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For all integers n ≥ 1 and k ≥ 2 , the Hadamard product v 1 ★ ⋯ ★ v k of k elements of K n + 1 (with K being the complex numbers or real numbers) is the element v ∈ K n + 1 which is the coordinate-wise product of v 1 , ... , v k (introduced by Cueto, Morton, and Sturmfels for a model in Algebraic Statistics). This product induces a rational map h : P n (K) k ⤏ P n (K) . When K = C , k = 2 and X i (C) ⊂ P n (C) , i = 1 , 2 are irreducible, we prove four theorems for the case dim X 2 (C) = 1 , three of them with X 2 (C) as a line. We discuss the existence (non-existence) of a cancellation law for ★-products and use the symmetry group of the Hadamard product. In the second part, we work over R. Under mild assumptions, we prove that by knowing X 1 (R) ★ ⋯ ★ X k (R) , we know X 1 (C) ★ ⋯ ★ X k (C) . The opposite, i.e., taking and multiplying a set of complex entries that are invariant for the complex conjugation and then seeing what appears in the screen P n (R) , very often provides real ghosts, i.e., images that do not come from a point of X 1 (R) × ⋯ × X k (R) . We discuss a case in which we certify the existence of real ghosts as well as a few cases in which we certify the non-existence of these ghosts, and ask several open questions. We also provide a scenario in which ghosts are not a problem, where the Hadamard data are used to test whether the images cover the full screen. [ABSTRACT FROM AUTHOR]

Sălăgean differential operator D κ plays an important role in the geometric function theory, where many studies are using this operator to introduce new subclasses of analytic functions defined in the open unit disk. Studies of Sălăgean differential operator D κ in connection with Stirling numbers are relatively new. In this paper, the differential operator D κ involving Stirling numbers is considered. A new sufficient condition involving Stirling numbers for the series Υ θ s (ϰ) written with the Pascal distribution are discussed for the subclass T κ (ϵ , ♭) . Also, we provide a sufficient condition for the inclusion relation I θ s R ϖ (E , D ) ⊂ T κ (ϵ , ♭) . Further, we consider the properties of an integral operator related to Pascal distribution series. New special cases as a consequences of the main results are also obtained. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define the linear operator based on the generalized Mittag-Leffler function and the Lambert series. By using this operator, we introduce a new subclass of β-uniformly starlike functions Τ J (α i) . Further, we obtain coefficient estimates, convex linear combinations, and radii of close-to-convexity, starlikeness, and convexity for functions f ∈ Τ J (α i) . In addition, we investigate the inclusion conditions of the Hadamard product and the integral transform. Finally, we determine the second Hankel inequality for functions belonging to this subclass. [ABSTRACT FROM AUTHOR]

This work presents a novel investigation that utilizes the integral operator I p , λ n in the field of geometric function theory, with a specific focus on sandwich theorems. We obtained findings about the differential subordination and superordination of a novel formula for a generalized integral operator. Additionally, certain sandwich theorems were discovered. [ABSTRACT FROM AUTHOR]

In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of Sturmfels and Sullivant. In the second part of the paper, we give a brief tutorial on the Hadamard.m2 package of Macaulay2. [ABSTRACT FROM AUTHOR]

A new subclass T X q [ λ , A , B ] of analytic functions is introduced by making use of the q-derivative operator associated with the Pascal distribution. Certain properties of analytic functions in the subclass T X q [ λ , A , B ] are derived. Some known results are generalized. [ABSTRACT FROM AUTHOR]

Deep edge detection is challenging, especially with the existing methods, like HED (holistic edge detection). These methods combine multiple feature side outputs (SOs) to create the final edge map, but they neglect diverse edge importance within one output. This creates a problem: to include desired edges, unwanted noise must also be accepted. As a result, the output often has increased noise or thick edges, ignoring important boundaries. To address this, we propose a new approach called the normalized Hadamard-product (NHP) operation-based deep network for edge detection. By multiplying the side outputs from the backbone network, the Hadamard-product operation encourages agreement among features across different scales while suppressing disagreed weak signals. This method produces additional Mutually Agreed Salient Edge (MASE) maps to enrich the hierarchical level of side outputs without adding complexity. Our experiments demonstrate that the NHP operation significantly improves performance, e.g., an ODS score reaching 0.818 on BSDS500, outperforming human performance (0.803), achieving state-of-the-art results in deep edge detection. [ABSTRACT FROM AUTHOR]

