Weak Pnictogen Bond with Bismuth: Experimental Evidence Based on Bi−P Through-Space Coupling

To study pnictogen bonding involving bismuth, flexible accordion-like molecular complexes of the composition [P(C₆H₄-o-CH₂SCH₃)₃BiX₃], (X=Cl, Br, I) have been synthesised and characterised. The strength of the weak and mainly electrostatic interaction between the Bi and P centres strongly depends on the character of the halogen substituent on bismuth, which is confirmed by single-crystal X-ray diffraction analyses, DFT and ab initio computations. Significantly, ²⁰⁹Bi–³¹P through-space coupling (J=2560 Hz) is observed in solid-state ³¹P NMR spectra, which is so far unprecedented in the literature, delivering direct information on the magnitude of this pnictogen interaction.     

Thermal behaviour of materials in interrupted phase change

Journal of Thermal Analysis and Calorimetry - The most critical part and barrier of phase change material (PCM) applications are the accuracy of simulations and the control of the process. The...     

Simple route to new oxadiazaboroles and oxadiazoles via amidoximes

Abstract

The novel push–pull alkene, the 2-(nitro-nitrosomethylene)-pyrrolidine with numerous aliphatic or aromatic amines as nucleophiles afforded amidoximes. Various substituted oxadiazaborole and oxadiazole derivatives were prepared starting from these amidoximes, widening the synthetic applicability of the push–pull alkenes. Acylation of the amidoximes was also examined. The mechanism of the amidoxime formation was investigated by computational methods.     

On norm dependent positive definite functions

In the first part of the paper we prove a decomposition theorem for positive definite functions (Theorem 2.3) generalizing a result of de Leeuw and Glicksberg. Using this theorem, we then show (Theorem 3.1) that certain norm dependent positive definite functions are automatically continuous at every point different from zero.     

The Stepanov differentiability theorem in metric measure spaces

We extend Cheeger’s theorem on differentiability of Lipschitz functions in metric measure spaces to the class of functions satisfying Stepanov’s condition. As a consequence, we obtain the analogue of Calderon’s differentiability theorem of Sobolev functions in metric measure spaces satisfying a Poincaré inequality. Communicated by Steven Krantz     

Development of chemically modified glass surfaces for nucleic acid,protein and small molecule microarrays

Microarrays have become a widely used tool to investigate the living cell at different levels. DNA microarrays enable the expression analysis of thousand of genes simultaneously, while protein arrays investigate the properties and interactions of proteins with other proteins and with non-proteinaceous molecules. One crucial step in producing such microarrays is the permanent immobilization of samples on a solid surface. Our goal was to develop diverse linker systems capable of anchoring different biological samples, especially DNA and drug-like small molecules. We developed 6 different chemical surfaces having a 3-D-like linker system for biomolecule immobilization, and compared them to previously described immobilization strategies. The attachment chemistry utilizes the amino reactive properties of acrylic and epoxy functions. The capacity of the support was increased by creating a branching structure holding the reactive functions. The method of anchoring was investigated through a model reaction. From HPLC and mass spectrometry measurements we concluded that the covalent binding of DNA occurs through nucleobases. The tested systems offer the capability to permanently immobilize several biomolecular species in an array format.     

A Radon–Nikodym type theorem for forms

The Lebesgue decomposition theorem and the Radon–Nikodym theorem are the cornerstones of the classical measure theory. These theorems were generalized in several settings and several ways. Hassi, Sebestyén, and de Snoo recently proved a Lebesgue type decomposition theorem for nonnegative sesquilinear forms defined on complex linear spaces. The main purpose of this paper is to formulate and prove also a Radon–Nikodym type result in this setting. As an application, we present a Lebesgue type decomposition theorem and solve a special case of the infimum problem for densely defined (not necessarily bounded) positive operators.     

On the Number of k‐Dominating Independent Sets

We study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erd?s and Moser—is widely investigated, much less is known in general. In this paper we settle the question for trees and prove that the maximum number of k‐dominating independent sets in n‐vertex graphs is between and if , moreover the maximum number of 2‐dominating independent sets in n‐vertex graphs is between and . Graph constructions containing a large number of k‐dominating independent sets are coming from product graphs, complete bipartite graphs, and finite geometries. The product graph construction is associated with the number of certain Maximum Distance Separable (MDS) codes.     

Design of a contact grating setup for mJ-energy THz pulse generation by optical rectification

According to the recent calculations, more efficient THz pulse generation is possible using relief grating on the front surface of the generating LiNbO₃ (LN) crystal for tilted-pulse-front-excitation rather than imaging the pump spot on a reflection grating into the LN crystal. Very recently, it was shown that—compared to a free-standing LN surface-relief grating—significantly higher diffraction efficiency can be reached if the grating profiles are filled with fused silica. Since realisation of such a setup is technically very challenging, in the present paper, we analyse the case where the input side of the LN grating is immersed into a refractive index matching liquid (RIML) instead of a solid material. Our results showed that the diffraction efficiency remains above 90?% for a refractive index ranging 1.45–1.60 of the applied RIML, and it is as high as 99?% for using the RIML for BK7. For this case, we carried out detailed calculations for various grating parameters. We propose a practical setup applying tilted input and slightly tilted output surfaces resulting in low losses and high diffraction efficiency for the pump. We conclude that a contact grating setup using BK7 RIML is suitable for producing THz pulses even in the mJ-energy range.