On a linear transcendence measure for the solutions of a universal differential equation at algebraic points

In this paper the author continues his work on arithmetic properties of the solutions of a universal differential equation at algebraic points. Every real continuous function on the real line can be uniformly approximated by C^∞-solutions of a universal differential equation. An algebraic universal differential equation of order five and degree 11 is explicitly given, such that every finite set of nonvanishing derivatives y^(k₁)(τ),…,y^(k_r)(τ) (1?k₁<?<k_r) at an algebraic point τ is linearly independent over the field of algebraic numbers. A linear transcendence measure for these values is effectively computed.     

Single-molecule conductance of redox molecules in electrochemical scanning tunneling microscopy

Experimental data and theoretical notions are presented for 6-[1'-(6-mercapto-hexyl)-[4,4']bipyridinium]-hexane-1-thiol iodide (6V6) "wired" between a gold electrode surface and tip in an in situ scanning tunneling microscopy configuration. The viologen group can be used to "gate" charge transport across the molecular bridge through control of the electrochemical potential and consequently the redox state of the viologen moiety. This gating is theoretically considered within the framework of superexchange and coherent two-step notions for charge transport. It is shown here that the absence of a maximum in the Itunneling versus electrode potential relationship can be fitted by a "soft" gating concept. This arises from large configurational fluctuations of the molecular bridge linked to the gold contacts by flexible chains. This view is incorporated in a formalism that is well-suited for data analysis and reproduces in all important respects the 6V6 data for physically sound values of the appropriate parameters. This study demonstrates that fluctuations of isolated configurationally "soft" molecules can dominate charge transport patterns and that theoretical frameworks for compact monolayers may not be directly applied under such circumstances.     

Factorization theorems for some scales of operator ideals

Let ??_p and ?_p denote the operator ideals generated by the approximation numbers and entropy numbers, respectively. If 0<p,q< ∞ and \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{p} + \frac{1}{q} = \frac{1}{r}, $\end{document} then ??_p °_q=??_r and ?_p °_q=?_r.     

The Application of NMR Spectroscopy and Chemometrics in Authentication of Spices

Spices and herbs are among the most commonly adulterated food types. This is because spices are widely used to process food. Spices not only enhance the flavor and taste of food, but they are also sources of numerous bioactive compounds that are significantly beneficial for health. The healing effects of spices are connected with their antimicrobial, anti-inflammatory and carminative properties. However, regular consumption of adulterated spices may cause fatal damage to our system because adulterants in most cases are unhealthy. For that reason, the appropriate analytical methods are necessary for quality assurance and to ensure the authenticity of spices. Spectroscopic methods are gaining interest as they are fast, require little or no sample preparation, and provide rich structural information. This review provides an overview of the application of NMR spectroscopy combined with chemometric analysis to determine the quality and adulteration of spices.