Punctured Plane Research Articles

Intraperitoneal mitoxantrone in the treatment of recurrent ascites from progressive epithelial ovarian cancer.

5051 Background: In patients with epithelial ovarian cancer (EOC), progression of disease is often characterized by recurrent ascites that does not respond neither to antineoplastic drugs nor to repeated paracentesis. We evaluated the effect of Mitoxantrone (MTZ) administered intraperitoneum (i.p.) to obtain control of recurrent ascites in this particular subset of pts. Methods: Seventy-four patients (median age 59 yrs, range 39–76) with EOC who progressed with ascites after 3 (42/74), 4 (23/74) or 5 (9/74) previous lines of chemotherapy were treated with MTZ i.p. delivered through a temporary catheter (EasyCyst puncture set,Ch 12, RUSCH France). After removing all the ascitic fluid, the drug was infused at the dose of 20 mg/m2, diluted in 1,500 mL of normal saline, via a 60-minute i.p. instillation and then it was left in situ. All the patients were controlled every 28 days and treatment was repeated in the presence of new developed ascites.The response of ascites to MTZ, was measured according these res...

퍼지 일반화된 위상 공간에서 FUZZY r-GENERALIZED ALMOST CONTINUITY에 관한 연구

In this paper, we introduce the concept of fuzzy r-generalized almost continuous mapping and obtain some characterizations of such a mapping. In particular, we investigate characterizations for the fuzzy r-generalized almost continuity by using the concept of fuzzy r-generalized regular open sets.

Scattered and hereditarily irresolvable spaces in modal logic

When we interpret modal ◊ as the limit point operator of a topological space, the Godel-Lob modal system GL defines the class Scat of scattered spaces. We give a partition of Scat into α-slices S α , where α ranges over all ordinals. This provides topological completeness and definability results for extensions of GL. In particular, we axiomatize the modal logic of each ordinal α, thus obtaining a simple proof of the Abashidze–Blass theorem. On the other hand, when we interpret ◊ as closure in a topological space, the Grzegorczyk modal system Grz defines the class HI of hereditarily irresolvable spaces. We also give a partition of HI into α-slices H α , where α ranges over all ordinals. For a subset A of a hereditarily irresolvable space X and an ordinal α, we introduce the α-representation of A, give an axiomatization of the α-representation of A, and characterize H α in terms of α-representations. We prove that \({X \in {\bf H}_{1}}\) iff X is submaximal. For a positive integer n, we generalize the notion of a submaximal space to that of an n-submaximal space, and prove that \({X \in {\bf H}_{n}}\) iff X is n-submaximal. This provides topological completeness and definability results for extensions of Grz. We show that the two partitions are related to each other as follows. For a successor ordinal α = β + n, with β a limit ordinal and n a positive integer, we have \({{\bf H}_{\alpha} \cap {\bf Scat} = {\bf S}_{\beta+2n-1} \cup {\bf S}_{\beta+2n}}\) , and for a limit ordinal α, we have \({{\bf H}_{\alpha} \cap {\bf Scat} = {\bf S}_{\alpha}}\) . As a result, we obtain full and faithful translations of ordinal complete extensions of Grz into ordinal complete extensions of GL, thus generalizing the Kuznetsov–Goldblatt–Boolos theorem.

HOMOGENIZATION OF ENERGIES DEFINED ON PAIRS SET-FUNCTION

In the present work, we deal with the problem of the asymptotic behavior of a sequence of non-homogeneous energies depending on a pair set-function of the form [Formula: see text] with u ∈ H1(Ω), E regular open set and the energy densities f and φ both 1-periodic in the first variable; this leads, in the Γ-limit, to a problem of homogenization. We prove a Γ-convergence result for the sequence {Fε}, showing that there is no interaction between the homogenized bulk and surface energy density; that is, even though the effect of the bulk and surface energies are at the same energy scale, oscillations in the bulk term can be neglected close to the surfaces ∂*E and S(u), where surface oscillations are dominant.

