Symmetry

18 pages, 1527 KiB

Open AccessArticle

Multiple-Attribute Decision Making Based on Intuitionistic Hesitant Fuzzy Connection Set Environment

by Wajid Ali, Tanzeela Shaheen, Iftikhar Ul Haq, Hamza Ghazanfar Toor, Faraz Akram, Saeid Jafari, Md. Zia Uddin and Mohammad Mehedi Hassan

Symmetry 2023, 15(3), 778; https://doi.org/10.3390/sym15030778 - 22 Mar 2023

Cited by 17 | Viewed by 2643

Abstract

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and [...] Read more.

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and handle situations more proficiently. Another related theory is the theory of set pair analysis (SPA), which considers both certainties and uncertainties as a cohesive system and represents them from three aspects: identity, discrepancy, and contrary. In this article, we explore the suitability of combining the IHFS and SPA theories in multi-attribute decision making (MADM) and present the hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). To facilitate the design of a novel MADM algorithm, we first develop several averaging and geometric aggregation operators on IHCS. Finally, we highlight the benefits of our proposed work, including a comparative examination of the recommended models with a few current models to demonstrate the practicality of an ideal decision in practice. Additionally, we provide a graphical interpretation of the devised attempt to exhibit the consistency and efficiency of our approach. Full article

(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications II)

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22 pages, 377 KiB

Open AccessArticle

Behavior as t → ∞ of Solutions of a Mixed Problem for a Hyperbolic Equation with Periodic Coefficients on the Semi-Axis

by Hovik A. Matevossian and Vladimir Yu. Smirnov

Symmetry 2023, 15(3), 777; https://doi.org/10.3390/sym15030777 - 22 Mar 2023

Cited by 5 | Viewed by 1391

Abstract

In this paper, we consider the asymptotic behavior (as

t \to \infty

) of solutions as an initial boundary value problem for a second-order hyperbolic equation with periodic coefficients on the semi-axis (

x > 0

). The main approach to studying the [...] Read more.

In this paper, we consider the asymptotic behavior (as

t \to \infty

) of solutions as an initial boundary value problem for a second-order hyperbolic equation with periodic coefficients on the semi-axis (

x > 0

). The main approach to studying the problem under consideration is based on the spectral theory of differential operators, as well as on the properties of the spectrum (

σ (H_{0})

) of the one-dimensional Schrödinger operator

H_{0}

with periodic coefficients

p (x)

and

q (x)

. Full article

(This article belongs to the Section Physics)

26 pages, 1417 KiB

Open AccessArticle

Topology and Emergent Symmetries in Dense Compact Star Matter

by Yong-Liang Ma and Wen-Cong Yang

Symmetry 2023, 15(3), 776; https://doi.org/10.3390/sym15030776 - 22 Mar 2023

Cited by 6 | Viewed by 1919

Abstract

It has been found that the topology effect and the possible emergent hidden scale and hidden local flavor symmetries at high density reveal a novel structure of compact star matter. When

N_{f} \geq 2

, baryons can be described by skyrmions when [...] Read more.

It has been found that the topology effect and the possible emergent hidden scale and hidden local flavor symmetries at high density reveal a novel structure of compact star matter. When

N_{f} \geq 2

, baryons can be described by skyrmions when the number of color

N_{c}

is regarded as a large parameter and there is a robust topology change—the transition from skyrmion to half-skyrmion—in the skyrmion matter approach to dense nuclear matter. The hidden scale and local flavor symmetries, which are sources introducing the scalar meson and vector mesons, are significant elements for understanding the nuclear force in nonlinear chiral effective theories. We review in this paper how the robust conclusions from the topology approach to dense matter and emergent hidden scale and hidden local flavor symmetries figure in generalized nuclear effective field theory (GnEFT), which is applicable to nuclear matter from low density to compact star density. The topology change encoded in the parameters of the effective field theory is interpreted as the hadron-quark continuity in the sense of the Cheshire Cat Principle. A novel feature predicted in this theory that has not been found before is the precocious appearance of the conformal sound velocity in the cores of massive stars, although the trace of the energy-momentum tensor of the system is not zero. That is, there is a pseudoconformal structure in the compact star matter and, in contrast to the usual picture, the matter is made of colorless quasiparticles of fractional baryon charges. A possible resolution of the longstanding

g_{A}

quench problem in nuclei transition and the compatibility of the predictions of the GnEFT with the global properties of neutron star and the data from gravitational wave detections are also discussed. Full article

(This article belongs to the Special Issue Symmetries and Ultra Dense Matter of Compact Stars)

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16 pages, 3196 KiB

Open AccessArticle

Influence of Asymmetric Agglomerations Effects over the Photothermal Release of Liposome-Encapsulated Nanodiamonds Assisted by Opto-Mechanical Changes

by Samuel Morales-Bonilla, Isaac I. Mota-Díaz, Janna Douda, Ariel Fuerte-Hernández, Juan Pablo Campos-López and Carlos Torres-Torres

Symmetry 2023, 15(3), 775; https://doi.org/10.3390/sym15030775 - 22 Mar 2023

Cited by 2 | Viewed by 1518

Abstract

An analysis of optical effects exhibited by blood plasma under healthy/unhealthy conditions, and of the penetrating evolution of nanovehicles conformed by nanodiamonds (NDs) encapsulating liposomes (L) within these biofluids, is presented. Optical ablation of liposome clusters was actuated and controlled by a standard [...] Read more.

