Axioms

Open AccessArticle

Spectral Problem of the Hamiltonian in Quantum Mechanics without Reference to a Potential Function

by

Ibraheem F. Al-Yousef

,

Moayad Ekhwan

,

H. Bahlouli

and

A. D. Alhaidari

Axioms 2023, 12(4), 334; https://doi.org/10.3390/axioms12040334 (registering DOI) - 29 Mar 2023

Abstract

Following the celebrated postulates of quantum mechanics, we write the quantum mechanical wavefunction as a convergent series of suitably selected complete square-integrable basis functions in configuration space. The expansion coefficients of the series are energy orthogonal polynomials that contain all spectral information about [...] Read more.

Following the celebrated postulates of quantum mechanics, we write the quantum mechanical wavefunction as a convergent series of suitably selected complete square-integrable basis functions in configuration space. The expansion coefficients of the series are energy orthogonal polynomials that contain all spectral information about the system. We exploit the properties of these polynomials to introduce physical systems with rich and highly nontrivial energy spectra. In this approach, no reference is made at all to the usual potential energy function. We consider, in this new approach, a few representative problems at the level of undergraduate students who took at least two courses in quantum mechanics and are familiar with the basics of orthogonal polynomials. Our aim is to expose students to quantum systems with rich energy spectra that goes beyond the very limited textbook examples of systems with very simple energy spectra (e.g., the harmonic oscillator, Coulomb, Morse, Pöschl–Teller, etc.) illustrating the physical significance of these energy polynomials in the description of a quantum system. To assist students, partial solutions are given in an appendix as tables and figures. Full article

(This article belongs to the Special Issue Computation Methods on Quantum Systems)

Open AccessArticle

Homogeneity Test of Many-to-One Relative Risk Ratios in Unilateral and Bilateral Data with Multiple Groups

by

Yuxin Li

,

Zhiming Li

and

Keyi Mou

Axioms 2023, 12(4), 333; https://doi.org/10.3390/axioms12040333 (registering DOI) - 29 Mar 2023

Abstract

In medical clinical studies, we often encounter paired organs’ unilateral or bilateral data. For bilateral data, there exists an intraclass correlation between paired organs. Under an intraclass correlation model, this paper proposes asymptotic statistics for testing the equality of many-to-one relative risk ratios [...] Read more.

In medical clinical studies, we often encounter paired organs’ unilateral or bilateral data. For bilateral data, there exists an intraclass correlation between paired organs. Under an intraclass correlation model, this paper proposes asymptotic statistics for testing the equality of many-to-one relative risk ratios in combined unilateral and bilateral data. Furthermore, we calculate the explicit expressions of these statistics. Moreover, these procedures are adequate to solve the hypothesis problems of unilateral or bilateral data. Through comparison, the simulation results show that the score test has a robust empirical type-I error rate and sufficient power. We provide a clinical trial of acute otitis media to illustrate our proposed methods. Full article

(This article belongs to the Special Issue Fuzzy Logic and Application in Multi-Criteria Decision-Making (MCDM))

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Open AccessArticle

Logarithmic Coefficients for Some Classes Defined by Subordination

by

Ebrahim Analouei Adegani

,

Ahmad Motamednezhad

,

Teodor Bulboacă

and

Nak Eun Cho

Axioms 2023, 12(4), 332; https://doi.org/10.3390/axioms12040332 - 29 Mar 2023

Abstract

In this paper, we obtain the sharp and accurate bounds for the logarithmic coefficients of some subclasses of analytic functions defined and studied in earlier works. Furthermore, we obtain the bounds of the second Hankel determinant of logarithmic coefficients for a class defined [...] Read more.

In this paper, we obtain the sharp and accurate bounds for the logarithmic coefficients of some subclasses of analytic functions defined and studied in earlier works. Furthermore, we obtain the bounds of the second Hankel determinant of logarithmic coefficients for a class defined by subordination, such as the class of starlike functions

S^{*} (φ)

. Some applications of our results, which are extensions of those reported in earlier papers are given here as special cases. In addition, the results given can be used for other popular subclasses. Full article

(This article belongs to the Special Issue Honorary Special Issue Dedicated to Prof. Anatolii Asirovich Gol’dberg (1930–2008))

Open AccessArticle

A New Reliability Class-Test Statistic for Life Distributions under Convolution, Mixture and Homogeneous Shock Model: Characterizations and Applications in Engineering and Medical Fields

by

,

,

,

and

Axioms 2023, 12(4), 331; https://doi.org/10.3390/axioms12040331 - 29 Mar 2023

Abstract

Over the past few decades, a new area of reliability known as classes of life distributions has developed as a result of the creation of metrics for evaluating the success or failure of reliability. This paper proposes a new reliability class-test statistic for [...] Read more.

