Publikační činnost IT4Innovations / Publications of IT4Innovations (9600)

Permanent URI for this collectionhttp://hdl.handle.net/10084/96109

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Now showing 1 - 20 out of 841 results

Unveiling solitons and dynamic patterns for a (3+1)-dimensional model describing nonlinear wave motion
(AIMS Press, 2024) Riaz, Muhammad Bilal; Kazmi, Syeda Sarwat; Jhangeer, Adil; Martinovič, Jan
In this study, the underlying traits of the new wave equation in extended (3 +1) dimensions, utilized in the field of plasma physics and fluids to comprehend nonlinear wave scenarios in various physical systems, were explored. Furthermore, this investigation enhanced comprehension of the characteristics of nonlinear waves present in seas and oceans. The analytical solutions of models under consideration were retrieved using the sub -equation approach and Sardar sub -equation approach. A diverse range of solitons, including bright, dark, combined dark -bright, and periodic singular solitons, was made available through the proposed methods. These solutions were illustrated through visual depictions utilizing 2D, 3D, and density plots with carefully chosen parameters. Subsequently, an analysis of the dynamical nature of the model was undertaken, encompassing various aspects such as bifurcation, chaos, and sensitivity. Bifurcation analysis was conducted via phase portraits at critical points, revealing the system's transition dynamics. Introducing an external periodic force induced chaotic phenomena in the dynamical system, which were visualized through time plots, twodimensional plots, three-dimensional plots, and the presentation of Lyapunov exponents. Furthermore, the sensitivity analysis of the investigated model was executed utilizing the Runge-Kutta method. The obtained findings indicated the e fficacy of the presented approaches for analyzing phase portraits and solitons over a wider range of nonlinear systems.
HyperQueue: Efficient and ergonomic task graphs on HPC clusters
(Elsevier, 2024) Beránek, Jakub; Böhm, Ada; Palermo, Gianluca; Martinovič, Jan; Jansík, Branislav
Task graphs are a popular method for defining complex scientific simulations and experiments that run on distributed and HPC (High-performance computing) clusters, because they allow their authors to focus on the problem domain, instead of low-level communication between nodes, and also enable quick prototyping. However, executing task graphs on HPC clusters can be problematic in the presence of allocation managers like PBS or Slurm, which are not designed for executing a large number of potentially short-lived tasks with dependencies. To make task graph execution on HPC clusters more efficient and ergonomic, we have created HYPERQUEUE, an open-source task graph execution runtime tailored for HPC use-cases. It enables the execution of large task graphs on top of an allocation manager by aggregating tasks into a smaller amount of PBS/Slurm allocations and dynamically load balances tasks amongst all available nodes. It can also automatically submit allocations on behalf of the user, it supports arbitrary task resource requirements and heterogeneous HPC clusters, it is trivial to deploy and does not require elevated privileges.
Controlling on-surface photoactivity: The impact of π-conjugation in anhydride-functionalized molecules on a semiconductor surface
(Wiley, 2024) Frezza, Federico; Sánchez-Grande, Ana; Canola, Sofia; Lamancová, Anna; Mutombo, Pingo; Chen, Qifan; Wäckerlin, Christian; Ernst, Karl-Heinz; Muntwiler, Matthias; Zema, Nicola; Di Giovannantonio, Marco; Nachtigallová, Dana; Jelínek, Pavel
On-surface synthesis has become a prominent method for growing low-dimensional carbon-based nanomaterials on metal surfaces. However, the necessity of decoupling organic nanostructures from metal substrates to exploit their properties requires either transfer methods or new strategies to perform reactions directly on inert surfaces. The use of on-surface light-induced reactions directly on semiconductor/insulating surfaces represents an alternative approach to address these challenges. Here, exploring the photochemical activity of different organic molecules on a SnSe semiconductor surface under ultra-high vacuum, we present a novel on-surface light-induced reaction. The selective photodissociation of the anhydride group is observed, releasing CO and CO2. Moreover, we rationalize the relationship between the photochemical activity and the π-conjugation of the molecular core. The different experimental behaviour of two model anhydrides was elucidated by theoretical calculations, showing how the molecular structure influences the distribution of the excited states. Our findings open new pathways for on-surface synthesis directly on technologically relevant substrates.