An analysis of optical effects exhibited by blood plasma under healthy/unhealthy conditions, and of the penetrating evolution of nanovehicles conformed by nanodiamonds (NDs) encapsulating liposomes (L) within these biofluids, is presented. Optical ablation of liposome clusters was actuated and controlled by a standard two-wave mixing (λ = 532 nm, τp = 4 ns) laser light method. Radiant time exposure effects (30 min) and threshold laser energy parameters (250 mJ/cm² numerical; 181 mJ/cm² experimental) necessary to release NDs were identified and confirmed with similar experiments in the literature. Interactions during the sedimentation process between nanovehicles and the laser beams barrier were considered as the principal thermal damage process to achieve the release and transportation of drugs within these static fluids. The mechanical response during the release of NDs focuses on the temperature propagation, dynamic effects of nanovehicles associated with the diffusion coefficient, and some agglomeration effects. The principal findings of this research concern the threshold temperature (51.85 °C) of liposomes for the release of NDs with respect to that typically quoted in the literature (40–70 °C) for pure liposomes. The assessment of the release of NDs focuses on the numerical magnitude of Quantum Yield. Furthermore, the optical contrast enhancement was associated with NDs size agglomerations and the healthy/unhealthy conditions of fluids. This research aims to be a first proof approximation for delivery and transportation approaches to guide and interpret outcomes when combined with the vectorial nature basis of laser light and further effects once the cargo is retained in the fluids. Full article

(This article belongs to the Special Issue Asymmetric and Symmetric Studies on Applied Physics)

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26 pages, 534 KiB

Open AccessReview

Sensitivity of Quantum-Enhanced Interferometers

by Dariya Salykina and Farid Khalili

Symmetry 2023, 15(3), 774; https://doi.org/10.3390/sym15030774 - 22 Mar 2023

Cited by 3 | Viewed by 2060

Abstract

We review various schemes of quantum-enhanced optical interferometers, both linear (SU(2)) and non-linear (SU(1,1)) ones, as well as hybrid SU(2)/SU(1,1) options, using the unified modular approach based on the Quantum Cramèr–Rao bound (QCRB), and taking into account the practical limitations pertinent to all [...] Read more.

We review various schemes of quantum-enhanced optical interferometers, both linear (SU(2)) and non-linear (SU(1,1)) ones, as well as hybrid SU(2)/SU(1,1) options, using the unified modular approach based on the Quantum Cramèr–Rao bound (QCRB), and taking into account the practical limitations pertinent to all real-world highly-sensitive interferometers. We focus on three important cases defined by the interferometer symmetry: (i) the asymmetric single-arm interferometer; (ii) the symmetric two-arm interferometer with the antisymmetric phase shifts in the arms; and (iii) the symmetric two-arm interferometer with the symmetric phase shifts in the arms. We show that while the optimal regimes for these cases differ significantly, their QCRBs asymptotically correspond to the same squeezing-enhanced shot noise limit (2), which first appeared in the pioneering work by C. Caves in 1981.We show also that in all considered cases the QCRB can be asymptotically saturated by the standard (direct or homodyne) detection schemes. Full article

(This article belongs to the Special Issue Quantum Mechanics and Symmetry/Asymmetry: Review Paper on Quantum Nonlinear Interferometers)

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12 pages, 304 KiB

Open AccessArticle

Application of Fixed-Point Results to Integral Equation through F-Khan Contraction

by Arul Joseph Gnanaprakasam, Gunaseelan Mani, Rajagopalan Ramaswamy, Ola A. Ashour Abdelnaby, Khizar Hyatt Khan and Stojan Radenović

Symmetry 2023, 15(3), 773; https://doi.org/10.3390/sym15030773 - 22 Mar 2023

Cited by 1 | Viewed by 1519

Abstract

In this article, we establish fixed point results by defining the concept of

F

-Khan contraction of an orthogonal set by modifying the symmetry of usual contractive conditions. We also provide illustrative examples to support our results. The derived results have been applied [...] Read more.

In this article, we establish fixed point results by defining the concept of

F

-Khan contraction of an orthogonal set by modifying the symmetry of usual contractive conditions. We also provide illustrative examples to support our results. The derived results have been applied to find analytical solutions to integral equations. The analytical solutions are verified with numerical simulation. Full article

(This article belongs to the Special Issue Symmetries in Differential Equation and Application)

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13 pages, 3526 KiB

Open AccessArticle

Numerical Simulation of the Effects of Reduced Gravity, Radiation and Magnetic Field on Heat Transfer Past a Solid Sphere Using Finite Difference Method

by Amir Abbas, Muhammad Ashraf, Ioannis E. Sarris, Kaouther Ghachem, Taher Labidi, Lioua Kolsi and Hafeez Ahmad

Symmetry 2023, 15(3), 772; https://doi.org/10.3390/sym15030772 - 22 Mar 2023

Cited by 14 | Viewed by 1624

Abstract

The current study deals with the reduced gravity and radiation effects on the magnetohydrodynamic natural convection past a solid sphere. The studied configuration is modeled using coupled and nonlinear partial differential equations. The obtained model is transformed to dimensionless form using suitable scaling [...] Read more.

The current study deals with the reduced gravity and radiation effects on the magnetohydrodynamic natural convection past a solid sphere. The studied configuration is modeled using coupled and nonlinear partial differential equations. The obtained model is transformed to dimensionless form using suitable scaling variables. The finite difference method is adopted to solve the governing equation and determine the velocity and temperature profiles in addition to the skin friction coefficient and Nusselt number. Furthermore, graphic and tabular presentations of the results are made. The verification of the numerical model is performed by comparing with results presented in the literature and a good concordance is encountered. The main objective of this investigation is to study the effect of the buoyancy force caused by the density variation on natural convective heat transfer past a solid sphere. The results show that the velocity increases with the reduced gravity parameter and solar radiation but decreases with Prandtl number and magnetic field parameter. It is also found that the temperature increases the with solar radiation and magnetic field but decreases with the reduced gravity parameter and Prandtl number. Full article

(This article belongs to the Special Issue Advances in Heat and Mass Transfer with Symmetry)

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15 pages, 7820 KiB

Open AccessArticle

Cross-Correlation Fusion Graph Convolution-Based Object Tracking

by Liuyi Fan, Wei Chen and Xiaoyan Jiang

Symmetry 2023, 15(3), 771; https://doi.org/10.3390/sym15030771 - 21 Mar 2023

Cited by 1 | Viewed by 2021

Abstract

Most popular graph attention networks treat pixels of a feature map as individual nodes, which makes the feature embedding extracted by the graph convolution lack the integrity of the object. Moreover, matching between a template graph and a search graph using only part-level [...] Read more.

