Inclusion Relations Research Articles

On a subclass of alpha-quasi convex mappings

In this paper, we introduce the class of α-quasi convex mappings on the unit ball in a complex Banach space, with the aim of providing a unified approach to the Fekete-Szegö problem for subclasses of normalized starlike mappings and normalized quasi-convex mappings of type B on the open unit ball B of a complex Banach space. In particular, using some restrictive assumptions, we investigate inclusion relations among the classes of alpha-quasi convex mappings, starlike mappings and quasi-convex mappings of type B.

Neutrosophic Fuzzy Tribonacci ℐ-Lacunary Statistical Convergent Sequence Spaces

Abstract The aim of this paper is to introduce and investigate some neutrosophic fuzzy tribonacci ℐ-lacunary statistical convergent sequence spaces by utilizing the domain of regular tribonacci matrix A = (ajk ). Morever, we also put forward various algebraic and topological features of these convergent sequence spaces and establish several interesting inclusion relations.

Certain topological properties for almost convergent Catalan-Motzkin sequence space

The purpose of this paper is to introduce a new almost convergent sequence space by means of a matrix involving Catalan and Motzkin numbers. It is demonstrated that this novel sequence space and the space of all almost convergent sequences are linearly isomorphic and the $\beta$-dual of this new space is deduced. In addition, by defining Catalan-Motzkin core of a complex-valued sequence, certain inclusion relations are derived for it.

Orlicz Amalgam Spaces on the Affine Group

Let A be the affine group, Φ1, Φ2 be Young functions. We study the Orlicz amalgam spaces W (LΦ1 (A), LΦ2 (A)) defined on A, where the local and global component spaces are the Orlicz spaces LΦ1 (A) and LΦ2 (A), respectively. We obtain an equivalent discrete norm on the amalgam space W (LΦ1 (A), LΦ2 (A)) using the constructions related to the affine group. Using the discrete norm we compute the dual space of W (LΦ1 (A), LΦ2 (A)). We also prove that the Orlicz amalgam space is a left L1(A)-module with respect to convolution under certain conditions. Finally, we investigate some inclusion relations between the Orlicz amalgam spaces.

Some aspects of 𝜆-weak convergence using difference operator

Abstract In this paper, we introduce generalized difference weak sequence space classes by utilizing the difference operator Δ ı ȷ \Delta^{\jmath}_{\imath} and the de la Vallée–Poussin mean, denoted as [ ( V , λ ) w , Δ ı ȷ ] m [(\mathscr{V},\lambda)_{w},\Delta^{\jmath}_{\imath}]_{m} for m = 0 m=0 , 1, and ∞. Further, we explore some algebraic and topological properties of these spaces, including their nature as linear, normed, Banach, and BK spaces. Additionally, we examine properties such as solidity, symmetry, and monotonicity. Finally, we define and establish some inclusion relations among generalized difference weak statistical convergence, generalized difference weak 𝜆-statistical convergence, and generalized difference weak [ V , λ ] [\mathscr{V},\lambda] -convergence.

Partial order on involutive permutations and double Schubert cells

As shown by Melnikov, the orbits of a Borel subgroup acting by conjugation on upper-triangular matrices with square zero are indexed by involutions in the symmetric group. The inclusion relation among the orbit closures defines a partial order on involutions. We observe that the same order on involutive permutations also arises while describing the inclusion order on [Formula: see text]-orbit closures in the direct product of two Grassmannians. We establish a geometric relation between these two settings.

Quadrilaterals hierarchical classification and properties of the diagonals: A study with pre-service mathematics teachers

The aim of this research is to investigate the main characteristics of the processes of constructing a hierarchical classification of quadrilaterals and identifying properties of their diagonals by pre-service middle and secondary school mathematics teachers (PMTs), when involved in whole-class discussions with the teacher educators, after having solved tasks focused on those topics. Data collection comprised video recordings of the sessions and PMTs’ written work, analyzed qualitatively. Findings indicate that constructing the hierarchical classification of quadrilaterals involved the PMTs in prototypical judgments, and dichotomous comparisons. In comparison the identification of the diagonals’ properties was influenced more by definitions and logical relationships, reflected in judgments and comparisons. It was concluded that participation in these processes, with whole-class discussions and development of schemes to illustrate inclusion relationships, may assist PMTs with prototypical phenomenon and dichotomous comparisons, benefiting their future teaching practice.

Lacunary weak convergence of sequences defined by Orlicz function

Abstract In this article, we introduced the idea of lacunary weak convergence of sequences defined by the class of Orlicz function. Various topological and algebraic properties, such as solidity, symmetry, and monotonicity, have been studied. To validate the failure instances, we gave appropriate examples and detailed discussions. Additionally, we have established some inclusion relationships between these spaces.