Reliable analysis for obtaining exact soliton solutions of (2+1)-dimensional Chaffee-Infante equation
(AIMS Press, 2024) Iqbal, Naveed; Riaz, Muhammad Bilal; Alesemi, Meshari; Hassan, Taher S.; Mahnashi, Ali M.; Shafee, Ahmad
The (2 + 1) -dimensional Cha ff ee -Infante equation (CIE) is a significant model of the ionacoustic waves in plasma. The primary objective of this paper was to establish and examine closedform soliton solutions to the CIE using the modified extended direct algebraic method (m -EDAM), a mathematical technique. By using a variable transformation to convert CIE into a nonlinear ordinary di ff erential equation (NODE), which was then reduced to a system of nonlinear algebraic equations with the assumption of a closed -form solution, the strategic m -EDAM was implemented. When the resulting problem was solved using the Maple tool, many soliton solutions in the shapes of rational, exponential, trigonometric, and hyperbolic functions were produced. By using illustrated 3D and density plots to evaluate several soliton solutions for the provided definite values of the parameters, it was possible to determine if the soliton solutions produced for CIE are cuspon or kink solitons. Additionally, it has been shown that the m -EDAM is a robust, useful, and user-friendly instrument that provides extra generic wave solutions for nonlinear models in mathematical physics and engineering.
Artificial neural network with Levenberg-Marquardt training algorithm for heat transfer analysis of Ag-TiO2/water hybrid nanofluid flow between two parallel rotating disks
(Ram Arti Publishers, 2024) Yaseen, Moh; Rawat, Sawan Kumar; Tyagi, Honey; Pant, Manish; Mishra, Ashish; Shafiq, Anum; Ujarari, Chandan Singh
The authors have investigated the axisymmetric and three-dimensional, steady, incompressible, and bioconvective flow of AgTiO 2 /water hybrid nanofluid between two infinite and parallel rotating disks. Practical uses of flows between two rotating disks include brake systems in vehicles, engines, disks in computers, atomizers, rotating air cleaners, gas turbines, and evaporators. This study was conducted within a Darcy-Forchheimer porous medium and considered the impact of a magnetic field, heat source, and thermal radiation. The governing mathematical equations are transformed into coupled and nonlinear ordinary differential equations through similarity transformations. Subsequently, these equations are numerically solved using MATLAB's built-in function "bvp4c". A multilayer perceptron based artificial neural network (ANN) model has been formulated to predict the Nusselt number (heat transfer rate) on both the lower and upper surfaces of the disk. The model utilizes the Levenberg-Marquardt training algorithm, renowned for its exceptional learning capability, as the training method for the ANN. Moreover, the authors generated a dataset consisting of 84 data points for each case using numerical methods to construct the proposed Multilayer Perceptron Artificial Neural Network. The computed mean squared error values for the developed ANN model, targeting Nusselt number predictions, were found to be 2x10 -6 , 5x10 -6 , 9x10 -6 , and 3x10 - 6. Additionally, the regression ( R 2 ) values, serving as an additional performance parameter, were determined as 0.999317, 0.997672, 0.999963, and 0.999840, respectively. A comprehensive assessment of these outcomes, strongly affirms that the ANN model has been crafted with a high degree of accuracy for predicting Nusselt numbers.
A statistical framework for a new Kavya-Manoharan Bilal distribution using ranked set sampling and simple random sampling
(Elsevier, 2024) Shafiq, Anum; Sindhu, Tabassum Naz; Riaz, Muhammad Bilal; Hassan, Marwa K. H.; Abushal, Tahani A.
In survival and stochastic lifespan modeling, numerous families of distributions are sometimes considered unnatural, unjustifiable theoretically, and occasionally superfluous. Here, a novel parsimonious survival model is developed using the Bilal distribution (BD) and the KavyaManoharan (KM) parsimonious transformation family. In addition to other analytical properties, the forms of probability density function (PDF) and behavior of the distributions ' hazard rates are analyzed. The insights are theoretical as well as practical. Theoretically, we offer explicit equations for the single and product moments of order statistics from Kavya-Manoharan Bilal Distribution. Practically, maximum likelihood (ML) technique, which is based on simple random sampling (SRS) and ranked set sampling (RSS) sample schemes, is employed to estimate the parameters. Numerical simulations are used as the primary methodology to compare the various sampling techniques.
