Mapping Class Research Articles

Random maps with sociological flavor

A map of a set to itself admits a representation by a graph with vertices being the elements of the set and an edge between every vertex and its image. Communities defined as the maximal connected components are uni-cyclic. The distributions of the sizes of communities and lengths of cycles for unconstrained random maps is a classical subject. We call experts the images and followers the remaining vertices, and we further define prophets, egocentrics, and introverts. We introduce and analyze classes of random maps with sociological flavor.

A novel iterative process for numerical reckoning of fixed points via generalized nonlinear mappings with qualitative study

Abstract This manuscript is devoted to constructing a novel iterative scheme and reckoning of fixed points for generalized contraction mappings in hyperbolic spaces. Also, we establish Δ \Delta and strong convergence results by the considered iteration under the class of mappings satisfying condition (E). Moreover, some qualitative results of the suggested iteration, like weak w 2 {w}^{2} -stability and data dependence results, are discussed. Furthermore, to test the efficiency and effectiveness of the proposed iteration, practical experiments are given. To support the theoretical results, illustrative examples are presented. Finally, our results improve and generalize several classical results in the literature of fixed point iterations.

Strategi Guru Mengefektifkan Kegiatan Pembelajaran Sosiologi pada Penerapan Kurikulum Merdeka di Sekolah Menengah Atas Negeri 2 Pandeglang

Abstrak The implementation of differentiated learning in sociology learning in the implementation of an independent curriculum at SMA Negeri 2 Pandeglang found several problems. Among them: students feel bored; lack of cooperation between students in each group; only a few students are active; and lack of interactive. The research aims to get an overview of the teacher’s strategy to streamline sociology learning activities in the implementation of the independent curriculum at SMA Negeri 2 Pandeglang. The research used a qualitative method with a descriptive approach. Data collection techniques were carried out through observation, interviews and documentation. The research was conducted at SMA Negeri 2 Pandeglang, Pandeglang Regency. Data analysis techniques used data reduction, data presentation and conclusion drawing or verification. The results showed that the teacher's strategy to streamline sociology learning activities in implementation the independent curriculum at SMA Negeri 2 Pandeglang was through differentiated learning. Differentiated learning is inseparable from several stages: the learning planning stage includes the implementation of diagnostic assessments, preparation of teaching modules, preparation of learning media and preparation of teaching materials. The learning implementation stage includes opening activities, core activities and closing activities. Various ways: appreciation and apperception, ice breaking, personal approach, varied learning methods and the use of mapping class techniques. Supporting factors: students motivation to learn, supportive learning media and teacher enthusiasm. Inhibiting factors: limited time, not all students actively participate and differences in students' abilitiy to understand learning.

An Algorithm for Nonlinear Problems Based on Fixed Point Methodologies With Applications

This research presents a highly efficient fixed point algorithm for the computation of fixed points for a very general class of nonexpansive mappings called generalized (α, β)-nonexpansive mappings within the context of uniformly convex Banach space. Our research establishes both weak and strong convergence theorems of the scheme. Furthermore, we demonstrate that the class of generalized (α, β)-nonexpansive mappings contain many classes of nonlinear mappings of the classical literature. Then, we perform various numerical computations to prove the efficiency of the proposed approach. We also study the convergence analysis of the scheme for two dimensional space with taxicab norm. Moreover, we show that our new result gives an alternative approach for solving Caputo fractional differential equation in a novel mappings setting.

A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness

Abstract In this article, we introduce Fibo-Pascal sequence spaces P p F {P_{p}^{F}} , 0 < p < ∞ {0<p<\infty} , and P ∞ F {P_{\infty}^{F}} through the utilization of the Fibo-Pascal matrix P F {P^{F}} . We establish that both P p F {P_{p}^{F}} and P ∞ F {P_{\infty}^{F}} are BK-spaces, enjoying a linear isomorphism with the classical spaces ℓ p {\ell_{p}} and ℓ ∞ {\ell_{\infty}} , respectively. Further contributing to the depth of our investigation, we proceed to derive the Schauder basis of the space P p F {P_{p}^{F}} , alongside an exhaustive computation of the α-, β-, and γ-duals for both spaces P p F {P_{p}^{F}} and P ∞ F {P_{\infty}^{F}} . Additionally, we undertake the task of characterizing certain classes of matrix mappings pertaining to the spaces P p F {P_{p}^{F}} and P ∞ F {P_{\infty}^{F}} . The final section of this study is dedicated to the meticulous characterization of compact operators acting in the spaces P 1 F {P_{1}^{F}} , P p F {P_{p}^{F}} , and P ∞ F {P_{\infty}^{F}} by using Hausdorff measure of non-compactness.

