Punctured Plane Research Articles

Existence result for a nonlinear mixed boundary value problem for the heat equation

In this paper we study the existence of solutions in parabolic Schauder space of a nonlinear mixed boundary value problem for the heat equation in a perforated domain. From a given regular open set Ω⊆Rn we remove a cavity ω⊆Ω. On the exterior boundary of Ω∖ω‾ we prescribe a Neumann boundary condition, while on the interior boundary we set a nonlinear Robin-type condition. Under suitable assumptions on the data and by means of Leray Schauder Fixed-Point Theorem, we prove the existence of (at least) one solution u∈C01+α2;1+α([0,T]×(Ω‾∖ω)).

Holonomy of the Planar Brownian Motion in a Poisson Punctured Plane

We define a family of diffeomorphism-invariant models of random connections on principal G-bundles over the plane, whose curvatures are concentrated on singular points. We study the limit when the number of points grows to infinity whilst the singular curvature on each point diminishes, and prove that the holonomy along a Brownian trajectory converges towards an explicit limit.

Identifying the Severity of Criminal Activity in Society Using Picture Fuzzy Baire Space

In this paper, the idea of picture fuzzy Baire space is explored and its properties are examined. The features of picture fuzzy semi-closed and semi-open sets, picture fuzzy nowhere dense sets, picture fuzzy first and second category sets, picture fuzzy residual sets, picture fuzzy submaximal spaces, picture fuzzy strongly irresolvable spaces, picture fuzzy Gδ set, picture fuzzy Fσ set, and picture fuzzy regular closed sets are analyzed. To understand the concepts, some examples are provided. An algorithm using picture fuzzy Baire space is developed to address real-world scenarios. This method is more effective in assessing criminal activity as it identifies an individual who has committed a more serious offense. This algorithmic approach proves its effectiveness in navigating the complexities of practical examples, showcasing its potential for real-world applications.

BIOPERATION ON 𝜹𝑷𝑺-OPEN SETS IN TOPOLOGICAL SPACES

The concept of a 𝝔 operation on a new class of 𝜹𝑷𝑺-open subsets was defined. The comparisons were made with all other existing open sets with this new open set. Here for the same topological space two different operations 𝝔 and 𝝔′are defined and a new concept of bioperation was introduced. The concepts of [𝝔,𝝔′]-open sets and [𝝔,𝝔′]-regular spaces along with some topological properties were analysed. Two types of [𝝔,𝝔′]-closures were studied with their properties, and the submaximal spaces were analyzed.

On Supra iR-Open Set in Topological Spaces and Some Applications

In this work we introduce the supra iR-open set in supra topological spaces. , a novel class of supra i-open sets. This class of sets exactly lies between supra regular open and supra i- open sets. We also look at its basic characteristics and compare it to other sorts of data supra semi open sets types as supra i- open set, supra regular open, regular open, regular closed, clopen, supra semi regular open set and supra clopen . By using this set , We introduce and define the notion of supra totally iR-continuous , supra iR-irresolute map and investigate some of its properties. We prove that every supra totally iR- continuous function is supra iR-irresolute, every totally i????-continuous function is supra totally iR continuous and any strongly continuous function is supra totally iR-continuous, on the other hand, we give examples to show that the convers may not be true. At last , We have proved some theorem to discuss the properties of supra iR-normal space and supra iR-regular space.

R-Compatible Ideals of topological spaces

Abstract. This paper's goal is to present the idea of regular-compatibility of ideals by replaced the open set is Regular-open set and with respect to topology, which is abbreviated as (τ ∼ R I ), Using a brand-new local function termed the regular-local function A(*R) (I, T), it is also possible to examine the connection between this idea and the idea of the R-compatibility of an ideal with I. A few comparable circumstances are established. By employing the new operator is Regular -psi set short (ΨR(A)), we further analyze the characterizations of Regular -compatibility with the aid of this local function. And the relationship between them. Several notions of compatibility between a partially ordered set and a topology on its underlying set are comparable to separation axioms and other well-known ideas from general topology.

Compute Nano topology by used the programing language python

The research aims to Compute the Nano topologies of any set, consisting of five or less elements, through the Python programming language, with finding the necessary algorithms for the solution steps, We explain the mechanism of action: In first we will find the equivalence relations on set, and then we must compute the nano topology, and end know who set was semi-open, alpha-open,beta-open Regular open ,pre open and gamma-open set .

Soft C-continuity and soft almost C-continuity between soft topological spaces

We present the notions of soft c-continuity and soft nearly c-continuity, which are weaker versions of soft continuity and soft almost continuity, respectively. We obtain several characterizations for these two concepts. We show that soft c-continuity and soft almost c-continuity are preserved under soft restrictions. In addition, we investigate the conditions under which the composition of two soft c-continuous and soft almost c-continuous functions is soft c-continuous and soft almost c-continuous. Moreover, via soft N-open sets, we give a characterization of the soft compactness of soft topological spaces over finite sets of parameters. In addition, we show that for a given soft topological space (L,Ω,F), the collection of soft regular open sets with soft compact complements forms a soft base for some coarser soft topology. We demonstrate that (L,Ω⁎,F) are all soft compacts. Furthermore, we demonstrate that Ω=Ω⁎ if (L,Ω,F) or (L,Ω⁎,F) is soft compact and soft Hausdorff. Finally, we investigate the correspondences between the novel notions in soft topology and their general topological analogs.

