Open string theory and planar algebras

In this note we show that abstract planar algebras are algebras over the topological operad of moduli spaces of stable maps with Lagrangian boundary conditions, which in the case of the projective line are described in terms of real rational functions. These moduli spaces appear naturally in the formulation of open string theory on the projective line. We also show two geometric ways to obtain planar algebras from real algebraic geometry, one based on string topology and one on Gromov-Witten theory. In particular, through the well known relation between planar algebras and subfactors, these results establish a connection between open string theory, real algebraic geometry, and subfactors of von Neumann algebras.Comment: 13 pages, LaTeX, 7 eps figure

Dynamic and structural stability of cubic vanadium nitride

Structural phase transitions in epitaxial stoichiometric VN/MgO(011) thin films are investigated using temperature-dependent synchrotron x-ray diffraction (XRD), selected-area electron diffraction (SAED), resistivity measurements, high-resolution cross-sectional transmission electron microscopy, and ab initio molecular dynamics (AIMD). At room temperature, VN has the B1 NaCl structure. However, below T_c=250K, XRD and SAED results reveal forbidden (001) reflections of mixed parity associated with a noncentrosymmetric tetragonal structure. The intensities of the forbidden reflections increase with decreasing temperature following the scaling behavior I∝(T_c−T)^(1/2). Resistivity measurements between 300 and 4 K consist of two linear regimes resulting from different electron/phonon coupling strengths in the cubic and tetragonal-VN phases. The VN transport Eliashberg spectral function α^(2)_(tr)F(ℏω), the product of the phonon density of states F(ℏω) and the transport electron/phonon coupling strengthα^(2)_(tr)(ℏω), is determined and used in combination with AIMD renormalized phonon dispersion relations to show that anharmonic vibrations stabilize the NaCl structure at T>T_c. Free-energy contributions due to vibrational entropy, often neglected in theoretical modeling, are essential for understanding the room-temperature stability of NaCl-structure VN, and of strongly anharmonic systems in general

Phase formation in CrFeCoNi nitride thin films

As a single-phase alloy, CrFeCoNi is a face centered cubic (fcc) material related to the archetypical high-entropy Cantor alloy CrFeCoNiMn. For thin films, CrFeCoNi of approximately equimolar composition tends to assume an fcc structure when grown at room temperature by magnetron sputtering. However, the single-phase solid solution state is typically not achieved for thin films grown at higher temperatures. The same holds true for Cantor alloy-based ceramics (nitrides and oxides), where phase formation is extremely sensitive to process parameters such as the amount of reactive gas. This study combines theoretical and experimental methods to understand the phase formation in nitrogen-containing CrFeCoNi thin films. Density functional theory calculations considering three competing phases (CrN, Fe-Ni and Co) show that the free energy of mixing, delta G of (CrFeCoNi)1-xNx solid solutions has a maximum at x = 0.20-0.25, and delta G becomes lower when x less than 0.20, greater than 0.25. Thin films of (CrFeCoNi)1-xNx (x = 0.14-0.41) grown by magnetron sputtering show stabilization of the metallic fcc when x lesser than or equal to 0.22 and the stabilization of the NaCl B1 structure when x is greater than 0.33, consistent with the theoretical prediction. In contrast, films with intermediate amounts of nitrogen (x = 0.22) grown at higher temperatures show segregation into multiple phases of CrN, Fe-Ni-rich and Co. These results offer an explanation for the requirement of kinetically limited growth conditions at low temperature for obtaining single-phase CrFeCoNi Cantor-like nitrogen-containing thin films and are of importance for understanding the phase-formation mechanisms in multicomponent ceramics

Лабораторна установка для дослідження ступеня очищення і пошкодження коренебульбоплодів

Патент України на корисну модель № 79083, МПК B65G 33/00, 2012.Лабораторна установка для дослідження ступеня очищення і пошкодження коренебульбоплодів, що містить раму, на якій з можливістю кутового та вертикального зміщення на підрамах встановлені секція пруткового транспортера-очисника та секція бітерних очисних валів, завантажувальний бункер, причому під секцією пруткового транспортера-очисника та секцією бітерних очисних валів на рамі розташовані поперечні лотки для відбору від сепарованих домішок, яка відрізняється тим, що кутовий зазор між центральною віссю барабана пруткового транспортера-очисника в зоні вивантаження коренебульбоплодів та центральною віссю першого бітерного очисного вала може змінюватись за рахунок використання різних отворів, які виконані на стійці та підрамі, а осьовий зазор – за рахунок кронштейна з отворами, причому над прутковим транспортером-очисником та секцією бітерних очисних валів встановлені вертикальні та похилі еластичні екрани, а для відбору очищених коренебульбоплодів в зоні вивантаження бітерних очисних валів розташована еластична ємність з можливістю вертикального переміщення та фіксації її задньої частини на вертикальному кронштейні

Uncertainty Relations in Deformation Quantization

Robertson and Hadamard-Robertson theorems on non-negative definite hermitian forms are generalized to an arbitrary ordered field. These results are then applied to the case of formal power series fields, and the Heisenberg-Robertson, Robertson-Schr\"odinger and trace uncertainty relations in deformation quantization are found. Some conditions under which the uncertainty relations are minimized are also given.Comment: 28+1 pages, harvmac file, no figures, typos correcte

Controls on the composition and lability of dissolved organic matter in Siberia's Kolyma River basin

High-latitude northern rivers export globally significant quantities of dissolved organic carbon (DOC) to the Arctic Ocean. Climate change, and its associated impacts on hydrology and potential mobilization of ancient organic matter from permafrost, is likely to modify the flux, composition, and thus biogeochemical cycling and fate of exported DOC in the Arctic. This study examined DOC concentration and the composition of dissolved organic matter (DOM) across the hydrograph in Siberia's Kolyma River, with a particular focus on the spring freshet period when the majority of the annual DOC load is exported. The composition of DOM within the Kolyma basin was characterized using absorbance-derived measurements (absorbance coefficienta330, specific UV absorbance (SUVA254), and spectral slope ratio SR) and fluorescence spectroscopy (fluorescence index and excitation-emission matrices (EEMs)), including parallel factor analyses of EEMs. Increased surface runoff during the spring freshet led to DOM optical properties indicative of terrestrial soil inputs with high humic-like fluorescence, SUVA254, and low SRand fluorescence index (FI). Under-ice waters, in contrast, displayed opposing trends in optical properties representing less aromatic, lower molecular weight DOM. We demonstrate that substantial losses of DOC can occur via biological (∼30% over 28 days) and photochemical pathways (>29% over 14 days), particularly in samples collected during the spring freshet. The emerging view is therefore that of a more dynamic and labile carbon pool than previously thought, where DOM composition plays a fundamental role in controlling the fate and removal of DOC at a pan-Arctic scale