Fixed point results for Geraghty–Ćirić-type contraction mappings in b-metric space with applications

In this study, we manifest a new class of mappings that satisfy Geraghty–Ćirić-type contractive conditions in the context of b-metric spaces and prove a theorem on the existence and uniqueness of fixed points. Our results unify and generalize the results of Geraghty; Ćirić; Dukic, Kadelburg, and Radenović; and Shu-fang Li, Fei Hi, and Ning Lu in the setting of b-metric spaces. Furthermore, we provide examples to verify the correctness and applicability of our results. We also utilize our findings to show the existence of a unique solution for a nonlinear integral equation.

Few-Shot Classification of Wafer Bin Maps Using Transfer Learning and Ensemble Learning

Abstract The high cost of collecting and annotating wafer bin maps (WBMs) necessitates few-shot WBM classification, i.e., classifying WBM defect patterns using a limited number of WBMs. Existing few-shot WBM classification algorithms mainly utilize meta-learning methods that leverage knowledge learned in several episodes. However, meta-learning methods require a large amount of additional real WBMs, which can be unrealistic. To help train a network with a few real-WBMs while avoiding this challenge, we propose the use of simulated WBMs to pre-train a classification model. Specifically, we employ transfer learning by pre-training a classification network with sufficient amounts of simulated WBMs and then fine-tuning it with a few real-WBMs. We further employ ensemble learning to overcome the overfitting problem in transfer learning by fine-tuning multiple sets of classification layers of the network. A series of experiments on a real-dataset demonstrate that our model outperforms the meta-learning methods that are widely used in few-shot WBM classification. Additionally, we empirically verify that transfer and ensemble learning, the two most important yet simple components of our model, reduce the prediction bias and variance in few-shot scenarios without a significant increase in training time.

Asymptotically ɑ hemicontractive mappings in Hilbert spaces and a new algorithm for solving associated split common fixed point problem

We introduce a novel class of asymptotically $\alpha-$hemicontractive mappings and demonstrate its relationship with the existing related families of mappings. We establish certain interesting properties of the fixed point set of the new class of mappings. Furthermore, we propose and investigate a new iterative algorithm for solving split common fixed point problem for the new class of mappings. In particular, weak and strong convergence theorems for solving split common fixed point problem for our new class of mappings in Hilbert spaces are proved. Moreover, using our method, we require no prior knowledge of norm of the transfer operator. The results presented in the paper extend and improve the results of Censor and Segal [Censor, Y.; Segal, A. The split common fixed point problem for directed operators. {\it J. Convex Anal.} {\bf 16 } (2009), no. 2, 587–600.], Moudafi [Moudafi, A. The split common fixed-point problem for demicontractive mappings. {\it Inverse Problems} {\bf 26} (2010), no. 5:055007.; Moudafi, A. A note on the split common fixed-point problem for quasi-nonexpansive operators. {\it Nonlinear Anal.} {\bf 74} (2011), no. 12, 4083–4087.], Chima and Osilike [Chima, E. E.; Osilike, M. O. Split common fixed point problem for class of asymptotically hemicontractive mappings. {\it J. Nigerian Math. Soc.} {\bf 38} (2019), no. 3, 363--390.], Fan \textit{et al} [Fan, Q.; Peng, J.; He, H. Weak and strong convergence theorems for the split common fixed point problem with demicontractive operators. {\it Optimization} {\bf 70} (2021), no. 5-6, 1409--1423.] and host of other related results in literature.

On the iterative scheme generating methods using mean-valued sequences

Using the Mann method and the shrinking projection method, we present generalized forms of iterative scheme generating methods and compared them with prior frameworks. To this end, the properties of mean-valued sequences are leveraged. Subsequently, we establish a convergence theorem similar to that developed by Martinez-Yanes and Xu. This approach highlights the difference between the conventional shrinking projection method and the Martinez-Yanes and Xu variant. The proposed frameworks yield various types of iterative schemes for finding common fixed points, including a three-step iterative scheme. The class of mappings considered incorporate general types, including nonexpansive mappings.

Involution Generators of the Big Mapping Class Group

Involution Generators of the Big Mapping Class Group

Retraction Note: Curves with prescribed symmetry and associated representations of mapping class groups

Retraction Note: Curves with prescribed symmetry and associated representations of mapping class groups

Invariant measures for random piecewise convex maps

We establish the existence of Lebesgue-equivalent conservative and ergodic σ -finite invariant measures for a wide class of one-dimensional random maps consisting of piecewise convex maps. We also estimate the size of invariant measures around a small neighbourhood of a fixed point where the invariant density functions may diverge. Application covers random intermittent maps with critical points or flat points. We also illustrate that the size of invariant measures tends to infinite for random maps whose right branches exhibit a strongly contracting property on average, so that they have a strong recurrence to a fixed point.

