Ideal matrices. III.

In this paper ideal matrices with respect to ideals in the maximal order of an algebraic number field are connected with the different of the field and with group matrices in the case of normal fields whose maximal order has a normal basis

Additive commutators of rational 2×2 matrices

AbstractThe expression of det (AB-BA) as a norm in both (Q(m) and Q(n) for 2×2 rational matrices with characteristic roots in Q(m), resp. Q(n), is studied here further, see [1]. A necessary and sufficient condition for this element to be also a norm in Q(m,n) is obtained

Delayed vasospasm after removal of a skull base meningioma

pre-printCerebral vasospasm is a well-known clinical entity associated with subarachnoid hemorrhage and traumatic brain injury [1,2]. In rare instances, vasospasm has been reported to occur after tumor resections, more specifically, after skull base tumor removal [3-5]. We report a rare case of a patient presenting with delayed clinical and angiographic vasospasm, 14 days after removal of a hyperostotic meningioma of the right sphenoid wing

Submandibular high-flow bypass in the treatment of skull base lesions: an analysis of long-term outcome

pre-printBackground: Cerebral bypass surgery remains an integral part of the treatment of complex skull base tumors and unclippable aneurysms. Objective: The authors retrospectively analyzed a single-surgeon experience using a high-flow submandibular-infratemporal saphenous vein graft bypass technique after carotid artery sacrifice in the resection of complex skull base tumors and carotid isolation in unclippable aneurysms. Methods: Data on indications, surgical technique, bypass patency, complications, and outcome were collected for patients treated with adjunctive submandibular high-flow bypass for skull base lesions. Results: Eleven patients (age range: 13-77 years) were treated for various skull base lesions: 4 patients were treated for skull base tumors with resection of the ICA, 6 were treated for aneurysms not amenable to clipping, and one was treated for invasive Mucor infection. Using a saphenous vein graft, a high-flow bypass was created from the high cervical internal carotid artery (ICA) or external carotid artery to ICA or middle cerebral artery by means of a submandibular-infratemporal route. Postoperative computed tomography angiography indicated bypass patency in 10/11 patients. There was no operative mortality. Follow-up of up to 12 years (mean 57 months) was achieved. Conclusion: Direct high-flow submandibular-infratemporal interpositional saphenous vein bypass graft is an effective and durable technique for the treatment of complex skull base lesions where internal carotid artery revascularization is indicated

When does a linear map belong to at least one orthogonal or symplectic group?

Given an endomorphism u of a finite-dimensional vector space over an arbitrary field K, we give necessary and sufficient conditions for the existence of a regular quadratic form (resp. a symplectic form) for which u is orthogonal (resp. symplectic). A solution to this problem being already known in the case char(K)2, our main contribution lies in the case char(K)=2. When char(K)=2, we also give necessary and sufficient conditions for the existence of a regular symmetric bilinear form for which u is orthogonal. In the case K is finite with characteristic 2, we give necessary and sufficient conditions for the existence of an hyperbolic quadratic form (resp. a regular non-hyperbolic quadratic form, resp. a regular non-alternate symmetric bilinear form) for which u is orthogonal.Comment: 32 pages (v4

Influence of body mass index and periprostatic fat on rectal dosimetry in permanent seed prostate brachytherapy

PURPOSE: We examined the influence of body mass index (BMI) and body fat distribution on rectal dose in patients treated with permanent seed brachytherapy for localized prostate cancer. METHODS AND MATERIALS: We analyzed 213 patients treated with I(125) seed brachytherapy for localized prostate cancer. BMI and rectal dosimetry data for all patients were available. Data on visceral and subcutaneous fat distribution at the level of the iliac crest (n = 140) as well as the distribution of periprostatic and subcutaneous fat at the symphysis pubis level were obtained (n = 117). Fat distribution was manually contoured on CT on day 30 after brachytherapy. The correlation between BMI, fat distribution and rectal dose (R100 (in cc), R150 (cc), D2 (Gy)) was analyzed using the Spearman correlation coefficient. Differences in rectal dose between tertiles of body fat distribution were calculated using nonparametric tests. RESULTS: Periprostatic adipose was only weakly correlated with BMI (r = 0.0.245, p = 0.008) and only weakly correlated with the other fat measurements (r = 0.31-0.37, p < 0.001). On the other hand, BMI was correlated with all other fat measurements (≥0.58, p < 0.001). All the other fat measurements were strongly correlated with each other (r = 0.5-0.87, p < 0.001). Patients with an R100 of >1.3 cc (23% of patients) had less visceral fat (p = 0.004), less subcutaneous fat at the level of the iliac crest (p = 0.046) and a lower BMI (26.8 kg/m(2) vs. 28.5 kg/m(2), p = 0.02) than patients with an R100 of <1.3 cc. Results were very similar when comparing an R100 of >1.0 cc (34% of patients) across the tertiles. None of the tested linear regression models were predictive (max 12%) of dose to the rectum. CONCLUSION: Dose to the rectum is dependent on BMI and body fat distribution. Periprostatic fat does not influence rectal dose. Dose to the rectum remains difficult to predict and depends on many factors, one of which is body fat distribution