Kolmogorov problem on widths asymptotics and pluripotential theory

Given a compact set K in an open set D on a Stein manifold Ω of dimension n, the set A[D,K] of all restriction of functions to K, analytic in D with absolute value bounded by 1 is a compact subset of C(K). The problem on the strict asymptotics for Kolmogorov diameters (widths): ln di(A[D,K]) ~ -σi[1/n],i —> ∞ was stated by Kolmogorov in an equivalent formulation for e-entropy of that set. For n = 1, this problem is solved by efforts of many authors (Erokhin, Babenko, Zahariuta, Levin-Tikhomirov, Widom, Nguyen, Skiba - Zahariuta, Fisher-Mic-cheli, et al) with σ = 1/τ where τ(K,D) := 1/2π ∫∆w (∆w is a positive measure supported on K). For n > 1 Zakharyuta conjectured that for "good" pairs (K, D) such an asymptotics holds with σ = 2π (n!/C(K,D))[1/n] where C(K,D) is the pluricapacity of the pairs (K, D) introduced by Bedford-Taylor [3]. In [31,35] Zakharyuta reduced this problem to a problem of pluripotential theory about approximating w(K, D; z) — 1 on any compact subset of D \ K by pluricomplex Green functions on D. The latter problem which is known as Zakharyuta's conjecture has been solved by Nivoche [23] and Poletsky [25]. In this thesis we give the detailed proofs of Zakharyuta's reduction of Kolmogorov problem to his conjecture and the Nivoche-Poletsky result

The diagnostic accuracy of the hounsfield unit value in pulmonary embolism

Objective: Pulmonary embolism (PE) a vascular disease. Computed tomography pulmonary angiography (CTPA) is the radiological imaging technique used to diagnose PE. In this study, we aimed to demonstrate the diagnostic accuracy of Hounsfield Unit (HU) value for PE based on the hypothesis that acute thrombosis causes an increase in HU value on computed tomography (CT). Methods: This research was as a single-center, retrospective study. Patients presenting to the emergency department (ED) diagnosed with PE on CTPA were enrolled as the study group. In addition, patients admitted to the same emergency department who were not diagnosed with PE and had non-contrast CT scans were included as the control group. A receiver operating curve (ROC) was produced to the diagnostic accuracy of HU values in predicting PE. Results: The study population (N=74) consisted of a study group (N=46) and a control group (N=28). The sensitivity and specificity of HU value for predicting PE on thoracic CT were found 61.5% and 96.4% at a value of 54.8 (Area Under the Curve (AUC):0.690) for right main pulmonary artery; 65.0% and 96.4% at a value of 55.9 (AUC:0.736) for left main pulmonary artery; 44.4% and 96.4% at a value of 62.7 (AUC:0.615) for right interlobar artery; and 60.0% and 92.9% at a value of 56.7 (AUC:0.736) for left interlobar artery. Conclusion: HU values may exhibit high diagnostic specificity on CT, for thrombi up to the interlobar level. An HU value exceeding 54.8 up to the interlobar level may raise suspicion of the presence of P

The role of repeated extended FAST in patients with stable blunt thoracoabdominal trauma

BACKGROUND: Thoracic and abdominal computed tomography scans are widely used modalities for trauma patients in emergency department (ED). However, alternative diagnostic and follow-up tools are also needed, due to limitations such as high cost and exces-sive radiation exposure. This study aimed to investigate the utility of repeated extended focused abdominal sonography for trauma (rE-FAST) performed by the emergency physician in patients with stable blunt thoracoabdominal trauma.METHODS: This was a prospective, single-center diagnostic accuracy study. Patients with blunt thoracoabdominal trauma admitted to the ED were included in the study. The E-FAST was performed on the patients included in the study at the 0th h, the 3rd h, and the 6th h during their follow-up. Then, the diagnostic accuracy metrics of E-FAST and rE-FAST were calculated.RESULTS: The sensitivity and specificity of E-FAST in determining thoracoabdominal pathologies were found to be 75% and 98.7%, respectively. The sensitivity and specificity for specific pathologies were 66.7% and 100% for pneumothorax, 66.7% and 98.8% for hemothorax, and 66.7% and 100% for hemoperitoneum, respectively. The sensitivity and specificity of rE-FAST in determining thoracal and/or abdominal hemorrhage in stable patients were found to be 100% and 98.7%, respectively.CONCLUSION: E-FAST successfully rules in thoracoabdominal pathologies in patients with blunt trauma, with its high specificity. However, only a rE-FAST might be sensitive enough to exclude traumatic pathologies in these stable patients

ACTIVE FOLLOW-UP DECISION IN PROSTATE CANCER; HOW SAFE IS THE BIOPSY GLEASON SCORE?

