Embedding Banach spaces into the space of bounded functions with countable support

We prove that a WLD subspace of the space consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into if and only if it does not contain isometric copies of . Moreover, a subspace of is constructed that has an unconditional basis, does not embed into , and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of ).     

On a nonlinear boundary value problem modeling corneal shape

In this paper we present some results concerning a boundary value problem for a nonlinear ordinary differential equation that was used before in modeling the topography of human cornea. These results generalize previously obtained theorems on existence and uniqueness. We show that our equation has a unique solution for all parameters and conditions that can arise in physical situation. In the second part of the article we derive some new estimates and approximate solutions. Numerical calculations verify that these approximations are very accurate.     

Erratum to: “Comparative studies of Pd, Ru, Ni, Cu/ZnAl2O4 catalysts for the water gas shift reaction”

The original version of the article was published in Cent. Eur. J. Chem. 11(6) (2013) pp. 912–919. Unfortunately, the original version of this article contains a mistake in the Acknowledgement section. It should be written as “Partially financed from grant number 0680/B/H03/2011/40 and gratefully acknowledged. Pawe? Mierczyński is a participant of START Programme.”     

Unravelling Structural Mysteries of Simple Organozinc Alkoxides

Simple RZnOR’ alkoxides are among the first known organozinc compounds, and widespread interest in their multifaced chemistry has been driven by their fundamental significance and potential applications including various catalytic reactions. Nevertheless, their chemistry in solution and in the solid state remains both relatively poorly understood and a subject of constant debate. Herein, the synthesis and structural characterization of long-sought structural forms, a roof-like trimer [(tBuZn)₃(μ-OC(H)Ph₂)₂(μ₃-OC(H)Ph₂)] and a ladder-type tetramer [(PhZn)₄(μ-OC(H)Ph₂)₂(μ₃-OC(H)Ph₂)₂], incorporating diphenylmethanolate as a model alkoxide ligand, are reported. Both novel aggregates are robust in the solid state and resistant towards mechanical force. By using ¹H NMR and diffusion-order spectroscopy, it is demonstrated that new RZnOR’ alkoxides are kinetically labile in solution and readily undergo ligand scrambling, such as in the case of Schlenk equilibrium. The elucidated key structural issues, which have remained undiscovered for decades, significantly advance the chemistry of RZnOR’ alkoxides and should support the rational design of zinc alkoxide-based applications.     

Thermographic imaging as alternative method in allergy diagnosis

Allergen sensitization is being diagnosed by commonly available methods in clinical practice—skin prick tests (SPTs) and specific immunoglobulin E test (sIgE). Recently, a new thermographic (TH) method for the assessment of SPT was developed, and it was demonstrated that the TH measurements of forearm temperature distribution during SPT, supported by a mathematical model, offer a new quantification method of allergen-induced skin reactions. The aim of this study is a comprehensive comparison of the TH method with SPT and sIgE techniques. The studies were performed for a group of 51 patients. The SPT and sIgE examinations were done in a routine way. For TH analyses, set of thermograms of both forearms were acquired after prick and analyzed with the use of developed software. All results were converted into categorized scale for comparison. The collected results indicate high correlation coefficients between methods equal to 0.76–0.99. Sensitivity and accuracy of TH assessment in respect of both SPT and sIgE methods is at good level (0.72–0.93). Acceptable level of specificity 0.60–0.88 was also achieved for most allergic responses. Excellent agreement between SPT and sIgE methods was observed which makes the TH assessment competitive. Due to higher precision and sensitivity of digital infrared technology, possibility of making error in diagnosis is significantly reduced. Additional advantage of the TH method relies on an estimation of the skin reactivity which allows highlighting the hypersensitivity patients and automatic correction of the diagnosis.     

Novel Method for HPLC Analysis of Triterpenic Acids Using 9-Anthryldiazomethane Derivatization and Fluorescence Detection

Triterpenic acids are a group of secondary plant metabolites which are part of the cuticular waxes covering fruits, leaves, and flowers. To date, quantitative analysis of these compounds has often been conducted using high-performance liquid chromatography coupled with spectrophotometric detection or mass spectrometry; however, these methods have some major drawbacks. This paper reports a new method of analysis implementing derivatization with 9-anthryldiazomethane and fluorescence detection. The method consists of the extraction of analytes from a matrix, purification with anion exchanging SPE columns, and an optional step of the alkaline hydrolysis of triterpenic acid esters. The paper also describes a fast and easy method for the synthesis of the derivatization agent. The detection limits of the method presented are approximately 100-fold lower than in a similar method using ultraviolet spectrophotometry as the mode of detection. The recovery and repeatability of the method are at satisfactory levels.     

Fractional electrical model for modified bismuth oxide

Modified bismuth oxide (Bi₂O₃) is of great importance to fuel cells and oxide varistors. The electrical parameters of Bi₂O₃ vary with its modifying components as well as with its aging temperature. This paper presents an analysis of impedance test results carried out to find an equivalent electric model and the relationship between the model's elements to various additives used to modify Bi₂O₃ and to changes in aging temperature. The proposed model was tested via computer simulation and the model parameters correlated to individual modifiers.