecture and silver back electrodes deposed by magnetron sputtering were constructed under environmental conditions. They were characterized by current-voltage (I–V) measurements, quantum efficiency, impedance spectroscopy, surface morphology, and time–degradation experiments. The control over morphology of active layer thin film was achieved by post-deposition thermal treatment at temperatures of 110–120 °C, which led to optimization of device morphology and electrical parameters. The impedance spectroscopy results of flexible photovoltaic elements were fitted using two R||CPE circuits in series. Polymer–organic solar cells prepared on plastic substrates showed comparable current–voltage characteristics and structural properties but need further device stability improvement according to traditionally constructed cells on glass substrates.