On the dual of the dual hyperoval from APN function f(x)=x3+Tr(x9)

AbstractUsing a quadratic APN function f on GF(2d+1), Yoshiara (2009) [15] constructed a d-dimensional dual hyperoval Sf in PG(2d+1,2). In Taniguchi and Yoshiara (2005) [13], we prove that the dual of Sf, which we denote by Sf⊥, is also a d-dimensional dual hyperoval if and only if d is even. In this note, for a quadratic APN function f(x)=x3+Tr(x9) on GF(2d+1) by Budaghyan, Carlet and Leander (2009) [2], we show that the dual Sf⊥ and the transpose of the dual Sf⊥T are not isomorphic to the known bilinear dual hyperovals if d is even and d⩾6

A new construction of the d-dimensional Buratti–Del Fra dual hyperoval

AbstractThe Buratti–Del Fra dual hyperoval Dd(F2) is one of the four known infinite families of simply connected d-dimensional dual hyperovals over F2 with ambient space of vector dimension (d+1)(d+2)/2 (Buratti and Del Fra (2003) [1]). A criterion (Proposition 1) is given for a d-dimensional dual hyperoval over F2 to be covered by Dd(F2) in terms of the addition formula. Using it, we provide a simpler model of Dd(F2) (Proposition 3). We also give conditions (Lemma 4) for a collection S[B] of (d+1)-dimensional subspaces of K⊕K constructed from a symmetric bilinear form B on K≅F2d+1 to be a quotient of Dd(F2). For when d is even, an explicit form B satisfying these conditions is given. We also provide a proof for the fact that the affine expansion of Dd(F2) is covered by the halved hypercube (Proposition 10)

人工距骨併用の人工足関節置換術

AIMS: Total ankle arthroplasty (TAA) has become the most reliable surgical solution for patients with end-stage arthritis of the ankle. Aseptic loosening of the talar component is the most common complication. A custom-made artificial talus can be used as the talar component in a combined TAA for patients with poor bone stock of the talus. The purpose of this study was to investigate the functional and clinical outcomes of combined TAA. PATIENTS AND METHODS: Ten patients (two men, eight women; ten ankles) treated using a combined TAA between 2009 and 2013 were matched for age, gender, and length of follow-up with 12 patients (one man, 11 women; 12 ankles) who underwent a standard TAA. All had end-stage arthritis of the ankle. The combined TAA features a tibial component of the TNK ankle (Kyocera, Kyoto, Japan) and an alumina ceramic artificial talus (Kyocera), designed using individualized CT data. The mean age at the time of surgery in the combined TAA and standard TAA groups was 71 years (61 to 82) and 75 years (62 to 82), respectively. The mean follow-up was 58 months (43 to 81) and 64 months (48 to 88), respectively. The outcome was assessed using the Japanese Society for Surgery of the Foot (JSSF) ankle-hindfoot scale, the Ankle Osteoarthritis Scale (AOS), and the Self-Administered Foot Evaluation Questionnaire (SAFE-Q). RESULTS: The mean preoperative JSSF score of the combined TAA and standard TAA groups was 44 (sd 11) and 49 (sd 10), respectively. The mean postoperative JSSF scores were 89 (sd 6.1) and 72 (sd 15), respectively. The mean postoperative JSSF score of the combined TAA group was significantly higher (p = 0.0034). The mean preoperative AOS scores for pain and function in the combined TAA and standard TAA groups were 5.8 (sd 3.3) and 5.5 (sd 3.1), and 8.6 (sd 1.3), and 7.1 (sd 2.9), respectively. The mean postoperative AOS scores of pain and function were 2.5 (sd 2.5) and 2.2 (sd 1.9), and 2.5 (sd 3.3) and 3.4 (sd 2.9), respectively. There were no significant differences between the two groups in terms of postoperative AOS scores. The mean postoperative SAFE-Q scores were: for pain, 76 (sd 23) and 70 (sd 23); for physical function, 66 (sd 25) and 55 (sd 27); for social function, 73 (sd 35) and 62 (sd 34); for shoe-related, 73 (sd 19) and 65 (sd 26); and for general health, 78 (sd 28) and 67 (sd 29), respectively. There were no significant differences between the two groups in terms of postoperative SAFE-Q scores. CONCLUSION: Combined TAA resulted in better clinical results than standard TAA. Cite this article: Bone Joint J 2019;101-B:443-446.博士（医学）・甲第717号・令和元年6月26日This is a non-final version of an article published in final form in "http://dx.doi.org/10.1302/0301-620X.101B4.BJJ-2018-0812.R2

Cerebrospinal fluid leakage and Chiari I malformation with Gorham's disease of the skull base: A case report

Background Gorham's syndrome is a rare bone disorder characterized by massive osteolysis of unknown etiology. There are no reports of comorbidity involving cerebrospinal fluid (CSF) leakage and Chiari I malformation with Gorham's syndrome. Here, we report an unusual case of an acute presyrinx state complicated by bacterial meningitis due to CSF leakage and Chiari I malformation associated with Gorham's disease of the skull base. Case presentation A 25-year-old woman with Chiari I malformation associated with Gorham's syndrome presented with aggressive paresthesia following bacterial meningitis. Axial magnetic resonance imaging (MRI) and computed tomography (CT) cisternography revealed CSF leakage in the right petrous apex. A presyrinx state was diagnosed based on the clinical symptoms and MRI findings. With resolution of the bacterial meningitis, the spinal edema and tonsillar ectopia also improved. Surgical repair of the CSF leakage was performed by an endoscopic endonasal transsphenoidal approach to prevent recurrence of meningitis. The postoperative course was uneventful. Conclusion Skull base osteolysis in Gorham's syndrome may induce Chiari I malformation and CSF leakage. We should pay attention to acute progression of clinical symptoms because Gorham's syndrome may predispose to development of Chiari I malformation and may be complicated by CSF leakage

Search for the field-induced magnetic instability around the upper critical field of superconductivity in H || c in CeCoIn5

We present nuclear spin-lattice relaxation rate (1/T1) at the Co site and ac-susceptibility results in the normal and superconducting (SC) states of CeCoIn5 for H || c near the SC upper critical field Hc2 above 0.1 K. At 4.2 T, 1/T1 rapidly decreases below the SC transition temperature, consistent with the previous reports. Although the field dependence of 1/T1T at 0.1 K shows a peak at 5.2 T above Hc2, the temperature dependence of 1/T1T at 5.2 T is independent of temperature below 0.2 K, showing a Fermi-liquid behavior. In addition, we found no NMR-spectrum broadening by the appearance of internal fields around Hc2 at 0.1 K. We could not detect any field-induced magnetic instability around Hc2 down to 0.1 K although the remarkable non-Fermi-liquid behavior towards Hc2 was observed in various physical quantities.Comment: 6 pages, 3 figure

Stress corrosion cracking of copper in swollen bentonite simulating nuclear waste disposal environment

Stress corrosion cracking (SCC) of pure copper in bentonite clay was examined using a slow strain rate test (SSRT). Bentonite was swollen with pure water or aqueous solutions containing NH₃ of 5 and 10 mM. Thick corrosion films and particulate deposits were formed on the copper surface after the SSRT. Typical tarnish rupture-type SCC occurred on pure copper in swollen bentonite with and without NH₃. The crack propagation rate was enhanced by NH₃. It is confirmed that a thick oxide layer was formed on copper during plastic deformation, resulting in tarnish crack-type SCC. Many particulate deposits observed on the surface were formed due to the rapid dissolution of Cu²⁺ ions to form porous CuO at local deformed sites, regardless of the SCC occurrence