Relative Thermodynamic Stabilities of Isomeric Vinyl Ethers Derived from 2-Acetyland 2-Isobutyryltetrahydrofurans. An Experimental and DFT Study

The relative thermodynamic stabilities of four isomeric vinyl ethers obtained by acid-catalyzed cleavage of MeOH from the dimethyl acetals of both 2-acetyltetrahydrofuran and 2-isobutyryltetrahydrofuran have been determined by chemical equilibration in cyclohexane solution. In addition, the structures and relative energies of many of these compounds have also been studied theoretically by DFT calculations. In each series of compounds, the endocyclic isomers, 5-(1-methoxyethyl)-2,3-dihydrofuran and 5-(1-methoxy-2-methylpropyl)-2,3-dihydrofuran, respectively, show the highest thermodynamic stabilities. This is particularly prominent for the vinyl ethers derived from 2-isobutyryltetrahydrofuran in which the equilibrium mixture consists of 90% of the endocyclic isomer at room temperature. The geometrical (exocyclic) isomers of the latter series of compounds show unexpected relative thermodynamic stabilities, but on the basis of the geometry-optimized structures provided by the DFT calculations, a reasonable explanation can be found.     

Linear viscoelastic models: Part II. Recovery of the molecular weight distribution using viscosity data

The constitutive models for the viscoelasticity of polymers are presented for determining molecular weight distributions (MWDs) from viscosity measurements. The inversion of this model derived from control theory and melt calibration procedure connects the relaxation modulus, viscosity, and other flow properties of a polymer. The linear principle enables simultaneous and accurate modelling of the relaxation modulus and of viscosity flow curves over a wide range. Starting from viscosity measurements, the new model is used to determine the MWD, linear viscoelastic relaxation moduli, and the relaxation spectra of polyethylene of different grades. In addition, two benchmark analyses of bimodal polystyrene are reported, and the capability of the model is proven by the two-box test of Malkin. The error of the modelled viscosity is smaller than that for previously reported models. One of the main features of this work is that no relaxation time or spectrum procedures were used to generate and model linear viscoelasticity.     

Fast and Ultraclean Approach for Measuring the Transport Properties of Carbon Nanotubes

In this work, a fast approach for the fabrication of hundreds of ultraclean field‐effect transistors (FETs) is introduced, using single‐walled carbon nanotubes (SWCNTs). The synthesis of the nanomaterial is performed by floating‐catalyst chemical vapor deposition, which is employed to fabricate high‐performance thin‐film transistors. Combined with palladium metal bottom contacts, the transport properties of individual SWCNTs are directly unveiled. The resulting SWCNT‐based FETs exhibit a mean field‐effect mobility, which is 3.3 times higher than that of high‐quality solution‐processed CNTs. This demonstrates that the hereby used SWCNTs are superior to comparable materials in terms of their transport properties. In particular, the on–off current ratios reach over 30 million. Thus, this method enables a fast, detailed, and reliable characterization of intrinsic properties of nanomaterials. The obtained ultraclean SWCNT‐based FETs shed light on further study of contamination‐free SWCNTs on various metal contacts and substrates.     

Analysis of the probe-fed annular microstrip antenna for hyperthermic applicators

The exact image theory is applied to obtain the exact field distribution of an annular microstrip radiator over a two layered biological medium. First, the image functions for the three layer structure (substrate-skin-fat) are derived by expanding the Fourier domain reflection coefficient into a sum of pole terms, known also as the Mittag-Leffler expansion. Secondly, the current distribution on the strip is solved by using the Galerkin’s method with continuous trigonometrical basis functions. In order to reduce the focus of the antenna, the dependence of the focus size on the radius of the antenna is calculated.     

Spectral characterization of the quadratic variation of mixed Brownian–fractional Brownian motion

Dzhaparidze and Spreij (Stoch Process Appl, 54:165–174, 1994) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This class contains both semimartingales and non-semimartingales. The motivation comes partially from the recent work by Bender et al. (Finance Stoch, 12:441–468, 2008), where it is shown that the quadratic variation of the log-returns determines the hedging strategy.     

Statistical Inference with Fractional Brownian Motion

We give a test between two complex hypothesis; namely we test whether a fractional Brownian motion (fBm) has a linear trend against a certain non-linear trend. We study some related questions, like goodness-of-fit test and volatility estimation in these models.     

Solvability of Minimal Graph Equation Under Pointwise Pinching Condition for Sectional Curvatures

We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan–Hadamard manifold M whose radial sectional curvatures outside a compact set satisfy an upper bound

$$\begin{aligned} K(P)\le - \frac{\phi (\phi -1)}{r(x)^2} \end{aligned}$$

and a pointwise pinching condition

$$\begin{aligned} |K(P) |\le C_K|K(P') | \end{aligned}$$

for some constants \(\phi >1\) and \(C_K\ge 1\), where P and \(P'\) are any 2-dimensional subspaces of \(T_xM\) containing the (radial) vector \(\nabla r(x)\) and \(r(x)=d(o,x)\) is the distance to a fixed point \(o\in M\). We solve the asymptotic Dirichlet problem with any continuous boundary data for dimensions \(n=\dim M>4/\phi +1\).