Some Non-standard Sobolev Spaces, Interpolation and Its Application to PDE

We consider some nonstandard Sobolev spaces in one dimension, in which functions have different regularity in different subsets. These spaces are useful in the study of some nonlinear parabolic equations where the nonlinearity is highly degenerate and depends on the smoothness of the solution at a certain subset (that may vary with time). An example of application is a diffusion equation with a smooth free boundary, and a moving source/sink where the solution has singularity. The main new idea here is to characterize the functional space setting that is needed for semigroup theory to apply.     

Nickel Nanopillar Arrays Electrodeposited on Silicon Substrates Using Porous Alumina Templates

Nickel nanopillar arrays were electrodeposited onto silicon substrates using porous alumina membranes as a template. The characterization of the samples was done by scanning electron microscopy, X-ray diffraction, and alternating force gradient magnetometry. Ni nanostructures were directly grown on Si by galvanostatic and potentiostatic electrodeposition techniques in three remarkable charge transfer configurations. Differences in the growth mechanisms of the nanopillars were observed, depending on the deposition method. A high correlation between the height of the nanopillars and the charge synthesis was observed irrespective of the electrochemical technique. The magnetization measurements demonstrated a main dependence with the height of the nanopillars. The synthesis of Ni nanosystems with a controllable aspect ratio provides an effective way to produce well-ordered networks for wide scientific applications.     

Ellipsoidal mixed-integer representability

Representability results for mixed-integer linear systems play a fundamental role in optimization since they give geometric characterizations of the feasible sets that can be formulated by mixed-integer linear programming. We consider a natural extension of mixed-integer linear systems obtained by adding just one ellipsoidal inequality. The set of points that can be described, possibly using additional variables, by these systems are called ellipsoidal mixed-integer representable. In this work, we give geometric conditions that characterize ellipsoidal mixed-integer representable sets.     

Differentiation of recurrent brain tumor versus radiation injury using diffusion tensor imaging in patients with new contrast-enhancing lesions

BACKGROUND AND PURPOSE: The purpose of this study was to assess the use of diffusion tensor imaging (DTI) in the evaluation of new contrast-enhancing lesions and perilesional edema in patients previously treated for brain neoplasm in the differentiation of recurrent neoplasm from treatment-related injury. METHODS: Twenty-eight patients with new contrast-enhancing lesions and perilesional edema at the site of previously treated brain neoplasms were retrospectively reviewed. Nine directional echoplanar DTIs with b=1000 s/mm(2) were obtained using a single-shot spin-echo echoplanar imaging. Standardized regions of interest were manually drawn in several regions. Mean apparent diffusion coefficient (ADC), fractional anisotropy (FA) and eigenvalue indices (lambda( parallel) and lambda( perpendicular)) and their ratios relative to the contralateral side were compared in patients with recurrent neoplasm versus patients with radiation injury, as established by histological examination or by clinical course, including long-term imaging studies and magnetic resonance spectroscopy. RESULTS: The ADC values in the contrast-enhancing lesions were significantly higher (P=.01) for the recurrence group (range=1.01 x 10(-3) to 1.66 x 10(-3) mm(2)/s; mean+/-S.D.=1.27+/-0.15) than for the nonrecurrence group (range=0.9 x 10(-3) to 1.31 x 10(-3) mm(2)/s; mean+/-S.D.=1.12+/-0.14). The ADC ratios in the white matter tracts in perilesional edema trended higher (P=.09) in treatment-related injury than in recurrent neoplasm (mean+/-S.D.=1.85+/-0.30 vs. 1.60+/-0.27, respectively). FA ratios were significantly higher in normal-appearing white matter (NAWM) tracts adjacent to the edema in the nonrecurrence group (mean+/-S.D.=0.89+/-0.15) than in those in the recurrence group (mean+/-S.D.=0.74+/-0.14; P=.03). Both eigenvalue indices lambda( parallel) and lambda( perpendicular) were significantly higher in contrast-enhancing lesions in the recurrence group than in those in the nonrecurrence group (P=.02). As well, both eigenvalue indices lambda( parallel) and lambda( perpendicular) were significantly higher in perilesional edema than in normal white matter (P<.01 and P<.001, respectively) in both groups. CONCLUSION: The assessment of diffusion properties, especially ADC values and ADC ratios, in contrast-enhancing lesions, perilesional edema and NAWM adjacent to the edema in the follow-up of new contrast-enhancing lesions at the site of previously treated brain neoplasms may add to the information obtained by other imaging techniques in the differentiation of radiation injury from tumor recurrence.     

