Convolution Properties Research Articles

Geometric Properties of Meromorphic Functions Involving Convolution Operator

We introduce and study a subclass of meromorphic univalent functions with positive coefficients defined by a novel operator and obtain coefficient estimates, closure theorems, convolution properties, partial sums, and δ- neighborhood for the class .

Subordination Results for the Second-Order Differential Polynomials of Meromorphic Functions

The outcome of the research presented in this paper is the definition and investigation of two new subclasses of meromorphic functions. The new subclasses are introduced using a differential operator defined considering second-order differential polynomials of meromorphic functions in U\{0}=z∈C:0<z<1. The investigation of the two new subclasses leads to establishing inclusion relations and the proof of convexity and convolution properties regarding each of the two subclasses. Further, involving the concept of subordination, the Fekete–Szegö problem is also discussed for the aforementioned subclasses. Symmetry properties derive from the use of the convolution and from the convexity proved for the new subclasses of functions.

FER-PCVT: Facial Expression Recognition with Patch-Convolutional Vision Transformer for Stroke Patients.

Early rehabilitation with the right intensity contributes to the physical recovery of stroke survivors. In clinical practice, physicians determine whether the training intensity is suitable for rehabilitation based on patients' narratives, training scores, and evaluation scales, which puts tremendous pressure on medical resources. In this study, a lightweight facial expression recognition algorithm is proposed to diagnose stroke patients' training motivations automatically. First, the properties of convolution are introduced into the Vision Transformer's structure, allowing the model to extract both local and global features of facial expressions. Second, the pyramid-shaped feature output mode in Convolutional Neural Networks is also introduced to reduce the model's parameters and calculation costs significantly. Moreover, a classifier that can better classify facial expressions of stroke patients is designed to improve performance further. We verified the proposed algorithm on the Real-world Affective Faces Database (RAF-DB), the Face Expression Recognition Plus Dataset (FER+), and a private dataset for stroke patients. Experiments show that the backbone network of the proposed algorithm achieves better performance than Pyramid Vision Transformer (PvT) and Convolutional Vision Transformer (CvT) with fewer parameters and Floating-point Operations Per Second (FLOPs). In addition, the algorithm reaches an 89.44% accuracy on the RAF-DB dataset, which is higher than other recent studies. In particular, it obtains an accuracy of 99.81% on the private dataset, with only 4.10M parameters.

Direct Solution of Black-Scholes-Merton European Put Option Model on Dividend Yield With Modified-Log Payoff Function

This paper proposes a framework based on the celebrated transform of Mellin type (MT) for the direct solution of the Black-Scholes-Merton European Put Option Model (BSMEPOM) on Dividend Yield (DY) with Modified-Log Payoff Function (MLPF) under the geometric Brownian motion. The focal goal of this paper is to use MT to obtain a valuation formula for the European Put Option (EPO) which pays a DY with MLPF. By means of the MT and its inversion formula, the price of EPO on DY was expressed in terms of integral equation. The valuation formula of EPO was obtained with the help of the convolution property of MT and final time condition. MT was tested on an illustrative example in order to measure its performance, effectiveness and suitability. The MLPF was compared with other existing payoff functions. Hence, the effect of DY on the pricing of EPO with MLPF was also investigated.

Fine‐Grained Scene Graph Generation with Overlap Region and Geometrical Center

AbstractScene graph generation refers to the task of identifying the objects and specifically the relationships between the objects from an image. Existing scene graph generation methods generally use the bounding boxes region features of objects to identify the relationships between objects. However, we feel that the overlap region features of two objects may play an important role in fine‐grained relationship identification. In fact, some fine‐grained relationships can only be obtained from the overlap region features of two objects. Therefore, we propose the Multi‐Branch Feature Combination (MFC) module and Overlap Region Transformer (ORT) module to comprehensively obtain the visual features contained in the overlap regions of two objects. Concretely, the MFC module uses deconvolution and multi‐branch dilation convolution to obtain high‐pixels and multi‐receptive field features in the overlap regions. The ORT module uses the vision transformer to obtain the self‐attention of the overlap regions. The joint use of these two modules achieves the mutual complementation of local connectivity properties of convolution and the global connectivity properties of attention. We also design a Geometrical Center Augmented (GCA) module to obtain the relative position information of the geometric centers between two objects, to prevent the problem that only relying on the scale of the overlap region cannot accurately capture the relationship between two objects. Experiments show that our model ORGC (Overlap Region and Geometrical Center), the combination of the MFC module, the ORT module, and the GCA module, can enhance the performance of fine‐grained relation identification. On the Visual Genome dataset, our model outperforms the current state‐of‐the‐art model by 4.4% on the R@50 evaluation metric, reaching a state‐of‐the‐art result of 33.88.

