Strategyproof matching with regional minimum and maximum quotas

This paper considers matching problems with individual/regional minimum/maximum quotas. Although such quotas are relevant in many real-world settings, there is a lack of strategyproof mechanisms that take such quotas into account. We first show that without any restrictions on the regional structure, checking the existence of a feasible matching that satisfies all quotas is NP-complete. Then, assuming that regions have a hierarchical structure (i.e., a tree), we show that checking the existence of a feasible matching can be done in time linear in the number of regions. We develop two strategyproof matching mechanisms based on the Deferred Acceptance mechanism (DA), which we call Priority List based Deferred Acceptance with Regional minimum and maximum Quotas (PLDA-RQ) and Round-robin Selection Deferred Acceptance with Regional minimum and maximum Quotas (RSDA-RQ). When regional quotas are imposed, a stable matching may no longer exist since fairness and nonwastefulness, which compose stability, are incompatible. We show that both mechanisms are fair. As a result, they are inevitably wasteful. We show that the two mechanisms satisfy different versions of nonwastefulness respectively; each is weaker than the original nonwastefulness. Moreover, we compare our mechanisms with an artificial cap mechanism via simulation experiments, which illustrate that they have a clear advantage in terms of nonwastefulness and student welfare

Polarography of Some Metal Ions in Fused LiCl-KCl-AlCl_3 System with a Dropping Mercury Electrode

Preparation and purification of fused LiCl-KCl-AlCl_3 System (m.p. 120℃) and polarographic behaviors of Pb(II), Cd(II), and Zn(II) ions in the fused salt at 160℃ were studied by using a dropping mercury electrode as an indicator electrode. All the current-voltage curves of these metal ions were reproducible and the electrode reactions were reversible. Each of log(i/i_d-i) vs. E plots gave a straight line with a slope of 43～45mV, which agreed well with the theoretical value of 43mV for two electron discharge at 160℃. The heights of the polarographic waves of Cd(II) and Zn(II) ions were proportional to their concentrations, and the diffusion current constants of Cd(II) and Zn(II) ions were 2.610±0.005 and 0.507±0.001, respectively

Trennung von Radioisotopen mit Ionenaustauscher-membranen I : Konzentrierung von Y-90 aus einer Sr-90-Y-90 Losung

Es gibt in der Literatur Berichte uber die Behandlung von radioaktiven Abfallen mit Ionenaustauschermembranen ; Beispiele von der Anwendung solcher Membranen fur die Trennung radioaktiver Nuklide jedoch sind nicht vorhanden. Die Verfasser der vorliegenden Arbeit haben die Konzentrierung von Y-90 aus einer Ausgangs-Sr-90-Y-90-Losung (im Gleichgewicht) untersucht. Es wurde festgestellt, daß Y-90 in einer schwefelsauren Losung durch eine Anionenaustauschermembrane diffundiert. Das Verhalten von Sr-89 gegenuber Ionenaustauschermembranen in verschiedenen Losungen wurde untersucht. Die Konzentrierung von Y-90 wurde unter den so ermittelten optimalen Bedingungen aus einer im Gleichgewichtszustand befindlichen Sr-90-Y-90-Losung durchgefuhrt. Aus den Versuchen mit Sr-89 wurde gefunden, daß es in einer waßrigen Losung mit einer Wasserstoffionenkonzentration von 10^ mol/l oder in einer NH_4Cl-HCl-Pufferlosung von pH 3.0 nicht durch eine Anionenaustauschermembrane diffundiert. Dem gegenuber wurde festgestellt, daß Y-90 aus einer Sr-90-Y-90-Losung wohl diffundiert. Die radio-chemische Reinheit des so gewonnenen Y-90 betragt uber 99%. Die Wanderungsge-schwindigkeit des radioaktiven Nuklids wird durch die elektrische Stromstarke, die Stromstarke durch die Gesamt-Ionenkonzentration der Losung beeinflußt. Die Y-90-Ausbeute ist folglich nicht von der primaren Y-90-Konzentration abhangig, sie wird durch die Stromstarke bestimmt

