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General Solutions of First-Order Algebraic ODEs in Simple Constant Extensions

系统科学与复杂性学报:英文版 2023年第4期36卷 1769-1788页

作者： mitteramskogler johann josef WINKLER Franz Research Institute for Symbolic Computation(RISC) Johannes Kepler Universität LinzA-4040 LinzAustria

If a first-order algebraic ODE is defined over a certain differential field,then the most elementary solution class,in which one can hope to find a general solution,is given by the adjunction of a single arbitrary constant to this *** of this type give rise to a particular kind of generic point—a rational parametrization—of an algebraic curve which is associated in a natural way to the ODE’s defining *** for the opposite direction,we show that a suitable rational parametrization of the associated curve can be extended to a general solution of the ODE if and only if one can find a certain automorphism of the solution *** automorphisms are determined by linear rational functions,i.e.,Möbius *** properties of rational parametrizations,in combination with the particular shape of such automorphisms,lead to a number of necessary conditions on the existence of general solutions in this solution ***,the desired linear rational function can be determined by solving a comparatively simple differential system over the ODE’s field of *** results hold for arbitrary differential fields of characteristic zero.

关键词： Algebraic curve algebraic differential equation general solution Möbius transformation rational parametrization

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Complicated small-bowel diverticulosis: A case report and review of the literature

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World Journal of Gastroenterology 2007年第15期13卷 2240-2242页

作者： Woubet T Kassahun josef Fangmann Jens Harms Michael Bartels johann Hauss Department of Surgery Ⅱ Faculty of Medicine University of LeipzigLiebig Strasse 20aLeipzig 04103Germany

While jejunoileal diverticula are rare and often asymptomatic, they may lead to chronic non-specific or acute symptoms. The large majority of complications present with an acute abdomen similar to appendicitis, cholecystitis or colonic diverticulitis but they also may appear with atypical symptoms. As a result, diagnosis of complicated jejunoileal diverticulosis can be quite difficult, and may solely depend on the result of surgical exploration. In the absence of contra-indications, diagnostic laparoscopy has the benefit of thorough examination of the abdominal contents and helps to reach an absolute diagnosis. Surgical resection of the involved small-bowel segment with primary anastomosis is the preferred treatment in patients with symptomatic complicated jejunoileal diverticular disease. An atypical presentation of complicated jejunal diverticulitis in conjunction with sigmoid diverticulitis diagnosed with laparoscopy and treated with surgical resection is presented.

关键词： Jejunoileal diverticulosis Diverticulitis, Small-bowel resection Perforation Laparoscopy

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Rapid solidification and metastable phase formation during surface modifications of composite Al-Cr cathodes exposed to cathodic arc plasma

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Journal of Materials Science & Technology 2021年第35期94卷 147-163页

作者： Mehran Golizadeh Francisca Mendez Martin Stefan Wurster johann P.Mogeritsch Abdellah Kharicha Szilard Kolozsvári Christian Mitterer Robert Franz Department of Materials Science Montanuniversitat LeobenFranz Josef-Straβe 188700 LeobenAustria Erich Schmid Institute of Materials Science Austrian Academy of SciencesJahnstraβe 12.8700 LeobenAustria Department of Metallurgy Montanuniversitat LeobenFranz Josef-Straβe 188700 LeobenAustria Plansee Composite Materials GmbH Siebenbiirgerstraβe 2386983 Lechbruck am SeeCermany

A combination of both conventional and advanced high-resolution characterization techniques was applied to study the modified layers on the surface of three composite Al-Cr arc cathodes with identical nominal composition of Al-50 at.%Cr but varying powder grain *** results revealed that the modified layers consist mainly of metastable phases such as Cr solid solution,high temperature cubic Al8 Cr5,supersaturated Al solid solution,and icosahedral *** metastable phase formation indicates that high cooling rates were involved during the solidification of molten material produced in the arc craters during cathode spot *** average cooling rate was estimated to be 10^(6)K/s based on secondary dendrite arm spacing measurements and supporting phase-field based *** formation mechanisms of the modified layers are discussed based on the obtained results and the current literature.

关键词： Cathodic arc Rapid solidification Quasicrystal Arc crater Macroparticle Phase-field simulation

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Transarterial administration of integrin inhibitor loaded nanoparticles combined with transarterial chemoembolization for treating hepatocellular carcinoma in a rat model

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World Journal of Gastroenterology 2016年第21期22卷 5042-5049页

作者： Jun Qian Elsie Oppermann Andreas Tran Ulli Imlau Kun Qian Thomas josef Vogl Department of Radiology Union Hospital Huazhong University of Science and Technology Institute for Diagnostic and Interventional Radiology Johann Wolfgang Goethe University

AIM: To compare the effect of transarterial chemoembolization(TACE) plus GRGDSP(Gly-Arg-Gly-Asp-SerPro, integrin-inhibitor) loaded nanoparticles with TACE alone or TACE + GRGDSP in a rat model of liver tumor. METHODS: Morris hepatoma 3924 A tumors were implanted in the livers of 30 ACI rats. The ACI rats were divided randomly into three groups(10 animals each). Tumor volume before treatment(V1) was examined by magnetic resonance imaging(MRI), and then, after laparotomy and placement of a PE-10 catheter into the hepatic artery, the following interventional protocols were performed: TACE(mitomycin C + lipiodol + degradable starch microspheres) + GRGDSP loaded nanoparticles for group A; TACE + GRGDSP for group B(control group 1); TACE alone for group C(control group 2). Tumor volume(V2) was assessed by MRI and the mean ratio of the post-treatment to pretreatment tumor volumes(V2/V1) was calculated. Immunohistochemical analysis was performed to assess the quantification of matrix metalloprotein 9(MMP-9) and vascular endothelial growth factor(VEGF) positive tumor cells in each treatment ***: The mean tumor growth ratios(V2/V1) were 1.3649 ± 0.1194 in group A, 2.0770 ± 0.1595 in group B, and 3.2148 ± 0.1075 in group C. Compared with groups B and C, group A showed a significant reduction in tumor volume. Lower expression of MMP-9 and VEGF in hepatocellular carcinoma was observed in group A than in groups B and C. The angiogenesis of tumor was evaluated using anti-VEGF antibodies, and the metastasis of tumor was assessed using antiMMP-9 antibody. MMP-9 and VEGF were expressed in all specimens. The immunoexpression of these proteins was confirmed by the presence of red cytoplasmic staining in tumor cells. Lower expression of MMP-9 and VEGF in hepatocellular carcinoma was observed in group A than in groups B and ***: Transarterial administration of integrin inhibitor loaded nanoparticles combined with TACE evidently retards tumor growth and intrahepatic met

关键词： Hepatocellular carcinoma Transarterial chemoembolization Integrin inhibitor Nanoparticles Matrix metalloprotein 9 Vascular endothelial growth factor ACI rats

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数学:与游戏相比

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书摘 2021年第4期 81-85页

作者： [奥]维特根斯坦韩林合(译) 不详

1.当人们说数学仅仅是游戏(或者:它是游戏)时,人们在否认它具有什么?2.游戏,与什么相对?--当人们说(它绝不是游戏)它的命题具有意义时,人们将什么归属给了它?

关键词：数学游戏命题

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