Lacunary Statistically Convergence via Modulus Function Sequences

Modifying the definition of density functions is one method used to generalise statistical convergence. In the present study, we use sequences of modulus functions and order $\alpha \in \left( 0,1\right] $ to introduce a new density. Based on this density framework, we define strong $(f_k)$-lacunary summability of order $\alpha $ and $(f_k)$-lacunary statistical convergence of order $\alpha $ for a sequence of modulus functions $(f_k)$. This concept holds an intermediate position between the usual convergence and the statistical convergence for lacunary sequences. We also establish inclusion theorems and relations between these two concepts in the study.

Irregular loci in the Emerton–Gee stack for GL2

Abstract Let K / Q p K/\mathbf{Q}_{p} be unramified. Inside the Emerton–Gee stack X 2 \mathcal{X}_{2} , one can consider the locus of two-dimensional mod 𝑝 representations of Gal ⁢ ( K ̄ / K ) \mathrm{Gal}(\overline{K}/K) having a crystalline lift with specified Hodge–Tate weights. We study the case where the Hodge–Tate weights are irregular, which is an analogue for Galois representations of the partial weight one condition for Hilbert modular forms. We prove that if the gap between each pair of weights is bounded by 𝑝 (the irregular analogue of a Serre weight), then this locus is irreducible. We also establish various inclusion relations between these loci.

Cross-region feature fusion with geometrical relationship for OCR-based image captioning

Automatically generating a readable sentence that describes the text-contained image is a challenging task. Compared to traditional image captioning algorithms, OCR-based image captioning focuses on reading OCR tokens in images and understanding them with the image content to generate descriptions. However, existing research mainly concentrate on improving the quantity and quality of obtaining OCR tokens and exploring their spatial relationships while lacking investigation into how to effectively join OCR tokens with image content. This paper proposes a cross-region feature fusion with a geometrical relationship Transformer(CFGR-Transformer) for OCR-based image captioning. The network first establishes the associations between the OCR and object regions of the image by constructing relative geometric relationships, including width/height difference, distance, IOU(Intersection over Union), inclusion relationships, and angles offset, and then incorporates intra-region and cross-region features to aggregate entities from different modalities by a multi-head attention mechanism based on relative relationships. Benefiting from the guidance of the relative relationship, visual entities like OCR tokens and object regions can consider multiple relative relationships as the attention weight for feature fusion within each subspace. Extensive experiments conducted on the TextCaps dataset demonstrate the effectiveness of the proposed CFGR-Transformer method. In particular, our results on the online testing of TextCaps achieve an improvement in CIDEr score from 93.0% to 98.2%.

Generalized Fuzzy-Valued Convexity with Ostrowski’s, and Hermite-Hadamard Type Inequalities over Inclusion Relations and Their Applications

Generalized Fuzzy-Valued Convexity with Ostrowski’s, and Hermite-Hadamard Type Inequalities over Inclusion Relations and Their Applications

Geometric Properties Connected with a Certain Multiplier Integral q−Analogue Operator

The topic concerning the introduction and investigation of new classes of analytic functions using subordination techniques for obtaining certain geometric properties alongside coefficient estimates and inclusion relations is enriched by the results of the present investigation. The prolific tools of quantum calculus applied in geometric function theory are employed for the investigation of a new class of analytic functions introduced by applying a previously defined generalized q−integral operator and the concept of subordination. Investigations are conducted on the new class, including coefficient estimates, integral representation for the functions of the class, linear combinations, forms of the weighted and arithmetic means involving functions from the class, and the estimation of the integral means results.

On the Inclusion Relations of Global Ultradifferentiable Classes Defined by Weight Matrices

We study and characterize the inclusion relations of global classes in the general weight matrix framework in terms of growth relations for the defining weight matrices. We consider the Roumieu and Beurling cases, and as a particular case, we also treat the classical weight function and weight sequence cases. Moreover, we construct a weight sequence which is oscillating around any weight sequence which satisfies some minimal conditions and, in particular, around the critical weight sequence (p!)1/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(p!)^{1/2}$$\\end{document}, related with the non-triviality of the classes. Finally, we also obtain comparison results both on classes defined by weight functions that can be defined by weight sequences and conversely.

