Work function of the adsorption system of potassium on tungsten

The work functions φ_hklof tungsten single crystal planes as functions of the surface densities N_hkl of the adsorbed potassium have been measured by means of the field emission method. Sealed-off field emission tubes with a Faraday collector and rotatable emitter were used. Another, special tube was made in order to determine the surface density of potassium. The unequilibrated adlayers on {110}, {112}, {100} and {111} tungsten single crystal planes have been investigated. For all the planes investigated the φ_hkl(N_hkl) dependence exhibited a distinct minimum. An attempt has been made to compare the experimental results with the theoretical models suggested recently.     

Lattice gas model for monolayer of amphipatic molecules

Using the molecular-field approximation for the lattice gas model in terms of a spin-one Ising model, we construct phase diagrams and show when the transition could be of first or second order. Possible relevance to the theoritical models of phase transitions in monolayers of amphipatic molecules is also discussed.     

Remark on the application of the effective hamiltonian method for random systems

We compare two versions of the effective Hamiltonian method applied to random bond systems. In one randomness is treated in a kind of the mean field approximation, whereas in the other the relevant arrangements of bonds are explicitly accounted for. Calculations for three dimensional systems of mixed ferromagnetic Heisenberg and Ising bonds show that although the T_c vs p (concentration of Heisenberg-loke interactions) curve in the second approach lies closer to the results of high temperature series general features in both approxsimations are quite similar.     

Polynomial Homogeneous Maps and Their Periods

We study the set of periods of the homogeneous polynomial maps $f: \R^n \to \R^n$ and $f: \C^n \to \C^n$ of degree $m>1$. For these complex maps, we also describe the number of invariant straight lines through the origin by $f^k$ for $k=1,2,\ldots$ and the dynamics of $f^k$ over them.     

High‐temperature study of superconducting hydrogen and deuterium sulfide

Hydrogen‐rich compounds are extensively explored as candidates for a high‐temperature superconductors. Currently, the measured critical temperature of 203 K in hydrogen sulfide (H₃S) is among the highest over all‐known superconductors. In present paper, using the strong‐coupling Eliashberg theory of superconductivity, we compared in detail the thermodynamic properties of two samples containing different hydrogen isotopes H₃S and D₃S at 150 GPa. Our research indicates that it is possible to reproduce the measured values of critical temperature 203 K and 147 K for H₃S and D₃S by using a Coulomb pseudopotential of 0.123 and 0.131, respectively. However, we also discuss a scenario in which the isotope effect is independent of pressure and the Coulomb pseudopotential for D₃S is smaller than for H₃S. For both scenarios, the energy gap, specific heat, thermodynamic critical field and related dimensionless ratios are calculated and compared with other conventional superconductors. We shown that the existence of the strong‐coupling and retardation effects in the systems analysed result in significant differences between values obtained within the framework of the Eliashberg formalism and the prediction of the Bardeen‐Cooper‐Schrieffer theory.     

A Sharp Weak-Type $$(\infty ,\infty )$$ Inequality for the Hilbert Transform

The paper is devoted to sharp weak type \((\infty ,\infty )\) estimates for \({\mathcal {H}}^{\mathbb {T}}\) and \({\mathcal {H}}^{\mathbb {R}}\), the Hilbert transforms on the circle and real line, respectively. Specifically, it is proved that

$$\begin{aligned} \left\| {\mathcal {H}}^{\mathbb {T}}f\right\| _{W({\mathbb {T}})}\le \Vert f\Vert _{L^\infty ({\mathbb {T}})} \end{aligned}$$

and

$$\begin{aligned} \left\| {\mathcal {H}}^{\mathbb {R}}f\right\| _{W({\mathbb {R}})}\le \Vert f\Vert _{L^\infty ({\mathbb {R}})}, \end{aligned}$$

where \(W({\mathbb {T}})\) and \(W({\mathbb {R}})\) stand for the weak-\(L^\infty \) spaces introduced by Bennett, DeVore and Sharpley. In both estimates, the constant \(1\) on the right is shown to be the best possible.