A study of self-adjointness, Lie analysis, wave structures, and conservation laws of the completely generalized shallow water equation
(Springer Nature, 2024) Ansari, Ali R.; Jhangeer, Adil; Imran, Mudassar; Beenish; Inc, Mustafa
This article explores the analysis of the completely generalized Hirota–Satsuma–Ito equation through Lie symmetry analysis. The equation under consideration represents a more comprehensive form of the (2+1)-dimensional HSI equation, encom passing four additional second-order derivative terms: 3H , 4H ι, 3H , 4H ι,and 6Hιι,emergingfromtheinclusion of second-order dissipative-type elements. We calculate the infinitesimal generators and determine the symmetry group for each generatorusingtheLiegroupinvariancecondition.EmployingtheconjugacyclassesoftheAbelianalgebra,wetransformtheconsid ered equation into an ordinary differential equation through similarity reduction. Subsequently, we solve these ordinary differential equations to derive closed-form solutions for the completely generalized Hirota–Satsuma–Ito equation under certain conditions. For other scenarios, we utilize the extended direct algebraic method to obtain soliton solutions. Furthermore, we rigorously calculated the conserved quantities corresponding to each symmetry generator, the conservation laws of the model are established using the multiplier approach. Additionally, we present the graphical representation of selected solutions for specific values of the physical parameters of the equation under scrutiny.
AggreProt: a web server for predicting and engineering aggregation prone regions in proteins
(Oxford University Press, 2024) Planas-Iglesias, Joan; Borko, Simeon; Swiatkowski, Jan; Eliáš, Matěj; Havlásek, Martin; Salamon, Ondřej; Grakova, Ekaterina; Kunka, Antonín; Martinovič, Tomáš; Damborský, Jiří; Martinovič, Jan; Bednář, David
Recombinant proteins play pivotal roles in numerous applications including industrial biocatalysts or therapeutics. Despite the recent progress in computational protein structure prediction, protein solubility and reduced aggregation propensity remain challenging attributes to design. Identification of aggregation-prone regions is essential for understanding misfolding diseases or designing efficient protein-based technologies, and as such has a great socio-economic impact. Here, we introduce AggreProt, a user-friendly webserver that automatically exploits an ensemble of deep neural networks to predict aggregation-prone regions (APRs) in protein sequences. Trained on experimentally evaluated hexapeptides, AggreProt compares to or outperforms state-of-the-art algorithms on two independent benchmark datasets. The server provides per-residue aggregation profiles along with information on solvent accessibility and transmembrane propensity within an intuitive interface with interactive sequence and structure viewers for comprehensive analysis. We demonstrate AggreProt efficacy in predicting differential aggregation behaviours in proteins on several use cases, which emphasize its potential for guiding protein engineering strategies towards decreased aggregation propensity and improved solubility. The webserver is freely available and accessible at https://loschmidt.chemi.muni.cz/aggreprot/.
Lie symmetry analysis, and traveling wave patterns arising the model of transmission lines
(AIMS Press, 2024) Jhangeer, Adil; Ansari, Ali R.; Imran, Mudassar; Beenish; Riaz, Muhammad Bilal
This work studies the behavior of electrical signals in resonant tunneling diodes through the application of the Lonngren wave equation. Utilizing the method of Lie symmetries, we have identified optimal systems and found symmetry reductions; we have also found soliton wave solutions by applying the tanh technique. The bifurcation and Galilean transformation are found to determine the model implications and convert the system into a planar dynamical system. In this experiment, the equilibrium state, sensitivity, and chaos are investigated and numerical simulations are conducted to show how the frequency and amplitude of alterations affect the system. Furthermore, local conservation rules are demonstrated in more detail to unveil the whole system of movements.
Unraveling the transformative impact of ternary hybrid nanoparticles on overlapped stenosis with electroosmotic vascular flow kinetics and heat transfer
(Elsevier, 2024) Hussain, Azad; Riaz, Muhammad Bilal; Dar, Muhammad Naveel Riaz; Cheema, Warda Khalid; Shflot, A. S.; Malik, M. Y.
