Regioselective acylation of aminoresorcinarenes

The acid catalyzed hydrolytic cleavage of the oxazine rings in the readily available tetraoxazine derivatives of resorcinarenes results in tetraaminoresorcinarenes. A similar process applied to C₂-symmetrical bisoxazine resorcinarene tetratosylates affords C_2v-symmetrical resorcinarenediamines. The mild acylation of these resorcinareneamines with BOC-anhydride or para-nitrophenyl ester proceeds selectively at the nitrogen atoms without affecting the hydroxyl groups. Most of the resulting resorcinareneamides are thus obtained in preparative yields and can be easily purified by simple crystallizations. In the crystalline state the compounds obtained are found to bind chloride anions through hydrogen bonds and electrostatic interactions and to display a chiral arrangement of hydrogen bonded functional groups at the wide rim of the macrocycle.     

Solution of linear equations with Hankel and Toeplitz matrices

Summary An algorithm is described for solving a linear equationA x=c, whereA is ann×n Hankel or Toeplitz matrix, inO (n ²) arithmetic operations. As contrasted with earlier such algorithms the present one does not require the principal minors ofA to be non-zero except detA.     

Model selection by sequentially normalized least squares

Model selection by means of the predictive least squares (PLS) principle has been thoroughly studied in the context of regression model selection and autoregressive (AR) model order estimation. We introduce a new criterion based on sequentially minimized squared deviations, which are smaller than both the usual least squares and the squared prediction errors used in PLS. We also prove that our criterion has a probabilistic interpretation as a model which is asymptotically optimal within the given class of distributions by reaching the lower bound on the logarithmic prediction errors, given by the so called stochastic complexity, and approximated by BIC. This holds when the regressor (design) matrix is non-random or determined by the observed data as in AR models. The advantages of the criterion include the fact that it can be evaluated efficiently and exactly, without asymptotic approximations, and importantly, there are no adjustable hyper-parameters, which makes it applicable to both small and large amounts of data.     

Exploring hurdles to transfer : student experiences of applying knowledge across disciplines

This paper explores the ways students perceive the transfer of learned knowledge to new situations – often a surprisingly difficult prospect. The novel aspect compared to the traditional transfer studies is that the learning phase is not a part of the experiment itself. The intention was only to activate acquired knowledge relevant to the transfer target using a short primer immediately prior to the situation where the knowledge was to be applied. Eight volunteer students from either mathematics or computer science curricula were given a task of designing an adder circuit using logic gates: a new context in which to apply knowledge of binary arithmetic and Boolean algebra. The results of a phenomenographic classification of the views presented by the students in their post-experiment interviews are reported. The degree to which the students were conscious of the acquired knowledge they employed and how they applied it in a new context emerged as the differentiating factors.     

Stock price dynamics and option valuations under volatility feedback effect

According to the volatility feedback effect, an unexpected increase in squared volatility leads to an immediate decline in the price–dividend ratio. In this paper, we consider the properties of stock price dynamics and option valuations under the volatility feedback effect by modeling the joint dynamics of stock price, dividends, and volatility in continuous time. Most importantly, our model predicts the negative effect of an increase in squared return volatility on the value of deep-in-the-money call options and, furthermore, attempts to explain the volatility puzzle. We theoretically demonstrate a mechanism by which the market price of diffusion return risk, or an equity risk-premium, affects option prices and empirically illustrate how to identify that mechanism using forward-looking information on option contracts. Our theoretical and empirical results support the relevance of the volatility feedback effect. Overall, the results indicate that the prevailing practice of ignoring the time-varying dividend yield in option pricing can lead to oversimplification of the stock market dynamics.     

Subcomponent Self-Assembly of a Cyclic Tetranuclear FeII Helicate in a Highly Diastereoselective Self-Sorting Manner

An enantiomerically pure diamine based on the 4,15-difunctionalized [2.2]paracyclophane scaffold and 2-formylpyridine self-assemble into an optically pure cyclic metallosupramolecular Fe₄L₆ helicate upon mixing with iron(II) ions in a diastereoselective subcomponent self-assembly process. The cyclic assembly results from steric strain that prevents the formation of a smaller linear dinuclear triple-stranded helicate, and hence, leads to the larger strain-free assembly that fulfils the maximum occupancy rule. Interestingly, use of the racemic diamine also leads to a racemic mixture of the homochiral cyclic helicates as the major product in a highly diastereoselective narcissistic chiral self-sorting manner given the fact that the assembly contains ten stereogenic elements, which can in principle give rise to 149 different diastereomers. The metallosupramolecular aggregates could be characterized by NMR, UV/Vis and CD spectroscopy, mass spectrometry, and X-ray crystallography.     

N‐Alkyl Ammonium Resorcinarene Salts as High‐Affinity Tetravalent Chloride Receptors

N‐Alkyl ammonium resorcinarene salts (NARYs, Y=triflate, picrate, nitrate, trifluoroacetates and NARBr) as tetravalent receptors, are shown to have a strong affinity for chlorides. The high affinity for chlorides was confirmed from a multitude of exchange experiments in solution (NMR and UV/Vis), gas phase (mass spectrometry), and solid‐state (X‐ray crystallography). A new tetra‐iodide resorcinarene salt (NARI) was isolated and fully characterized from exchange experiments in the solid‐state. Competition experiments with a known monovalent bis‐urea receptor ( 5 ) with strong affinity for chloride, reveals these receptors to have a much higher affinity for the first two chlorides, a similar affinity as 5 for the third chloride, and lower affinity for the fourth chloride. The receptors affinity toward chloride follows the trend K₁?K₂?K₃≈ 5 >K₄, with K_a=5011 m ^?1 for 5 in 9:1 CDCl₃/[D₆]DMSO.     

Control of N‐Heterocyclic Carbene Catalyzed Reactions of Enals: Asymmetric Synthesis of Oxindole‐γ‐Amino Acid Derivatives

A strategy to control the switch between a non‐cycloaddition reaction and a cycloaddition reaction of enals, using N‐heterocyclic carbene (NHC) catalyisis, has been developed. The new scalable protocol leads to γ‐amino‐acid esters bearing a tetrasubstituted stereocenter in good yields and high stereoselectivities by homo‐Mannich reactions of enals and isatin‐derived ketimines. By simply changing the N‐ketimine substituent to an ortho‐hydroxy phenyl group, the corresponding spirocyclic oxindolo‐γ‐lactams are obtained.