Polarographic Studies of Some Metal Ions in Fused LiCl-KCl and NaF-KF-LiF Eutectics by Using Improved Molybdenum Microelectrode of Dipping Type

In the first place, polarographic Studies of various metallic ions in fused LiCl-KCl eutectic at 450℃ were carried out by using improved molybdenum microelectrode of dipping type. By using a spiral molybdenum wire or a chlorine reference electrode as anode, effects of temperature, concentration of reducible species, microelectrode area and gas bubbling rate over the microelectrode surface were examined with Zn(II) as an example. The limiting current was independent of the gas bubbling rate from 0.5 to 3.5 sec/bubble and directly proportional to the microelectrode area and to the concentration of Zn(II). From the result of the temperature dependence of limiting current, the activation energy of the electrode process at the voltage showing limiting current was determined as 4.6 kcal/mole of Zn(II). This value may show that the limiting current obtained by this electrode is diffusion-controlled. From the polarographic behavior of Zn(II), it was concluded that this electrode reaction should be completely irreversible, because the relationship of log(i_d-i)/i vs. E was linear, the slope being 150mV at 450℃. Following the above fundamental studies, polarographic behaviors of T1(I), Cu(II), Cd(II), Al(III) and U(IV) were examined mainly on the relation between i～E curves and half-wave potentials. In the second place, polarographic studies of lead(II) ion in fused KF-NaF-LiF eutectic at 650℃ were carried out by improving the microelectrode mentioned above. The polarogram obtained showed an S-shaped form without a bend, and resembled that in the fused chloride. The relation between applied voltage and log(i_d-i)/i was linear. The half-wave potential was -0.55±0.01V vs. the molybdenum anode and the limiting current was proportional to the concentration of lead(II) ion ranging from 1.95～4.60m moles per 1000g fused salt

Requirement of Gαq/Gα11 Signaling in the Preservation of Mouse Intestinal Epithelial Homeostasis

Background & AimsProliferation, differentiation, and morphogenesis of the intestinal epithelium are tightly regulated by a number of molecular pathways. Coordinated action of intestine is achieved by gastrointestinal hormones, most of which exert these actions through G-protein–coupled receptors. We herein investigated the role of Gαq/11-mediated signaling in intestinal homeostasis.MethodsIntestinal tissues from control (Gnaqflox/floxGna11+/+), Int-Gq knock-out (KO) (VilCre+/-Gnaqflox/floxGna11+/+), G11 KO (Gnaqflox/floxGna11-/-), and Int-Gq/G11 double knock-out (DKO) (VilCre+/-Gnaqflox/floxGna11-/-) mice were examined by microscopy, transmission electron microscopy, and immunohistochemistry. The effect of Gαq/11-mediated signaling was studied in the cell lineage, proliferation, and apoptosis. Dextran sodium sulfate (DSS) colitis was induced to study the role of Gαq/11 in colon.ResultsPaneth cells were enlarged, increased in number, and mislocalized in Int-Gq/G11 DKO small intestine. Paneth cells also reacted with PAS and Muc2 antibody, indicating an intermediate character of Paneth and goblet cells. The nuclear β-catenin, T-cell factor 1, and Sox9 expression were reduced severely in the crypt base of Int-Gq/G11 DKO intestine. Proliferation was activated in the crypt base and apoptosis was enhanced along the crypt. Int-Gq/G11 DKO mice were susceptible to DSS colitis. Proliferation was inhibited in the crypt of unaffected and regenerative areas. Cystic crypts, periodic acid–Schiff–positive cells, and Muc2-positive cells were unusually observed in the ulcerative region.ConclusionsThe Gαq/11-mediated pathway plays a pivotal role in the preservation of intestinal homeostasis, especially in Paneth cell maturation and positioning. Wnt/β-catenin signaling was reduced significantly in the crypt base in Gαq/G11-deficient mice, resulting in the defective maturation of Paneth cells, induction of differentiation toward goblet cells, and susceptibility to DSS colitis