New research findings in biotechnology for fuels and chemical production

Applied Biochemistry and Biotechnology -     

Deleting Outliers in Robust Regression with Mixed Integer Programming

In robust regression we often have to decide how many are the unusual observations, which should be removed from the sample in order to obtain better fitting for the rest of the observations. Generally, we use the basic principle of LTS, which is to fit the majority of the data, identifying as outliers those points that cause the biggest damage to the robust fit. However, in the LTS regression method the choice of default values for high break down-point affects seriously the efficiency of the estimator. In the proposed approach we introduce penalty cost for discarding an outlier, consequently, the best fit for the majority of the data is obtained by discarding only catastrophic observations. This penalty cost is based on robust design weights and high break down-point residual scale taken from the LTS estimator. The robust estimation is obtained by solving a convex quadratic mixed integer programming problem, where in the objective function the sum of the squared residuals and penalties for discarding observations is minimized. The proposed mathematical programming formula is suitable for small-sample data. Moreover, we conduct a simulation study to compare other robust estimators with our approach in terms of their efficiency and robustness.     

Sharp general local estimates for dyadic-like maximal operators and related Bellman functions

For each 1?q<p we precisely evaluate the main Bellman functions associated with the local Lp→Lq estimates of the dyadic maximal operator on Rn. Actually we do that in the more general setting of tree-like maximal operators and with respect to general convex and increasing growth functions. We prove that these Bellman functions equal to analogous extremal problems for the Hardy operator which can be viewed as a symmetrization principle for such operators. Under certain mild conditions on the growth functions we show that for the latter extremals exist (although for the original Bellman functions do not) and analyzing them we give a determination of the corresponding Bellman function.     

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.