AppliedMath, Volume 5, Issue 1 (March 2025) – 31 articles

Two classes of series involving differences of harmonic numbers and the binomial coefficients $C(3n,n)$ are evaluated in closed form. The classes under consideration are ${\sum }_{k=0}^{\infty }{\displaystyle \frac{H_{3k+1}-H_k}{(3k+1)\left(\genfrac{}{}{0pt}{}{3k}{k}\right)}}\left({\displaystyle \genfrac{}{}{0pt}{}{k}{m}}\right)z^k\mathrm{and}{\sum }_{k=0}^{\infty }{\displaystyle \frac{H_{2k}-H_k}{(3k+1)\left(\genfrac{}{}{0pt}{}{3k}{k}\right)}}\left({\displaystyle \genfrac{}{}{0pt}{}{k}{m}}\right)z^k,$ where z is a complex number and m (a non-negative integer) is an additional parameter. The tool that will be applied is integration in combination with complex analysis and partial fraction decomposition. Several remarkable integral values and difficult series identities are stated as special cases of the main results. Full article

We examine the modified Hill three-body problem by incorporating the oblateness of the primary body and focus on its asymptotic orbits. Specifically, we analyze and characterize homoclinic and heteroclinic connections associated with the collinear equilibrium points. By systematically varying the oblateness parameter, we determine conditions for the existence and location of these orbits. Our results confirm the presence of both homoclinic orbits, where trajectories asymptotically connect an equilibrium point to itself, and heteroclinic orbits, which establish connections between two distinct equilibrium points, via their stable and unstable invariant manifolds, which are computed both analytically and numerically. To achieve precise computations, we employ differential correction techniques and leverage the system’s inherent symmetries. Numerical calculations are carried out for orbit multiplicities up to twelve, ensuring a comprehensive exploration of the dynamical properties. Full article

In the context of holonomic systems, the identification of virtual displacements is clear and consolidated. This provides the possibility, once the class of displacements have been coupled with Newton’s equations, for us to write the correct equations of motion. This method combines the d’Alembert principle with Lagrange formalism. As far as nonholonomic systems are concerned, the conjecture that dates back to $\check{\mathrm{C}}$etaev actually defines a class of virtual displacements through which the d’Alembert–Lagrange method can be applied again. A great deal of literature is dedicated to the $\check{\mathrm{C}}$etaev rule from both the theoretical and experimental points of view. The absence of a rigorous (mathematical) validation of the rule inferable from the constraint equations has been declared to have expired in a recent publication; one of our objectives is to produce a critical comment on this stated result. Finally, we explore the role of the $\check{\mathrm{C}}$etaev condition within the significant class of nonholonomic homogeneous constraints. Full article

This work presents the Leal method for the approximation of integrals without known exact solutions, capable of multi-expanding simultaneously at different points. This method can be coupled with asymptotic approximations and the least squares method to extend the domain of convergence. The complete elliptic integral of the first kind, the Gamma function, and the error function are treated with this new method, resulting in highly accurate and easily computable approximations, exhibiting a wide region of convergence compared to other reported works. Finally, a comparison of computing time using Fortran between our proposals and other approximations from the literature is presented and discussed. Full article

Artificial neural networks have proven to be an important machine learning model that has been widely used in recent decades to tackle a number of difficult classification or data fitting problems within real-world areas. Due to their significance, several techniques have been developed to efficiently identify the parameter vectors for these models. These techniques usually come from the field of optimization and, by minimizing the training error of artificial neural networks, can estimate the vector of their parameters. However, these techniques often either get trapped in the local minima of a training error or lead to overfitting in the artificial neural network, resulting in poor performance when applied to data that were not present during the training process. This paper presents an innovative training technique for artificial neural networks based on the differential evolution optimization method. This new technique creates an initial population of artificial neural networks that evolve, as well as periodically applies a local optimization technique in order to accelerate the training of these networks. The application of the local minimization technique was performed in such a way as to avoid the phenomenon of overfitting. This new method was successfully applied to a series of classification and data fitting problems, and a comparative study was conducted with other training techniques from the relevant literature. Full article

Technical systems, which form the basis of modern technology, are structures designed to achieve a specific purpose by bringing together different components. In this respect, they have a wide field of study. Our study is aimed at the general evaluation of technical systems operating under stress. The reliability of technical systems is directly related to order statistics. Therefore, first of all, when the moment of failure is observed, a life time distribution is proposed, which is revised at each moment of failure. Secondly, a new expected value operator is proposed. Thanks to this operator, the average working time under stress can be calculated easily without deforming the working time distribution. Finally, the differential structure of the stress factor is examined in detail, and two different differential equations and solutions are proposed depending on the working time distribution. The numerical calculations presented in the study include detailed information on the applications of the proposed methods. Full article

