Punctured Plane Research Articles

Genuses of cluster quivers of finite mutation type

In this paper, we study the distribution of the genuses of cluster quivers of finite mutation type. First, we prove that in the 11 exceptional cases, the distribution of genuses is 0 or 1. Next, we consider the relationship between the genus of an oriented surface and that of cluster quivers from this surface. It is verified that the genus of an oriented surface is an upper bound for the genuses of cluster quivers from this surface. Furthermore, for any nonnegative integer n and a closed oriented surface of genus n, we show that there always exist a set of punctures and a triangulation of this surface such that the corresponding cluster quiver from this triangulation is exactly of genus n.

On (<mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mrow><mml:msup><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup><mml:mtext>,</mml:mtext><mml:msup><mml:mrow><mml:mi>β</mml:mi></mml:mrow><mml:mrow><mml:mo>∗</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>)-almost-pre-continuous mappings in topological spaces

Abstract In this paper, we introduced the notion of γ ∗ -regular-open sets and γ ∗ - δ .open sets and studied some of their basic properties and investigated the relationship between them. Also we introduced the notion of γ ∗ - δ - T i i = 0 , 1 2 , 1 , 2 spaces and characterized them using γ ∗ - δ .open sets and γ ∗ - δ .closed sets. Finally the concepts of ( γ ∗ , β ∗ )-almost-pre-continuous mappings and ( γ ∗ , β ∗ )-almost-pre-open (closed) mappings and studied some of their basic properties.

Regular open sets in fuzzifying topology redefined

In 2000 [1], Zahran introduced the concept of regular open sets in fuzzifying topology. In 2004 [2], Sayed and Zahran, gave an example to illustrate that the statements: (1) ⊨ A ∈ R τ → A ∈ τ (Lemma 2.2 [1]); and (2) ⊨ ( A ∈ R τ ∧ B ∈ R τ ) → A ∩ B ∈ R τ ( Theorem 2.4 [1]), are incorrect. In the present paper we redefine this concept to make these statements correct. Furthermore, by making use of our definition of regular open sets, the concepts of almost continuity and δ -continuity are introduced and studied in fuzzifying topology.

Nonlocal Variational Principles with Variable Growth

This paper is concerned with the functionalJdefined byJ(u)=∫Ω×ΩW(x,y,∇u(x),∇u(y))dx dy, whereΩ⊂ℝNis a regular open bounded set andWis a real-valued function with variable growth. After discussing the theory of Young measures in variable exponent Sobolev spaces, we study the weak lower semicontinuity and relaxation ofJ.

PS-Regular Sets in Topology and Generalized Topology

We define and study a new class of regular sets calledPS-regular sets. Properties of these sets are investigated for topological spaces and generalized topological spaces. Decompositions of regular open sets and regular closed sets are provided usingPS-regular sets. Semiconnectedness is characterized by usingPS-regular sets.PS-continuity and almostPS-continuity are introduced and investigated.

Almost separation axioms in fuzzifying topology

In the present paper, we introduced topological notions defined by means of regular open sets when these are planted into the framework of Ying's fuzzifying topological spaces (in Lukasiewicz fuzzy logic). We used fuzzy logic to introduce almost separation axioms \(T_{0}^{R}\)-, \(T_{1}^{R}\)-, \(T_{2}^{R}\) (almost Hausdorff)-, \(T_{3}^{R}\) (almost-regular)- and \(T_{4}^{R}\) (almost-normal). Furthermore, the \(R_{0}^{R}\)- and \(R_{1}^{R}\)-separation axioms have been studied and their relations with the \(T_{1}^{R}\)- and \(T_{2}^{R}\)-separation axioms have been introduced. Moreover, we gave the relations of these axioms with each other as well as the relations with other fuzzifying separation axioms.

F-door spaces and F-submaximal spaces

Submaximal spaces and door spaces play an enigmatic role in topology. In this paper, reinforcing this role, we are concerned with reaching two main goals:The first one is to characterize topological spaces X such that F(X) is a submaximal space (resp., door space) for some covariant functor Ff rom the category Top to itself. T0, and FH functors are completely studied.Secondly, our interest is directed towards the characterization of maps f given by a flow (X, f) in the category Set, such that (X,P(f)) is submaximal (resp., door) where P(f) is a topology on X whose closed sets are exactly the f-invariant sets.