Roots in the mapping class groups

The purpose of this paper is the study of the roots in the mapping class groups. Let $\Sigma$ be a compact oriented surface, possibly with boundary, let $\PP$ be a finite set of punctures in the interior of $\Sigma$, and let $\MM (\Sigma, \PP)$ denote the mapping class group of $(\Sigma, \PP)$. We prove that, if $\Sigma$ is of genus 0, then each $f \in \MM (\Sigma)$ has at most one $m$-root for all $m \ge 1$. We prove that, if $\Sigma$ is of genus 1 and has non-empty boundary, then each $f \in \MM (\Sigma)$ has at most one $m$-root up to conjugation for all $m \ge 1$. We prove that, however, if $\Sigma$ is of genus $\ge 2$, then there exist $f,g \in \MM (\Sigma, \PP)$ such that $f^2=g^2$, $f$ is not conjugate to $g$, and none of the conjugates of $f$ commutes with $g$. Afterwards, we focus our study on the roots of the pseudo-Anosov elements. We prove that, if $\partial \Sigma \neq \emptyset$, then each pseudo-Anosov element $f \in \MM(\Sigma, \PP)$ has at most one $m$-root for all $m \ge 1$. We prove that, however, if $\partial \Sigma = \emptyset$ and the genus of $\Sigma$ is $\ge 2$, then there exist two pseudo-Anosov elements $f,g \in \MM (\Sigma)$ (explicitely constructed) such that $f^m=g^m$ for some $m\ge 2$, $f$ is not conjugate to $g$, and none of the conjugates of $f$ commutes with $g$. Furthermore, if the genus of $\Sigma$ is $\equiv 0 (\mod 4)$, then we can take $m=2$. Finally, we show that, if $\Gamma$ is a pure subgroup of $\MM (\Sigma, \PP)$ and $f \in \Gamma$, then $f$ has at most one $m$-root in $\Gamma$ for all $m \ge 1$. Note that there are finite index pure subgroups in $\MM (\Sigma, \PP)$.

Note on % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBqj3BWbIqubWexLMBb50ujbqegm0B % 1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr % Ffpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0F % irpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaa % GcbaWefv3ySLgznfgDOfdarCqr1ngBPrginfgDObYtUvgaiuaacqWF % qessryqr1ngBPrgaiyGacqGFsbGuaaa!4796! $$ \mathcal{I}R $$ -closed and % MathType!MTEF!2!1!+- % feaagaart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBqj3BWbIqubWexLMBb50ujbqegm0B % 1jxALjharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqr % Ffpeea0xe9Lq-Jc9vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0F % irpepeKkFr0xfr-xfr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaa % GcbaGaamyqamaaBaaaleaatuuDJXwAK1uy0HwmaeXbfv3ySLgzG0uy % 0Hgip5wzaGqbaiab-brijfHbfv3ySLgzaGGbciab+jfasbqabaaaaa!4888! $$ A_{\mathcal{I}R} $$ -sets

We characterize and discuss the properties of \( \mathcal{I}R \)-closed sets and \( A_{\mathcal{I}R} \)-sets. Also, we give characterizations of weakly \( \mathcal{I} \)-locally closed sets and \( \mathcal{I} \)-submaximal spaces. A characterization of codense ideals in terms of \( \mathcal{I}R \)-closed sets is also given.

FINE HIERARCHY OF REGULAR APERIODIC ω-LANGUAGES

We develop a theory of regular aperiodic ω-languages in parallel with the theory around the Wagner hierarchy. In particular, we characterize the Wadge degrees of regular aperiodic ω-languages, find an effective version of the Wadge reducibility adequate for this class of languages and prove "aperiodic analogs" of the Büchi-Landweber determinacy theorem and of the Landweber's characterization of regular open and regular Gδ sets.

SUBMAXIMAL AND SPECTRAL SPACES

A topological space X is said to be submaximal if every dense subset of X is open. In this paper, descriptions of submaximal spectral spaces and Stone submaximal spaces are given. Throughout this paper a number of illustrative examples are given.

SUBMAXIMAL AND SPECTRAL SPACES

A topological space X is said to be submaximal if every dense subset of X is open. In this paper, descriptions of submaximal spectral spaces and Stone submaximal spaces are given. Throughout this paper a number of illustrative examples are given.

Realcompactness in maximal and submaximal spaces

We study realcompactness in the classes of submaximal and maximal spaces. It is shown that a normal submaximal space of cardinality less than the first measurable is realcompact. ZFC examples of submaximal not realcompact and maximal not realcompact spaces are constructed. These examples answer questions posed in [O.T. Alas, M. Sanchis, M.G. Tkačenko, V.V. Tkachuk, R.G. Wilson, Irresolvable and submaximal spaces: homogeneity versus σ -discreteness and new ZFC examples, Topology Appl. 107 (3) (2000) 259–273] and generalize some results from [D.P. Baturov, On perfectly normal dense subspaces of products, Topology Appl. 154 (2) (2007) 374–383].

