Concept Of Symmetry Research Articles

What Does Symmetry Look Like? A Qualitative Research Based on Mental Images

Symmetry, located within the field of transformation geometry, is a mathematical concept that plays an extremely important role as a problem-solving technique. Despite this, it seems that it is rarely used in solving mathematical problems in secondary school. This research was carried out to reveal the mental images of secondary school students regarding the concept of symmetry in the secondary school mathematics curriculum. In the study conducted based on a qualitative perspective, the metaphors developed by the students regarding the concept of symmetry and the visuals they drew were examined. The study was conducted in the spring semester of the 2022-2023 academic year with 223 students studying in the 5th, 6th and 7th grades at a public school in Ankara, selected according to the convenient sampling method. Content analysis was used to analyze and interpret the data obtained from the students. Looking at the results of the research; It turns out that secondary school students generally perceive the concept of symmetry as "having similar functionality", "visually overlapping" and "perfect and meeting in differences".

Exploring Cybersecurity Education and Training Techniques: A Comprehensive Review of Traditional, Virtual Reality, and Augmented Reality Approaches

Considering the alarming increase in cyberattacks and their potential financial implications, the importance of cybersecurity education and training cannot be overstated. This paper presents a systematic literature review that examines different cybersecurity education and training techniques with a focus on symmetry. It primarily focuses on traditional cybersecurity education techniques and emerging technologies, such as virtual reality (VR) and augmented reality (AR), through the lens of symmetry. The main objective of this study is to explore the existing cybersecurity training techniques, identify the challenges involved, and assess the effectiveness of cybersecurity training based on VR and AR while emphasizing the concept of symmetry. Through careful selection criteria, 66 primary studies were selected from a total of 150 pertinent research studies. This article offers valuable insights into the pros and cons of conventional training approaches, explores the use of VR and AR in cybersecurity education concerning symmetry, and thoroughly discusses the challenges associated with these technologies. The findings of this review contribute significantly to the continuing efforts in cybersecurity education by offering recommendations for improving employees’ knowledge, engagement, and motivation in cybersecurity training programs while maintaining symmetry in the learning process.

Higher category theory and n-groups as gauge symmetries for quantum gravity

Higher category theory can be employed to generalize the notion of a gauge group to the notion of a gauge n-group. This novel algebraic structure is designed to generalize notions of connection, parallel transport and holonomy from curves to manifolds of dimension higher than one. Thus it generalizes the concept of gauge symmetry, giving rise to a topological action called nBF action, living on a corresponding n-principal bundle over a spacetime manifold. Similarly as for the Plebanski action, one can deform the topological nBF action by adding appropriate simplicity constraints, in order to describe the correct dynamics of both gravity and matter fields. Specifically, one can describe the whole Standard Model coupled to gravity as a constrained 3BF or 4BF action. The split of the full action into a topological sector and simplicity constraints sector is adapted to the spinfoam quantization technique, with the aim to construct a full model of quantum gravity with matter. In addition, the properties of the gauge n-group structure open up a possibility of a nontrivial unification of all fields. An n-group naturally contains additional novel gauge groups which specify the spectrum of matter fields present in the theory, in a similar way to the ordinary gauge group that prescribes the spectrum of gauge vector bosons in the Yang-Mills theory. The presence and the properties of these new gauge groups has the potential to explain fermion families, and other structure in the matter spectrum of the theory.

New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities

It is well known that both concepts of symmetry and convexity are directly connected. Similarly, in fuzzy theory, both ideas behave alike. It is important to note that real and interval-valued mappings are exceptional cases of fuzzy number-valued mappings (FNVMs) because fuzzy theory depends upon the unit interval that make a significant contribution to overcoming the issues that arise in the theory of interval analysis and fuzzy number theory. In this paper, the new class of p-convexity over up and down (UD) fuzzy relation has been introduced which is known as UD-p-convex fuzzy number-valued mappings (UD-p-convex FNVMs). We offer a thorough analysis of Hermite–Hadamard-type inequalities for FNVMs that are UD-p-convex using the fuzzy Aumann integral. Some previous results from the literature are expanded upon and broadly applied in our study. Additionally, we offer precise justifications for the key theorems that Kunt and İşcan first deduced in their article titled “Hermite–Hadamard–Fejer type inequalities for p-convex functions”. Some new and classical exceptional cases are also discussed. Finally, we illustrate our findings with well-defined examples.