This study examines how ternary hybrid nanoparticles affect electroosmotic vascular flow kinetics and heat transfer. Through a meticulous exploration of their intricate interplay, this research unveils unprecedented insights into their transformative impact. By comprehensively analyzing the dynamics of vascular flow and thermal behavior under the influence of ternary hybrid nanoparticles, novel advancements are revealed. The assessment is innovative because it incorporates electroosmotic force on blood flow that contains three different nanoparticles (Ti O 2 , Al 2 O 3 ) and Si O 2 . To evaluate the numerical solution, an unraveled approach using the finite element method is employed, ensuring both stability and convergence of the solution. The computed numerical results are presented in graphs and tables, showcasing the relationship between key factors. The comparative analysis uncovers the unparalleled performance and remarkable efficacy of these nanoparticles in enhancing the electroosmotic vascular flow and optimizing heat transfer. The electric field due to the electroosmosis flow interacts with flow pattern and influence the potential flow and vortex formation. This research presents a paradigm shift in the understanding of biomedical engineering and fluid dynamics, offering promising prospects for revolutionizing healthcare technologies and achieving unprecedented levels of thermal management efficiency across diverse applications.
Optimization of micro-rotation effect on magnetohydrodynamic nanofluid flow with artificial neural network
(Wiley, 2024) Shafiq, Anum; Çolak, Andaç Batur; Sindhu, Tabassum Naz
It is a major research area in mathematics, physics, engineering, and computer science to study the heat and mass transfer properties of flow. Suspensions containing multiple nanoparticles or nanocomposites have recently gained a wide range of applications in biological research and clinical trials under certain conditions. Nanofluids are important suspensions that allow nanoparticles to disseminate and behave in a homogeneous and stable environment. Therefore, here magnetohydrodynamic micropolar nanofluid flow towards the stretching surface with artificial neural network has been considered. In this study, radiation and heat source phenomena have been presented in heat convection. Brownian and thermophoresis effects and micro-rotational particles are also taking into account. The non-linear simplified equations have been calculated numerically via Runge-Kutta fourth-order shooting process. The calculation of the Sherwood number, Nusselt number, couple stress coefficient, and skin friction coefficient has been conducted utilizing diverse parameters. Furthermore, the outcomes have been employed to create four distinct artificial neural networks. Our observation indicates that an increase in the heat source quantity leads to a rise in heat generation, resulting in a greater total heat output and an increase in the temperature field. Coefficient of determination “R” values higher than 0.99 have been obtained for the artificial neural network models. The obtained findings have shown that artificial neural networks can predict thermal parameters with high accuracy.
Evaluating energy transmission characteristics of Non-Newtonian fluid flow in stratified and non-stratified regimes: A comparative study
(Elsevier, 2024) Bilal, S.; Asadullah; Riaz, Muhammad Bilal
Considering the natural and industrial importance of flow characterization in stratified media, the current study is articulated. This work highlights the influence of linear stratification as well as convective surfaces in both thermal and solutal fields on the rheological attributes of Williamson fluid flow through an inclined surface. Novel physical aspects of a uniformly provided magnetic field of strength B and chemically reactive species are also included. The concerned transport equations are derived from the associated conservation laws in dimensional forms. Modification in the developed couple system is achieved by using a set of similar variables. Levenberg-Marquardt Scheme (LMS) and Bayesian Regularization Scheme (BRS) are utilized in comparative manner to analyze initial data accessed for quantities of interest. The data used in the generation of MLP was 80 percent for model training and 20 percent for testing and validation. Error histograms, performance plots, fitness curves, and regression plots for training, testing, and validation are presented. Data in the form of tables and graphs are presented, which express an excellent match between the ANN-predicted and targeted values. It is revealed that an artificial neural network approach can provide highly efficient forecasting for such problems by providing accurate data for quantities of interest. It is noticed that Nusselt number and Sherwood number enhances up to 33 % and 29 % versus respective stratification parameters. Velocity profile declines against magnetic field parameter (M) whereas, skin friction coefficient increments up to 25 %. Appliance of convective boundary constraints at the surface of inclined sheet tends to enhance the temperature and concentration fields.