Amaç: Prostat spesifik antijenin tanımlanmasından sonra insidental prostat kanseri oranı yükselmiş ve hastalar gereksiz tedavilere maruz kalabilmişlerdir. İnsidental prostat kanseri olan hastalarda herhangi bir tedavi uygulanmadan yakın izlem kılavuzlara girmiş ve hastalara uygulanmaya başlamıştır. Ancak transrektal ultrasonografi eşliğinde biyopsi patolojilerindeki veriler ile radikal prostatektomi spesimen patolojilerindeki verilerin uyumsuzluğu, küratif tedavi ihtiyacı olabilecek hastaları riske atmaktadır. Bu çalışmada; radikal prostatektomi spesimenlerindeki Gleason skorları ile TRUS-bx Gleason skorlarının karşılaştırılması amaçlanmıştır. Materyal – Metot: Mart 2011 ile Haziran 2016 tarihleri arasında, kliniğimizde radikal prostatektomi cerrahisi geçirmiş hastaların verileri retrospektif olarak değerlendirildi. Hastaların transrektal ultrasonografi eşliğinde biyopsi öncesi PSA değerleri, biyopsi kor sayıları, kanser pozitif biyopsi kor sayıları, biyopsideki kanser yüzdeleri ve Gleason skorları tespit edilerek, radikal prostatektomi sonrası Gleason skorları, doku kanser oranları, cerrahi sınırlar ve patolojik evre ile karşılaştırıldı. Bulgular: Toplam 44 hastanın verileri değerlendirildi. Transrektal ultrasonografi eşliğinde biyopsi patolojisinde Gleason skoru 7 olan hastaların 1’inde (%16,6) prostat spesimen Gleason skoru >7 olarak tespit edildi Sonuç: Transrektal ultrasonografi eşliğinde biyopsi patolojilerinde bildirilen Gleason skorları ile radikal prostatektomi Gleason skorları arasında fark olabilmekte, bu fark özellikle biyopsi Gleason skoru 7 at 1 (16,6%) patient in both transrectal ultrasonography guided biopsy and radical prostatectomy Conclusion: There are differences between transrectal ultrasonography guided biopsy Gleason scores and the radical prostatectomy Gleason scores. This differences especially are obvious in patients with Gleason score <7. The reliability of gleason scores reported by the pathologists might be questionable so, in order to decide active surveillance for patients, other variables (core-tumor ratio, tumor core number, PSA) must also be considered

Comparison of Long-Term Efficacy and Reliability of Mid-Urethral Sling Surgeries in Stress Type Urinary Incontinence Treatment