Multivalent harmonic functions Involving multiplier transformation

In the present investigation we study a subclass of multivalent harmonic functions involving multiplier transformation. An equivalent convolution class condition and a sufficient coefficient condition for this class is acquired. We also show that this coefficient condition is necessary for functions belonging to its subclass. As an application of coefficient condition, a necessary and sufficient hypergeometric inequality is also given. Further, results on bounds, inclusion relation, extreme points, a convolution property and a result based on the integral operator are obtained.

On Certain Subclass of Analytic Functions

In the present investigation, a new general subclass $M_{\alpha ,\beta }\left( \phi \right) $ of analytic functions is defined. Some subordination relations, inclusion relations, integral preserving properties, convolution properties and some other interesting properties are studied.

Bourgain–Morrey spaces and their applications to boundedness of operators

A class of function spaces related to Bourgain–Morrey spaces was recently introduced. Here, this class is investigated from the viewpoints of harmonic analysis and functional analysis. Specifically, this paper is oriented to certain inclusion, approximation, and interpolation properties as well as the boundedness of operators such as the Hardy–Littlewood maximal operator, fractional integral operators, fractional maximal operators, and singular integral operators. In particular, the embedding result by Bégout and Vargas is refined. Another important feature of this class of function spaces is that it can describe the convolution property. In addition, we give a description of the dual of Bourgain–Morrey spaces and we combine this with existing results to conclude the reflexivity of these spaces.

Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator

In this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our results generalized many previous results obtained by different authors. We obtain convolution and inclusion properties for new subclasses of multivalent functions defined by using the Dziok-Srivatava operator. Moreover, using a result connected with the Briot-Bouquet differential subordination, we obtain an inclusion relation between some of these classes of functions.

Properties of analytic functions associated with Mitttag-Leffler-type Borel distribution series

Keeping in view of the latest trends toward special functions, due its various applications in Physics and applied Mathematics, we introduce a subclass of analytic functions with the help of Borel distribution series. Furthermore, we investigate some useful geometric and algebric properties of these functions. We discuss coefficient estimates, growth and distortion theorems, radii of close-to-convexity, starlikeness, convexity and convolution properties to this subclass. subject classification numbers as needed.

The attractivity of functional hereditary integral equations

In this paper, the problem of attractivity of solutions for functional hereditary integral equations is initiated. A hereditary integral equation is converted into a second kind Volterra integral equation of convolution type by use of the property of convolution. Sufficient conditions for the existence of attractive solutions are established according to the fixed point theorem. The conclusions presented in this paper extend some published results. The effectiveness of the proposed results is illustrated by three numerical examples.

A New Class of Holomorphic Univalent Functions Defined by Linear Operator

In the present work, we submit and study a new class AN(τ, λ, η, ρ) containing holomorphic univalent functions defined by linear operator in the open unit disk Λ={s ϵ C :|s | <1} We get some geometric properties, such as, coefficient inequality, growth, and distortion bounds, convolution properties, convex set, neighborhood property, radii of starlikeness and convexity , weighted mean and arithmetic mean for functions belonging to the class AN(τ, λ, η, ρ)

6DCNN with Roto-Translational Convolution Filters for Volumetric Data Processing

In this work, we introduce 6D Convolutional Neural Network (6DCNN) designed to tackle the problem of detecting relative positions and orientations of local patterns when processing three-dimensional volumetric data. 6DCNN also includes SE(3)-equivariant message-passing and nonlinear activation operations constructed in the Fourier space. Working in the Fourier space allows significantly reducing the computational complexity of our operations. We demonstrate the properties of the 6D convolution and its efficiency in the recognition of spatial patterns. We also assess the 6DCNN model on several datasets from the recent CASP protein structure prediction challenges. Here, 6DCNN improves over the baseline architecture and also outperforms the state of the art.