Exact Solutions of Nonlinear Partial Differential Equations Using the Extended Kudryashov Method and Some Properties

In this paper, we consider how to find new exact solutions for nonlinear partial differential equations using the extended Kudryashov method. This method mainly uses the Riccati equation and the Bernoulli equation where there are some underdetermined constant parameters. And we also use the concept of symmetry to study its reduction equation, Lie transformation group, self-adjointness, and conservation laws. This paper mainly studies the Boussinesq class and the shallow water wave equation in (1 + 1) dimensions and tries to find new exact solutions and symmetry properties of them.

When the Conception of Symmetry Deceives Us: A Case Report on the Perioperative Diagnosis of Subclavian Artery Stenosis

When the Conception of Symmetry Deceives Us: A Case Report on the Perioperative Diagnosis of Subclavian Artery Stenosis

Statistical Analyses of a Class of Random Cyclooctatetraene Chain Networks with Respect to Several Topological Properties

In recent years, the research on complex networks has created a boom. The objective of the present paper is to study a random cyclooctatetraene chain whose graph-theoretic mathematical properties arose scientists’ interests. By applying the concept of symmetry and probability theory, we obtain the explicit analytical expressions for the variances of Schultz index, multiplicative degree-Kirchhoff index Gutman index, and additive degree-Kirchhoff index of a random cyclooctatetraene chain with n octagons, which plays a crucial role in the research and application of topological indices.

Методика вивчення симетрії елементарних частинок в ЗВО

The article addresses the current issue of teaching symmetry in elementary particles within technicalhigher education institutions. The study of symmetry in elementary particles plays a vital role in helpingstudents understand the fundamental laws of nature and the properties of fundamental particles. However,symmetry is a complex concept that requires deep understanding and analysis. To successfully master thisintricate topic in an educational environment, effective teaching methods and tools need to be developed.Modern students demand an active and engaging approach to learning, making the use of innovative methodscritically important.The article presents an analysis of contemporary approaches to teaching symmetry in elementaryparticles within higher education institutions. It places significant emphasis on innovative methodologiesdesigned to help students grasp complex symmetry concepts in physics. Specifically, it discusses the utilizationof modern pedagogical technologies, interactive tools, virtual laboratories, and computer simulations. Thepractical aspects of conducting laboratory work and experimental research focused on studying symmetry arealso explored.The article explores possible ways to enhance the effectiveness of teaching in this field. An essentialpart of the article involves analyzing the impact of symmetry education on the professional training of futureexperts in the field of physics and related sciences. Achievements in the study of symmetry also necessitate an33effective assessment system. It is crucial to consider the knowledge and skills acquired by students in this fieldso that they can independently analyze and apply symmetrical principles in their further research.The prospects for further scientific research involve the investigation of modern approaches to physicseducation, including the use of computer simulations, virtual laboratories, and interactive learning tools. Theseinnovations contribute to a better understanding of complex symmetry concepts. Research in this direction canhelp develop effective pedagogical approaches and tools that support students in the process of studyingsymmetry in elementary particles and enhance the quality of physics education.

Задача о беспорядках

The problem of characterizing symmetric necklaces as disorders is considered. Such an idea is an alternative approach to the one using Poya's enumeration theorem, including Burnside's lemma. The relationship between partitions of numbers and permutation types is shown. Disorder types are associated with necklace types considered as permutations in which no element remains in place, as well as with disorders with fixed elements. The distributions of disorders by types for necklaces up to the seventh degree are studied. The number and enumeration of disorders of each type is carried out, and their evenness is established. Particular attention is paid to the study of the symmetric necklaces properties. Classes of symmetry and asymmetry are enumerated for each necklace type considered. At the same time, the concepts of chiral and achiral symmetry are introduced as varieties of axial symmetry. Relationships between the power of symmetry classes and the order of symmetry of necklaces are revealed. The concept of symmetry diagrams for necklaces is introduced. Diagrams could be applied for determining the properties of invariance of symmetric and asymmetric necklaces of a given length. The concept of congruence is used as an equivalence relation between necklaces. It allows implementing a geometric approach to the study of necklaces and the visualization of the results obtained. For this purpose, necklaces are associated with multiconnected non-oriented graphs, the vertices of which are the vertices of regular polygons. In this case, the number of vertices in the graph corresponds to the necklace’s length, and the number of connected components coincides with the number of bead colors. As an application of the results obtained, the possibility of studying the accent dynamics of poetic stanzas vertically using necklaces is considered. Empirical data on the use of various types of seven-line stanzas in poetic practice are presented. It is noted that approximately a quarter of the existing symmetric types of necklaces for various reasons do not find practical application.