Over the past few decades, a new area of reliability known as classes of life distributions has developed as a result of the creation of metrics for evaluating the success or failure of reliability. This paper proposes a new reliability class-test statistic for life distributions. In some reliability processes, such as convolution, mixture, and homogeneous shock models, the closure characteristics of the proposed class-test statistic are investigated. To compare the proposed class-test against some competitive tests, the Weibull, linear failure rate (LFR), and Makeham distributions are evaluated. In addition, the relationship between sample size, level of confidence, and critical values is considered to assess the efficacy of the proposed class-test. Furthermore, a Monte Carlo null distribution critical points simulation and some applications of the censored and uncensored data are performed to demonstrate the validity of the proposed class-test in reliability analysis. Full article

(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)

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Open AccessSystematic Review

Systematic Review of Aggregation Functions Applied to Image Edge Detection

by

,

,

,

,

Cedric Marco-Detchart

,

Giancarlo Lucca

and

Humberto Bustince

Axioms 2023, 12(4), 330; https://doi.org/10.3390/axioms12040330 - 28 Mar 2023

Abstract

Edge detection is a crucial process in numerous stages of computer vision. This field of study has recently gained momentum due to its importance in various applications. The uncertainty, among other characteristics of images, makes it difficult to accurately determine the edge of [...] Read more.

Edge detection is a crucial process in numerous stages of computer vision. This field of study has recently gained momentum due to its importance in various applications. The uncertainty, among other characteristics of images, makes it difficult to accurately determine the edge of objects. Furthermore, even the definition of an edge is vague as an edge can be considered as the maximum boundary between two regions with different properties. Given the advancement of research in image discontinuity detection, especially using aggregation and pre-aggregation functions, and the lack of systematic literature reviews on this topic, this paper aims to gather and synthesize the current state of the art of this topic. To achieve this, this paper presents a systematic review of the literature, which selected 24 papers filtered from 428 articles found in computer databases in the last seven years. It was possible to synthesize important related information, which was grouped into three approaches: (i) based on both multiple descriptor extraction and data aggregation, (ii) based on both the aggregation of distance functions and fuzzy C-means, and (iii) based on fuzzy theory, namely type-2 fuzzy and neutrosophic sets. As a conclusion, this review provides interesting gaps that can be explored in future work. Full article

(This article belongs to the Special Issue New Trends in Fusion Processes Based on Aggregation and Pre-aggregation Functions: Theory and Applications)

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Open AccessArticle

C-R Immersions and Sub-Riemannian Geometry

by

Elisabetta Barletta

,

Sorin Dragomir

and

Francesco Esposito

Axioms 2023, 12(4), 329; https://doi.org/10.3390/axioms12040329 (registering DOI) - 28 Mar 2023

Abstract

On any strictly pseudoconvex CR manifold M, of CR dimension n, equipped with a positively oriented contact form

θ

, we consider natural

ϵ

-contractions, i.e., contractions

g_{ϵ}^{M}

of the Levi form

G_{θ}

, such that the norm [...] Read more.

On any strictly pseudoconvex CR manifold M, of CR dimension n, equipped with a positively oriented contact form

θ

, we consider natural

ϵ

-contractions, i.e., contractions

g_{ϵ}^{M}

of the Levi form

G_{θ}

, such that the norm of the Reeb vector field T of

(M, θ)

is of order

O (ϵ^{- 1})

. We study isopseudohermitian (i.e.,

f^{*} Θ = θ

) Cauchy–Riemann immersions

f : M \to (A, Θ)

between strictly pseudoconvex CR manifolds M and A, where

Θ

is a contact form on A. For every contraction

g_{ϵ}^{A}

of the Levi form

G_{Θ}

, we write the embedding equations for the immersion

f : M \to (A, g_{ϵ}^{A})