This paper presents a method for hedging in markets of two-factor diffusion and jump diffusion models under the restriction of a specified probability of success. In addition, a method for hedging with a given shortfall amount is developed. A maximal perfect hedging set is constructed for options involving the exchange of one asset for another. The developed method is applied to the pricing of equity-linked life insurance contracts, such as “pure endowments with a guarantee”. Traditional pricing approaches for hedging options often yield minimal returns for investors. By accepting a predefined level of risk, investors can achieve higher returns. In light of this, this paper proposes risk management strategies applicable to these hybrid financial and insurance products. Full article

We compare, mathematically, the text of a famous Italian novel, I promessi sposi, written by Alessandro Manzoni (source text), to its most recent English translation, The Betrothed by Michael F. Moore (target text). The mathematical theory applied does not measure the efficacy and beauty of texts; only their mathematical underlying structure and similarity. The translation theory adopted by the translator is the “domestication” of the source text because English is not as economical in its use of subject pronouns as Italian. A domestication index measures the degree of domestication. The modification of the original mathematical structure produces several consequences on the short–term memory buffers required for the reader and on the theoretical number of patterns used to construct sentences. The geometrical representation of texts and the related probability of error indicate that the two texts are practically uncorrelated. A fine–tuning analysis shows that linguistic channels are very noisy, with very poor signal–to–noise ratios, except the channels related to characters and words. Readability indices are also diverse. In conclusion, a blind comparison of the linguistic parameters of the two texts would unlikely indicate they refer to the same novel. Full article

There has been considerable debate about whether contemporary Western societies are experiencing an increase in narcissistic tendencies, often referred to as a “narcissism epidemic”. This rise highlights the importance of understanding the origins of narcissism, particularly regarding its potential association with parenting styles. Such insights can inform treatment approaches and contribute to paradigm shifts in developmental psychology. This systematic review and meta-analysis examine how different parenting styles are associated with the development of narcissistic traits, using both partial and zero-order correlations as measures of effect. To ensure a consistent conceptualization of parenting styles, the results were evaluated using Baumrind’s parental styles typology. The review follows PRISMA guidelines and is registered in PROSPERO (CRD42024516395). Studies published in English or Portuguese since 2000 were sourced from PubMed (1039 articles) and Scopus (2120 articles), resulting in a final sample of 53 studies across 38 articles. Data synthesis included assessment of statistical heterogeneity (${\mathrm{I}}^2$ statistic), publication bias (funnel plots, Egger’s test, and the trim and fill method), and methodological quality (adapted Newcastle–Ottawa Scale, NOS). Additionally, sensitivity analyses were conducted to evaluate the effect of excluding studies scoring below eight on the NOS by comparing results from analyses with all studies versus high-quality studies only. Results indicate a significant, albeit weak, association between parenting styles and narcissistic traits, with notable variations between maternal and paternal influences. This analysis provides a comprehensive perspective on the interplay between parenting approaches and the emergence of narcissistic characteristics, underscoring the complexity of factors that contribute to narcissism in contemporary society. Full article

In this article, we analyze some curvature restrictions satisfying by the concircular curvature tensor in $(2n+1)$-dimensional Sasakian manifolds with the generalized Tanaka–Webster connection $\overline{\nabla }$ admitting Ricci–Yamabe solitons. Finally, we give an example of three-dimensional Sasakian manifolds which verifies some of our findings. Full article

Based on a recent representation of the psi function due to Guillera and Sondow and independently Boyadzhiev, new closed forms for various series involving harmonic numbers and inverse factorials are derived. A high point of the presentation is the rediscovery, by much simpler means, of a famous quadratic Euler sum originally discovered in 1995 by Borwein and Borwein. In addition, the following series ${\sum }_{n=1}^{\infty }{\displaystyle \frac{1}{n(n+1)\left(\genfrac{}{}{0pt}{}{n+z}{n}\right)}},{\sum }_{n=1}^{\infty }{\displaystyle \frac{1}{n(n+1)(n+2)\left(\genfrac{}{}{0pt}{}{n+z}{n}\right)}},{\sum }_{n=1}^{\infty }{\displaystyle \frac{1}{n(n+1)(n+2)(n+3)\left(\genfrac{}{}{0pt}{}{n+z}{n}\right)}}$, as well as the harmonic and odd harmonic number series associated with them are evaluated. Full article

