An adaptive finite element method for singular parabolic equations

Summary. In this paper we consider additive Schwarz-type iteration methods for saddle point problems as smoothers in a multigrid method. Each iteration step of the additive Schwarz method requires the solutions of several small local saddle point problems. This method can be viewed as an additive version of a (multiplicative) Vanka-type iteration, well-known as a smoother for multigrid methods in computational fluid dynamics. It is shown that, under suitable conditions, the iteration can be interpreted as a symmetric inexact Uzawa method. In the case of symmetric saddle point problems the smoothing property, an important part in a multigrid convergence proof, is analyzed for symmetric inexact Uzawa methods including the special case of the additive Schwarz-type iterations. As an example the theory is applied to the Crouzeix-Raviart mixed finite element for the Stokes equations and some numerical experiments are presented. Mathematics Subject Classification (1991):65N22, 65F10, 65N30Supported by the Austrian Science Foundation (FWF) under the grant SFB F013}\and Walter Zulehner     

Prediction problem in quantum mechanics is intractable (NP-Hard)

It is proved that both the prediction problem and the problem of reconstructing the state from the observations in quantum mechanics are NP-hard.     

Identification of pyrrolo-pyridine derivatives as novel class of antibacterials

Molecular Diversity - A series of 5-oxo-4H-pyrrolo[3,2-b]pyridine derivatives was identified as novel class of highly potent antibacterial agents during an extensive large-scale high-throughput...     

Triangle Geometry of the Qubit State in the Probability Representation Expressed in Terms of the Triada of Malevich’s Squares

We map the density matrix of the qubit (spin-1/2) state associated with the Bloch sphere and given in the tomographic probability representation onto vertices of a triangle determining Triada of Malevich’s squares. The three triangle vertices are located on three sides of another equilateral triangle with the sides equal to\( \sqrt{2} \). We demonstrate that the triangle vertices are in one-to-one correspondence with the points inside the Bloch sphere and show that the uncertainty relation for the three probabilities of spin projections +1/2 onto three orthogonal directions has the bound determined by the triangle area introduced. This bound is related to the sum of three Malevich’s square areas where the squares have sides coinciding with the sides of the triangle. We express any evolution of the qubit state as the motion of the three vertices of the triangle introduced and interpret the gates of qubit states as the semigroup symmetry of the Triada of Malevich’s squares. In view of the dynamical semigroup of the qubit-state evolution, we constructed nonlinear representation of the group U(2).     

Anomalous capacitance of quantum well double-barrier diodes

The S-parameters of several different quantum well double barrier diodes have been measured. A technique has been developed for measuring whisker contacted diodes with and HP 8510B automatic network analyzer. Special coaxial mounts using K-connectors were designed to enable measurements up to 20 GHz. The voltage-dependent conductance and capacitance were derived from the measured reflection coefficient of each device. The C/V characteristics were observed to exhibit an anomalous increase at voltages corresponding the the negative differential resistance region (NDR). These are the first reported S-parameter measurements in the negative differential resistance region of quantum well double barrier diodes. A theory is presented that explains, in part, the observed results.     

Acoustic Radiation Force Impulse-Imaging for the evaluation of the thyroid gland: a limited patient feasibility study

Purpose

Real-time tissue elastography, a qualitative elastography method, has shown promising results in the diagnostic work up of thyroid nodules. However, to our knowledge no study has evaluated a quantitative elastography method in the thyroid gland. The present study is a feasibility study evaluating Acoustic Radiation Force Impulse-Imaging, a novel quantitative elastography method in the thyroid gland.

Methods

ARFI-imaging involves the mechanical excitation of tissue using short-duration acoustic pulses to generate localized displacements in tissue. The displacements induce a lateral shear-wave propagation which is tracked using multiple laterally positioned ultrasound “tracking“ beams. Inclusion criteria were: thyroid nodules ?1 cm, non-functioning or hypo-functioning on radionuclide scanning, and cytological/histological assessment of thyroid nodule as reference method. All patients received conventional ultrasound, and examination of the thyroid gland including Power Doppler Ultrasound using a 9 MHz linear transducer, in addition real-time elastography (RTE) was performed at 9 MHz frequency and ARFI-imaging was performed at 4 MHz using Siemens (ACUSON S2000) B-mode-ARFI combination transducer.

Results

Sixty nodules in 55 patients were analyzed. Three nodules were papillary carcinoma. The stiffer the tissue the faster the shear wave propagates. The results obtained indicated that the shear wave velocity in thyroid lobes ranged between 0.5 and 4.9 m/s. The median velocity of ARFI-imaging in the healthy nodule-free thyroid gland, as well as in benign and malignant thyroid nodules was 1.98 m/s (range: 1.20-3.63 m/s), 2.02 m/s (range: 0.92-3.97 m/s), and 4.30 m/s (range: 2.40-4.50 m/s), respectively. While no significant difference in median velocity was found between healthy thyroid tissue and benign thyroid nodules, a significant difference was found between malignant thyroid nodules on the one hand and healthy thyroid tissue (p = 0.018) or benign thyroid nodules (p = 0.014) on the other hand. Specificity of ARFI-imaging for the differentiation of benign and malignant thyroid nodules was comparable with RTE (91-95%).

Conclusions

ARFI can be performed in the thyroid tissue with reliable results.     

Comparative ultrastructural study of spermatozoa in some oyster species from the Asian-Pacific Coast

Sperm organization in the oysters Crassostrea gigas, Crassostrea nippona, Crassostrea cf. rivularis and Saccostrea cf. mordax inhabiting Asian Pacific coast was studied. The spermatozoa of all studied species had a number of common morphological characters such as a cup-like acrosome with heterogeneous matrix on its top, an axial rod in the subacrosomal space, a barrel-shaped nucleus, four mitochondria in the midpiece, pericentriolar complexes, and a 9+2-organized flagellum. The spermatozoa of C. cf. rivularis differed from the other species by having cytoplasm processes in the midpiece region. Such structures have never been described in the Ostreidae. Additionally, each species could be identified by the shape and size of sperm compartments (acrosome, nucleus, anterior nuclear fossa). The most significant interspecific difference was found in the size of an anterior nuclear fossa. The smallest anterior nuclear fossa was found in C. cf. rivularis (about 0.24 μm in length reaching about 22% of the nuclear length) while the biggest in C. gigas from the Sea of Japan (about 0.53 μm in length reaching about 46% of the nuclear length). The spermatozoa of C. gigas collected from the Sea of Japan and Taiwan Strait differed significantly in almost all the studied parameters. Since sperm morphology has been successfully used for species differentiation, this suggests the existence of two species rather than two populations. The data obtained indicate the species-specific difference in the sperm ultrastructure within the Ostreidae, which may be identified both ultrastructurally and morphometrically.     

Coherent States of a Free Particle with Varying Mass in the Probability Representation of Quantum Mechanics

Journal of Russian Laser Research - We construct Gaussian coherent states of a free particle with time-dependent mass, using symplectic tomographic probability distribution and integrals of motion...     

Ionization penalty in nonlinear Raman neuroimaging

Light-assisted ionization accompanying coherent anti-Stokes Raman scattering (CARS) of ultrashort laser pulses in brain tissue is shown to manifest itself in a detectable blueshift of the anti-Stokes signal. This blueshift can serve as an indicator of ionization processes in CARS-based neuroimaging.