Most popular graph attention networks treat pixels of a feature map as individual nodes, which makes the feature embedding extracted by the graph convolution lack the integrity of the object. Moreover, matching between a template graph and a search graph using only part-level information usually causes tracking errors, especially in occlusion and similarity situations. To address these problems, we propose a novel end-to-end graph attention tracking framework that has high symmetry, combining traditional cross-correlation operations directly. By utilizing cross-correlation operations, we effectively compensate for the dispersion of graph nodes and enhance the representation of features. Additionally, our graph attention fusion model performs both part-to-part matching and global matching, allowing for more accurate information embedding in the template and search regions. Furthermore, we optimize the information embedding between the template and search branches to achieve better single-object tracking results, particularly in occlusion and similarity scenarios. The flexibility of graph nodes and the comprehensiveness of information embedding have brought significant performance improvements in our framework. Extensive experiments on three challenging public datasets (LaSOT, GOT-10k, and VOT2016) show that our tracker outperforms other state-of-the-art trackers. Full article

(This article belongs to the Special Issue Advances in Computer Vision, Pattern Recognition, Machine Learning and Symmetry)

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14 pages, 1363 KiB

Open AccessArticle

Algebraic Morphology of DNA–RNA Transcription and Regulation

by Michel Planat, Marcelo M. Amaral and Klee Irwin

Symmetry 2023, 15(3), 770; https://doi.org/10.3390/sym15030770 - 21 Mar 2023

Cited by 3 | Viewed by 2301

Abstract

Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. To discover the symmetries and invariants of the transcription and regulation at the scale of the genome, in this paper, we introduce tools of infinite [...] Read more.

Transcription factors (TFs) and microRNAs (miRNAs) are co-actors in genome-scale decoding and regulatory networks, often targeting common genes. To discover the symmetries and invariants of the transcription and regulation at the scale of the genome, in this paper, we introduce tools of infinite group theory and of algebraic geometry to describe both TFs and miRNAs. In TFs, the generator of the group is a DNA-binding domain while, in miRNAs, the generator is the seed of the sequence. For such a generated (infinite) group

π

, we compute the

S L (2, C)

character variety, where

S L (2, C)

is simultaneously a ‘space-time’ (a Lorentz group) and a ‘quantum’ (a spin) group. A noteworthy result of our approach is to recognize that optimal regulation occurs when

π

looks similar to a free group

F_{r}

(

r = 1

to 3) in the cardinality sequence of its subgroups, a result obtained in our previous papers. A non-free group structure features a potential disease. A second noteworthy result is about the structure of the Groebner basis

G

of the variety. A surface with simple singularities (such as the well known Cayley cubic) within

G

is a signature of a potential disease even when

π

looks similar to a free group

F_{r}

in its structure of subgroups. Our methods apply to groups with a generating sequence made of two to four distinct DNA/RNA bases in

{A, T / U, G, C}

. We produce a few tables of human TFs and miRNAs showing that a disease may occur when either

π

is away from a free group or

G

contains surfaces with isolated singularities. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2023)

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16 pages, 4390 KiB

Open AccessArticle

A Novel Heteromorphic Ensemble Algorithm for Hand Pose Recognition

by Shiruo Liu, Xiaoguang Yuan, Wei Feng, Aifeng Ren, Zhenyong Hu, Zuheng Ming, Adnan Zahid, Qammer H. Abbasi and Shuo Wang

Symmetry 2023, 15(3), 769; https://doi.org/10.3390/sym15030769 - 21 Mar 2023

Cited by 3 | Viewed by 1663

Abstract

Imagining recognition of behaviors from video sequences for a machine is full of challenges but meaningful. This work aims to predict students’ behavior in an experimental class, which relies on the symmetry idea from reality to annotated reality centered on the feature space. [...] Read more.

Imagining recognition of behaviors from video sequences for a machine is full of challenges but meaningful. This work aims to predict students’ behavior in an experimental class, which relies on the symmetry idea from reality to annotated reality centered on the feature space. A heteromorphic ensemble algorithm is proposed to make the obtained features more aggregated and reduce the computational burden. Namely, the deep learning models are improved to obtain feature vectors representing gestures from video frames and the classification algorithm is optimized for behavior recognition. So, the symmetric idea is realized by decomposing the task into three schemas including hand detection and cropping, hand joints feature extraction, and gesture classification. Firstly, a new detector method named YOLOv4-specific tiny detection (STD) is proposed by reconstituting the YOLOv4-tiny model, which could produce two outputs with some attention mechanism leveraging context information. Secondly, the efficient pyramid squeeze attention (EPSA) net is integrated into EvoNorm-S0 and the spatial pyramid pool (SPP) layer to obtain the hand joint position information. Lastly, the D–S theory is used to fuse two classifiers, support vector machine (SVM) and random forest (RF), to produce a mixed classifier named S–R. Eventually, the synergetic effects of our algorithm are shown by experiments on self-created datasets with a high average recognition accuracy of 89.6%. Full article

(This article belongs to the Section Computer)

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34 pages, 15543 KiB

Open AccessArticle

A Novel Row Index Mathematical Procedure for the Mitigation of PV Output Power Losses during Partial Shading Conditions

by Muhammad Zeeshan, Naeem Ul Islam, Faiz Faizullah, Ihsan Ullah Khalil and Jaebyung Park

Symmetry 2023, 15(3), 768; https://doi.org/10.3390/sym15030768 - 21 Mar 2023

Cited by 3 | Viewed by 1790

Abstract

Energy demand forecasted for the next several years has been bench marked due to the massive need for electrical energy. Solar power plants have earned a great marketplace position in recent years, but also face challenges in terms of power dissipation due to [...] Read more.

Energy demand forecasted for the next several years has been bench marked due to the massive need for electrical energy. Solar power plants have earned a great marketplace position in recent years, but also face challenges in terms of power dissipation due to the frequent occurrence of shade. As a result, the per unit solar electricity price increases drastically. There is an immense need to ensure the maximum dependable power conversion efficiency of Photovoltaic (PV) systems by mitigating power output losses during partial shading conditions. The reconfiguration of PV arrays is a useful, effective, and promising approach in this context. Though several reconfiguration techniques have been developed in recent years, their applicability to real-time power plants is debatable due to the requirement of many physical relocations, long interconnecting ties, and complexity. This research work proposes a novel row index mathematical procedure followed by a technique in which the reconfiguration matrix indexes are filled with a unique number so that no row number repeats in the same row and column. Additionally, the proposed approach uses small number of switches that reduce the cost as well as the computational complexity. To strengthen the analysis, very recent techniques such as Sudoku, Total Cross Tied (TCT), Chess-Knight, and Particle Swarm Optimization (PSO) based reconfiguration are compared against five different shading patterns. It has been observed that approximately 68% power loss is mitigated in TCT configuration. It is worth noting that it results in higher PV output power than the existing latest reconfiguration techniques such as PSO, Chess-Knight, Sudoku, and others. Full article

(This article belongs to the Section Engineering and Materials)

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16 pages, 7890 KiB

Open AccessArticle

A Numerical Solution of Symmetric Angle Ply Plates Using Higher-Order Shear Deformation Theory

by Saira Javed

Symmetry 2023, 15(3), 767; https://doi.org/10.3390/sym15030767 - 21 Mar 2023

Viewed by 1463

Abstract

This research aims to provide the numerical analysis solution of symmetric angle ply plates using higher-order shear deformation theory (HSDT). The vibration of symmetric angle ply composite plates is analyzed using differential equations consisting of supplanting and turning functions. These supplanting and turning [...] Read more.