Acoustic realization of projective mirror Chern insulators

Symmetry plays a key role in classifying topological phases. Recent theory shows that in the presence of gauge fields, the algebraic structure of crystalline symmetries needs to be projectively represented, which brings extra chance for topological physics. Here, we report a concrete acoustic realization of mirror Chern insulators by exploiting the concept of projective symmetry. Specifically, we introduce a simple but universal recipe for constructing projective mirror symmetry, and conceive a minimal model for achieving the projective symmetry-enriched mirror Chern insulators. Based on our selective-excitation measurements, we demonstrate unambiguously the projective mirror eigenvalue-locked topological nature of the bulk states and associated chiral edge states. We extract the non-abelian Berry curvature and identify the mirror Chern number directly, providing experimental evidence for this exotic topological phase. All experimental results agree well with the theoretical predictions. Our findings give insights into topological systems equipped with gauge fields.

Design of Active Disturbance Rejection Controller for Trajectory-Following of Autonomous Ground Electric Vehicles

In this paper, the concept of symmetry is utilized in the promising trajectory-following control design of autonomous ground electric vehicles—that is, the construction and the solution of active disturbance rejection controllers are symmetrical. This paper presents an active disturbance rejection controller (ADRC) for improving the trajectory-following performance of autonomous ground electric vehicles (AGEV) with an advanced active front steering system. Since AGEV trajectory dynamics are inherently affected by complex traffic conditions, various driving maneuvers, and other road environment, the main control objective is to deal with the AGEV trajectory control challenges of system uncertainties, system nonlinearities, and external disturbance. First, the vehicle dynamics trajectory-following model and its state space representation system are established. Then, the augmented control-oriented vehicle-trajectory-following system with dynamic error is developed. The resulting active disturbance rejection controller of the vehicle-trajectory-following system is finally designed using the trajectory performance index and active disturbance compensation, and the stability of the active disturbance rejection controller is also analyzed and derived via Lyapunov stability theory. The effectiveness of the proposed controller is validated through double lane change and serpentine maneuvers under the co-simulation platform of MATLAB/Simulink-Carsim®. Simulation results show that the designed controller provides enhanced vehicle-trajectory-following performance compared to the linear quadratic regulator controller (LQR) and model predictive controller (MPC). It will provide a certain guidance for the controller engineering design of the AGEV trajectory-following system.

Automatic Trajectory Determination in Automated Robotic Welding Considering Weld Joint Symmetry

The field of inspection for welded structures is currently in a state of rapid transformation driven by a convergence of global technological, regulatory, and economic factors. This evolution is propelled by several key drivers, including the introduction of novel materials and welding processes, continuous advancements in inspection technologies, innovative approaches to weld acceptance code philosophy and certification procedures, growing demands for cost-effectiveness and production quality, and the imperative to extend the lifespan of aging structures. Foremost among the challenges faced by producers today is the imperative to meet customer demands, which entails addressing both their explicit and implicit needs. Furthermore, the integration of emerging materials and technologies necessitates the exploration of fresh solutions. These solutions aim to enhance inspection process efficiency while providing precise quantitative insights into defect identification and location. To this end, our project proposes cutting-edge technologies, some of which have yet to gain approval within the sector. Noteworthy among these innovations is the integration of vision systems into welding robots, among other solutions. This paper introduces a groundbreaking algorithm for tool path selection, leveraging profile scanning and the concept of joint symmetry. The application of symmetry principles for trajectory determination represents a pioneering approach within this expansive field.

Fuzzy-Based Active Queue Management Using Precise Fuzzy Modeling and Genetic Algorithm

Active Queue Management (AQM) methods significantly impact the network performance, as they manage the router queue and facilitate the traffic flow through the network. This paper presents a novel fuzzy-based AQM method developed with a computationally efficient precise fuzzy modeling optimized using the Genetic Algorithm. The proposed method focuses on the concept of symmetry as a means to achieve a more balanced and equitable distribution of the resources and avoid bandwidth wasting resulting from unnecessary packet dropping. The proposed method calculates the dropping probability of each packet using a precise fuzzy model that was created and tuned in advance and based on the previous dropping probability value and the queue length. The tuning process is implemented as an optimization problem formulated for the b0, b1, and b2 variables of the precise rules with an objective function that maximizes the performance results in terms of loss, dropping, and delay. To prove the efficiency of the developed method, the simulation was not limited to the common Bernoulli process simulation; instead, the Markov-modulated Bernoulli process was used to mimic the burstiness nature of the traffic. The simulation is conducted on a machine operated with 64-bit Windows 10 with an Intel Core i7 2.0 GHz processor and 16 GB of RAM. The simulation used Java programming language in Apache NetBeans Integrated Development Environment (IDE) 11.2. The results showed that the proposed method outperformed the existing methods in terms of computational complexity, packet loss, dropping, and delay. As such, in low congested networks, the proposed method maintained no packet loss and dropped 22% of the packets with an average delay of 7.57, compared to the best method, LRED, which dropped 21% of the packets with a delay of 10.74, and FCRED, which dropped 21% of the packets with a delay of 16.54. In highly congested networks, the proposed method also maintained no packet loss and dropped 48% of the packets, with an average delay of 16.23, compared to the best method LRED, which dropped 47% of the packets with a delay of 28.04, and FCRED, which dropped 46% of the packets with a delay of 40.23.

