The Quantum Mellin transform

We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary change of basis from the position x on the half line to the Hyperbolic momentum $p_\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\eta$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.Comment: 23 pages, 6 Figure

Investigation of the thermal expansion and heat capacity of the CaCu3Ti4O12 ceramics

The thermal expansion of the CaCu3Ti4O12 ceramics has been measured over a wide temperature range 120–1200 K. The high quality of the samples under study has been confirmed by good agreement of the results of measurements of the heat capacity in the range 2–300 K and in the vicinity of the phase transition of magnetic nature at 25 K with the data for the single crystal. No anomalies in the thermal expansion that can be associated with the phase transition at 726–732 K assumed by other investigators have been found. The influence exerted on the thermal expansion by the heat treatment of the sample in a helium atmosphere and in air has been investigated

IL-6 and IL-8 secretion by human glioma cells proliferating after Gamma-knife irradiation

One of the modern methods of treating patients with primary and recurrent brain tumors is radiosurgical irradiation using Gamma Knife, which allows therapeutic doses to be delivered to tumors not exceeding 2.5 cm in diameter in 1–2 sessions. Tumor cells on the periphery of this tissue volume that receive lower radiation doses can resume proliferation and serve as a source of recurrence. The increase of radiation dose may cause necroses formation and a worsening prognosis. The properties of glioblastoma cells that survive and resume proliferation long after stereotactic irradiation are still poorly known. The aim of the work was to evaluate the expression of IL-6 and IL-8 by glioblastoma A172, R1, T2, and T98G cell lines that resumed proliferation after sublethal Gamma Knife irradiation. Cells were irradiated once at doses ranging from 6 to 16 Gy, and then cultured for 40 days. Cell number was counted weekly; lethal and sublethal irradiation doses for each glioblastoma cell line were determined. In cultures descendant from proliferation of single most resistant cells, the level of IL-6 and IL-8 secretion after 96 hours cultivation (ng/1000 cells) was determined by ELISA. The cells of all four glioblastoma lines secreted IL-6 and IL-8 into culture medium. The highest production of cytokines, never before demonstrated for glioblastomas, was discovered in R1 cells. Glioblastoma T2 also had high interleukin production levels. In contrast to these lines, glioblastoma A172 (highly sensitive to the action of cytostatic drugs and radiation) secreted IL-6 at 30 times lower level than R1 cells. Glioblastoma T98G (highly resistant to the action of cytostatic drugs and radiation) also exhibited low interleukins production level. R1, T2, and T98G glioblastoma cells that resumed proliferation after irradiation had increased secretion of IL-6 and, to a lesser extent, IL-8. The dependence of cytokine production increase on irradiation dose for these cells was not linear. In contrast, A172 cells reduced IL-6 and IL-8 secretion under irradiation. The multidirectional changes in IL-6 and IL-8 production by cells of different glioblastoma lines were long-term and persisted for more than a month. The presented results cast doubt on the possibility to use IL-6 and IL-8 production by glioblastoma cells as potential biomarkers for early diagnosis, therapy monitoring as well as prognostic markers of the disease course

Fifth European Dirofilaria and Angiostrongylus Days (FiEDAD) 2016

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