Application of neutrosophic Poisson distribution series on harmonic classes of analytic functions defined by q− derivative operator and sigmoid function

There are several authors who have obtained various forms of properties for some subclasses of analytic univalent functions related to different distribution series, such as Binomial, Generalized Discrete Probability, Geometric, Mittag-Leffler, Pascal, and Poisson distribution series. The authors, in this paper, proved the inclusion relation of the harmonic analytic function class $H_{q}^{\alpha}(\theta, \gamma(s), \Psi)$ established by applying convolution operators regarding neutrosophic distribution series equipped with the Sigmoid function (activation function). The present results are capable of handling both accurate (determinate) data and inaccurate (indeterminate) data.

Multi-Target Recognition of Substation Infrared Image Based on Improved Faster RCNN

Abstract This study presents a multi-target recognition approach for substation infrared images based on enhanced Faster RCNN, which addresses the challenge of identifying several high-voltage electrical equipment in substation infrared images simultaneously. This method uses VGG16 to extract image features of a variety of electrical equipment in infrared images. Generate regional suggestions through the regional suggestion network and adjust the regional suggestions through border regression. ROI Pooling maps regional suggestions of different scales to fixed-size output vectors and sends them to Softmax for classification, and corrects the incorrectly identified parts categories according to the inclusion relationship of the regional suggestions. In the experiment, 27586 infrared photos are chosen to create an infrared data set in the voc207 format. Then, statistical analysis is performed on the recognition outcomes of 5517 infrared images in the test set. Based on the testing data, the upgraded rapid RCNN has a 92.8% recognition accuracy, which is 9.7% higher than that before, and has higher engineering practical value.

GNN-MgrPool: Enhanced graph neural networks with multi-granularity pooling for graph classification

Graph neural networks (GNNs) have gained sufficient attention and are applied to various domain tasks. At present, numerous pooling approaches are being proposed to aggregate node features and obtain node embeddings. However, current GNNs are black-box models that typically use a flat or single pooling step to aggregate nodes, which only considers the similarity between nodes within the cluster. These approaches ignore the influence of relationships within and between clusters in the learning process. To address this issue, we propose a novel multi-granular pooling method that aggregates nodes by simultaneously considering density and relationships among nodes and clusters. This method allows us to obtain multi-granular node-embedding clusters from GNN layers. The clusters in the current layer are built upon those in the previous layer, and these clusters change from fine to coarse as the number of clusters decreases during learning, which is achieved by using multi-granular pooling (MgrPool). Additionally, there is an inclusion relation between adjacent layers, and the node representation of each layer is established through the ratio of node distance within clusters to that between clusters. Finally, we conducted several experiments on node and graph classification tasks by combining GNN models with this pooling approach. The results demonstrate that our GNN-MgrPool model outperforms similar state-of-the-art algorithms and largely improves the interpretability of the learning process.

On The Monotony of Struve Functions

Cotîrlă and Szász (Comput Methods Funct Theory: 2023) solved a conjecture related with inclusion relation for Bessel functions, proposed by Baricz and András (Complex Var Elliptic Equ 54(7): 689–696, 2009). In this paper, we prove this conjecture for normalized Struve functions by using subordination factor sequences.

Depth for Multi‐Modal Contour Ensembles

AbstractThe contour depth methodology enables non‐parametric summarization of contour ensembles by extracting their representatives, confidence bands, and outliers for visualization (via contour boxplots) and robust downstream procedures. We address two shortcomings of these methods. Firstly, we significantly expedite the computation and recomputation of Inclusion Depth (ID), introducing a linear‐time algorithm for epsilon ID, a variant used for handling ensembles with contours with multiple intersections. We also present the inclusion matrix, which contains the pairwise inclusion relationships between contours, and leverage it to accelerate the recomputation of ID. Secondly, extending beyond the single distribution assumption, we present the Relative Depth (ReD), a generalization of contour depth for ensembles with multiple modes. Building upon the linear‐time eID, we introduce CDclust, a clustering algorithm that untangles ensemble modes of variation by optimizing ReD. Synthetic and real datasets from medical image segmentation and meteorological forecasting showcase the speed advantages, illustrate the use case of progressive depth computation and enable non‐parametric multimodal analysis. To promote research and adoption, we offer the contour‐depth Python package.

Results for Analytic Function Associated with Briot–Bouquet Differential Subordinations and Linear Fractional Integral Operators

In this paper, we present a new class of linear fractional differential operators that are based on classical Gaussian hypergeometric functions. Then, we utilize the new operators and the concept of differential subordination to construct a convex set of analytic functions. Moreover, through an examination of a certain operator, we establish several notable results related to differential subordination. In addition, we derive inclusion relation results by employing Briot–Bouquet differential subordinations. We also introduce a perspective study for developing subordination results using Gaussian hypergeometric functions and provide certain properties for further research in complex dynamical systems.