On some properties of generalized open sets in generalized topological spaces

Abstract In [8], Császár introduced some generalized open sets in generalized topological spaces, namely, μ-semi-open, μ-preopen, μ-β-open, and μ-α-open. The primary purpose of this paper is to study some new properties and characterizations of these concepts as we also introduce and study a new generalized open set in generalized topological spaces, namely, μ-b-open. We also investigate some relationships between these concepts.

FUZZY INTUITIONISTIC ALMOST (r, s)-CONTINUOUS MAPPINGS

We introduce the concepts of fuzzy -regular open sets and fuzzy almost -continuous mappings on the intuitionistic fuzzy topological spaces in sense. Also we investigate the equivalent conditions of the fuzzy almost -continuity.

Meromorphic mappings of torus onto the Riemann sphere

The meromorphic mappings of the two dimensional torus onto the Riemann sphere are studied. Their connections with loxodromic meromorphic functions in the punctured plane are considered.

Submaximal operator space structures on Banach spaces

Subspaces of maximal operator spaces are called submaximal spaces and in general, they need not be maximal. We call those maximal operator spaces with the property that all submaximal spaces turn out to be maximal as hereditarily maximal spaces. Any two Banach isomorphic subspaces of a hereditarily maximal space will be completely isomorphic as operator spaces. We derive a characterization of these spaces. We introduce a notion of distance of an operator space to the class of submaximal spaces and discuss some related results. Mathematics subject classification (2010): 46L07, 47L25.

Multi topological approximations of rough set theory

In this paper, we generalise Pawlak’s approximation spaces to topological approximation spaces. These topological approximation spaces are generated using many topological notions such as regular open sets, semi-open sets, pre-open sets, γ-open sets, α-open sets and β-open sets and others. The basic definitions and properties of these topological approximation spaces are introduced and sufficiently illustrated. We put all topological generalisations in one generalisation called m-generalisation spaces.

Weaker forms of the Menger property

In this paper we study a weaker form of the classical concept of Menger property. This property, called weakly Menger, is independent from the Menger property and the almost Menger property. In particular, for Tychonoff spaces weaker Menger spaces are not equivalent to almost Menger spaces. We give some characterizations in terms of regular open sets and almost continuous mappings. We also introduce a weaker form of the star-Menger property and the notion of almost γk -set. Some open questions are given.

Ureteroscopy-Assisted Retrograde Nephrostomy

Introduction: Lawson et al first developed retrograde nephrostomy in 1983.1 Hunter et al reported 30 cases of retrograde nephrostomy in 1985.2 Ureteroscopy (URS)-assisted retrograde nephrostomy (UARN) was reported as a new technique for percutaneous nephrolithotomy (PCNL) in 2011, and this institute performed more than 30 cases of UARN.3 This video presents the details of the UARN technique based on this experience. Materials and Methods: The patient is placed in the Galdakao-modified Valdivia position under general and epidural anesthesia.4 A ureteral access sheath (UAS) is inserted and a flexible ureteroscope (Flex-X2®; Karl Storz) is inserted through the UAS. The target calculi are carefully observed to identify the appropriate renal calyx to be punctured. A Lawson retrograde nephrostomy puncture wire (Lawson Retrograde Nephrostomy Wire Puncture Set; COOK Urological) is carefully set into the flexible URS. The flexible ureteroscope approaches the desired renal calyx again, and the route from the renal calyx to the exit skin is then confirmed under fluoroscopy. The puncture is performed under ultrasonography after rechecking the preoperative computed tomography to avoid injury to the spleen, liver, intestines, or pleural cavity. The puncture wire passes through the muscle easily and tents the skin at the posterior axillary line. The skin is incised and the needle is delivered. Next, 22G and 18G needle dilators are placed over the puncture wire, which is advanced through the skin, subcutaneous fat, abdominal wall musculature, and perinephric fat until it reaches the renal parenchyma. The catheter is dilated up to 12F and a safety guidewire is placed through the UAS. A 30F percutaneous nephroaccess sheath (NAS; X-Force®N30 Nephrostomy Balloon Dilation Catheter; BARD) is passed over the balloon into the calyx under ureteroscopic and fluoroscopic guidance, and then the balloon is removed. PCNL is then performed. Results: A total of 32 patients were treated by UARN from September 2010 to November 2011. According to this procedure, 81.3% of the patients achieved a stone-free outcome and there were no blood transfusions or any complications in patients with a Clavien score of two or more. The median operation time was 160 minutes. Nephrostomy was therefore not performed on patients who achieved a stone-free outcome, and ureteral stents were put in place at the conclusion of this procedure in all patients.5 UARN was abandoned in one case because of URS mechanical trouble. These patients included two cases of horseshoe kidney, one case of complete staghorn calculi, and two cases of obese patients. Conclusions: UARN is considered to be the most suitable procedure for puncturing the middle calix. UARN is a safe, effective, and minimally invasive procedure for PCNL because continuous observation can be obtained with URS. No competing financial interests exist. Runtime of video: 5 mins 17 secs