. A pseudohermitan version of the Gauss equation for an isopseudohermitian C-R immersion is obtained by an elementary asymptotic analysis as

ϵ \to 0^{+}

. For every isopseudohermitian immersion

f : M \to S^{2 N + 1}

into a sphere

S^{2 N + 1} \subset C^{N + 1}

, we show that Webster’s pseudohermitian scalar curvature R of

(M, θ)

satisfies the inequality

R \leq 2 n [(f^{*} g_{Θ}) (T, T) + n + 1] + \frac{1}{2} {∥ H (f) ∥_{g_{Θ}^{f}}^{2} + ∥ {trace}_{G_{θ}} Π_{H (M)} (\nabla^{⊤} - \nabla) ∥_{f^{*} g_{Θ}}^{2}}

with equality if and only if

B (f) = 0

and

\nabla^{⊤} = \nabla

on

H (M) \otimes H (M)

. This gives a pseudohermitian analog to a classical result by S-S. Chern on minimal isometric immersions into space forms. Full article

(This article belongs to the Special Issue Research in Differential Geometry and Singularity Theory)

Open AccessArticle

Linguistic Complex Fuzzy Sets

by

Songsong Dai

Axioms 2023, 12(4), 328; https://doi.org/10.3390/axioms12040328 - 28 Mar 2023

Abstract

Complex fuzzy sets (CFSs) are a suitable tool to manage spatial directional information which includes distance and direction. However, spatial directional information is given by linguistic values. It is very awkward for the CFS to describe this type of spatial directional information. To [...] Read more.

Complex fuzzy sets (CFSs) are a suitable tool to manage spatial directional information which includes distance and direction. However, spatial directional information is given by linguistic values. It is very awkward for the CFS to describe this type of spatial directional information. To overcome this limitation, we first propose a novel concept called a linguistic complex fuzzy set (LCFS) to serve as an extension of the CFS. Then we put forward some basic operational laws for LCFSs. After that, we define three operators for LCFSs: the linguistic complex fuzzy weighted averaging (LCFWA) operator, the linguistic amplitude max (Amax) operator and the linguistic amplitude min (Amin) operator. In actual application, we use the LCFWA operator to deal with group decision making when the importance weights of experts are known. For the situation in which the weights of experts are unknown, we develop an Amax-Amin method for group decision making. Full article

(This article belongs to the Special Issue Fuzzy Set Theory and Its Applications in Decision Making)

Open AccessArticle

Modeling COVID-19 Real Data Set by a New Extension of Haq Distribution

by

,

,

,

,

Mahmoud M. Abd El-Raouf

and

Md Moyazzem Hossain

Axioms 2023, 12(4), 327; https://doi.org/10.3390/axioms12040327 - 28 Mar 2023

Abstract

Modeling real-life pandemics is very important; this study focuses on introducing a new superior flexible extension of the asymmetric Haq distribution known as the power Haq distribution (PHD). The most fundamental mathematical properties are derived. We determine its parameters using ten estimation methods. [...] Read more.

Modeling real-life pandemics is very important; this study focuses on introducing a new superior flexible extension of the asymmetric Haq distribution known as the power Haq distribution (PHD). The most fundamental mathematical properties are derived. We determine its parameters using ten estimation methods. The asymptotic behavior of its estimators is investigated through simulation, and a comparison is done to find out the most efficient method for estimating the parameters of the distribution under consideration. We use a sample for the COVID-19 data set to evaluate the proposed model’s performance and usefulness in fitting the data set in comparison to other well-known models. Full article

(This article belongs to the Special Issue Mathematical and Statistical Analysis Methods with Multidisciplinary Applications)

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Open AccessReview

Advancements in Numerical Methods for Forward and Inverse Problems in Functional near Infra-Red Spectroscopy: A Review

by

Abida Hussain

,

Ibrahima Faye

,

Mohana Sundaram Muthuvalu

,

Tong Boon Tang

and

Mudasar Zafar

Axioms 2023, 12(4), 326; https://doi.org/10.3390/axioms12040326 - 28 Mar 2023

Abstract

A In the field of biomedical image reconstruction, functional near infra-red spectroscopy (fNIRs) is a promising technology that uses near infra-red light for non-invasive imaging and reconstruction. Reconstructing an image requires both forward and backward problem-solving in order to figure out what the [...] Read more.

