SHc^c Realization of Minimal Model CFT: Triality, Poset and Burge Condition

Recently an orthogonal basis of $\mathcal{W}_N$-algebra (AFLT basis) labeled by $N$-tuple Young diagrams was found in the context of 4D/2D duality. Recursion relations among the basis are summarized in the form of an algebra SH$^c$ which is universal for any $N$. We show that it has an $\mathfrak{S}_3$ automorphism which is referred to as triality. We study the level-rank duality between minimal models, which is a special example of the automorphism. It is shown that the nonvanishing states in both systems are described by $N$ or $M$ Young diagrams with the rows of boxes appropriately shuffled. The reshuffling of rows implies there exists partial ordering of the set which labels them. For the simplest example, one can compute the partition functions for the partially ordered set (poset) explicitly, which reproduces the Rogers-Ramanujan identities. We also study the description of minimal models by SH$^c$. Simple analysis reproduces some known properties of minimal models, the structure of singular vectors and the $N$-Burge condition in the Hilbert space.Comment: 1+38 pages and 12 figures. v2: typos corrected + comments adde

Über den N- und Harnsäurestoffwechsel bei der Leberpräparatgabe

Von manchen Autoren wurde klar gestellt, dass das Leberpräparat bei perniziöser Anämie, bei sekundärer Anämie und auch bei Nephrose wirksam ist Wir haben je einem Patienten von Gicht, amyotrophischer Lateralsklerose und Fettsucht, sowie einem Gesunden Hepatose (eine Art Leberpräparat) gegeben und den Einfluss der Hepatose auf den Harnsäure-, Harnstoff-, Ammoniak-, Rest-N-, Gesamt-, N-Gehalt im Blut und auch auf den Gesamt-N-, Harnstoff- und Harnsäure-Gehalt im Harn untersucht. Die Ergebnisse sind folgende: Beim Gichtkranken stieg der Harnsäurespiegel im Blut stark an und es zeigten sich vermehrte Gichtanfälle und eine Neubildung der Gichttophen. Bei den anderen war die Harnsäurevermehrung im Blut nicht so deutlich, aber die Harnsäureausscheidung im Harn nahm ziemlich auffallend zu. Der Ammoniakgehalt im Blut neigte zu leichter Verminderung, ausgenommen beim Gichtkranken. Beim Gichtkranken, welcher eine Funktionsstörung der Leber und der Niere aufwies, stieg der Rest-N-Gehalt im Blut deutlich an, während das bei den anderen nicht der Fall war. Der Gesamt-N-Gehalt im Harn vermehrte sich bei allen ohne Ausnahme. Der Harnstoff im Blut zeigte beim Gichtkranken eine geringe Vermehrung, bei den anderen blieb er dagegen fast unverändert. Für diese Ergebnisse soll der Faktor, dass Hepatose N-reich ist, eine grosse Rolle spielen, aber auch die Tatsache, dass Hepatose Vitamins und andere noch unklare wirksame Substanzen enthält, wie von uns schon an anderen Orten veröffentlicht wurde, mag einen Einfluss ausüben

Reflection states in Ding-Iohara-Miki algebra and brane-web for D-type quiver

Reflection states are introduced in the vertical and horizontal modules of the Ding-Iohara-Miki (DIM) algebra (quantum toroidal $\mathfrak{gl}_1$). Webs of DIM representations are in correspondence with $(p,q)$-web diagrams of type IIB string theory, under the identification of the algebraic intertwiner of Awata, Feigin and Shiraishi with the refined topological vertex. Extending the correspondence to the vertical reflection states, it is possible to engineer the $\mathcal{N}=1$ quiver gauge theory of D-type (with unitary gauge groups). In this way, the Nekrasov instanton partition function is reproduced from the evaluation of expectation values of intertwiners. This computation leads to the identification of the vertical reflection state with the orientifold plane of string theory. We also provide a translation of this construction in the Iqbal-Kozcaz-Vafa refined topological vertex formalism.Comment: 27 pages, 11 figures. Details of translation in terms of IKV refined topological vertex added in the second versio

(p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters

Instanton partition functions of $\mathcal{N}=1$ 5d Super Yang-Mills reduced on $S^1$ can be engineered in type IIB string theory from the $(p,q)$-branes web diagram. To this diagram is superimposed a web of representations of the Ding-Iohara-Miki (DIM) algebra that acts on the partition function. In this correspondence, each segment is associated to a representation, and the (topological string) vertex is identified with the intertwiner operator constructed by Awata, Feigin and Shiraishi. We define a new intertwiner acting on the representation spaces of levels $(1,n)\otimes(0,m)\to(1,n+m)$, thereby generalizing to higher rank $m$ the original construction. It allows us to use a folded version of the usual $(p,q)$-web diagram, bringing great simplifications to actual computations. As a result, the characterization of Gaiotto states and vertical intertwiners, previously obtained by some of the authors, is uplifted to operator relations acting in the Fock space of horizontal representations. We further develop a method to build qq-characters of linear quivers based on the horizontal action of DIM elements. While fundamental qq-characters can be built using the coproduct, higher ones require the introduction of a (quantum) Weyl reflection acting on tensor products of DIM generators.Comment: 42 page

Ultraviolet Laser Oscillations of Multiple Ionized Ions in Z-Pinch Discharge

Pulse laser oscillations from multiple ionized N, O and rare gases were observed in the ultraviolet region for the Z-pinch discharge. Optimum value of gas pressure, oscillation time and its pressure dependence were examined for laser oscillations. It has been found that oscillations from different ions occur in the increasing order of ionization after the breakdown of discharge. The line Aril λ4765 A showed an anomalous behavior. Calculation is made on two different models for ionization and excitation of plasma. The first one is concerned with ionization and excitation by thermal electrons during plasma compression. The second one is concerned with direct excitation of laser oscillation by runaway electrons. The calculation based on the former explains the temporal sequence of laser oscillations ; and that on the latter explains the anomalous behavior of ArII λ4765 A line

Rocuronium has a suppressive effect on platelet function via the p2y12 receptor pathway in vitro that is not reversed by sugammadex

Rocuronium is an aminosteroid nondepolarizing neuromuscular blocker that is widely used for anesthesia and intensive care. In this study, we investigated the effect of rocuronium on human platelet functions in vitro. The effects of rocuronium on platelet aggregation, P-selectin expression, and cyclic adenosine monophosphate (cAMP) levels in platelets were measured using an aggregometer, an enzyme immunoassay, and flow cytometry, respectively. Rocuronium inhibited ADP-induced platelet aggregation, P-selectin expression and suppression of cAMP production. These effects were not antagonized by equimolar sugammadex, a synthetic γ-cyclodextrin derivative that antagonizes rocuronium-induced muscle relaxation by encapsulating the rocuronium molecule. Morpholine, which constitutes a part of the rocuronium molecule but is not encapsulated by sugammadex, inhibited ADP-induced platelet aggregation. Vecuronium, which has a molecular structure similar to that of rocuronium but does not possess a morpholine ring, had no significant effect on ADP-induced platelet aggregation. These results indicate that rocuronium has a suppressive effect on platelet functions in vitro that is not reversed by sugammadex and suggest that this effect is mediated by blockade of the P2Y12 receptor signaling pathway via the morpholine ring of rocuronium

Observation of the Electrode Surface Microbes in Microbial Fuel Cells

Poster Presentation