This research aims to provide the numerical analysis solution of symmetric angle ply plates using higher-order shear deformation theory (HSDT). The vibration of symmetric angle ply composite plates is analyzed using differential equations consisting of supplanting and turning functions. These supplanting and turning functions are numerically approximated through spline approximation. The obtained global eigenvalue problem is solved numerically to find the eigenfrequency parameter and a related eigenvector of spline coefficients. The plates of different constituent components are used to study the parametric effects of the plate’s aspect ratio, side-to-thickness ratio, assembling sequence, number of composite layers, and alignment of each layer on the frequency of the plate. The obtained results are validated by existing literature. Full article

(This article belongs to the Special Issue Symmetry and Approximation Methods II)

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16 pages, 1153 KiB

Open AccessArticle

The Reliability of Stored Water behind Dams Using the Multi-Component Stress-Strength System

by Hanan Haj Ahmad, Dina A. Ramadan, Mahmoud M. M. Mansour and Mohamed S. Aboshady

Symmetry 2023, 15(3), 766; https://doi.org/10.3390/sym15030766 - 21 Mar 2023

Cited by 4 | Viewed by 1566

Abstract

Dams are essential infrastructure for managing water resources and providing entry to clean water for human needs. However, the construction and maintenance of dams require careful consideration of their reliability and safety, specifically in the event of extreme weather conditions such as heavy [...] Read more.

Dams are essential infrastructure for managing water resources and providing entry to clean water for human needs. However, the construction and maintenance of dams require careful consideration of their reliability and safety, specifically in the event of extreme weather conditions such as heavy rainfall or flooding. In this study, the stress-strength model provides a useful framework for evaluating the reliability of dams and their ability to cope with external stresses such as water pressure, earthquake activity, and erosion. The Shasta reservoir in the United States is a prime example of a dam that requires regular assessment of its reliability to guarantee the safety of communities and infrastructure. The Gumbel Type II distribution has been suggested as a suitable model for fitting the collected data on the stress and strength of the reservoir behind the Shasta dam. Both classical and Bayesian approaches have been used to estimate the reliability function under the multi-component stress-strength model, and Monte Carlo simulation has been employed for parameter estimation. In addition, some measures of goodness-of-fit are employed to examine the suitability of the suggested model. Full article

(This article belongs to the Special Issue Symmetrical and Asymmetrical Distributions in Statistics and Data Science)

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23 pages, 1842 KiB

Open AccessArticle

Enhancing Interval-Valued Pythagorean Fuzzy Decision-Making through Dombi-Based Aggregation Operators

by Ghaliah Alhamzi, Saman Javaid, Umer Shuaib, Abdul Razaq, Harish Garg and Asima Razzaque

Symmetry 2023, 15(3), 765; https://doi.org/10.3390/sym15030765 - 20 Mar 2023

Cited by 17 | Viewed by 1810

Abstract

The success of any endeavor or process is heavily contingent on the ability to reconcile and satisfy balance requirements, which are often characterized by symmetry considerations. In practical applications, the primary goal of decision-making processes is to efficiently manage the symmetry or asymmetry [...] Read more.

The success of any endeavor or process is heavily contingent on the ability to reconcile and satisfy balance requirements, which are often characterized by symmetry considerations. In practical applications, the primary goal of decision-making processes is to efficiently manage the symmetry or asymmetry that exists within different sources of information. In order to address this challenge, the primary aim of this study is to introduce novel Dombi operation concepts that are formulated within the framework of interval-valued Pythagorean fuzzy aggregation operators. In this study, an updated score function is presented to resolve the deficiency of the current score function in an interval-valued Pythagorean fuzzy environment. The concept of Dombi operations is used to introduce some interval-valued Pythagorean fuzzy aggregation operators, including the interval-valued Pythagorean fuzzy Dombi weighted arithmetic (IVPFDWA) operator, the interval-valued Pythagorean fuzzy Dombi ordered weighted arithmetic (IVPFDOWA) operator, the interval-valued Pythagorean fuzzy Dombi weighted geometric (IVPFDWG) operator, and the interval-valued Pythagorean fuzzy Dombi ordered weighted geometric (IVPFDOWG) operator. Moreover, the study investigates many important properties of these operators that provide new semantic meaning to the evaluation. In addition, the suggested score function and newly derived interval-valued Pythagorean fuzzy Dombi aggregation (IVPFDA) operators are successfully employed to select a subject expert in a certain institution. The proposed approach is demonstrated to be successful through empirical validation. Lastly, a comparative study is conducted to demonstrate the validity and applicability of the suggested approaches in comparison with current techniques. This research contributes to the ongoing efforts to advance the field of evaluation and decision-making by providing novel and effective tools and techniques. Full article

(This article belongs to the Special Issue Recent Developments on Fuzzy Sets Extensions)

16 pages, 2995 KiB

Open AccessArticle

Bio-Inspired Machine Learning Approach to Type 2 Diabetes Detection

by Marwan Al-Tawil, Basel A. Mahafzah, Arar Al Tawil and Ibrahim Aljarah

Symmetry 2023, 15(3), 764; https://doi.org/10.3390/sym15030764 - 20 Mar 2023

Cited by 15 | Viewed by 2577

Abstract

Type 2 diabetes is a common life-changing disease that has been growing rapidly in recent years. According to the World Health Organization, approximately 90% of patients with diabetes worldwide have type 2 diabetes. Although there is no permanent cure for type 2 diabetes, [...] Read more.