A In the field of biomedical image reconstruction, functional near infra-red spectroscopy (fNIRs) is a promising technology that uses near infra-red light for non-invasive imaging and reconstruction. Reconstructing an image requires both forward and backward problem-solving in order to figure out what the image’s optical properties are from the boundary data that has been measured. Researchers are using a variety of numerical methods to solve both the forward and backward problems in depth. This study will show the latest improvements in numerical methods for solving forward and backward problems in fNIRs. The physical interpretation of the forward problem is described, followed by the explanation of the state-of-the-art numerical methods and the description of the toolboxes. A more in-depth discussion of the numerical solution approaches for the inverse problem for fNIRs is also provided. Full article

(This article belongs to the Special Issue Mathematical Methods in the Applied Sciences)

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Open AccessArticle

Higher-Order Nabla Difference Equations of Arbitrary Order with Forcing, Positive and Negative Terms: Non-Oscillatory Solutions

by

Jehad Alzabut

,

Said R. Grace

,

Jagan Mohan Jonnalagadda

,

Shyam Sundar Santra

and

Bahaaeldin Abdalla

Axioms 2023, 12(4), 325; https://doi.org/10.3390/axioms12040325 - 27 Mar 2023

Abstract

This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities and the properties of discrete fractional calculus serve as the fundamental foundation to our approach. To help establish the main [...] Read more.

This work provides new adequate conditions for difference equations with forcing, positive and negative terms to have non-oscillatory solutions. A few mathematical inequalities and the properties of discrete fractional calculus serve as the fundamental foundation to our approach. To help establish the main results, an analogous representation for the main equation, called a Volterra-type summation equation, is constructed. Two numerical examples are provided to demonstrate the validity of the theoretical findings; no earlier publications have been able to comment on their solutions’ non-oscillatory behavior. Full article

(This article belongs to the Special Issue Advances in Difference Equations)

Open AccessArticle

Fuzzy Algebras of Concepts

by

Manuel Ojeda-Hernández

,

Domingo López-Rodríguez

and

Pablo Cordero

Axioms 2023, 12(4), 324; https://doi.org/10.3390/axioms12040324 - 26 Mar 2023

Abstract

Preconcepts are basic units of knowledge that form the basis of formal concepts in formal concept analysis (FCA). This paper investigates the relations among different kinds of preconcepts, such as protoconcepts, meet and join-semiconcepts and formal concepts. The first contribution of this paper, [...] Read more.

Preconcepts are basic units of knowledge that form the basis of formal concepts in formal concept analysis (FCA). This paper investigates the relations among different kinds of preconcepts, such as protoconcepts, meet and join-semiconcepts and formal concepts. The first contribution of this paper, is to present a fuzzy powerset lattice gradation, that coincides with the preconcept lattice at its 1-cut. The second and more significant contribution, is to introduce a preconcept algebra gradation that yields different algebras for protoconcepts, semiconcepts, and concepts at different cuts. This result reveals new insights into the structure and properties of the different categories of preconcepts. Full article

(This article belongs to the Special Issue Non-classical Logics and Related Algebra Systems)

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Open AccessArticle

A Coupled PDE-ODE Model for Nonlinear Transient Heat Transfer with Convection Heating at the Boundary: Numerical Solution by Implicit Time Discretization and Sequential Decoupling

by

,

,

and

Axioms 2023, 12(4), 323; https://doi.org/10.3390/axioms12040323 - 24 Mar 2023

Abstract

This article considers heat transfer in a solid body with temperature-dependent thermal conductivity that is in contact with a tank filled with liquid. The liquid in the tank is heated by hot liquid entering the tank through a pipe. Liquid at a lower [...] Read more.

