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Povzetek: We show that if $E$ is a closed convex set in $\mathbb C^n$, $n>1$ contained in a closed halfspace $H$ such that ▫$E\cap bH$▫ is nonempty and bounded, then the concave domain $\Omega=\mathbb C^n\setminus E$ contains images of proper holomorphicmaps $f : X \to \mathbb C^n$ from any Stein manifold $X$ of dimension $< n$, with approximation of a givenmap on closed compact subsets of $X$. If in addition $2 {\rm dim} X+1 \le n$ then $f$ can be chosen an embedding, and if $2 {\rm dim} X = n$, then it can be chosen an immersion. Under a stronger condition on $E$, we also obtain the interpolation property for such maps on closed complex subvarieties.
Ključne besede: Stein manifolds, holomorphic embeddings, Oka manifold, minimal surfaces, convexity
Objavljeno v DiRROS: 15.03.2024; Ogledov: 261; Prenosov: 129
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Povzetek: In this paper we present the main developments in Oka theory since the publication of my book "Stein Manifolds and Holomorphic Mappings (The Homotopy Principle in Complex Analysis)", 2nd ed., Springer, 2017. We also give several new results, examples and constructions of Oka domains in Euclidean and projective spaces. Furthermore, we show that for $n > 1$ the fibre $\mathbb C^n$ in a Stein family can degenerate to a non-Oka fibre, thereby answering a question of Takeo Ohsawa. Several open problems are discussed.
Ključne besede: Oka manifold, Oka map, Stein manifold, elliptic manifold, algebraically subelliptic manifold, Calabi–Yau manifold, density property
Objavljeno v DiRROS: 14.03.2024; Ogledov: 657; Prenosov: 552
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Povzetek: Background. To analyze the efficacy of postoperative radiochemotherapy with 5-florouracil (5-FU) and leucovorin (LV) applied in the patients with gastric carcinoma treated in a single institution. Patients and methods. Between 2001 and 2004, 123 patients with resected gastric adenocarcinoma were treated with postoperative concomitant radiochemotherapy with 5-FU and LV. The adjuvant treatment consisted of five cycles of chemotherapy with 5-FU (425mg/m2 IV) andLV (20 mg/m2 IV) and concomitant radiotherapy with the total dose of 45 Gy.Results. The treatment was completed according to the protocol in 82% of patients. The frequency and severity of early toxic effects induced by radiochemotherapy were manageable. Median follow-up time of 56 survivors was 64.5 months (range: 51.7-96.4 months). The 5-year locoregional control (LRC), diseasefree survival (DFS), disease-specific survival (DSS) and overall survival (OS) were 81%, 48.3%, 50.4%, and 48.4%, respectively. The multivariate analysis showed that the tumor involvement of cardia and low intensity of chemotherapy were independent adverse prognostic factors for DSS and OS. More advanced pT-stage and tumors with diffuse growth type according to Lauren were identified as negative independent prognostic factor for OS. They were also on the threshold of statistical significance for DSS. Conclusions. Postoperative radiochemotherapy for gastric carcinoma has acceptable toxicity, and is effective particularly in regard to LRC. High incidence of distant metastases calls for more effective systemic regimens.
Objavljeno v DiRROS: 08.03.2024; Ogledov: 276; Prenosov: 81
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Povzetek: In this paper, we find surprisingly small Oka domains in Euclidean spaces $\mathbb C^n$ of dimension $n>1$ at the very limit of what is possible. Under a mild geometric assumption on a closed unbounded convex set $E$ in $\mathbb C^n$, we show that $\mathbb C^n\setminus E$ is an Oka domain. In particular, there are Oka domains only slightly bigger than a halfspace, the latter being neither Oka nor hyperbolic. This gives smooth families of real hypersurfaces $\Sigma_t \subset \mathbb C^n$ for $t \in \mathbb R$ dividing $\mathbb C^n$ in an unbounded hyperbolic domain and an Oka domain such that at $t=0$, $\Sigma_0$ is a hyperplane and the character of the two sides gets reversed. More generally, we show that if $E$ is a closed set in $\mathbb C^n$ for $n>1$ whose projective closure $\overline E \subset \mathbb{CP}^n$ avoids a hyperplane $\Lambda \subset \mathbb{CP}^n$ and is polynomially convex in $\mathbb{CP}^n\setminus \Lambda\cong\mathbb C^n$, then $\mathbb C^n\setminus E$ is an Oka domain.
Ključne besede: Oka manifold, hyperbolic manifolds, density property, projectively convex sets
Objavljeno v DiRROS: 19.02.2024; Ogledov: 516; Prenosov: 154
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Povzetek: Background. Breast cancer is the most frequent malignant disease in the majority of developed countries. In the last few years the introduction of mammography screening programmes has resulted in an improved survival of breast cancer patients. However, the incidence of the disease in these countries is still on the increase. Present focus on secondary breast cancer prevention activities, consisting of early detection and treatment, cannot ensure a decrease of breast cancer incidence. Improved breast health awarenesscould therefore represent a part of specific health promotion activities aimed at decreasing the incidence of breast cancer. Conclusions. Indeveloped countries breast cancer is a significant health care issue. Secondary breast cancer prevention activities should therefore be complementedby specific health promotion activities in order to reduce its incidence in the future. Primary breast cancer prevention would include healthpromotion activities aimed at enhancement of the individual as well as collective breast health awareness. Properly enlightened members of the influential population groups could attain appropriate changes in the fields of legislation, taxation, customs and commercial regulations that would enablewomen to control their own breast health.
Objavljeno v DiRROS: 07.02.2024; Ogledov: 503; Prenosov: 85
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