Type 2 diabetes is a common life-changing disease that has been growing rapidly in recent years. According to the World Health Organization, approximately 90% of patients with diabetes worldwide have type 2 diabetes. Although there is no permanent cure for type 2 diabetes, this disease needs to be detected at an early stage to provide prognostic support to allied health professionals and develop an effective prevention plan. This can be accomplished by analyzing medical datasets using data mining and machine-learning techniques. Due to their efficiency, metaheuristic algorithms are now utilized in medical datasets for detecting chronic diseases, with better results than traditional methods. The main goal is to improve the performance of the existing approaches for the detection of type 2 diabetes. A bio-inspired metaheuristic algorithm called cuttlefish was used to select the essential features in the medical data preprocessing stage. The performance of the proposed approach was compared to that of a well-known bio-inspired metaheuristic feature selection algorithm called the genetic algorithm. The features selected from the cuttlefish and genetic algorithms were used with different classifiers. The implementation was applied to two datasets: the Pima Indian diabetes dataset and the hospital Frankfurt diabetes dataset; generally, these datasets are asymmetry, but some of the features in these datasets are close to symmetry. The results show that the cuttlefish algorithm has better accuracy rates, particularly when the number of instances in the dataset increases. Full article

(This article belongs to the Special Issue Machine Learning and Data Analysis)

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18 pages, 319 KiB

Open AccessArticle

Sharp Coefficient Bounds for a New Subclass of q-Starlike Functions Associated with q-Analogue of the Hyperbolic Tangent Function

by Chetan Swarup

Symmetry 2023, 15(3), 763; https://doi.org/10.3390/sym15030763 - 20 Mar 2023

Cited by 6 | Viewed by 1547

Abstract

In this study, by making the use of q-analogous of the hyperbolic tangent function and a Sălăgean q-differential operator, a new class of q-starlike functions is introduced. The prime contribution of this study covers the derivation of sharp coefficient bounds [...] Read more.

In this study, by making the use of q-analogous of the hyperbolic tangent function and a Sălăgean q-differential operator, a new class of q-starlike functions is introduced. The prime contribution of this study covers the derivation of sharp coefficient bounds in open unit disk

U,

especially the first three coefficient bounds, Fekete–Szego type functional, and upper bounds of second- and third-order Hankel determinant for the functions to this class. We also use Zalcman and generalized Zalcman conjectures to investigate the coefficient bounds of a newly defined class of functions. Furthermore, some known corollaries are highlighted based on the unique choices of the involved parameters l and q. Full article

(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis II)

26 pages, 7620 KiB

Open AccessArticle

A New Technique to Uniquely Identify the Edges of a Graph

by Hafiz Muhammad Ikhlaq, Rashad Ismail, Hafiz Muhammad Afzal Siddiqui and Muhammad Faisal Nadeem

Symmetry 2023, 15(3), 762; https://doi.org/10.3390/sym15030762 - 20 Mar 2023

Cited by 4 | Viewed by 1981

Abstract

Graphs are useful for analysing the structure models in computer science, operations research, and sociology. The word metric dimension is the basis of the distance function, which has a symmetric property. Moreover, finding the resolving set of a graph is NP-complete, and the [...] Read more.

Graphs are useful for analysing the structure models in computer science, operations research, and sociology. The word metric dimension is the basis of the distance function, which has a symmetric property. Moreover, finding the resolving set of a graph is NP-complete, and the possibilities of finding the resolving set are reduced due to the symmetric behaviour of the graph. In this paper, we introduce the idea of the edge-multiset dimension of graphs. A representation of an edge is defined as the multiset of distances between it and the vertices of a set,

B \subseteq V (Γ)

. If the representation of two different edges is unequal, then B is an edge-multiset resolving a set of

Γ

. The least possible cardinality of the edge-multiset resolving a set is referred to as the edge-multiset dimension of

Γ

. This article presents preliminary results, special conditions, and bounds on the edge-multiset dimension of certain graphs. This research provides new insights into structure models in computer science, operations research, and sociology. They could have implications for developing computer algorithms, aircraft scheduling, and species movement between regions. Full article

(This article belongs to the Special Issue Theoretical Computer Science and Discrete Mathematics II)

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18 pages, 716 KiB

Open AccessArticle

Complexity Analysis of Benes Network and Its Derived Classes via Information Functional Based Entropies

by Jun Yang, Asfand Fahad, Muzammil Mukhtar, Muhammad Anees, Amir Shahzad and Zahid Iqbal

Symmetry 2023, 15(3), 761; https://doi.org/10.3390/sym15030761 - 20 Mar 2023

Cited by 6 | Viewed by 2321

Abstract

The use of information–theoretical methodologies to assess graph-based systems has received a significant amount of attention. Evaluating a graph’s structural information content is a classic issue in fields such as cybernetics, pattern recognition, mathematical chemistry, and computational physics. Therefore, conventional methods for determining [...] Read more.

The use of information–theoretical methodologies to assess graph-based systems has received a significant amount of attention. Evaluating a graph’s structural information content is a classic issue in fields such as cybernetics, pattern recognition, mathematical chemistry, and computational physics. Therefore, conventional methods for determining a graph’s structural information content rely heavily on determining a specific partitioning of the vertex set to obtain a probability distribution. A network’s entropy based on such a probability distribution is obtained from vertex partitioning. These entropies produce the numeric information about complexity and information processing which, as a consequence, increases the understanding of the network. In this paper, we study the Benes network and its novel-derived classes via different entropy measures, which are based on information functionals. We construct different partitions of vertices of the Benes network and its novel-derived classes to compute information functional dependent entropies. Further, we present the numerical applications of our findings in understanding network complexity. We also classify information functionals which describe the networks more appropriately and may be applied to other networks. Full article

(This article belongs to the Special Issue Combinatorics, Discrete Mathematics, Symmetry and Regularity in Graphs, Graph Indices, Graph Parameters and Applications of Graph Theory)

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11 pages, 449 KiB

Open AccessFeature PaperArticle

New Features in the Differential Cross Sections Measured at the LHC

by Oleg Selyugin

Symmetry 2023, 15(3), 760; https://doi.org/10.3390/sym15030760 - 20 Mar 2023

Cited by 6 | Viewed by 1078

Abstract

The critical analysis of the new experimental data obtained by the ATLAS Collaboration group at 13 TeV is presented and the problem of the tension between data of the ATLAS and TOTEM Collaborations is considered. The analysis of new effects discovered on the [...] Read more.