New possibilities of Gramian computation, by means of canonical transformations into diagonal, controllable, and observable canonical forms, are shown. Using such a technique, the Gramian matrices can be represented as products of the Hadamard matrices of multipliers and the matrices of the transformed right-hand sides of Lyapunov equations. It is shown that these multiplier matrices are invariant under various canonical transformations of linear continuous systems. The modal Lyapunov equations for continuous SISO LTI systems in diagonal form are obtained, and their new solutions based on Hadamard decomposition are proposed. New algorithms for the element-by-element computation of Gramian matrices for stable, continuous MIMO LTI systems are developed. New algorithms for the computation of controllability Gramians in the form of Xiao matrices are developed for continuous SISO LTI systems, given by the equations of state in the controllable and observable canonical forms. The application of transformations to the canonical forms of controllability and observability allowed us to simplify the formulas of the spectral decompositions of the Gramians. In this paper, new spectral expansions in the form of Hadamard products for solutions to the algebraic and differential Sylvester equations of MIMO LTI systems are obtained, including spectral expansions of the finite and infinite cross - Gramians of continuous MIMO LTI systems. Recommendations on the use of the obtained results are given. [ABSTRACT FROM AUTHOR]

Using the Salagean q-differential operator, we investigate a novel subclass of analytic functions in the open unit disc, and we use the Hadamard product to provide some inclusion relations. Furthermore, the coefficient conditions, convolution properties, and applications of the q-fractional calculus operators are investigated for this class of functions. In addition, we extend the Miller and Mocanu inequality to the q-theory of analytic functions. [ABSTRACT FROM AUTHOR]

The selection of a demand forecasting method is critical for companies aiming to avoid manufacturing overproduction or shortages in pursuit of sustainable development. Various qualitative and quantitative criteria with different weights must be considered during the evaluation of a forecasting method. The qualitative criteria and criteria weights are usually assessed in linguistic terms. Aggregating these various criteria and linguistic weights for evaluating and selecting demand forecasting methods in sustainable manufacturing is a major challenge. This paper proposes an extension of fuzzy elimination and choice translating reality (ELECTRE) I to resolve this problem. In the proposed method, fuzzy weighted ratings are defuzzified with the signed distance to develop a crisp ELECTRE I model. Moreover, an extension to ELECTRE I is developed by suggesting an extended modified discordance matrix and a closeness coefficient for ranking alternatives. The proposed extension can overcome the problem of information loss, which can lead to incorrect ranking results when using the Hadamard product to combine concordance and modified discordance matrices. A comparison is conducted to show the advantage of the proposed extension. Finally, a numerical example is used to demonstrate the feasibility of the proposed method. Furthermore, a numerical comparison is made to display the advantage of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the present study employs the utilization of the concepts pertaining to (x , y) -symmetrical functions, Janowski type functions, and q-calculus in order to establish a novel subclass within the open unit disk. Specifically, we delve into the examination of convolution properties, which serve as a tool for investigating and inferring adequate and equivalent conditions. Moreover, we also explore specific characteristics of the class S ˜ q x , y (α , β , λ) , thereby further scrutinizing the convolution properties of these newly defined classes. [ABSTRACT FROM AUTHOR]

The objective of the current paper is to find the necessary and sufficient conditions for Miller–Ross-type Poisson distribution series to be in the classes S T * (γ , β) and K T (γ , β) of analytic functions with negative coefficients. Furthermore, we investigate several inclusion properties of the class Y σ (V , W) associated of the operator I α , c ε defined by this distribution. We also take into consideration an integral operator connected to series of Miller–Ross-type Poisson distributions. Special cases of the main results are also considered. [ABSTRACT FROM AUTHOR]

The aim of this research study is to establish a novel subclass of meromorphic functions in the mean of q-derivatives in combination with the well-known polylogarithm function. Two additional subfamilies for this class are also defined. Furthermore, the coefficient inequality and distortion bounds are highlighted. Finally, the convex families and related set structures are thoroughly investigated. [ABSTRACT FROM AUTHOR]

In this paper, we prove some Banach fixed point theorems in generalized metric space where the contractive conditions are endowed with the Hadamard product of real symmetric positive definite matrices. Since the condition that a matrix A converges to zero is not needed, this produces stronger results than those of Perov. As an application of our results, we study the existence and uniqueness of the solution for a system of matrix equations. [ABSTRACT FROM AUTHOR]

