Cohomological properties of multinorm-one tori

In this paper we investigate the Tate--Shafarevich group Sha^1(k, T) of a multinorm-one torus $T$ over a global field $k$. We establish a few functorial maps among cohomology groups and explore their relations. Using these properties and relations we obtain a few basic structural results for Sha^1(k, T) and extend a few results of Bayer-Fluckiger--Lee--Parimala [Adv. in Math., 2019] to some more general multinorm-one tori. We also give a uniform proof of a result of Demarche--Wei for a criterion of the vanishing of Sha^1(k, T), and of the main result of Pollio [Pure App. Math. Q., 2014] for the case where the \'etale $k$-algebra in question is a product of two abelian extensions. Moreover, we improve the explicit description of Sha^1(k, T) in Lee [J. Pure Appl. Alg., 2022] by removing an intersection condition.Comment: 26 pages, comments welcom

Design for data acquisition system of gear measuring center

A data acquisition system for Computerized Numerical Control Gear Measurement Center was developed, in which Field-Programmable Gate Array was used as the control core instead of traditional single-chip microcomputer or Digital Signal Processor, First-In First-Out buffer to hold data, and personal computer bus as data transmission unit. The system performs multichannel data acquisition more efficiently, higher precision and higher rate in real time than the traditional ones. Experimental comparison indicates that the data gathering rate increase twice to 10 kHz, and the uniformly-spaced error is in 1 μm

Computing Tate-Shafarevich groups of multinorm one tori of Kummer type

A multinorm one torus associated to a commutative \'etale algebra $L$ over a global field $k$ is of Kummer type if each factor of $L$ is a cyclic Kummer extension. In this paper we compute the Tate-Shafarevich group of such tori based on recent works of Bayer-Fluckiger, T.-Y. Lee and Parimala, and of T.-Y.~Lee. We also implement an effective algorithm using SAGE which computes the Tate-Shafarevich groups when each factor of $L$ is contained in a fixed concrete bicyclic extension of $k$.Comment: 17 pages, 3 figures, comments are welcom

Optimization of microsatellite DNA Gelred fluorescence imaging technology

Gelred fluorescent dye has broader prospects of application in DNA experiment because of its high sensitivity, security and stability. In order to explore the best microsatellite DNA Gelred imaging technology, this study compared its dosage by using three methods; precasting gels method (PG), staining sample method (SS) and immersion gels method (IG). The results show that agarose gel electrophoresis (AGE) fluorescence imaging technology can use the first method (PG) and the concentration of Gelred was 1X, because of the best banding and easy operation. The polyacrylamide gel electrophoresis (PAGE) can use the third method (IG), for the advantages of clear and bright image, saving dye and easily redying to image. The orthogonal test showed that the parameters of IG method were: the concentration of Gelred was 2X, that of sodium chloride was 10% and immersion time was 40 min. The optimization of microsatellite DNA Gelred fluorescence imaging technology would lay a technical foundation in DNA banding related experiments.Key word: Agarose gel electrophoresis (AGE), polyacrylamide gel electrophoresis (PAGE), fluorescence imaging technology of Gelred, simple sequence repeat (SSR)

Design for data acquisition system of gear measuring center

A data acquisition system for Computerized Numerical Control Gear Measurement Center was developed, in which Field-Programmable Gate Array was used as the control core instead of traditional single-chip microcomputer or Digital Signal Processor, First-In First-Out buffer to hold data, and personal computer bus as data transmission unit. The system performs multichannel data acquisition more efficiently, higher precision and higher rate in real time than the traditional ones. Experimental comparison indicates that the data gathering rate increase twice to 10 kHz, and the uniformly-spaced error is in 1 μm

The effect of drainage tube on bleeding and prognosis after total knee arthroplasty: a prospective cohort study

BACKGROUND: To evaluate the effect of drainage tube on prognosis after total knee arthroplasty (TKA) and explore an effective treatment with favorable prognosis. METHODS: In a prospective study, 18 patients with TKA for the first time were included and randomly divided into three groups, group A (no placement of drainage tube), group B (negative pressure drainage), and group C (4 h clamping drainage). Intraoperative and postoperative blood loss, operation time, and the drainage volume were recorded and analyzed. Arthrocele, ecchymosis, and range of motion (ROM) were examined postoperatively. The degree of pain was scored by Visual Analog Scale (VAS) after 6, 12, and 24 h of operation. The complications were examined and HSS (hospital for special surgery) knee score was taken during the follow-up period. RESULTS: There was no significant difference in operation time, total blood loss, intraoperative blood loss, and VAS score among three groups. Meanwhile, the hidden blood loss in group B was significantly decreased compared with group A (P = 0.0015). The postoperative drainage volume of group B was significantly increased compared with group C (P = 0.0002). No drainage increased the rate of arthrocele and ecchymosis. Compared with group A, ROM after 3 days of operation in groups B and C was significantly increased (P = 0.0357, P = 0.0372, respectively). During follow-up study, no deep infection or deep venous thrombosis was found. CONCLUSION: After TKA, early clamping of the drainage tube reduced the bleeding loss without adverse effect on prognosis, which might be useful for clinical application in future

catena-Poly[[diaquacadmium(II)]bis­(μ-pyridine-3-sulfonato)-κ2 N:O;κ2 O:N]

In the title polymeric complex, [Cd(C5H4NO3S)2(H2O)2]n, the Cd atom is located on a centre of inversion and is coordinated by two O atoms and two N atoms, derived from four different pyridine-3-sulfonate ligands, and two O atoms derived from two water mol­ecules, forming a distorted trans-N2O4 octa­hedral geometry. The topology of the polymer is a one-dimensional chain mediated by bridging pyridine-3-sulfonate anions. These are connected into a three-dimensional architecture via hydrogen bonds

catena-Poly[[aqua­[3-(3-pyrid­yl)acrylato]gadolinium(III)]-bis­[μ-3-(3-pyrid­yl)acrylato]]

In the title compound, [Gd(C8H6NO2)3(H2O)]n, the gadolinium(III) ion is coordinated by eight carboxyl­ate O atoms and one water mol­ecule. The carboxyl­ate ligands bridge pairs of gadolinium(III) ions, forming a zigzag chain along [100]. Hydrogen bonds link the chains into sheets parallel to (001)

[2,2′-(1,1′-Binaphthyl-2,2′-diyldiimino)­diethanol-κ3 N,N′,O]dichloridocopper(II)

In the title complex, [CuCl2(C24H24N2O2)], the CuII cation is N,N′,O-chelated by a 2,2′-(1,1′-binaphthyl-2,2′-diyldiimino)­diethanol ligand and coordinated by two chloride anions in a distorted square-pyramidal geometry. In the diethanol ligand, the two naphthalene ring systems are twisted with respect to each other at a dihedral angle of 68.30 (9)°. The uncoord­inated hy­droxy group links with a coordinated chloride anion via an intra­molecular O—H⋯Cl hydrogen bond. Inter­molecular N—H⋯O and N—H⋯Cl hydrogen bonds occur in the crystal structure