Exploring travelling wave solutions, bifurcation, chaos, and sensitivity analysis in the (3+1)-dimensional gKdV-ZK model: A comprehensive study using Lie symmetry methodology
(Elsevier, 2024) Jhangeer, Adil; Jamal, Tahira; Talafah, Abdallah M.; Riaz, Muhammad Bilal
This article presents a study on the generalized Korteweg-de Vries-Zakharov-Kuznetsov (gKdV-ZK) model, which is a nonlinear system that demonstrates the effect of magnetic fields on weak ion-acoustic waves in plasma consisting of cold and hot electrons. The research entails investigating the reduction of symmetry through Lie group analysis, scrutinizing the characteristics of the dynamic structure using bifurcation phase diagrams, and examining the dynamic behaviour of the perturbed dynamical system employing chaos theory. Methods such as 3D and 2D phase portraits, time series analysis, Poincar & eacute; maps, exploration of multistability in the autonomous structure across various initial conditions, Lyapunov exponents, and bifurcation diagrams are exercised to demonstrate chaotic behaviour. Additionally, the research establishes general forms of solitary wave solutions, encompassing hyperbolic, trigonometric, and rational soliton solutions, through the utilization of a modified auxiliary equation approach to analytically address the examined problem. These findings are visually depicted as 2D and 3D graphs with carefully selected parameters, accompanied by their corresponding constraint conditions. Furthermore, the sensitivity analysis of the studied equation is deliberated upon and visually illustrated. The uncovered findings are captivating, innovative, and potentially beneficial for comprehending various physical phenomena in engineering and science.
On favorable bounds on the spectrum of discretized Steklov-Poincaré operator and applications to domain decomposition methods in 2D
(Elsevier, 2024) Vodstrčil, Petr; Lukáš, Dalibor; Dostál, Zdeněk; Sadowská, Marie; Horák, David; Vlach, Oldřich; Bouchala, Jiří; Kružík, Jakub
The efficiency of numerical solvers of PDEs depends on the approximation properties of the discretization methods and the conditioning of the resulting linear systems. If applicable, the boundary element methods typically provide better approximation with unknowns limited to the boundary than the Schur complement of the finite element stiffness matrix with respect to the interior variables. Since both matrices correctly approximate the same object, the Steklov-Poincar & eacute; operator, it is natural to assume that the matrices corresponding to the same fine boundary discretization are similar. However, this note shows that the distribution of the spectrum of the boundary element stiffness matrix is significantly better conditioned than the finite element Schur complement. The effect of the favorable conditioning of BETI clusters is demonstrated by solving huge problems by H-TBETI-DP and H-TFETI-DP.
Symmetry and complexity: a Lie symmetry method to bifurcation, chaos, multistability and soliton solutions of the nonlinear generalized advection-diffusion-reaction equation
(IOP Publishing, 2024) Samina, Samina; Jhangeer, Adil; Chen, Zili
This paper deals with the complexities of nonlinear dynamics within the nonlinear generalized advection-diffusion-reaction equation, which describes intricate transport phenomena involving advection, diffusion, and reaction processes occurring simultaneously. Through the utilization of the Lie symmetry approach, we thoroughly examine this proposed model, transforming the partial differential equation into an ordinary differential equation using similarity reduction techniques to facilitate a more comprehensive analysis. Exact solutions for this transformed equation are derived employing the extended simplest equation method and the new extended direct algebraic method. To enhance understanding, contour plots along with 2D and 3D visualizations of solutions are employed. Additionally, we explore bifurcation and chaotic behaviors through a qualitative analysis of the model. Phase portraits are meticulously scrutinized across various parameter values, offering insights into system behavior. The introduction of an external periodic strength allows us to utilize various tools including time series, 3D, and 2D phase patterns to discern chaotic and quasi-periodic behaviors. Furthermore, a multistability analysis is conducted to examine the impacts of diverse initial conditions. These findings underscore the efficacy and practicality of the proposed methodologies in evaluating soliton solutions and elucidating phase dynamics across a spectrum of nonlinear models, offering novel perspectives on intricate physical phenomena.
Impact of windfall tax on market dynamics: A Cournot oligopoly model with exogenous shocks
(Elsevier, 2024) Nálepová, Veronika; Lampart, Marek
This study explores the nuanced impact of windfall taxes on market equilibrium, introducing an innovative approach within the Cournot oligopoly framework. The paper uses the 0–1 test for chaos to dissect how profit taxation can stabilize market behaviors under bounded rationality. It suggests that higher taxes may prevent collusion, thereby promoting a more competitive environment. The paper demonstrates that while windfall taxes leave regular markets almost unaffected, they can protect firms in chaotic states from adverse outcomes. This research underscores the necessity for policymakers to tailor windfall tax strategies to specific market conditions, potentially driving enhanced market efficiency. Our insights advocate for the judicious application of windfall taxes, which could significantly shape future economic policies.