Laser-induced thermotherapy for lung tissue—evaluation of two different internally cooled application systems for clinical use

Thermal ablation techniques like radiofrequency or laser-induced thermotherapy (LITT) are increasingly used to treat tumors of parenchymatous organs. Minimal access, parenchymal preservation, and a low complication rate render them suitable for pulmonary tumors as well. Their successful clinical application depends on the induction of sufficiently large lesions and a knowledge of the energy parameters required for complete thermal ablation. The aim of this study was to establish a dose-response relationship for a percutaneous and an intraoperative system for LITT of lung tissue. Thermal lesions were induced in healthy porcine lungs using an Nd:YAG laser (1,064 nm). LITT was performed with a percutaneous application system in group I (n = 18) and an intraoperative application system in group II (n = 90). Laser energy was applied for 600-1,200 s in a power range of 20-32 W (12,000-38,400 J). The lesions were longitudinally and transversally measured, and the volume was calculated after the intervention. Furthermore, an open application system was used to perform LITT under in vivo conditions during lung perfusion and ventilation in domestic pigs. Lesion volumes in both groups showed a plateau-like curve when the laser power increased from an initial level of 25 W. With the percutaneous puncture system (group I), the application of 28 W (16,800 J) for 10 min generated the largest lesions with a volume of 12.54 +/- 1.33 cm(3), an axial diameter of 39.33 +/- 2.52 mm, and a diametrical diameter of 24.67 +/- 1.15 mm. A longer application time was not possible due to thermal instability of the applicator. Moreover, group I started developing extensive carbonizations at a laser power of 22 W (13,200 J). The intraoperative application system (group II) achieved the largest lesion volumes of 11.03 +/- 2.54 cm(3) with diameters of 34.6 +/- 4.22 mm (axial) and 25.6 +/- 2.51 mm (diametrical) by an exposure time of 20 min and a power of 32 W (38,400 J). Here extensive carbonizations only started to occur at 28 W (33,600 J). Under in vivo conditions, all pigs tolerated the LITT procedure well without complications. Besides a typical cooling effect in the vicinity of blood vessels, the thermal lesions were about three times smaller than the ex vivo lesions. Both the percutaneous and the open LITT application system induced reproducible, clinically relevant lung lesions. The percutaneous puncture set generated large relevant lesions, although its usability is limited by its restricted capacity and high carbonization risk. It is suitable for powers up to 22 W. The intraoperative application system allows higher energy exposure to induce larger lesion volumes. This study elucidates the dose-effect relation of two clinically relevant puncture sets.

Canonical Universes and Intuitions About Probabilities

This paper consists of three parts supplementing the papers of K. Hauser 2002 and D. Mumford 2000: (1) There exist regular open sets of points in R 3 with paradoxical properties, which are constructed without using the axiom of choice or the continuum hypothesis. (2) There exist canonical universes of sets in which one can define essentially all objects of mathematical analysis and in which all our intuitions about probabilities are true. (3) Models satisfying the full axiom of choice cannot satisfy all those intuitions and they violate them in a very similar way as those models which satisfy also the continuum hypothesis.

The group of parenthesized braids

We investigate a group B • that includes Artin's braid group B ∞ and Thompson's group F. The elements of B • are represented by braids diagrams in which the distances between the strands are not uniform and, besides the usual crossing generators, new rescaling operators shrink or stretch the distances between the strands. We prove that B • is a group of fractions, that it is orderable, admits a nontrivial self-distributive structure, i.e., one involving the law x ( yz ) = ( xy ) ( xz ) , it embeds in the mapping class group of a sphere with a Cantor set of punctures, and that Artin's representation of B ∞ into the automorphisms of a free group extends to B • .

Gradient estimates for Dirichlet parabolic problems in unbounded domains

We consider autonomous parabolic Dirichlet problems in a regular unbounded open set Ω ⊂ R N involving second-order operator A with (possibly) unbounded coefficients. We determine new conditions on the coefficients of A yielding global gradient estimates for the bounded classical solution.