Zadeh's fuzzy set theory offers a logical, adaptable solution to the challenge of defining, assessing and contrasting various sustainability scenarios. The results presented in this paper use the fuzzy set concept embedded into the theories of differential subordination and superordination established and developed in geometric function theory. As an extension of the classical concept of differential subordination, fuzzy differential subordination was first introduced in geometric function theory in 2011. In order to generalize the idea of fuzzy differential superordination, the dual notion of fuzzy differential superordination was developed later, in 2017. The two dual concepts are applied in this article making use of the previously introduced operator defined as the convolution product of the generalized Sălgean operator and the Ruscheweyh derivative. Using this operator, a new subclass of functions, normalized analytic in U, is defined and investigated. It is proved that this class is convex, and new fuzzy differential subordinations are established by applying known lemmas and using the functions from the new class and the aforementioned operator. When possible, the fuzzy best dominants are also indicated for the fuzzy differential subordinations. Furthermore, dual results involving the theory of fuzzy differential superordinations and the convolution operator are established for which the best subordinants are also given. Certain corollaries obtained by using particular convex functions as fuzzy best dominants or fuzzy best subordinants in the proved theorems and the numerous examples constructed both for the fuzzy differential subordinations and for the fuzzy differential superordinations prove the applicability of the new theoretical results presented in this study. [ABSTRACT FROM AUTHOR]

This research aims to present a linear operator L p , q ρ , σ , μ f utilizing the q-Mittag–Leffler function. Then, we introduce the subclass of harmonic (p , q) -convex functions HT p , q (ϑ , W , V) related to the Janowski function. For the harmonic p-valent functions f class, we investigate the harmonic geometric properties, such as coefficient estimates, convex linear combination, extreme points, and Hadamard product. Finally, the closure property is derived using the subclass HT p , q (ϑ , W , V) under the q-Bernardi integral operator. [ABSTRACT FROM AUTHOR]

Using convolution (or Hadamard product), we define the El-Ashwah and Drbuk linear operator, which is a multivalent function in the unit disk U = w : w < 1   and   w ∈ ₵ , and satisfy its specific relationship to derive the subordination, superordination, and sandwich results for this operator by using properties of subordination and superordination concepts. [ABSTRACT FROM AUTHOR]

Using the results of third-order differential subordination, we introduce certain families of admissible functions and discuss some applications of third-order differential subordination for meromorphic functions associated with a linear operator containing a generalized Mittag-Leffler function. [ABSTRACT FROM AUTHOR]

In this paper, we make use of the concept of q − calculus in the theory of univalent functions, to obtain the bounds for certain coefficient functional problems of Janowski type starlike functions and to find the Fekete–Szegö functional. A similar results have been done for the function ℘ − 1. Further, for functions in newly defined class we determine coefficient estimates, distortion bounds, radius problems, results related to partial sums. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to define new classes of analytic functions by amalgamating the concepts of q-calculus, Janowski type functions and (x , y) -symmetrical functions. We use the technique of convolution and quantum calculus to investigate the convolution conditions which will be used as a supporting result for further investigation in our work, we deduce the sufficient conditions, P o ´ lya-Schoenberg theorem and the application. Finally motivated by definition of the neighborhood, we give analogous definition of neighborhood for the classes S ˜ q x , y (α , β) and K ˜ q x , y (α , β) , and then investigate the related neighborhood results, which are also pointed out. [ABSTRACT FROM AUTHOR]

The goal of this article is to contemplate coefficient estimates for a new class of analytic functions f associated with generalized telephone numbers to originate certain initial Taylor coefficient estimates and Fekete–Szegö inequality for f in the new function class. Comparable results have been attained for the function f − 1. Further application of our outcomes to certain functions demarcated by convolution products with certain normalized analytic functions in the open unit disk are specified, and we obtain Fekete–Szegö variations for this new function class defined over Poisson and Borel distribution series. [ABSTRACT FROM AUTHOR]

This paper is concerned with studying some results by introducing a new Hadamard product M γ , b , v , δ C , η operator for differential subordination and superordination for certain univalent functions in the open unit disc U. Firstly, we state some basic definitions and required theorems. Furthermore. Some sandwich theorems are derived. The differential subordination theory's features and outcomes are symmetric to those derived using the differential superordination theory. [ABSTRACT FROM AUTHOR]