Unveiling multi-wave patterns: dynamic characterization and sensitivity analysis of the Yu-Toda-Sasa-Fukuyama model in lattice and liquid
(IOP Publishing, 2024) Riaz, Muhammad Bilal; Kazmi, Syeda Sarwat; Jhangeer, Adil
In this study, an examination of the Yu-Toda-Sasa-Fukuyama equation is undertaken, a model that characterizes elastic waves in a lattice or interfacial waves in a two layer liquid. Our emphasis lies in conducting a comprehensive analysis of this equation through various viewpoints, including the examination of soliton dynamics, exploration of bifurcation patterns, investigation of chaotic phenomena, and a thorough evaluation of the model's sensitivity. Utilizing a simplified version of Hirota's approach, multi-soliton pattens, including 1-wave, 2-wave, and 3-wave solitons, are successfully derived. The identified solutions are depicted visually via 3D, 2D, and contour plots using Mathematica software. The dynamic behavior of the discussed equation is explored through the theory of bifurcation and chaos, with phase diagrams of bifurcation observed at the fixed points of a planar system. Introducing a perturbed force to the dynamical system, periodic, quasi-periodic and chaotic patterns are identified using the RK4 method. The chaotic nature of perturbed system is discussed through Lyapunov exponent analysis. Sensitivity and multistability analysis are conducted, considering various initial conditions. The results acquired emphasize the efficacy of the methodologies used in evaluating solitons and phase plots across a broader spectrum of nonlinear models.
Some new characterizations of boundedness of commutators of p-adic maximal-type functions on p-adic Morrey spaces in terms of Lipschitz spaces
(AIMS Press, 2024) Sarfraz, Naqash; Riaz, Muhammad Bilal; Malik, Qasim Ali
In this note, we investigate some new characterizations of the p-adic version of Lipschitz spaces via the boundedness of commutators of the p-adic maximal -type functions, including padic sharp maximal functions, p-adic fractional maximal functions, and p-adic fractional maximal commutators on p-adic Morrey spaces, when a symbol function b belongs to the Lipschitz spaces.
Federated learning for privacy-preserving intrusion detection in software-defined networks
(IEEE, 2024) Raza, Mubashar; Saeed, Muhammad Jasim; Riaz, Muhammad Bilal; Sattar, Muhammad Awais
Software-defined networking (SDN) is an innovative network technology. It changed the world of computer networking by providing solutions to many challenges. SDN provides programmability, easy and centralized network management, dynamic configuration, and improved security. Although SDN offers remarkable benefits but it provides centralized network management which is prone to attacks. So, intrusion detection systems (IDS) are essential to detect and prevent security attacks in SDN. Traditional IDS follow a centralized machine learning approach which causes vulnerabilities in IDS. Old-style IDS lack data privacy preservation, and solution for training data unavailability due to privacy. Federated learning (FL) is a distributed machine learning approach which provides a collaborative training approach without data sharing. In FL, training is performed on multiple nodes creating a global model without sharing the data. ToaddresschallengesandthelimitationsoftraditionalIDS,weproposedaFLbasedmulticlassclassification IDS for SDN. FL delivers an efficient and scalable solution to address challenges of traditional IDS. The proposed model enhances security of SDN by not requiring the centralization of data. To test the impact and efficiency of proposed model, we used a latest and realistic cybersecurity dataset. We also compared the proposed model with state of art existing multi class classification studies. The results and their comparison with existing studies highlight the potential of proposed model to enhance network security while providing a privacy-preserving learning environment for intrusion detection.
On 14-regular distance magic graphs
(Institut Teknologi Bandung, 2024) Kovář, Petr; Krbeček, Matěj
Let G be a graph with n vertices. By N(v) we denote the set of all vertices adjacent to v. A bijection f : V(G) -> {1, 2, ... , n} is a distance magic labeling of G if there exists an integer k such that the sum of labels of all vertices adjacent to v is k for all vertices v in V(G). A graph which admits a distance magic labeling is a distance magic graph. In this paper, we completely characterize all orders for which a 14 -regular distance magic graph exists. Hereby we extended similar results on 2-, 4-, 6-, 8-, 10-, and 12 -regular distance magic graphs.

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