On Regular**-Open Separation Axioms In Ideal Topological Space

The concern of this study focuses on constructing a new classes of separation axioms by using the notion of Regular**− open set of ideal topological space. Using the concept of regular-open sets and Regular-local functions with *R-closure operator in an ideal topological space (X, T, I), analogous to the usual separation axioms. A few characteristics and attributes are investigated. Like separation axioms works.

Generalized Investigated in Topological Space

Abstract: In this paper, some characterizations and proportion of notion a investigated. Throughout this paper (X, τ) and (Y, σ ) (simply, X and Y) represent topological spaces on which separation axioms are assumed unless otherwise mentioned. We introduce a new class of sets called regular generalized open sets which is properly placed in between the class of open sets and the class of - open sets. Throughout this paper (X, ) represents a topological space on which no separation axiom is assumed unless otherwise mentioned. For a subset A of a topological space X, cl (A) and int (A) denote the closure of A and the interior of A respectively. X/A or Ac denotes the complement of A in X. introduced and investigated semi open sets, generalized closed sets, regular semi open sets, weakly closed sets, semi generalized closed sets , weakly generalized closed sets, strongly generalized closed sets, generalized pre - regular closed sets, regular generalized closed sets, and generalized -generalized closed sets respectively.

Regular Open Sets on The Intuitionistic Fuzzy Topological Spaces in Sostak's Sense

The aim of this paper is to introduce and study the concepts of intuitionistic r-fuzzy regular open sets and their related notions in topological spaces.

Abstract Number ‐ 81: Safety and Efficacy of Trans‐carotid Intervention in Multiple Scenarios: Medellin Experience Direct Carotid access.

Introduction Direct carotid puncture has been validated such as an alternative route to reach the intracranial vasculature. However, this approach has not been considered routinely in INR. A believe of higher risk for neurovascular procedures or major accesssite related complications restrict its use. This study was conducted to investigate the feasibility and safety of trans carotid Neurointervention for a variety of pathologies. Methods Since 2018 we implemented a direct carotid access under special considerations to perform a therapeutic approach. A total of 14 patients from our centers were analyzed. Patients were divided into a variety of neurovascular conditions: Carotid Stenting CAS (n = 2), Mechanical Thrombectomy MT (n = 5), AVM´s treatment (n = 2), intracranial Aneurysms treatment (n = 5). Patient demographics, technical data, intervention time, type of intervention, closure device used, local or systemic complications and a patient perception assessment were registered. Results Mean age was 64.3 ± 10.3 years. all cases but two we treated the patients under General Anesthesia GA. Major indication to this approach was : anatomical and access limitations. (in 12 cases wasn’t possible to reach the ICA through femoral or radial access due to extreme aortic arc tortuosity. Two patients with Leriche Syndrome) All cases performed with ultrasound US assistance. A 4 Fr. Micro‐ puncture set were used in all procedures and posteriorly a 6Fr. Introducer was inserted. Technical success in all cases (100%). Two patients presented mild vasospasm and resolved using IA vasodilators. Both CAS were performed without any complications and none embolic protection device used. For MT(n = 5): a SOFIA 6Fr for ADAPT was used in 3 cases with TICI 2b‐3 in all cases. Combined approach ¨Solumbra¨ solitaire and aspiration catheter was used in two cases, one TICI 2a and one TICI 3. For the AVM´s treatment we use a 6Fr guiding catheter and non‐detachable microcatheters to inject Onix with a high grade of obliteration. Five aneurysms were treated with this approach (2 ICA – ophthalmic; 2 MCA and one AcomA) Mean average time of the procedure was 34.5 min. (ranged 9–59 min) just one bleeding complication observed at the closure device use. In all cases but one we use Angio‐Seal 6Fr as closure device, in a single case where we used a ProGlide suture device we had a serious complication at the puncture site. Conclusions Trans Carotid Intervention TCI. was feasible and safe in selected patients in this small series. A multiple variety of neurovascular conditions would be treated successfully by this way improving the learning curve. Complication rates and clinical outcomes were comparable with those in trans femoral or radial approach.

Submaximality on Bigeneralized Topological Spaces

In this article, in a bigeneralized topological space, we introduce a new space namely, (s, v)-bigeneralized submaximal space, and analyze its nature. Also, the characterization theorem for a (s, v)-bigeneralized submaximal space, image and preimage of (s, v) bigeneralized submaximal is a (s, v)-bigeneralized submaximal space under (µ, η)-open, (µ, η)-continuous map, respectively are proved. Further, the relationship between hyperconnected space and submaximal space in a pairwise bigeneralized submaximal space is given.

