Corona-type theorems and division in some function algebras on planar domains

Let $A$ be an algebra of bounded smooth functions on the interior of a compact set in the plane. We study the following problem: if $f,f_1,\dots,f_n\in A$ satisfy $|f|\leq \sum_{j=1}^n |f_j|$, does there exist $g_j\in A$ and a constant $N\in\N$ such that $f^N=\sum_{j=1}^n g_j f_j$? A prominent role in our proofs is played by a new space, C_{\dbar, 1}(K), which we call the algebra of \dbar-smooth functions. In the case $n=1$, a complete solution is given for the algebras $A^m(K)$ of functions holomorphic in $K^\circ$ and whose first $m$-derivatives extend continuously to \ov{K^\circ}. This necessitates the introduction of a special class of compacta, the so-called locally L-connected sets. We also present another constructive proof of the Nullstellensatz for $A(K)$, that is only based on elementary \dbar-calculus and Wolff's method.Comment: 23 pages, 6 figure

A subalgebra of the Hardy algebra relevant in control theory and its algebraic-analytic properties

We denote by A_0+AP_+ the Banach algebra of all complex-valued functions f defined in the closed right half plane, such that f is the sum of a holomorphic function vanishing at infinity and a ``causal'' almost periodic function. We give a complete description of the maximum ideal space M(A_0+AP_+) of A_0+AP_+. Using this description, we also establish the following results: (1) The corona theorem for A_0+AP_+. (2) M(A_0+AP_+) is contractible (which implies that A_0+AP_+ is a projective free ring). (3) A_0+AP_+ is not a GCD domain. (4) A_0+AP_+ is not a pre-Bezout domain. (5) A_0+AP_+ is not a coherent ring. The study of the above algebraic-anlaytic properties is motivated by applications in the frequency domain approach to linear control theory, where they play an important role in the stabilization problem.Comment: 17 page

A fibered description of the vector-valued spectrum

For Banach spaces X and Y we study the vector-valued spectrum (Formula presented.), that is the set of non null algebra homomorphisms from (Formula presented.) to (Formula presented.), which is naturally projected onto the closed unit ball of (Formula presented.). The aim of this article is to describe the fibers defined by this projection, searching for analytic balls and considering Gleason parts.Fil: Dimant, Veronica Isabel. Universidad de San Andrés. Departamento de Matemáticas y Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Singer, Joaquín Camilo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin

Partial regularity and t-analytic sets for Banach function algebras

In this note we introduce the notion of t-analytic sets. Using this concept, we construct a class of closed prime ideals in Banach function algebras and discuss some problems related to Alling’s conjecture in H infinity. A description of all closed t-analytic sets for the disk-algebra is given. Moreover, we show that some of the assertions in [8] concerning the O-analyticity and S-regularity of certain Banach function algebras are not correct. We also determine the largest set on which a Douglas algebra is pointwise regular

Expression study of receptor tyrosine kinase targets of Imatinib mesylate in skull base chordomas

Chordomas are rare neoplasms arising along the axial skeleton. Up to now, the most suitable therapeutic approach is based on a combination of surgical excision and radiotherapy. Chemotherapy in not applied due to its reported low efficacy. Recently, evidence on the efficacy of Imatinib mesylate in two patients has been reported. We analyzed 14 chordoma samples for the expression of the Imatinib mesylate targets by means of RT-PCR and immunohistochemistry and found that PDGFR\u3b1 and PDGFR\u3b2 are in some cases expressed in neoplastic cells, while the stromal counterpart of the same tumor shows the above receptors. Findings on the PDGFA/PDGFB expression suggest a receptor-activated status. Our study provides new insights into the specific localization of Imatinib mesylate targets in skull base chordomas that could be taken into account for the setting up of a pharmacological treatment for this tumor

Acromegaly is associated with increased cancer risk: A survey in Italy

It is debated if acromegalic patients have an increased risk to develop malignancies. The aim of the present study was to assess the standardized incidence ratios (SIRs) of different types of cancer in acromegaly on a large series of acromegalic patients managed in the somatostatin analogs era. It was evaluated the incidence of cancer in an Italian nationwide multicenter cohort study of 1512 acromegalic patients, 624 men and 888 women, mean age at diagnosis 45 \uc2\ub1 13 years, followed up for a mean of 10 years (12573 person-years) in respect to the general Italian population. Cancer was diagnosed in 124 patients, 72 women and 52 men. The SIRs for all cancers was significantly increased compared to the general Italian population (expected: 88, SIR 1.41; 95% CI, 1.18-1.68, P < 0.001). In the whole series, we found a significantly increased incidence of colorectal cancer (SIR 1.67; 95% CI, 1.07-2.58, P = 0.022), kidney cancer (SIR 2.87; 95% CI, 1.55-5.34, P < 0.001) and thyroid cancer (SIR 3.99; 95% CI, 2.32-6.87, P < 0.001). The exclusion of 11 cancers occurring before diagnosis of acromegaly (all in women) did not change remarkably the study outcome. In multivariate analysis, the factors significantly associated with an increased risk of malignancy were age and family history of cancer, with a non-significant trend for the estimated duration of acromegaly before diagnosis. In conclusion, we found evidence that acromegaly in Italy is associated with a moderate increase in cancer risk