HPLC micro-fractionation coupled to a cell-based assay for automated on-line primary screening of calcium antagonistic components in plant extracts

High performance liquid chromatography (HPLC) micro-fractionation was successfully coupled to an automated ⁴⁵Ca²⁺ uptake assay using GH₄C₁ cells for the separation of natural product extracts and for the primary detection of their calcium antagonistic components. The reliability of the procedure was first established with a reference solution consisting of pure compounds with a known effect on the Ca²⁺ uptake. No loss of activity was observed to occur after HPLC micro-fractionation. Extracts of Peucedanum palustre and Pinus sylvestris, showing high and no inhibition of Ca²⁺ uptake as total extracts, respectively, were analysed and the inhibitory activity of the P. palustre extract could be traced to two components, identified as columbianadin and isoimperatorin. As expected, no significant inhibition was observed with the micro-fractionated P. sylvestris samples. In summary, the procedure was found to be applicable for primary detection of calcium antagonistic components in complex matrices and to significantly reduce the time previously needed for bioactivity-guided isolation.     

Proteome analysis of conditioned medium from cultured adult hippocampal progenitors

It is known that proliferation and survival of neural stem/progenitor cells in vitro not only depend on exogenous factors, but also on autocrine factors secreted into the conditioned medium. It is also well known that the identification of bioactive proteins secreted into the conditioned medium poses a substantial challenge. Recently, neural stem/progenitor cells were shown to secrete a survival factor, cystatin C, into the conditioned medium. Here, we demonstrate an approach to identify other low molecular weight proteins in conditioned medium from cultured adult rat hippocampal progenitor cells. A combination of preparative two-dimensional gel electrophoresis (2-DE) and mass spectrometry was utilized in the analysis. We were able to identify a number of proteins, which include Rho-guanine nucleotide dissociation inhibitor 1, phosphatidylethanolamine binding protein (PEBP), also termed Raf-1 kinase interacting protein, polyubiquitin, immunophilin FK506 binding protein 12 (FKBP12) and cystatin C. The presence of PEBP and FKBP12 in conditioned medium was confirmed immunologically. All nestin-positive progenitor cells showed immunoreactivity for antibodies against PEBP and FKBP12. To our knowledge we are the first to use this preparative proteomic approach to search for stem cell factors in conditioned medium. The method could be used to identify novel bioactive proteins secreted by stem/progenitor cells in vitro. Identification of bioactive proteins in vitro is of potential importance for the understanding of the regulatory mechanisms of the cells in vivo.     

Porphyrazines with annulated diazepine rings. 2. Alternative synthetic route to tetrakis-2,3-(5,7-diphenyl-1,4-diazepino)porphyrazines: new metal complexes, general physicochemical data, ultraviolet-visible linear and optical limiting behavior, and electrochemical and spectroelectrochemical properties

Following a previous report on the synthesis and physicochemical characterization of a novel class of porphyrazines carrying peripherally annulated seven-membered rings, i.e., tetrakis-2,3-(5,7-diphenyl-1,4-diazepino)porphyrazine [Ph(8)DzPzH(2)].4H(2)O and its metal derivatives [Ph(8)DzPzM].xH(2)O (x = 2-7, M = Mg(II)(H(2)O), Cu(II), and Zn(II)), a new more convenient procedure is reported here, allowing the preparation in high yields of the Li(I) and Na(I) derivatives of formulas [Ph(8)DzPzLi(2)].5H(2)O and [Ph(8)DzPzNa(2)].6H(2)O, which can be directly converted into other metal derivatives under mild conditions (room temperature) and in good yields. The series studied has been extended to include the Mn(II) and Co(II) complexes also reported here for the first time. Physicochemical characterization of the new "diazepinoporphyrazines" was based on fast atom bombardment (FAB) mass spectrometry and X-ray powder patterns, infrared (IR), electron paramagnetic resonance (EPR), and room-temperature magnetic susceptibility measurements. A detailed discussion of the UV-vis spectra emphasizes the role played by the external diazepine rings in electron delocalization through their tautomeric or protonated forms present in neutral, basic, and acidic media. The nonlinear optical effect of optical limiting for the different species [M = 2H, Mg(II)(H(2)O), Mn(II), Co(II), Cu(II), and Zn(II)] has also been measured. It has been observed that the extent of the optical limiting depends on the specific M center. The observed nonlinear optical features are analyzed and discussed in terms of the electronic and magnetic properties exhibited by some of the metal ions and taking into account the model of the excited-state absorption in which the nature of M determines the kinetics of formation of the highly absorbing state of the specific complex examined. As evidenced by the detailed electrochemical and spectroelectrochemical study carried out on this new class of macrocycles, one of the most important aspects is the facilitated electron delocalization for the oxidized and reduced species allowed by a 1H-6Htautomerism taking place on the peripheral diazepine rings.