Tensor Products and Crossed Differential Graded Lie Algebras in the Category of Crossed Complexes

The study of algebraic structures endowed with the concept of symmetry is made possible by the link between Lie algebras and symmetric monoidal categories. This relationship between Lie algebras and symmetric monoidal categories is useful and has resulted in many areas, including algebraic topology, representation theory, and quantum physics. In this paper, we present analogous definitions for Lie algebras within the framework of whiskered structures, bimorphisms, crossed complexes, crossed differential graded algebras, and tensor products. These definitions, given for groupoids in existing literature, have been adapted to establish a direct correspondence between these algebraic structures and Lie algebras. We show that a 2-truncation of the crossed differential graded Lie algebra, obtained from our adapted definitions, gives rise to a braided crossed module of Lie algebras. We also construct a functor to simplicial Lie algebras, enabling a systematic mapping between different Lie algebraic categories, which supports the validity of our adapted definitions and establishes their compatibility with established categories.

Symmetric Strange Attractors: A Review of Symmetry and Conditional Symmetry

A comprehensive review of symmetry and conditional symmetry is made from the core conception of symmetry and conditional symmetry. For a dynamical system, the structure of symmetry means its robustness against the polarity change of some of the system variables. Symmetric systems typically show symmetrical dynamics, and even when the symmetry is broken, symmetric pairs of coexisting attractors are born, annotating the symmetry in another way. The polarity balance can be recovered through combinations of the polarity reversal of system variables, and furthermore, it can also be restored by the offset boosting of some of the system variables if the variables lead to the polarity reversal of their functions. In this case, conditional symmetry is constructed, giving a chance for a dynamical system outputting coexisting attractors. Symmetric strange attractors typically represent the flexible polarity reversal of some of the system variables, which brings more alternatives of chaotic signals and more convenience for chaos application. Symmetric and conditionally symmetric coexisting attractors can also be found in memristive systems and circuits. Therefore, symmetric chaotic systems and systems with conditional symmetry provide sufficient system options for chaos-based applications.

A New Technique to Achieve Torsional Anchor of Fractional Torsion Equation Using Conservation Laws

The main idea in this research is introducing another approximate method to calculate solutions of the fractional Torsion equation, which is one of the applied equations in civil engineering. Since the fractional order is closed to an integer, we convert the fractional Torsion equation to a perturbed ordinary differential equation involving a small parameter epsilon. Then we can find the exact solutions and approximate symmetries for the alternative approximation equation. Also, with help of the definition of conserved vector and the concept of nonlinear self-adjointness, approximate conservation laws(ACL) are obtained without approximate Lagrangians by using their approximate symmetries. In order to apply the presented theory, we apply the Lie symmetry analysis (LSA) and concept of nonlinear self-adjoint Torsion equation, which are very important in mathematics and engineering sciences, especially civil engineering.

Evaluation of Thermodynamic Parameters for Cu(II) Ions Biosorption on Algae Biomass and Derived Biochars

The removal of metal ions by biosorption on inexpensive materials is still a challenge for environmental engineering research. In this study, marine green algae biomass (Ulva lactuca sp.) and the biochars obtained from this biomass, at 320 °C (BC-320) and 550 °C (BC-550), were used as biosorbents for the removal of Cu(II) ions from aqueous solution. In addition to comparing the biosorption capacities, the determination of the thermodynamic parameters allows the choice of the most suitable material for the biosorption processes. The experimental results, obtained for Cu(II) ions biosorption on each biosorbent (algae biomass (AB), BC-320 and BC-550), at three different temperatures (10, 30 and 50 °C) were analyzed using Langmuir and Freundlich isotherm models, while pseudo-first order, pseudo-second order and intra-particle diffusions models were used to model the kinetic data. The biosorption of Cu(II) ions is best described by the Langmuir model and the pseudo-second kinetic model, regardless of the type of biosorbent. Such behavior is characteristic for the retention of metal ions on low-cost materials, and is explained in the literature using the concepts of molecular symmetry. The maximum biosorption capacity (qmax, mg/g) depends on the temperature, but also on the type of biosorbent, and follow the order: BC-320 < AB < BC-550. Using the experimental isotherms, the thermodynamic parameters (ΔG0, ΔH0 and ΔS0) for the biosorption of Cu(II) ions on each biosorbent were calculated. The analysis of the obtained values constitutes the main arguments in choosing BC-550 as the most effective biosorbent for the removal of Cu(II) ions from aqueous media.