A new class of NeutroOpen, NeutroClosed, AntiOpen and AntiClosed sets in NeutroTopological and AntiTopological spaces

A lot of research has been done on the types of open and closed sets in general topological spaces and also in general bitopological spaces. Types of sets like pre-open sets and pre-closed sets, semi-open sets and semi-closed sets, Alpha-open sets, and Alpha-closed sets, regular open sets and regular closed sets, g-open sets and g-closed sets, and many more have been defined and studied. In the current study, an attempt has been made to define and give examples of a new category of open and closed sets, namely, NeutroOpen and NeutroClosed sets. Further, the concept of neutron-topology is used to define NeutroPreOpen and NeutroPreClosed sets, NeutroSemiOpen and NeutroSemiClosed sets, NeutroAlphaOpen and NeutroAlphaClosed sets, NeutroRegularOpen and NeutroRegularClosed sets, NeutroBetaOpen, and NeutroBetaClosed sets, and several examples have been given to illustrate each of the new classes of sets. Also, the concept of AntiTopology has been used to define another class of sets, namely, AntiOpen and AntiClosed sets of the above five classes of sets, namely, regular-openclosed; semi-openclosed, Alpha-openclosed, Beta-openclosed pre-openclosed sets. Further, a new class of subsets is identified which are named as NeutroTauOpen and NeutroTauClosed sets. Similar subsets in anti-topological spaces are named as AntiTauOpen and AntiTauClosed sets.

δ-open sets in Neutrosophic Hypersoft Topological Spaces

In this paper, neutrosphic hypersoft δ-open sets are introduced by defining the neutrosophic hypersoft regular open sets, pre-open sets, δ-interior and δ-closure. Under the guidance of these definitions, neutrosophic hyper- soft δ semi-open sets and δ pre-open sets are also introduced. Further, we have deduced inuitionistic hypersoft topology and fuzzy hypersoft topology from the neutrosophic hypersoft topology. Moreover, we discuss about the relations between neutrosphic hypersoft δ-open sets, δ semi-open sets, δ pre-open sets, semi-open sets and pre-open sets and their properties with examples.

On Regular Semi Supra Open set and Regular Semi Supra Continuity

The aim of this paper is to present the concepts of -supra continuous function, -semi supra continuous function, -regular open set and -regular semi supra open set in -supra topological space. We studied relations between these functions and check up from some of its characteristics.

Hölder regularity and Liouville properties for nonlinear elliptic inequalities with power-growth gradient terms

This note studies local integral gradient bounds for distributional solutions of a large class of partial differential inequalities with diffusion in divergence form and power-like first-order terms. The applications of these estimates are two-fold. First, we show the (sharp) global Hölder regularity of distributional semi-solutions to this class of diffusive PDEs with first-order terms having supernatural growth and right-hand side in a suitable Morrey class posed on a bounded and regular open set$\Omega$. Second, we provide a new proof of entire Liouville properties for inequalities with superlinear first-order terms without assuming any one-side bound on the solution for the corresponding homogeneous partial differential inequalities. We also discuss some extensions of the previous properties to problems arising in sub-Riemannian geometry and also to partial differential inequalities posed on noncompact complete Riemannian manifolds under appropriate area-growth conditions of the geodesic spheres, providing new results in both these directions. The methods rely on integral arguments and do not exploit maximum and comparison principles.

On soft submaximal spaces

In the present paper, detailed properties of soft submaximal topological spaces have been discussed. It starts by examining how well soft submaximal spaces behave when subjected to some operations, such as: taking soft subspaces, soft products, soft topological sum and images/preimages under certain soft mappings. Furthermore, several characterizations of soft submaximal spaces are obtained with respect to various types of soft subsets of soft topological spaces and their simple extensions.

On Sw*- Regular Spaces

The purpose of this paper is to present and investigate a new class of topological spaces known as Sw*-regular spaces, by utilizing the concept of Sw-regular sets and some of its properties. which is introduced in 2009 by L. S. Abddullah and A. B. Khalaf [1], the new class is properly contained in S*- regular space [2], [3], means that Sw*- regular spaces is a stronger form to the space S*- regular. Several characterizations, properties and relationships of Sw*- regular space with other spaces such as, Sw-compact, extremally disconnected, regular, semi-regular, Sw-T2 and Urysohn spaces has been studied. Furthermore, several properties of Sw*- regular spaces with some functions such as, continuous, strongly continuous, open, clopen and Somewhat open functions are also explored. In addition we investigate that Sw*- regular space has a topological property, while it has not a hereditary property, only by adding certain conditions such as, a subspace is open or, if the subspace of an Sw*-regular submaximal space is preopen, then it becomes an Sw*- regular.

Some Open Sets and Related Topics in Topological Spaces

Our purpose is to investigate some properties of (Λ, b)-open sets. Several characterizations of (Λ, b)- extremally disconnected spaces, (Λ, b)-hyperconnected spaces and (Λ, b)-submaximal spaces are established. Es- pecially, several characterizations of (Λ, b)-continuous functions are discussed.