Determination of Naphthazarin Derivatives in 16 Alkanna Species by RP-LC Using UV and MS for Detection

As part of our ongoing studies, a new and validated method for analysis of isohexenyl-naphthazarines in Turkish Alkanna species was developed. By using reversed phase material (Synergi MAX RP) it was possible to determine four known isohexenylnaphthazarin-derivatives, namely alkannin, acetylalkannin, deoxyalkannin, and β,β-dimethylacrylalkannin within 25 min in n-hexane extracts of the roots. The quantification of these compounds in 16 Anatolian Alkanna species is described for the first time. In order to assure peak identity LC-MS experiments were performed. Quantitative results revealed that the most dominant compound in the extracts was β,β-dimethylacrylalkannin.     

Regularization of diffusion tensor MRI via local coordinates

We propose a novel framework for regularization of symmetric positive-definite (SPD) tensors (e.g., diffusion tensors). This framework is based on differential geometry. The space of SPD matrices, P_n, is described as a Riemannian manifold that is parameterized via the Iwasawa coordinate system. Then, distances on P_n are measured in terms of a natural GL (n)-invariant Riemannian metric. Using the Beltrami framework we construct a set of coupled geometric PDEs with respect to the Iwasawa coordinates. Then, by means of the gradient descent method these equations define the regularization flow over P_n. It appears to be that the local coordinate approach via that coordinate system results in very simple numerics that leads to fast convergence of the algorithm. We demonstrate the efficiency of this algorithm on real volumetric DTI datasets. Results of fibers tractography before and afterthe regularization process arepresented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cylindrical Tank Filled With a Liquid in a Three-Dimensional Temperature Field

In the cylindrical coordinate system, we construct an exact solution of the threedimensional thermoelasticity problem for a tank filled with a liquid. After determining the temperature field from the heat conduction equation, we solve the equations of the asymmetrical problem of the theory of elasticity. In doing so, the system of resolving equations is reduced to four separate equations with respect to the displacements of the construction. Several exact solutions of boundary-value problems are found. The results are presented in the form of rather simple formulas.     

The Limitations of Nonlinear Fluorescence Effect in Super Resolution Saturated Structured Illumination Microscopy System

Classically, optical systems are considered to have a fundamental resolution limit due to diffraction. Many strategies for improving both axial and lateral resolutions are based on a priori information about the input signal. These strategies lead to a numerical aperture improvement. However these are still limited by the wave nature of light. By using fluorescence technique one theoretically can reach unlimited resolution. The key point is to use the nonlinear dependence of the fluorescence emission rate on the intensity of the applied illumination. In this paper we present simulation as well as experimental results which show the advantage and the problems of using the nonlinear fluorescence effect in super resolution systems as well as discussing the nonlinear phenomena concerning the fluorescence process. The results show that the nonlinear fluorescence effect is accompanied by severe quenching, bleaching and saturation phenomena. As consequence, super resolution using saturated structured illumination method in living biological samples becomes severely restricted.     

Fluctuations and the onset of chaos

We consider the role of fluctuations on the onset and characteristics of chaotic behavior associated with period doubling subharmonic bifurcations. By studying the problem of forced dissipative motion of an anharmonic oscillator we show that the effect of noise is to produce a bifurcation gap in the set of available states. We discuss the possible experimental observation of this gap in many systems which display turbulent behavior.     

3D Euler spirals for 3D curve completion

Shape completion is an intriguing problem in geometry processing with applications in CAD and graphics. This paper defines a new type of 3D curve, which can be utilized for curve completion. It can be considered as the extension to three dimensions of the 2D Euler spiral. We prove several properties of this curve - properties that have been shown to be important for the appeal of curves. We illustrate its utility in two applications. The first is “fixing” curves detected by algorithms for edge detection on surfaces. The second is shape illustration in archaeology, where the user would like to draw curves that are missing due to the incompleteness of the input model.     

Due-date assignment on uniform machines

The classical weighted minsum scheduling and due-date assignment problem (with earliness, tardiness and due-date costs) was shown to be polynomially solvable on a single machine, more than two decades ago. Later, it was shown to have a polynomial time solution in the case of identical processing time jobs and parallel identical machines. We extend the latter setting to parallel uniform machines. We show that the two-machine case is solved in constant time. Furthermore, the problem remains polynomially solvable for a given (fixed) number of machines.