Some computer-assisted proofs of nontrivial steady-state solutions for the Kolmogorov flows are presented. The method is based on the infinite-dimensional fixed-point theorem using a Newton-like ...operator with a numerical verification algorithm that automatically generates a set that includes the exact nontrivial solution. When discussing the numerical results, we consider the effects of rounding errors in the floating point computations. This is a continuation of our study that was presented in Watanabe (2009).
We propose a computer-assisted method to prove the existence of a symmetry-breaking bifurcation point for the Kolmogorov problem. First, we numerically show that a symmetry-breaking bifurcation point ...exists. Then, according to the symmetric property, we define a symmetric operator. Using this operator, we divide the space into a symmetric space and an antisymmetric space. Then, considering the Reynolds number as a variable, we construct an extended system. We confirm the existence of the symmetry-breaking bifurcation point by computer-assisted proofs of the extended system that satisfies both conditions of a bifurcation theorem. The first condition is that the system has an isolated solution and the second is that a linearized operator is bijective. We numerically construct a set containing solutions that satisfy the hypothesis of Banach’s fixed-point theorem in a certain Sobolev space and thus the first condition is satisfied. The second condition is equivalent to an equation having the unique trivial solution zero. We prove that this condition is equivalent to an inequality.
This paper presents a computer-assisted proof of the existence and unimodality of steady-state solutions for the Proudman–Johnson equation which is representative of two-dimensional fluid flow. The ...proposed approach is based on an infinite-dimensional fixed-point theorem with interval arithmetic, and is another proof by Miyaji and Okamoto (Jpn J Ind Appl Math 36:287–298, 2019). Verification results show the validity of both proofs.
On admission, his height was 166.4 cm, body weight 52.1 kg (no weight gain), temperature 36.7°C, heart rate 122 beats/min, respiratory rate 18 breaths/min, blood pressure 122/64 mmHg, and oxygen ...saturation of peripheral artery, 97%–99% (on room air). Additionally, Levi et al. reported that SARS-CoV-2 infection promotes severe systemic disease, which accompanies coagulation abnormalities. 5 In this study, the SARS-CoV-2 infection possibly triggered the recurrence of refractory NS with hemoconcentration, which caused coagulation abnormalities. ...intravenous heparin was selected since the antithrombin III level was maintained, and immediate anticoagulation was required. No coagulation abnormalities, such as elevated D-dimer levels or an acute platelet count reduction, occurred.
This paper describes some numerical verification procedures to prove the invertibility of a linear operator in Hilbert spaces and to compute a bound on the norm of its inverse. These approaches ...improve on previous procedures that use an orthogonal projection of the Hilbert space and its a priori error estimations. Several verified examples which confirm the effectiveness of the new procedures are presented.
In the present paper, we propose a computer-assisted procedure to prove the invertibility of a linear operator in a Hilbert space and to compute a verified norm bound of its inverse. A number of the ...authors have previously proposed two verification approaches that are based on projection and constructive a priori error estimates. The approach of the present paper is expected to bridge the gap between the two previous procedures in actual numerical verifications. Several verification examples that confirm the actual effectiveness of the proposed procedure are reported.
...Inoue reported 4 a 5-year-old boy diagnosed with KD (Day 5). Because of IVIG resistance, he received repeated IVIG, intravenous methylprednisolone pulse (IVMP; Days 6–9), plasma exchange, and 5 ...mg/kg infliximab (Day 13). ...Ishikawa 5 reported a 2-month-old girl diagnosed with KD (Day 5). Because of IVIG resistance, she received repeated IVIG, IVMP (Days 8–9, 15–16), and plasma exchange. Table 1 Cases of Kawasaki disease complicated with aspergillosis References Age Sex Infliximab Cyclosporine IVMP Plasma exchange Antifungal medicine CAL Inoue 4 5 years Male (+) (−) (+) (+) Voriconazole (+) Ishikawa 5 2 months Female (−) (−) (+) (+) L-AMB (+) Our patient 14 months Female (+) (+) (−) (−) Micafungin (−) CAL, coronary artery lesions; IVIG, intravenous immunoglobulin; IVMP, intravenous methylprednisolone pulse; L-AMB, liposomal amphotericin B. As far as we are aware, this is the first report on aspergillosis after treatment with cyclosporine and infliximab for refractory KD. ...in cases of recurrent fever and poor improvement of inflammation in blood tests after acute KD treatment with cyclosporine or infliximab, complications of aspergillosis should be considered.
On admission, he developed fever and his family doctor suggested that he undergo urine leukocyte elastase test. The following observations were noted: height: 73.2 cm, bodyweight: 10.8 kg, body ...temperature: 39.5 °C, heart rate: 176 beats/min, respiratory rate: 36 breaths/min, and blood pressure: 101/59 mmHg. ...Raoultella ornithinolytica isolated from the living environment may cause UTI.
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