Stabilization of mixture of two rigid solids modeling temperature and porosity

In this paper we investigate the asymptotic behavior of solutions to the initial boundary value problem for a mixture of two rigid solids modeling temperature and porosity. Our main result is to establish conditions which ensure the analyticity and the exponential stability of the corresponding semigroup.     

Improving motion estimation by accounting for local image distortion

Cardiac elastography is a useful diagnostic technique for detection of heart function abnormalities, based on analysis of echocardiograms. The analysis of the regional heart motion allows assessing the extent of myocardial ischemia and infarction. In this paper, a new two-stage algorithm for cardiac motion estimation is proposed, where the data is taken from a sequence of 2D echocardiograms. The method combines the advantages of block-matching and optical flow techniques. The first stage employs a standard block-matching algorithm (sum of absolute differences) to provide a displacement estimate with accuracy of up to one pixel. At the second stage, this estimate is corrected by estimating the parameters of a local image transform within a test window. The parameters of the image transform are estimated in the least-square sense. In order to account for typical heart motions, like contraction/expansion, translation and rotation, a local affine model is assumed within the test window. The accuracy of the new algorithm is evaluated using a sequence of 500 grayscale B-mode images, which are generated as distorted, but known copies of an original ROI, taken from a real echocardiogram. The accuracy of the motion estimation is expressed in terms of errors: maximum absolute error, root-mean-square error, average error and standard deviation. The errors of the proposed algorithm are compared with these of the known block-matching technique with cross-correlation and interpolation in the sub-pixel space. Statistical analysis of the errors shows that the proposed algorithm provides more accurate estimates of the heart motion than the cross-correlation technique with interpolation in the sub-pixel space.     

Redox-Active Supramolecular Heteroleptic M4L2L′2 Assemblies with Tunable Interior Binding Site

Three Pt₄L₂L′₂ heteroleptic rectangles ( 1 – 3 ), containing ditopic redox-active bis-pyridine functionalized perylene bisimide (PBI) ligands PBI-pyr₂ ( L ) are reported. Co-ligand L′ is a dicarboxylate spacer of varying length, leading to modified overall size of the assemblies. ¹H NMR spectroscopy reveals a trend in the splitting and upfield chemical shift of the PBI-hydrogens in the rectangles with respect to free PBI, most pronounced with the largest strut length ( 3 ) and least with the smallest strut length ( 1 ). This is attributed to increased rotational freedom of the PBI-pyr ₂ ligand over its longitudinal axis (N_py-N_py), due to increased distance between the PBI-surfaces, which is corroborated by VT-NMR measurements and DFT calculations. The intramolecular motion entails desymmetrization of the two PBI-ligands, in line with cyclic voltammetry (CV) data. The first (overall two-electron) reduction event and re-oxidation for 1 display a subtle peak-to-peak splitting of 60 mV, whilst increased splitting of this event is observed for 2 and 3 . The binding of pyrene in 1 is probed to establish proof of concept of host-guest chemistry enabled by the two PBI-motifs. Fitting the binding curve obtained by ¹H NMR titration with a 1:1 complex formation model led to a binding constant of 964±55 m ⁻¹. Pyrene binding is shown to directly influence the redox-chemistry of 1 , resulting in a cathodic and anodic shift of approximately 46 mV on the first and second reduction event, respectively.     

Crystal structures of 2,4-dimethylthioxanthene 10,10-dioxide, 2,4,9-trimethylthioxanthene 10,10-dioxide,and 2,4-dimethyl-9-isopropylthioxanthene 10,10-dioxide

The structures of 2,4-dimethylthioxanthene 10,10-dioxide, 1 , 2,4,9-trimethylthioxanthene 10,10-dioxide, 2 , and 2,4-dimethyl-9-isopropylthioxanthene 10,10-dioxide, 3 , have been determined by x-ray diffraction. The central ring of the thioxanthene ring system is in a boat conformation. The 9-methyl substituent in 2 and the 9-isopropyl substituent in 3 are both in the boat-axial conformation with respect to the central ring. The folding angles between the planes of the two benzo rings are 136.6°, 142.9°, and 134.3° for 1, 2 , and 3 , respectively.     

A reduction method for atypical representations of classical Lie superalgebras

We introduce a reduction method for studying representations of classical Lie superalgebras with atypical central character. We show that the atypical quotient of universal enveloping algebra has a non-trivial Jacobson radical. The factor by this radical has a new center, which is calculated for sl(1|n) and psl(2|2). Using this center we obtain new character formulae, generalization of Borel-Weil-Bott and Beilinson-Bernstein localization theorems.     

Specification of oscillating chemical models starting from a given linearized form

The Lotka-Volterra model is shown to be the simplest unique model among those models having the same linearized form. We also show that the two-dimensional explodator model is not unique in its own class: there are four models possessing the same linearized form. Finally, we propose a method for the construction of formal chemical models having prescribed properties (i.e. having prescribed a type of one or more equilibrium points).