     

Imine‐Based Architectures at Surfaces and Interfaces: From Self‐Assembly to Dynamic Covalent Chemistry in 2D

Within the last two decades, dynamic covalent chemistry (DCC) has emerged as an efficient and versatile strategy for the design and synthesis of complex molecular systems in solution. While early examples of supramolecularly assisted covalent synthesis at surfaces relied strongly on kinetically controlled reactions for post‐assembly covalent modification, the DCC method takes advantage of the reversible nature of bond formation and allows the generation of the new covalently bonded structures under thermodynamic control. These structurally complex architectures obtained by means of DCC protocols offer a wealth of solutions and opportunities in the generation of new complex materials that possess sophisticated properties. In this focus review we examine the formation of covalently bonded imine‐based discrete nanostructures as well as one‐dimensional (1D) polymers and two‐dimensional (2D) covalent organic frameworks (COFs) physisorbed on solid substrates under various experimental conditions, for example, under ultra‐high vacuum (UHV) or at the solid–liquid interface. Scanning tunneling microscopy (STM) was used to gain insight, with a sub‐nanometer resolution, into the structure and properties of those complex nanopatterns.     

Particular concentration profiles at the electrode with respect to interferometric investigations

The variations of concentration profiles at the working electrode as a consequence of Fick's law and the electroneutrality maintaining rule as considered. The conclusion is drawn that the cause of reversed or twofold interference fringe shifts may be, among others, the effect of the superposition of the concentration gradients of particular species. The calculations are illustrated by original interferograms.     

On functional which are orthogonally additive modulo Z

Let E be a real inner product space with dimension at least 2, D ? E, f: E → R with f(x+y)?f(x)?f(y) ∈ Z for all orthogonal x,y ∈ E, and f(D) ? (?γ,γ)+Z witn some real γ > 0. We prove that, under some additional assumptions, there are a unique linear functional A: E → R and a unique constant d ∈ R with f(x)?d∥x∥²?A(x) ∈ Z for x ∈ E. We also show some applications of this result to the determination of solutions F: E → C of the conditional equation: F(x+y) = F(x)F(y) for all orthogonal x,y ∈ E.     

Analyzing the Carotenoid Composition of Melilot (Melilotus officinalis (L.) Pall.) Extracts and the Effects of Isolated (All-E)-lutein-5,6-epoxide on Primary Sensory Neurons and Macrophages

Melilotus officinalis is known to contain several types of secondary metabolites. In contrast, the carotenoid composition of this medicinal plant has not been investigated, although it may also contribute to the biological activities of the drug, such as anti-inflammatory effects. Therefore, this study focuses on the isolation and identification of carotenoids from Meliloti herba and on the effect of isolated (all-E)-lutein 5,6-epoxide on primary sensory neurons and macrophages involved in nociception, as well as neurogenic and non-neurogenic inflammatory processes. The composition of the plant extracts was analyzed by high performance liquid chromatography (HPLC). The main carotenoid was isolated by column liquid chromatography (CLC) and identified by MS and NMR. The effect of water-soluble lutein 5,6-epoxide-RAMEB (randomly methylated-β-cyclodextrin) was investigated on Ca²⁺-influx in rat primary sensory neurons induced by the activation of the transient receptor potential ankyrin 1 receptor agonist to mustard-oil and on endotoxin-induced IL-1β release from isolated mouse peritoneal macrophages. (all-E)-Lutein 5,6-epoxide significantly decreased the percent of responsive primary sensory neurons compared to the vehicle-treated stimulated control. Furthermore, endotoxin-evoked IL-1β release from macrophages was significantly decreased by 100 µM lutein 5,6-epoxide compared to the vehicle-treated control. The water-soluble form of lutein 5,6-epoxide-RAMEB decreases the activation of primary sensory neurons and macrophages, which opens perspectives for its analgesic and anti-inflammatory applications.