Certain subclasses of meromorphic multivalent q-starlike and q-convex functions

Abstract In this paper, we extend the idea of q-derivative (or q-difference) operator for meromorphic p-valent functions and introduce certain new subclasses of meromorphic multivalent q-starlike and q-convex functions. We investigate subordination properties, coefficient inequalities, convolution properties and integral representations. We also derive sufficient conditions for meromorphic multivalent q-starlike and q-convex functions and highlight some known consequence of our main results.

Unifying discrete and integral transforms through the use of a Banach algebra

A weighted space is introduced and some of its properties are highlighted. This is done with the aim of defining a space such that the transform of a class of functions exists. Certain properties of a new class of discrete and integral transforms are highlighted, including the codomain of the transform being a set of continuous functions and continuity of the operator associated with the space. The shifting and convolution properties are introduced and it is proven that the weighted space is closed under the convolution operation. Several examples which fall in this class of transforms are given, including the Dirichlet series, the Z transform and the Laplace transform. Some conditions are stated which imply that any member of a class of discrete operators is injective. Following this, it is established that the weighted space is a Banach algebra where the convolution is the underlying product.

Spectral statistics of Dirac ensembles

In this paper, we find spectral properties in the large N limit of Dirac operators that come from random finite noncommutative geometries. In particular, for a Gaussian potential, the limiting eigenvalue spectrum is shown to be universal, regardless of the geometry, and is given by the convolution of the semicircle law with itself. For simple non-Gaussian models, this convolution property is also evident. In order to prove these results, we show that a wide class of multi-trace multimatrix models have a genus expansion.

Harmonic Multivalent Functions Associated with Generalized Hypergeometric Functions

In this paper , certain subclass of harmonic multivalent function defined in the exterior of the unit disk by used generalize hypergeometric functions is introduced . In This study an attempting have been made to investigate several geometric properties such as coefficient property , growth bounds , extreme points , convolution property , and convex linear combination .

Jumping hedges on the strength of the Mellin transform

With more looming uncertainties in our present financial climate and environment, models with jump–diffusion more than ever are necessary. They are suited to reproduce the large and sudden fluctuations in the level of the underlying variable, and mimic various statistical properties in observed time series. The jump–diffusion modelling setup, however, brings complexity to the valuation and hedging of derivative securities. This paper delves into the subject of hedging along with the illustration of hedging’s intimate interplay with pricing. We harness the power of the Mellin transform and its convolution property to establish hedging sensitivities that capture the many dimensions of risk in option positions. Our methodology allows for a wide class of generalised payoffs (i.e. all piecewise linear functions). Each hedging parameter is shown to contain the impact of jumps and an explicit metric to quantify the jump risk is defined. The systematic and efficient calculations of higher-order sensitivities are demonstrated and their implications, from a practical perspective, are also considered. Inclusion of some numerical examples illustrates the ease of implementation of our results.

CONVOLUTION CONDITIONS FOR CERTAIN SUBCLASSES OF MEROMORPHIC p-VALENT FUNCTIONS

In the present paper we introduce two subclasses MSp q;λ(b; A; B) and MKp q;λ(b; A; B) of meromorphic multivalent functions by using q-derivative operator defined in the punctured unit disc. Also, we derive several properties including convolution properties, the necessary and sufficient condition and coefficient estimates for these subclasses.

An improved finite integration method for nonlocal nonlinear Schrödinger equations

In this paper, we study the nonlocal nonlinear Schrödinger equation (NNLSE), which is an important extension of the nonlinear Schrödinger equation (NLSE). Since the nonlinearity of NNLSE involves a convolution, numerical approximation of its solution is very expensive. To achieve an efficient numerical method for solving the NNLSE, according to the property of convolution, we firstly present a partial differential equation (PDE) method to transfer the NNLSE from an integro-differential equation to an equivalent or approximate system of PDEs, and the numerical solution of the NNLSE can then be obtained by solving these PDEs. Based on the recently developed finite integration method (FIM), we derive an improved method (IFIM) in this paper. The novelty of this IFIM is that the quadrature method is only used once instead of multiple times for multi-layer integral, so it consumes less running time and provides higher accuracy. In addition, we adapt a second-order operator-splitting method (OS2) at each time-step to ensure a convergent solution for long-time integration. Several numerical experiments are given to verify the efficiency and accuracy of the proposed IFIM for solving the NNLSE.