The critical analysis of the new experimental data obtained by the ATLAS Collaboration group at 13 TeV is presented and the problem of the tension between data of the ATLAS and TOTEM Collaborations is considered. The analysis of new effects discovered on the basis of experimental data at 13 TeV MDPI: ref is not allowed in abstract, please correct. and associated with the specific properties of the hadron potential at large distances is carried out taking account of all sets of experimental data on elastic proton-proton scattering obtained by the TOTEM and ATLAS Collaborations in a wide momentum transfer region. It also gives quantitative descriptions of all examined experimental data with a minimum of fitting parameters. It is shown that the new features determined at a high statistical level give an important contribution to the differential cross sections and allow the research analytic properties and symmetries into hadron interactions at large distances. Full article

(This article belongs to the Section Physics)

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3 pages, 180 KiB

Open AccessEditorial

Asymmetry of Movement and Postural Balance and Underlying Functions in Humans

by Thierry Paillard

Symmetry 2023, 15(3), 759; https://doi.org/10.3390/sym15030759 - 20 Mar 2023

Cited by 1 | Viewed by 3139

Abstract

Human movements and posture often show lateral asymmetries. Although symmetry [...] Full article

(This article belongs to the Special Issue Neuroscience, Neurophysiology and Symmetry)

19 pages, 3716 KiB

Open AccessArticle

A Malware Detection Approach Based on Deep Learning and Memory Forensics

by Shuhui Zhang, Changdong Hu, Lianhai Wang, Miodrag J. Mihaljevic, Shujiang Xu and Tian Lan

Symmetry 2023, 15(3), 758; https://doi.org/10.3390/sym15030758 - 19 Mar 2023

Cited by 11 | Viewed by 6449

Abstract

As cyber attacks grow more complex and sophisticated, new types of malware become more dangerous and challenging to detect. In particular, fileless malware injects malicious code into the physical memory directly without leaving attack traces on disk files. This type of attack is [...] Read more.

As cyber attacks grow more complex and sophisticated, new types of malware become more dangerous and challenging to detect. In particular, fileless malware injects malicious code into the physical memory directly without leaving attack traces on disk files. This type of attack is well concealed, and it is difficult to find the malicious code in the static files. For malicious processes in memory, signature-based detection methods are becoming increasingly ineffective. Facing these challenges, this paper proposes a malware detection approach based on convolutional neural network and memory forensics. As the malware has many symmetric features, the saved training model can detect malicious code with symmetric features. The method includes collecting executable static malicious and benign samples, running the collected samples in a sandbox, and building a dataset of portable executables in memory through memory forensics. When a process is running, not all the program content is loaded into memory, so binary fragments are utilized for malware analysis instead of the entire portable executable (PE) files. PE file fragments are selected with different lengths and locations. We conducted several experiments on the produced dataset to test our model. The PE file with 4096 bytes of header fragment has the highest accuracy. We achieved a prediction accuracy of up to 97.48%. Moreover, an example of fileless attack is illustrated at the end of the paper. The results show that the proposed method can detect malicious codes effectively, especially the fileless attack. Its accuracy is better than that of common machine learning methods. Full article

(This article belongs to the Section Computer)

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37 pages, 8111 KiB

Open AccessReview

Green IoT: A Review and Future Research Directions

by Mohammed H. Alsharif, Abu Jahid, Anabi Hilary Kelechi and Raju Kannadasan

Symmetry 2023, 15(3), 757; https://doi.org/10.3390/sym15030757 - 19 Mar 2023

Cited by 57 | Viewed by 11169

Abstract

The internet of things (IoT) has a significant economic and environmental impact owing to the billions or trillions of interconnected devices that use various types of sensors to communicate through the internet. It is well recognized that each sensor requires a small amount [...] Read more.

The internet of things (IoT) has a significant economic and environmental impact owing to the billions or trillions of interconnected devices that use various types of sensors to communicate through the internet. It is well recognized that each sensor requires a small amount of energy to function; but, with billions of sensors, energy consumption can be significant. Therefore, it is crucial to focus on developing energy-efficient IoT technology and sustainable solutions. The contribution of this article is to support the implementation of eco-friendly IoT solutions by presenting a thorough examination of energy-efficient practices and strategies for IoT to assist in the advancement of sustainable and energy-efficient IoT technologies in the future. Four framework principles for achieving this are discussed, including (i) energy-efficient machine-to-machine (M2M) communications, (ii) energy-efficient and eco-sustainable wireless sensor networks (WSN), (iii) energy-efficient radio-frequency identification (RFID), and (iv) energy-efficient microcontroller units and integrated circuits (IC). This review aims to contribute to the next-generation implementation of eco-sustainable and energy-efficient IoT technologies. Full article

(This article belongs to the Special Issue Next-Generation Green Wireless Networks and Industrial IoT)

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26 pages, 1303 KiB

Open AccessArticle

Comparing the Min–Max–Median/IQR Approach with the Min–Max Approach, Logistic Regression and XGBoost, Maximising the Youden Index

by Rocío Aznar-Gimeno, Luis M. Esteban, Gerardo Sanz and Rafael del-Hoyo-Alonso

Symmetry 2023, 15(3), 756; https://doi.org/10.3390/sym15030756 - 19 Mar 2023

Cited by 2 | Viewed by 2288

Abstract

Although linearly combining multiple variables can provide adequate diagnostic performance, certain algorithms have the limitation of being computationally demanding when the number of variables is sufficiently high. Liu et al. proposed the min–max approach that linearly combines the minimum and maximum values of [...] Read more.

Although linearly combining multiple variables can provide adequate diagnostic performance, certain algorithms have the limitation of being computationally demanding when the number of variables is sufficiently high. Liu et al. proposed the min–max approach that linearly combines the minimum and maximum values of biomarkers, which is computationally tractable and has been shown to be optimal in certain scenarios. We developed the Min–Max–Median/IQR algorithm under Youden index optimisation which, although more computationally intensive, is still approachable and includes more information. The aim of this work is to compare the performance of these algorithms with well-known Machine Learning algorithms, namely logistic regression and XGBoost, which have proven to be efficient in various fields of applications, particularly in the health sector. This comparison is performed on a wide range of different scenarios of simulated symmetric or asymmetric data, as well as on real clinical diagnosis data sets. The results provide useful information for binary classification problems of better algorithms in terms of performance depending on the scenario. Full article

(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering IV)

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25 pages, 3854 KiB

Open AccessArticle

Omnidimensional Convex Polytopes

by Szymon Łukaszyk and Andrzej Tomski

Symmetry 2023, 15(3), 755; https://doi.org/10.3390/sym15030755 - 19 Mar 2023

Cited by 2 | Viewed by 2228

Abstract

The study shows that the volumes and surfaces of n-balls, n-simplices, and n-orthoplices are holomorphic functions of n, which makes those objects omnidimensional, that is well defined in any complex dimension. Applications of these formulas to the omnidimensional polytopes [...] Read more.