Sub-Riemannian Coarea Formula for Classes of Noncontact Mappings of Carnot Groups

Sub-Riemannian Coarea Formula for Classes of Noncontact Mappings of Carnot Groups

Solutions of Fuzzy Fractional Differential Equations

The concept of generalized conformable fractional derivative is used to explore fuzzy fractional differential equations in this research. The extension of the class of differentiable fuzzy mappings underpins this concept. The summations and differences of two functions are produced using this derivative, and we prove the existence and uniqueness of a solution to a fuzzy fractional differential equation.

Big Mapping Class Groups and the Co-Hopfian Property

We study injective homomorphisms between big mapping class groups of infinite-type surfaces. First, we construct (uncountably many) examples of surfaces without boundary whose (pure) mapping class groups are not co-Hopfian; these are first such examples of injective endomorphisms of mapping class groups that fail to be surjective. We then prove that, subject to some topological conditions on the domain surface, any continuous injective homomorphism between (arbitrary) big mapping class groups that sends Dehn twists to Dehn twists is induced by a subsurface embedding. Finally, we explore the extent to which, in stark contrast to the finite-type case, superinjective maps between curve graphs impose no topological restrictions on the underlying surfaces.

On T-continuous map

It is no secret to the observer that the new open sets play a role in general topology. and they represent research topic for many topologists in different parts of the world. In fact, there is an important topics in general topology and real analysis that deals with continuity of maps and their different forms by relying on new open set. In this work, we presented and studied a new class of continuous maps called T-continuous by using the concepts of T-open sets and T-closed sets, where important and basic properties of T-continuous map and its relationship with other maps were verified.

Sample size adaptation designs and efficiency comparison with group sequential designs.

This study is to give a systematic account of sample size adaptation designs (SSADs) and to provide direct proof of the efficiency advantage of general SSADs over group sequential designs (GSDs) from a different perspective. For this purpose, a class of sample size mapping functions to define SSADs is introduced. Under the two-stage adaptive clinical trial setting, theorems are developed to describe the properties of SSADs. Sufficient conditions are derived and used to prove analytically that SSADs based on the weighted combination test can be uniformly more efficient than GSDs in a range of likely values of the true treatment difference . As shown in various scenarios, given a GSD, a fully adaptive SSAD can be obtained that has sufficient statistical power similar to that of the GSD but has a smaller average sample size for all in the range. The associated sample size savings can be substantial. A practical design example and suggestions on the steps to find efficient SSADs are also provided.

Generalized second order vectorial ∞-eigenvalue problems

We consider the problem of minimizing the $L^\infty$ norm of a function of the hessian over a class of maps, subject to a mass constraint involving the $L^\infty$ norm of a function of the gradient and the map itself. We assume zeroth and first order Dirichlet boundary data, corresponding to the “hinged” and the “clamped” cases. By employing the method of $L^p$ approximations, we establish the existence of a special $L^\infty$ minimizer, which solves a divergence PDE system with measure coefficients as parameters. This is a counterpart of the Aronsson-Euler system corresponding to this constrained variational problem. Furthermore, we establish upper and lower bounds for the eigenvalue.

Fekete and Szegö Inequalities for a Class of Holomorphic Mappings

Fekete and Szegö Inequalities for a Class of Holomorphic Mappings

Meta-analysis Influence of Integrated Mind Mapping Inquiry Based Learning Model on Student Problem Solving Skills

A This study aims to determine the effect of inquiry-based learning model integrated mind mapping on students' problem-solving skills. This type of research is quantitative research with meta-analysis methods. Data comes from international journals or proceedings published 2015-2023. Data search through ScienceDirect, Springer, ProQuest, ERIC and Taylor of Francis databases. Research should be selected for data in meta-analyses. The inclusion criteria are that research must be experimental methods or quasi-experiments, research indexed by Scopus, Sinta, Web of Science, Microsoft Academic and EBSCO, Research has an experimental class inquiry learning model integrated mind mapping and conventional model control class, research has a number of samples (N), correlation values (r), t, and F and a sample consisting of 1021 participants. Data analysis with the help of JASP to determine the value of effect size, heterogeneity test and publication bias. The results showed a positive influence of minde mapping-based inquiry learning model on students' problem solving skills ( z = 7.019; p < 0.001; 95% CI [0.61; 1.26]. This finding shows that the influence of mind mapping-based inquiry learning models is included in the very high category (rRE = 1.31).