Amaç: Transobturator tape (TOT) ve tension free vaginal tape (TVT) operasyonları stres tipte idrar kaçırma (StİK) tedavisinde kullanılan standart orta üretra askı cerrahileridir. Çalışmamızda, TOT/TVT operasyonlarının; klinik başarı, komplikasyon ve uzun dönem etkinlik/güvenilirliğini değerlendirmeyi amaçladık.Materyal ve Metot: Tek bir cerrah tarafından 2011-2020 tarihleri arasında spinal anestezi altında orta üretral askı (TOT ve TVT) cerrahisi uygulanan toplam 79 hasta retrospektif olarak değerlendirildi. Hastaların pre-operatif anamnez, fizik muayene, laboratuvar değerlendirmesi ve ürodinamik incelemeleri yapıldı. Hastaların cerrahi başarısı, per-operatif komplikasyonları, post-operatif erken dönem ve geç dönem komplikasyonları değerlendirildi.Bulgular: Orta üretra askı operasyonu uygulanan 41(%51,9) hastaya TOT ve 38 (%48,1) hastaya TVT cerrahisi uygulandı. Hastaların ortalama yaşı 54,5±9,5 yıl ve ortalama takip süresi 55,4 (min 2,9-max 113,7) aydır. Cerrahi sonrası 77 hastada (%97,5) StİK şikayetinin tamamen ortadan kalktığı gözlenirken, TVT uygulanan 2 (%2,5) hastada sıklığı azalmış olsa da StİK’nın devam ettiği gözlendi. Postoperatifdönemde 4 (%5) TVT hastasında ve 5 (%6,3) TOT hastasında de-nova sıkışma tipi idrar kaçırma gözlendi.Sonuç: Orta üretra askı operasyonlarından TOT ve TVT cerrahileri StİK tedavisinde başarı oranları yüksek tedavi seçenekleridir. TVT operasyonunda TOT cerrahisine göre komplikasyon oranlarının düşük oranda da olsa yüksek olmasına rağmen uzun dönem izlem sonrası her iki operasyonun da etkili ve güvenilir olduğu tespit edildi.Aim: Trans-obturator tape (TOT) and tension free vaginal tape (TVT) operations are standard mid urethral sling surgeries used in stress type urinary incontinence (STUI) treatment. We aimed to evaluate the clinical success, complications and long-term efficacy / reliability of TOT / TVT surgeries. Materials and Methods: A total of 79 patients who underwent middle urethral sling (TOT and TVT) operation by a single surgeon under spinal anesthesia between 2011-2020 were evaluated retrospectively. Pre-operative anamnesis, physical examination, laboratory evaluation and urodynamic examinations of the patients were analysed. Surgical success, per-operative complications, post-operative early and late complications were evaluated. Results: Trans-obturator tape and TVT surgery was performed in 41 (51.9%) and 38 (48.1%) patients respectively. The average age of the patients was 54.5 ± 9.5 years and the mean follow-up period was 55.4 (min 2.9-max 113.7) months. It was observed that STUI symptoms disappeared completely in 77 patients (97.5%) after surgery, while STUI symptoms continued in 2 (2.5%) patients with TVT. De-novo urgency incontinence was observed in 4 (5%) TVT patients and 5 (6.3%) TOT patients at post-operative period. Conclusion: Mid-urethral sling operations (TOT and TVT surgeries) are the treatment options with high success rates in STUI treatment. Although complication rates were higher in TVT operation compared to TOT surgery, after long-term follow-up, it was found that both operations were effective and reliable

Local Boundedness of Catlin q-Type

In D'Angelo (Ann Math 115:615-637, 1982) introduced the notion of finite type for points p of a real hypersurface M of C-n by defining the order of contact Delta(q)(M, p) of complex-analytic q-dimensional varieties with M at p. Later, Catlin (Ann Math 126(1):131-191, 1987) defined q-type, D-q(M, p) for points of hypersurfaces by considering generic (n - q + 1)-dimensional complex aline subspaces of C-n. We define a generalization of the Catlin's q-type for an arbitrary subset M of C-n in a similar way that D'Angelo's 1-type, (M, p), is generalized in Lamel and Mir (Adv Math 335:696-734, 2018). Using recent results connecting the D'Angelo and Catlin q-types in Brinzanescu and Nicoara (Relating Catlin and D'Angelo q-types. arXiv:1707.08294, 2021) and building on D'Angelo's work on the openness of the set of points of finite Delta(q)-type, we prove the openness of the set of points of finite Catlin q-type for an arbitrary subset M subset of C-n

Holomorphic extension of meromorphic mappings along real analytic hypersurfaces

Let M subset of C-n be a real analytic hypersurface, M' subset of C-N (N >= n) be a strongly pseudoconvex real algebraic hypersurface of the special form, and F be a meromorphic mapping in a neighborhood of a point p is an element of M which is holomorphic in one side of M. Assuming some additional conditions for the mapping F on the hypersurface M, we proved that F has a holomorphic extension to p. This result may be used to show the regularity of CR mappings between real hypersurfaces of different dimensions

Dynamical estimates on a class of quadratic polynomial automorphisms of C-3

Quadratic automorphisms of C3 are classified up to affine conjugacy into seven classes by Fornss and Wu. Five of them contain irregular maps with interesting dynamics. In this paper, we focus on the maps in the fifth class and make some dynamical estimates for these maps

Extension of plurisubharmonic functions in the Lelong class

Let X be an algebraic subvariety of Cn and X be its closure in Pn. In their paper (J. Reine Angew. Math. 676 (2013), 33-49), Coman, Guedj and Zeriahi proved that any plurisub- harmonic function with logarithmic growth on X extends to a plurisubharmonic function with logarithmic growth on Cn when the germs (X, a) in Pn are irreducible for all a ∈ X\X. In this pa- per we consider X for which the germ (X, a) is reducible for some a ∈ X \X and we give a necessary and sufficient condition for X so that any plurisubharmonic function with logarithmic growth on X extends to a plurisubharmonic function with logarithmic growth on Cn