Tomb towers and minarets: analysis of symmetries and geometries of Iranian geometrical ornaments of the Seljuq era. Pictorial requiem for the Kharraqan towers

Ornamental adornment of the Kharraqan tomb towers, the most outstanding funeral monuments of the Seljuk era in NW Iran, and those of four best-preserved Seljuq brick minarets in northern Iran, documents the artistic canon of the pre-glaze stage of Iranian Islamic architecture. Despite some later interruptions, these monuments and their plain-brick ornaments, as well as the ‘virtually interlaced’ brick ornaments, stand at the beginnings of a rich development that led to the Safavid architecture of Iran. Besides documentation and study of the geometric character of early Islamic art, which was based on limited technical resources, this study offers insight into symmetry concepts developed at this stage of art and architecture development. This is the last and most complete study of the Kharraqan towers performed before their overwhelming destruction in the 2002 earthquake.

Scaling Symmetries and Parameter Reduction in Epidemic SI(R)S Models

Symmetry concepts in parametrized dynamical systems may reduce the number of external parameters by a suitable normalization prescription. If, under the action of a symmetry group G, parameter space A becomes a (locally) trivial principal bundle, A≅A/G×G, then the normalized dynamics only depends on the quotient A/G. In this way, the dynamics of fractional variables in homogeneous epidemic SI(R)S models, with standard incidence, absence of R-susceptibility and compartment independent birth and death rates, turns out to be isomorphic to (a marginally extended version of) Hethcote’s classic endemic model, first presented in 1973. The paper studies a 10-parameter master model with constant and I-linear vaccination rates, vertical transmission and a vaccination rate for susceptible newborns. As recently shown by the author, all demographic parameters are redundant. After adjusting time scale, the remaining 5-parameter model admits a 3-dimensional abelian scaling symmetry. By normalization we end up with Hethcote’s extended 2-parameter model. Thus, in view of symmetry concepts, reproving theorems on endemic bifurcation and stability in such models becomes needless.

The art and science of scholarly writing: framing symmetry of specificity beyond IMRAD

PurposeThe purpose of this paper is to provide scholars with a robust, easy-to-follow structural model for crafting compelling academic publications. Recognizing the diversity of research methodologies and genres, the paper proposes the symmetry of specificity framework as a guide to maintaining coherence, depth and relevance across different sections of an academic paper.Design/methodology/approachThis paper presents a theoretical framework – “symmetry of specificity” – through an iterative approach inspired by supervision and examination of theses, writing and reviewing research papers and editorial work. The framework builds upon the established IMRAD model and uses the concept of symmetry to explain the structural elements of academic publications. Its unique contribution lies in elucidating the two-dimensional funneling process that takes place within academic writing, and providing a nuanced understanding of how to maintain balance between different sections.FindingsThe symmetry of specificity framework introduces a novel perspective on academic writing, emphasizing the concept of “symmetry in specificity”. It shows how maintaining a balance in detail and focus across different sections of a research paper can significantly enhance its coherence and relevance. By elucidating the interaction between theory and data in research writing, it provides valuable insights into the nuances of crafting a compelling academic paper.Research limitations/implicationsWhile the proposed symmetry of specificity framework may not be universally applicable across all types of research, it provides a solid foundation for the development of alternate structures tailored to specific research paradigms. There is ample opportunity for future research to explore adaptations of this model for various types of academic writing, offering a fresh perspective on structuring academic publications and potentially sparking new discussions and innovations in this realm.Practical implicationsThis framework can aid both novice and experienced scholars in structuring their research papers effectively. By offering a conceptual roadmap, it guides the writer through the complex process of academic writing, from crafting the methodology and analysis sections to articulating compelling conclusions. Thus, it serves as a useful tool in enhancing the quality and impact of research communication.Originality/valueThis paper presents a unique approach to structuring academic publications that goes beyond the conventional IMRAD model. By offering a theory-based structural model, it contributes to an underexplored area in academic writing and opens up new avenues for pedagogy and practice in research communication.