Continuous lattices and Whiteheadian theory of space

In this paper a solution ofWhitehead’s problem is presented: Starting with a purely mereological system of regions a topological space is constructed such that the class of regions is isomorphic to the Boolean lattice of regular open sets of that space. This construction may be considered as a generalized completion in analogy to the well-known Dedekind completion of the rational numbers Qyielding the real numbers R. The argument of the paper relies on the theories of continuous lattices and “pointless” topology.

Subspaces of Maximal Operator Spaces

We explore subspaces of maximal operator spaces ( submaximal spaces) and give a new characterization of such spaces. We show that the set of n-dimensional submaximal spaces is closed in the topology of c.b. distance, but not compact. We also investigate subspaces of MAX(L ∞) and prove that any homogeneous Hilbertian subspace of MAX(L 1) is completely isomorphic to R + C.

Laser-induced Thermotherapy (LITT): Dose-Effect Relation on Lung Tissue

Summary Laser-induced thermotherapy (LITT) is an established minimally invasive technique which has been proven to be successful for many years, especially in the treatment of liver metastases. The lung is the organ most affected by metastases, next to the liver. Many patients do not meet the criteria of inclusion for metastasectomy which is considered the gold standard (3, 4). LITT could be a safe and effective alternative for these inoperable patients. In case of bilateral lung disease, segmental excision or lobectomy can be complemented by LITT of solitary focuses in other lobes. For a successful therapy management of lung metastases, lesion sizes are required for creating situations comparable to RO excision. For this purpose, the dose-effect relation between the applied Nd:YAG laser power and the coagulation size attainable was investigated for a clinically established applicator system. The tests were made ex vivo on porcine lungs using a LITT puncture set for open surgery. The laser power ranging from 20 to 32 watts was applied to the tissue through an internally cooled diffusor-tip applicator. The induced coagulation lesions were measured for volumes and maximum extensions. While the tested LITT system proved to be suitable for application with powers up to 32 watts, its maximum efficacy had been reached already at 25 watts and an exposure time of 20 minutes. Higher powers did not generate substantially larger lesions, but caused a temperature holdup and subsequent carbonisation. The data on the dose-effect relation obtained by this study contribute essentially to clinical application and lay the ground for a safe and validated therapy control.

Parfaits Miroirs De L'univers'': A `Virtual' Interpretation of Leibnizian Metaphysics

In "Virtual Modality" (in press) a long technical article I developed an adequate metalogical semantics for modal extensions of a recursively axiomatisable first-order theory T, and called the motivations for this se mantic framework 'Leibnizian". The purpose of this somewhat less formal essay will be to offer a partial justification my invocation of one of the more venerable names in the history of western philosophy. To this end, let T be such an incomplete axiomatisable theory, and C the completion of T's Lindenbaum algebra the (Dedekind-MacNeill) completion of the the boolean algebra of formulas of T modulo T-provable equivalence. In the present context, C may be concretely realised as the Stone algebra, or boolean algebra of regular open sets in T's Stone space, where the latter is construed as the (metatheoretically defined) space of Henkin interpretations of T. Detailed information about Stone algebras and Stone spaces (so named for their twentieth-century discoverer and investigator, Marshall Stone), as well as the notions of boolean-valued 'randomness' which underlie these results, may be found in (Bell) and (Bell and Machover), (Jech) and other articles, textbooks and monographs cited in (Boos 1998).

Existence of algebraic minimal surfaces for an arbitrary puncture set

We will show that any punctured Riemann surface can be conformally immersed into a Euclidean 3-space as a branched complete minimal surface of finite total curvature called an algebraic minimal surface.

Digital Topology: Regular Sets and Root Images of the Cross-Median Filter

In the study of topological properties of digital images, which is the central topic of digital topology, one is often interested in special operations on object boundaries and their properties. Examples are contour filling or border following. In classical topology there exists the strong concept of regularity: regular sets in R2 show no “exotic behaviour” and are extensively used in the theory of boundary value problems. In this paper we transfer the concept of regularity to digital topology within the framework of semi-topology. It is shown that regular open sets in (a special) semi-topology can be characterized graphically. A relationship between digital topology and image processing is established by showing that regular open digital sets, interpreted as digital pictures, are left unchanged when the cross-median filter is applied.