We present several new results for fourth-order differential subordination and superordination in this paper by using the differential linear operator Γ π , ρ , β , μ f z . Relevant connections between the new results presented here and those considered in previous works are addressed. The properties and results concerning the differential subordination theory are symmetric to the properties obtained using the differential superordination theory, and by combining them, sandwich-type theorems are obtained. [ABSTRACT FROM AUTHOR]

In this paper, two new integral operators are defined using the operator D R λ m , n , introduced and studied in previously published papers, defined by the convolution product of the generalized Sălăgean operator and Ruscheweyh operator. The newly defined operators are used for introducing several new classes of functions, and properties of the integral operators on these classes are investigated. Subordination results for the differential operator D R λ m , n are also obtained. [ABSTRACT FROM AUTHOR]

Multivariate skew-symmetric-normal (MSSN) distributions have been recognized as an appealing tool for modeling data with non-normal features such as asymmetry and heavy tails, rendering them suitable for applications in diverse areas. We introduce a richer class of MSSN distributions based on a scale-shape mixture of (multivariate) flexible skew-symmetric normal distributions, called the SSMFSSN distributions. This very general class of SSMFSSN distributions can capture various shapes of multimodality, skewness, and leptokurtic behavior in the data. We investigate some of its probabilistic characterizations and distributional properties which are useful for further methodological developments. An efficient EM-type algorithm designed under the selection mechanism is advocated to compute the maximum likelihood (ML) estimates of parameters. Simulation studies as well as applications to a real dataset are employed to illustrate the usefulness of the presented methods. Numerical results show the superiority of our proposed model in comparison to several existing competitors. [ABSTRACT FROM AUTHOR]

Traditionally, the special function theory has many applications in various areas of mathematical physics, economics, statistics, engineering, and many other branches of science. Inspired by certain recent extensions of the k-analogue of gamma, the Pochhammer symbol, and hypergeometric functions, this work is devoted to the study of the k-analogue of Gauss hypergeometric functions by the Hadamard product. We give a definition of the Hadamard product of k-Gauss hypergeometric functions (HPkGHF) associated with the fourth numerator and two denominator parameters. In addition, convergence properties are derived from this function. We also discuss interesting properties such as derivative formulae, integral representations, and integral transforms including beta transform and Laplace transform. Furthermore, we investigate some contiguous function relations and differential equations connecting the HPkGHF. The current results are more general than previous ones. Moreover, the proposed results are useful in the theory of k-special functions where the hypergeometric function naturally occurs. [ABSTRACT FROM AUTHOR]

This paper introduces a new integral operator in q-analog for multivalent functions. Using as an application of this operator, we study a novel class of multivalent functions and define them. Furthermore, we present many new properties of these functions. These include distortion bounds, sufficiency criteria, extreme points, radius of both starlikness and convexity, weighted mean and partial sum for this newly defined subclass of multivalent functions are discussed. Various integral operators are obtained by putting particular values to the parameters used in the newly defined operator. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to find the upper bound of the third Hankel determinant for a family of q-starlike functions which are associated with the Ruscheweyh-type q-derivative operator. The work is motivated by several special cases and consequences of our main results, which are pointed out herein. [ABSTRACT FROM AUTHOR]

This study defines a new linear differential operator via the Hadamard product between a q-hypergeometric function and Mittag–Leffler function. The application of the linear differential operator generates a new subclass of meromorphic function. Additionally, the study explores various properties and features, such as convex properties, distortion, growth, coefficient inequality and radii of starlikeness. Finally, the work discusses closure theorems and extreme points. [ABSTRACT FROM AUTHOR]

In this paper, an upper bound on the spectral radius ρ (A ∘ B) for the Hadamard product of two nonnegative matrices (A and B) and the minimum eigenvalue τ (C ★ D) of the Fan product of two M-matrices (C and D) are researched. These bounds complement some corresponding results on the simple type bounds. In addition, a new lower bound on the minimum eigenvalue of the Fan product of several M-matrices is also presented. These results and numerical examples show that the new bounds improve some existing results. [ABSTRACT FROM AUTHOR]

In this article, a new class of harmonic univalent functions, defined by the differential operator, is introduced. Some geometric properties, like, coefficient estimates, extreme points, convex combination and convolution (Hadamard product) are obtained. [ABSTRACT FROM AUTHOR]