This article considers heat transfer in a solid body with temperature-dependent thermal conductivity that is in contact with a tank filled with liquid. The liquid in the tank is heated by hot liquid entering the tank through a pipe. Liquid at a lower temperature leaves the tank through another pipe. We propose a one-dimensional mathematical model that consists of a nonlinear PDE for the temperature along the solid body, coupled to a linear ODE for the temperature in the tank, the boundary and the initial conditions. All equations are converted into a dimensionless form reducing the input parameters to three dimensionless numbers and a dimensionless function. A steady-state analysis is performed. To solve the transient problem, a nontrivial numerical approach is proposed whereby the differential equations are first discretized in time. This reduces the problem to a sequence of nonlinear two-point boundary value problems (TPBVP) and a sequence of linear algebraic equations coupled to it. We show that knowing the temperature in the system at time level n − 1 allows us to decouple the TPBVP and the corresponding algebraic equation at time level n. Thus, starting from the initial conditions, the equations are decoupled and solved sequentially. The TPBVPs are solved by FDM with the Newtonian method. Full article

(This article belongs to the Special Issue Computational Heat Transfer and Fluid Dynamics)

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Open AccessArticle

Comparative Study with Applications for Gompertz Models under Competing Risks and Generalized Hybrid Censoring Schemes

by

Laila A. Al-Essa

,

Ahmed A. Soliman

,

Gamal A. Abd-Elmougod

and

Huda M. Alshanbari

Axioms 2023, 12(4), 322; https://doi.org/10.3390/axioms12040322 - 24 Mar 2023

Abstract

In reliability and survival analysis, the time-to-failure data play an important role in the development of the reliability and life characteristics of the products. In some cases, these kinds of data are modeled using a competing risks model. The problem of conducting comparative [...] Read more.

In reliability and survival analysis, the time-to-failure data play an important role in the development of the reliability and life characteristics of the products. In some cases, these kinds of data are modeled using a competing risks model. The problem of conducting comparative life testing under a competing risks model when the units come from different lines of production has recently been addressed. In this paper, we address this problem when the life of the unit is distributed using the Gompertz distribution, noting that the units come from two lines of production and two independent causes of failure are activated. The data are collected under a joint generalized type-II hybrid censoring scheme. Maximum likelihood estimators of the unknown parameters are derived, along with the corresponding asymptotic confidence intervals. We also adopt two bootstrap confidence intervals. Using independent gamma priors, the Bayes estimators relative to squared error loss function are obtained with credible intervals. The properties and quality of estimators are measured by performing a Monte Carlo simulation study. Finally, a real-life data set is analyzed to discuss the applicability of the proposed methods to real phenomena. The optimal plan with respect to comments on the numerical results is discussed in the conclusion. Full article

(This article belongs to the Special Issue Recent Advances in Statistical Modeling and Simulations with Applications)

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Open AccessArticle

Fractional–Order Modeling and Control of COVID-19 with Shedding Effect

by

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and

Axioms 2023, 12(4), 321; https://doi.org/10.3390/axioms12040321 - 24 Mar 2023

Abstract

A fractional order COVID-19 model consisting of six compartments in Caputo sense is constructed. The indirect transmission of the virus through susceptible populations by the shedding effect is studied. Equilibrium solutions are calculated, and basic reproduction ratio (that depends both on direct and [...] Read more.

A fractional order COVID-19 model consisting of six compartments in Caputo sense is constructed. The indirect transmission of the virus through susceptible populations by the shedding effect is studied. Equilibrium solutions are calculated, and basic reproduction ratio (that depends both on direct and indirect mode of transmission), existence and uniqueness, as well as stability analysis of the solution of the model, are studied. The paper studies the effect of optimal control policy applied to shedding effect. The control is the observation of standard hygiene practices and chemical disinfectants in public spaces. Numerical simulations are carried out to support the analytic result and to show the significance of the fractional order from the biological viewpoint. Full article

(This article belongs to the Special Issue Recent Advances in Fractional Calculus)

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Open AccessArticle

Renyi Entropy of the Residual Lifetime of a Reliability System at the System Level

by

Mhamed Mesfioui

,

Mohamed Kayid

and

Mansour Shrahili

Axioms 2023, 12(4), 320; https://doi.org/10.3390/axioms12040320 - 23 Mar 2023

Abstract

The measurement of uncertainty across the lifetimes of engineering systems has drawn more attention in recent years. It is a helpful metric for assessing how predictable a system’s lifetime is. In these circumstances, Renyi entropy, a Shannon entropy extension, is particularly appealing. In [...] Read more.