Development and (pre-) clinical assessment of a novel surgical tool for primary and secondary tracheoesophageal puncture with immediate voice prosthesis insertion, the Provox Vega Puncture Set

Development and (pre-) clinical assessment were performed of a novel surgical tool for primary and secondary tracheoesophageal puncture (TEP) with immediate voice prosthesis (VP) insertion in laryngectomized patients, the Provox Vega Puncture Set (PVPS). After preclinical assessment in fresh frozen cadavers, a multicenter prospective clinical feasibility study in two stages was performed. Stage-1 included 20 patients, and stage-2 had 27. Based on observations in stage-1, the PVPS was re-designed (decrease in diameter of the dilator from 23.5 to 18 Fr.) and further used in stage-2. Primary outcome measure was immediate VP insertion without requiring additional instruments. Secondary outcome measures for comparison of the new with the traditional TEP procedure were: appreciation, ease of use, time consumption, estimated surgical risks and overall preference. A mini-max two-stage study design was used to establish the required sample size. In stage-1, dilatation forces were considered too high in patients with a fibrotic TE wall. With the final thinner version of the PVPS, VPs were successfully inserted into the TEP in ‘one-go’ in 24/27 (89%) of TEPs: 20 primary and 7 secondary. Participating surgeons rated appreciation, ease of use, time consumption and estimated surgical risks as better. Related adverse events were few and minor. The new PVPS appeared to be the preferred device by all participating surgeons. This study shows that the novel, disposable PVPS is a useful TEP instrument allowing quick and easy insertion of the VP in the vast majority of cases without requiring additional instruments.

On various classes of bitopological spaces

Bitopological spaces in which every subset is -open in its -closure (i.e., (i,j)-submaximal spaces) are introduced and their properties are studied. Based on the investigations by Arhangel'skiĭ, Collins and the author, the necessary conditions are found for bitopological spaces to be p-connected. Furthermore, (i,j)-I-spaces are introduced and the relations between (i,j)-submaximal, (i,j)-nodec and (i,j)-I-spaces are established when two topologies on a set are either independent of each other or interconnected by the inclusion, -, - and -relations. The preservation of (i,j)-submaximal and (2,1)-I-spaces under morphisms is also considered.

Generalized submaximal spaces

The notion of generalized submaximal spaces is introduced and studied. Properties and characterizations of generalized submaximal spaces are discussed.

\(rw\)-Locally Closed Sets in Bitopological Spaces

The aim of this paper is to introduce the concepts of \(rw\)-locally closed sets, \(rw\)-submaximal spaces and study their basic properties in bitopological spaces.

On Fuzzifying Nearly Compact Spaces

This paper considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies) introduced by Ying [16, (I)]. It investigates topological notions defined by means of regular open sets when these are planted into the frame-work of Ying's fuzzifying topological spaces (in <TEX>${\L}$</TEX>ukasiewwicz fuzzy logic). The concept of fuzzifying nearly compact spaces is introduced and some of its properties are obtained. We use the finite intersection property to give a characterization of fuzzifying nearly compact spaces. Furthermore, we study the image of fuzzifying nearly compact spaces under fuzzifying completely continuous functions, fuzzifying almost continuity and fuzzifying R-map.

SEVERAL KINDS OF INTUITIONISTIC FUZZY OPEN SETS AND INTUITIONISTIC FUZZY INTERIORS

The notion of intuitionistic fuzzy semi-pre interior (semi-pre closure) is introduced, and several related properties are investigated. Characterizations of an intuitionistic fuzzy regular open set, an intuitionistic fuzzy semi-open set and an intuitionistic fuzzy <TEX>${\gamma}$</TEX>-open set are provided. A method to make an intuitionistic fuzzy regular open set (resp. intuitionistic fuzzy regular closed set) is established. A relation between an intuitionistic fuzzy <TEX>${\gamma}$</TEX>-open set and an intuitionistic fuzzy semi-preopen set is considered. A condition for an intuitionistic fuzzy set to be an intuitionistic fuzzy <TEX>${\gamma}$</TEX>-open set is discussed.