The study shows that the volumes and surfaces of n-balls, n-simplices, and n-orthoplices are holomorphic functions of n, which makes those objects omnidimensional, that is well defined in any complex dimension. Applications of these formulas to the omnidimensional polytopes inscribed in and circumscribed about n-balls reveal previously unknown properties of these geometric objects. In particular, for

0 < n < 1

, the volumes of the omnidimensional polytopes are larger than those of circumscribing n-balls, and both their volumes and surfaces are smaller than those of inscribed n-balls. The surface of an n-simplex circumscribing a unit diameter n-ball is spirally convergent to zero with real n approaching negative infinity but first has a local maximum at

n = - 3.5

. The surface of an n-orthoplex circumscribing a unit diameter n-ball is spirally divergent with real n approaching negative infinity but first has a local minimum at

n = - 1.5

, where its real and imaginary parts are equal to each other; similarly, is its volume, where the similar local minimum occurs at

n = - 3.5

. Reflection functions for volumes and surfaces of these polytopes inscribed in and circumscribed about n-balls are proposed. Symmetries of products and quotients of the volumes in complex dimensions n and

- n

and of the surfaces in complex dimensions n and

2 - n

are shown to be independent of the metric factor and the gamma function. Specific symmetries also hold between the volumes and surfaces in dimensions

n = - 1 / 2

and

n = 1 / 2

. Full article

(This article belongs to the Special Issue Mathematical Modelling of Physical Systems 2021)

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18 pages, 324 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Expansion-Free Dissipative Fluid Spheres: Analytical Solutions

by Luis Herrera, Alicia Di Prisco and Justo Ospino

Symmetry 2023, 15(3), 754; https://doi.org/10.3390/sym15030754 - 19 Mar 2023

Cited by 10 | Viewed by 1492

Abstract

We search for exact analytical solutions of spherically symmetric dissipative fluid distributions satisfying the vanishing expansion condition (vanishing expansion scalar

Θ

). To accomplish this, we shall impose additional restrictions allowing integration of the field equations. The solutions are analyzed, and possible applications [...] Read more.

We search for exact analytical solutions of spherically symmetric dissipative fluid distributions satisfying the vanishing expansion condition (vanishing expansion scalar

Θ

). To accomplish this, we shall impose additional restrictions allowing integration of the field equations. The solutions are analyzed, and possible applications to astrophysical scenarios as well as alternative approaches to obtaining new solutions are discussed. Full article

(This article belongs to the Special Issue Symmetry in Cosmology and Gravity: Topic and Advance)

11 pages, 277 KiB

Open AccessArticle

Tangent Bundles of P-Sasakian Manifolds Endowed with a Quarter-Symmetric Metric Connection

by Mohammad Nazrul Islam Khan, Fatemah Mofarreh and Abdul Haseeb

Symmetry 2023, 15(3), 753; https://doi.org/10.3390/sym15030753 - 19 Mar 2023

Cited by 13 | Viewed by 1592

Abstract

The purpose of this study is to evaluate the curvature tensor and the Ricci tensor of a P-Sasakian manifold with respect to the quarter-symmetric metric connection on the tangent bundle

T M

. Certain results on a semisymmetric P-Sasakian manifold, generalized [...] Read more.

The purpose of this study is to evaluate the curvature tensor and the Ricci tensor of a P-Sasakian manifold with respect to the quarter-symmetric metric connection on the tangent bundle

T M

. Certain results on a semisymmetric P-Sasakian manifold, generalized recurrent P-Sasakian manifolds, and pseudo-symmetric P-Sasakian manifolds on

T M

are proved. Full article

(This article belongs to the Special Issue Symmetry and Its Application in Differential Geometry and Topology, 2nd Edition)

17 pages, 7780 KiB

Open AccessArticle

Electrochemistry of Rhodanine Derivatives as Model for New Colorimetric and Electrochemical Azulene Sensors for the Detection of Heavy Metal Ions

by Ovidiu-Teodor Matica, Cornelia Musina (Borsaru), Alina Giorgiana Brotea, Eleonora-Mihaela Ungureanu, Mihaela Cristea, Raluca Isopescu, George-Octavian Buica and Alexandru C. Razus

Symmetry 2023, 15(3), 752; https://doi.org/10.3390/sym15030752 - 18 Mar 2023

Cited by 3 | Viewed by 1598

Abstract

Rhodanine (R) is a heterocycle having complexing properties for heavy metal (HM) ions. Considering the similar electron-donating character of diethylaminobenzene and azulene, electrochemical characterization of (Z)-5-(azulen-1-ylmethylene)-2-thioxo-thiazolidin-4-one (R1) and 5-(4 diethylamino-benzylidene)-2-thioxo-thiazolidin-4-one (R2) was performed to establish [...] Read more.

Rhodanine (R) is a heterocycle having complexing properties for heavy metal (HM) ions. Considering the similar electron-donating character of diethylaminobenzene and azulene, electrochemical characterization of (Z)-5-(azulen-1-ylmethylene)-2-thioxo-thiazolidin-4-one (R1) and 5-(4 diethylamino-benzylidene)-2-thioxo-thiazolidin-4-one (R2) was performed to establish their common features. Chemically modified electrodes based on R1 and R2 were compared for HM recognition. Evidence for the formation of films was provided by scanning and controlled potential electrolysis, and HM recognition experiments were performed using their films. Parallel studies for analysis of HMs by complexation in solution were performed by UV-Vis. The analogy between R1 and R2 created the premise for easier selection of compounds for certain applications. The performance of the chemically modified electrodes was evaluated as detection limits for HMs. The azulene monomer (R1) proved to be the best candidate for Pb(II) detection, being about eight times more sensitive than R2. However, in solution, R2 proved to be a good choice for optical measurements, having a higher absorption coefficient. These results support the two ligands having different behaviors in homogeneous and heterogeneous systems. Full article

(This article belongs to the Section Chemistry: Symmetry/Asymmetry)

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17 pages, 356 KiB

Open AccessArticle

Five Generalized Rough Approximation Spaces Produced by Maximal Rough Neighborhoods

by A. A. Azzam and Tareq M. Al-shami

Symmetry 2023, 15(3), 751; https://doi.org/10.3390/sym15030751 - 18 Mar 2023

Cited by 4 | Viewed by 1322

Abstract

In rough set theory, the multiplicity of methods of calculating neighborhood systems is very useful to calculate the measures of accuracy and roughness. In line with this research direction, in this article we present novel kinds of rough neighborhood systems inspired by the [...] Read more.