The measurement of uncertainty across the lifetimes of engineering systems has drawn more attention in recent years. It is a helpful metric for assessing how predictable a system’s lifetime is. In these circumstances, Renyi entropy, a Shannon entropy extension, is particularly appealing. In this paper, we develop the system signature to give an explicit formula for the Renyi entropy of the residual lifetime of a coherent system when all system components have lived to a time t. In addition, several findings are studied for the aforementioned entropy, including the bounds and order characteristics. It is possible to compare the residual lifespan predictability of two coherent systems with known signatures using the findings of this study. Full article

(This article belongs to the Special Issue Information Theory in Economics, Finance, and Management)

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Open AccessArticle

New Generalization of Geodesic Convex Function

by

Ohud Bulayhan Almutairi

and

Wedad Saleh

Axioms 2023, 12(4), 319; https://doi.org/10.3390/axioms12040319 - 23 Mar 2023

Abstract

As a generalization of a geodesic function, this paper introduces the notion of the geodesic

φ_{E}

-convex function. Some properties of the

φ_{E}

-convex function and geodesic

φ_{E}

-convex function are established. The concepts of a geodesic

φ_{E}

-convex [...] Read more.

As a generalization of a geodesic function, this paper introduces the notion of the geodesic

φ_{E}

-convex function. Some properties of the

φ_{E}

-convex function and geodesic

φ_{E}

-convex function are established. The concepts of a geodesic

φ_{E}

-convex set and

φ_{E}

-epigraph are also given. The characterization of geodesic

φ_{E}

-convex functions in terms of their

φ_{E}

-epigraphs, are also obtained. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

Open AccessArticle

An Asymmetric Model Position Dependent Mass: Quantum Mechanical Study

by

,

,

,

,

and

Axioms 2023, 12(4), 318; https://doi.org/10.3390/axioms12040318 - 23 Mar 2023

Abstract

We propose an asymmetric model position dependent mass and study its quantum mechanical behaviour on different potentials such as harmonic oscillator potential, double well potential, Gaussian single well potential and triangular single well model potential. It is observed from our study that the [...] Read more.

We propose an asymmetric model position dependent mass and study its quantum mechanical behaviour on different potentials such as harmonic oscillator potential, double well potential, Gaussian single well potential and triangular single well model potential. It is observed from our study that the model asymmetric mass works well for weak coupling preserving the symmetric phase portrait. However, the dominance of asymmetric feature of the mass in the system clearly visible for higher values of the constant associated with the mass. Though, both position dependent mass and potential have significant role in controlling the spectral feature of the system, one may dominate over other for certain cases. Full article

(This article belongs to the Special Issue Applied Mathematics in Energy and Mechanical Engineering)

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Open AccessArticle

Coefficient Bounds for a Family of s-Fold Symmetric Bi-Univalent Functions

by

,

,

,

,

and

Axioms 2023, 12(4), 317; https://doi.org/10.3390/axioms12040317 - 23 Mar 2023

Abstract

We present a new family of s-fold symmetrical bi-univalent functions in the open unit disc in this work. We provide estimates for the first two Taylor–Maclaurin series coefficients for these functions. Furthermore, we define the Salagean differential operator and discuss various applications [...] Read more.

We present a new family of s-fold symmetrical bi-univalent functions in the open unit disc in this work. We provide estimates for the first two Taylor–Maclaurin series coefficients for these functions. Furthermore, we define the Salagean differential operator and discuss various applications of our main findings using it. A few new and well-known corollaries are studied in order to show the connection between recent and earlier work. Full article

(This article belongs to the Special Issue Dedicated to Professor Hari Mohan Srivastava on the Occasion of His 82nd Birthday)

Open AccessArticle

Inequalities and Reverse Inequalities for the Joint A-Numerical Radius of Operators

by

Najla Altwaijry

,

Silvestru Sever Dragomir

and

Kais Feki

Axioms 2023, 12(3), 316; https://doi.org/10.3390/axioms12030316 - 22 Mar 2023

Abstract

In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space

H

, which leads to the special case of the well-known A-numerical radius [...] Read more.

In this paper, we aim to establish several estimates concerning the generalized Euclidean operator radius of d-tuples of A-bounded linear operators acting on a complex Hilbert space

H

, which leads to the special case of the well-known A-numerical radius for

d = 1

. Here, A is a positive operator on

H

. Some inequalities related to the Euclidean operator A-seminorm of d-tuples of A-bounded operators are proved. In addition, under appropriate conditions, several reverse bounds for the A-numerical radius in single and multivariable settings are also stated. Full article

(This article belongs to the Special Issue A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi)

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