Ranking the effect of [1A(ax), 1B(eq)] versus [1A(eq), 1B(ax)] cyclohexane ring substitution on the H chemical shifts of γ-methylene cyclohexane ring protons using 2,2-disubstituted adamantanes as models

When two different substituents are placed in the nonbridgehead position of adamantane, the two [1A(ax), 1B(eq)] and [1A(eq), 1B(ax)] cyclohexane chair conformers are modeled and features of their NMR spectra can be studied from a single spectrum at 298 K. The effect of [1A(ax), 1B(eq)] and [1A(eq), 1B(ax)] cyclohexane ring substitution on the ¹H resonance separation within the γ-CH₂s of cyclohexane ring is compared for various substituent pairs; this aim is approached by measuring the ¹H chemical shift separation within the 4′,9′-H and 8′,10′-H methylenes from the ¹H NMR spectrum of the model 2A,2B-disubstituted adamantane at 298 K.     

The Sedimentation of Colloidal Nanoparticles in Solution and Its Study Using Quantitative Digital Photography

Sedimentation and diffusion are important aspects of the behavior of colloidal nanoparticles in solution, and merit attention during the synthesis, characterization, and application of nanoparticles. Here, the sedimentation of nanoparticles is studied quantitatively using digital photography and a simple model based on the Mason–Weaver equation. Good agreement between experimental time‐lapse photography and numerical solutions of the model is found for a series of gold nanoparticles. The new method is extended to study for the first time the gravitational sedimentation of DNA‐linked gold nanoparticle dimers as a model system of a higher complexity structure. Additionally, simple formulas are derived for estimating suitable parameters for the preparative centrifugation of nanoparticle solutions.     

Restricted Universality of Power Series

We prove the existence of a power series having radius of convergence0, whose partial sums have universal approximation propertieson any compact set with connected complement that is containedin a finite union of circles centred at 0 and having rationalradii, but do not have such properties on any compact set withnonempty interior. This relates to a theorem of A. I. Seleznev.2000 Mathematics Subject Classification 30B30 (primary), 30B10,30E60 (secondary).     

On the Vekua Pair in Spheroidal Geometry and its Role in Solving Boundary Value Problems

The Vekua pair forms a transformation between the kernel of the Laplace's and the kernel of the Helmholtz's operator. In fact, it provides an interior solution of the Helmholtz's equation once an interior harmonic function is given, and conversely, given an interior solution of the Helmhotz's equation an interior harmonic function is constructed. Consequently, it seems that the Vekua connection offers the perfect ground to obtain solutions of boundary value problems connected with Helmholtz operator. Vekua expressed his transformation in spherical coordinates. Nevertheless, when a change of coordinates is applied, the transformation assumes a much more complicated form, but it still remains a very useful technique for dealing with solutions of the equations of Laplace and Helmholtz. Here we extend the Vekua theory to a new integral transformation pair concerning solutions of the aforementioned operators in exterior domains. In addition, the form of the Vekua transformation is analyzed in spheroidal coordinates and its implication to boundary value problems is investigated.     

Essential oils of Satureja species: insecticidal effect on Culex pipiens larvae (Diptera: Culicidae)

The chemical composition of the essential oils of the wild growing plants of Greek S. spinosa L., S. parnassica subsp. parnassica Heldr.& Sart ex Boiss., S. thymbra and S. montana were determined by GC and GC/MS analysis. The larvicidal activities of the essential oils were assayed against Culex pipiens biotype molestus. The analytical data indicated that various monoterpene hydrocarbons and phenolic monoterpenes constitute the major constituents of the oils, but their concentration varied greatly among the oils examined. The bioassay results indicated that the oils possess significant larvicidal activities and represent an inexpensive source of natural substances mixture that exhibit potentials for use to control the mosquito larvae.     

The concept of material forces in phase transition problems within the level-set framework

The dynamics of a phase transition front in solids using the level set method is examined in this paper. Introducing an implicit representation of singular surfaces, a regularized version of the sharp interface model arises. The interface transforms into a thin transition layer of nonzero thickness where all quantities take inhomogeneous expressions within the body. It is proved that the existence of an inhomogeneous energy of the material predicts inhomogeneity forces that drive the singularity. The driving force is a material force entering the canonical momentum equation (pseudo-momentum) in a natural way. The evolution problem requires a kinetic relation that determines the velocity of the phase transition as a function of the driving force. Here, the kinetic relation is produced by invoking relations that can be considered as the regularized versions of the Rankine–Hugoniot jump conditions. The effectiveness of the method is illustrated in a shape memory alloy bar.     

In Vitro and In Vivo Enzyme‐Mediated Biomineralization of Oligo(poly(ethylene glycol) Fumarate Hydrogels

The enzyme alkaline phosphatase (ALP) is added at different concentrations (i.e., 0, 2.5, and 10 mg · ml^?1) to oligo(poly(ethylene glycol)fumarate) (OPF) hydrogels. The scaffolds are either incubated in 10 mM calcium glycerophosphate (Ca–GP) solution for 2 weeks or implanted in a rat subcutaneous model for 4 weeks. Fourier transform infrared (FTIR) spectroscopy, X‐ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and alizarin red staining show a strong ability to form minerals exclusively in ALP‐containing hydrogels in vitro. Additionally, the calcium content increases with increasing ALP concentration. Similarly, only ALP‐containing hydrogels induce mineralization in vivo. Specifically, small (≈5–20 µm) mineral deposits are observed at the periphery of the hydrogels near the dermis/scaffold interface using Von Kossa and alizarin red staining.

     

Coarse topological transitivity on open cones and coarsely J-class and D-class operators

We generalize the concept of coarse hypercyclicity, introduced by Feldman in [13], to that of coarse topological transitivity on open cones. We show that a bounded linear operator acting on an infinite dimensional Banach space with a coarsely dense orbit on an open cone is hypercyclic and a coarsely topologically transitive (mixing) operator on an open cone is topologically transitive (mixing resp.). We also “localize” these concepts by introducing two new classes of operators called coarsely J-class and coarsely D  -class operators and we establish some results that may make these classes of operators potentially interesting for further studying. Namely, we show that if a backward unilateral weighted shift on l²(N)$l^2(\mathbb{N})$ is coarsely J-class (or D  -class) on an open cone then it is hypercyclic. Then we give an example of a bilateral weighted shift on l^∞(Z)$l^{\infty }(\mathbb{Z})$ which is coarsely J-class, hence it is coarsely D-class, and not J  -class. Note that, concerning the previous result, it is well known that the space l^∞(Z)$l^{\infty }(\mathbb{Z})$ does not support J-class bilateral weighted shifts, see [10]. Finally, we show that there exists a non-separable Banach space which supports no coarsely D-class operators on open cones. Some open problems are added.