In rough set theory, the multiplicity of methods of calculating neighborhood systems is very useful to calculate the measures of accuracy and roughness. In line with this research direction, in this article we present novel kinds of rough neighborhood systems inspired by the system of maximal neighborhood systems. We benefit from the symmetry between rough approximations (lower and upper) and topological operators (interior and closure) to structure the current generalized rough approximation spaces. First, we display two novel types of rough set models produced by maximal neighborhoods, namely, type 2

m_{ξ}

-neighborhood and type 3

m_{ξ}

-neighborhood rough models. We investigate their master properties and show the relationships between them as well as their relationship with some foregoing ones. Then, we apply the idea of adhesion neighborhoods to introduce three additional rough set models, namely, type 4

m_{ξ}

-adhesion, type 5

m_{ξ}

-adhesion and type 6

m_{ξ}

-adhesion neighborhood rough models. We establish the fundamental characteristics of approximation operators inspired by these models and discuss how the properties of various relationships relate to one another. We prove that adhesion neighborhood rough models increase the value of the accuracy measure of subsets, which can improve decision making. Finally, we provide a comparison between Yao’s technique and current types of adhesion neighborhood rough models. Full article

22 pages, 4003 KiB

Open AccessArticle

A Robust-Reliable Decision-Making Methodology Based on a Combination of Stakeholders’ Preferences Simulation and KDD Techniques for Selecting Automotive Platform Benchmark

by Asad Saghari, Ivana Budinská, Masoud Hosseinimehr and Shima Rahmani

Symmetry 2023, 15(3), 750; https://doi.org/10.3390/sym15030750 - 18 Mar 2023

Cited by 8 | Viewed by 1686

Abstract

The automotive family design is known as one of the most complex engineering design problems with multiple groups of stakeholders involved from different domains of interest and contradictory attributes. Taking into account all stakeholders’ preferences, which are generally symmetrical, non-deterministic distributions around a [...] Read more.

The automotive family design is known as one of the most complex engineering design problems with multiple groups of stakeholders involved from different domains of interest and contradictory attributes. Taking into account all stakeholders’ preferences, which are generally symmetrical, non-deterministic distributions around a mean value, and determining the right value of attributes for each alternative are two basic challenges for these types of decision-making problems. In this research, the possibility to achieve a robust-reliable decision by focusing on the two aforementioned challenges is explored. In the proposed methodology, a random simulation technique is used to elicit stakeholders’ preferences and determine the relative importance of attributes. The decision space and values of attributes are determined using the Knowledge Discovery in Databases (KDD) technique, and to achieve a robust-reliable decision, statistical and sensitivity analyses are performed. By implementing this methodology, the decision-maker is assured that the preferences of all stakeholders are taken into account and the determined values for attributes are reliable with the least degree of uncertainty. The proposed methodology aims to select benchmark platforms for the development of an automotive family. The decision space includes 546 automobiles in 11 different segments based on 34 platforms. There are 6223 unique possible states of stakeholders’ preferences. As a result, five platforms with the highest degree of desirability and robustness to diversity and uncertainty in the stakeholders’ preferences are selected. The presented methodology can be implemented in complex decision-making problems, including a large and diverse number of stakeholders and multiple attributes. In addition, this methodology is compatible with many Multi-Attribute Decision-Making (MADM) techniques, including SAW, AHP, SWARA, and TOPSIS. Full article

(This article belongs to the Special Issue Algorithms for Multi-Criteria Decision-Making under Uncertainty)

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14 pages, 2787 KiB

Open AccessFeature PaperArticle

Energy Transfer Processes in NASICON-Type Phosphates under Synchrotron Radiation Excitation

by Nataliya Krutyak, Vitali Nagirnyi, Ivo Romet, Dina Deyneko and Dmitry Spassky

Symmetry 2023, 15(3), 749; https://doi.org/10.3390/sym15030749 - 18 Mar 2023

Cited by 1 | Viewed by 1567

Abstract

The luminescence properties of NASICON-type Na_3.6M_1.8(PO₄)₃ (M = Y, Lu) and Na₃Sc₂(PO₄)₃ phosphates, undoped and rare earth-doped (RE = Tb³⁺, Dy³⁺, Eu³⁺, Ce [...] Read more.

The luminescence properties of NASICON-type Na_3.6M_1.8(PO₄)₃ (M = Y, Lu) and Na₃Sc₂(PO₄)₃ phosphates, undoped and rare earth-doped (RE = Tb³⁺, Dy³⁺, Eu³⁺, Ce³⁺), were studied using synchrotron radiation in a wide energy region of 4.5–45 eV. Intrinsic emission originating from self-trapped excitons with electron component localized at the 3d Sc states was detected in both doped and undoped Na₃Sc₂(PO₄)₃ while only defect-related emission was registered in Na_3.6M_1.8(PO₄)₃. Emission of RE ions substituting three-valent cations in low-symmetry sites was detected in all doped phosphates. The efficiency and pass ways of energy transfer from the host to emission centres were analysed based on luminescence excitation spectra. It is shown that the most efficient energy transfer is realized in Tb³⁺-doped phosphors, while it was poor for other RE ions. The differences in energy transfer efficiencies are explained by different position of RE f states in the crystal electronic band structure influencing the efficiency of charge carrier trapping in the substance. Based on excitation spectra analysis, the bandgap values were estimated to ~8 eV for all studied phosphates. Full article

(This article belongs to the Special Issue Advances in Synchrotron and Undulator Radiation Studies Ⅱ)

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