Mortality and pulmonary complications in patients undergoing surgery with perioperative sars-cov-2 infection: An international cohort study

Background The impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on postoperative recovery needs to be understood to inform clinical decision making during and after the COVID-19 pandemic. This study reports 30-day mortality and pulmonary complication rates in patients with perioperative SARS-CoV-2 infection. Methods This international, multicentre, cohort study at 235 hospitals in 24 countries included all patients undergoing surgery who had SARS-CoV-2 infection confirmed within 7 days before or 30 days after surgery. The primary outcome measure was 30-day postoperative mortality and was assessed in all enrolled patients. The main secondary outcome measure was pulmonary complications, defined as pneumonia, acute respiratory distress syndrome, or unexpected postoperative ventilation. Findings This analysis includes 1128 patients who had surgery between Jan 1 and March 31, 2020, of whom 835 (740%) had emergency surgery and 280 (248%) had elective surgery. SARS-CoV-2 infection was confirmed preoperatively in 294 (261%) patients. 30-day mortality was 238% (268 of 1128). Pulmonary complications occurred in 577 (512%) of 1128 patients; 30-day mortality in these patients was 380% (219 of 577), accounting for 817% (219 of 268) of all deaths. In adjusted analyses, 30-day mortality was associated with male sex (odds ratio 175 [95% CI 128-240], p<00001), age 70 years or older versus younger than 70 years (230 [165-322], p<00001), American Society of Anesthesiologists grades 3-5 versus grades 1-2 (235 [157-353], p<00001), malignant versus benign or obstetric diagnosis (155 [101-239], p=0046), emergency versus elective surgery (167 [106-263], p=0026), and major versus minor surgery (152 [101-231], p=0047). Interpretation Postoperative pulmonary complications occur in half of patients with perioperative SARS-CoV-2 infection and are associated with high mortality. Thresholds for surgery during the COVID-19 pandemic should be higher than during normal practice, particularly in men aged 70 years and older. Consideration should be given for postponing non-urgent procedures and promoting non-operative treatment to delay or avoid the need for surgery. Funding National Institute for Health Research (NIHR), Association of Coloproctology of Great Britain and Ireland, Bowel and Cancer Research, Bowel Disease Research Foundation, Association of Upper Gastrointestinal Surgeons, British Association of Surgical Oncology, British Gynaecological Cancer Society, European Society of Coloproctology, NIHR Academy, Sarcoma UK, Vascular Society for Great Britain and Ireland, and Yorkshire Cancer Research

Pituitary society expert Delphi consensus: operative workflow in endoscopic transsphenoidal pituitary adenoma resection

Abstract: Purpose: Surgical workflow analysis seeks to systematically break down operations into hierarchal components. It facilitates education, training, and understanding of surgical variations. There are known educational demands and variations in surgical practice in endoscopic transsphenoidal approaches to pituitary adenomas. Through an iterative consensus process, we generated a surgical workflow reflective of contemporary surgical practice. Methods: A mixed-methods consensus process composed of a literature review and iterative Delphi surveys was carried out within the Pituitary Society. Each round of the survey was repeated until data saturation and > 90% consensus was reached. Results: There was a 100% response rate and no attrition across both Delphi rounds. Eighteen international expert panel members participated. An extensive workflow of 4 phases (nasal, sphenoid, sellar and closure) and 40 steps, with associated technical errors and adverse events, were agreed upon by 100% of panel members across rounds. Both core and case-specific or surgeon-specific variations in operative steps were captured. Conclusions: Through an international expert panel consensus, a workflow for the performance of endoscopic transsphenoidal pituitary adenoma resection has been generated. This workflow captures a wide range of contemporary operative practice. The agreed “core” steps will serve as a foundation for education, training, assessment and technological development (e.g. models and simulators). The “optional” steps highlight areas of heterogeneity of practice that will benefit from further research (e.g. methods of skull base repair). Further adjustments could be made to increase applicability around the world