The study of contagion dynamics is a well-established domain within epidemiology, where the spread of infectious diseases is modeled and analyzed. In recent years, similar methodologies have been applied to the financial sector to understand and predict the propagation of risks within banking systems better. This paper examines the application of contagion models to assessing liquidity risk in the banking sector, leveraging optimal control theory to evaluate potential interventions by central banks. Using data from the largest European banks, we simulate the impact of central bank measures on liquidity risk. By employing optimal control techniques, we construct a model capable of simulating various scenarios to evaluate the effectiveness of policy interventions in mitigating financial contagion. Our approach provides a robust framework for analyzing the systemic risk propagation within the banking network, offering qualitative insights into the contagion mechanisms and their implications for the financial and macroeconomic landscape. The model simulates three distinct scenarios, with each representing varying levels of intervention and market conditions. The results demonstrate the model’s ability to capture the intricate interactions among major European banks, reflecting the complex realities of the financial system. These findings emphasize the critical role of central bank policies in maintaining financial stability and underscore the necessity of coordinated international efforts to manage systemic risks. This analysis contributes to a broader understanding of financial contagion, offering valuable insights for policymakers and financial institutions aiming to strengthen their resilience against future crises. The data used for the parameters are historical, which may not reflect recent changes in the banking system. The model could also be improved by incorporating non-financial factors, such as the behaviors of market actors. For future research, several improvements are possible. One improvement would be to make the bank interactions more dynamic to reflect rapid market changes better. It would also be interesting to add financial crisis scenarios to test the system’s resilience. Using more up-to-date data and incorporating new regulations would help refine the model. Finally, it would be relevant to examine the impact of external events, such as geopolitical crises, on the propagation of systemic risk. In conclusion, while the model is useful, there are several avenues for improving it and making it more suitable for our current realities. Full article

This article focuses on both classical and Bayesian inference of traffic intensity in a single-server Markovian queueing model considering balking. To reflect real-world situations, the article introduces the concept of balking, where customers opt not to join the queue due to the perceived waiting time. The essence of this article involves a comprehensive analysis of different loss functions, namely, the squared error loss function (SELF) and the precautionary loss function (PLF), on the accuracy of the Bayesian estimation. To evaluate the performance of the Bayesian method with various priors such as inverted beta, gamma, and Jeffreys distributions, an assessment is performed using the Markov Chain Monte Carlo (MCMC) simulation technique. The efficacy of the Bayesian estimators is assessed by comparing the mean squared errors (MSEs). Full article

The modeling of the one-dimensional wave equation is the fundamental model for characterizing the behavior of vibrating strings in different physical systems. In this work, we investigate numerical solutions for the one-dimensional wave equation employing both explicit and implicit finite difference schemes. To evaluate the correctness of our numerical schemes, we perform extensive error analysis looking at the $L^1$ norm of error and relative error. We conduct thorough convergence tests as we refine the discretization resolutions to ensure that the solutions converge in the correct order of accuracy to the exact analytical solution. Using the von Neumann approach, the stability of the numerical schemes are carefully investigated so that both explicit and implicit schemes maintain the stability criteria over simulations. We test the accuracy of our numerical schemes and present a few examples. We compare the solution with the well-known spectral and finite element method. We also show theoretical proof of the stability and convergence of our numerical scheme. Full article

This study investigates M/M/n:(m/FIFO) systems with a limited queue capacity (incorporating both “waiting and rejection”). This category of systems can be considered to be mixed-service systems. They operate as queuing systems for customers admitted to the system awaiting service, as well as systems that implement rejection or loss for customers who are denied when the system is full (when all servers and the buffer capacity are occupied). The correlation between the system size and a set of performance measures is analysed for the given arrival and service rates. The system size is determined based on a threshold rate of rejected customers. The correlation between the buffer size and the utilisation factor has direct relevance in the design of real systems (e.g., when the dynamics of the arrival rate can be estimated, it provides a solution for phasing the building of physical waiting places for a specific service capacity). In addition, the analysis of customer rejection probability and average waiting time as a function of the effective utilisation factor could yield practical insights for designing and operating real systems. The second part of this study presents a model for optimising the size of a multi-server system with a finite queue capacity. Initially, the number of servers is determined, assuming that the existing situation does not allow for an increase in the buffer capacity. Then, the case in which both server and buffer capacities become decision variables is presented. The operating losses (which are more straightforward to measure than the related costs) are used as an optimisation criterion. Full article

Among the many (mostly randomized) models proposed in the last decades to study how opinions of a set of individuals interconnected by pairwise relations evolve, a novel deterministic model is introduced in this paper that is able to encompass individual choices, strength and sign of relations, and asynchronism. In particular, asynchronism has been considered until now only in randomized settings. It is here studied in which cases the behavior of the resulting dynamical network is predictable, that is, in which cases the number of opinion configurations encountered by the set of individuals before the dynamical network enters a loop is polynomially bounded by the network size. Full article

An efficient linearization method for solving a system of nonlinear equations was developed, showing good stability and convergence properties. It uses an unconventional and simple strategy to improve the performance of classic methods by a full-rank update of the Jacobian approximates. It can be considered both as a discretized Newton’s method or as a quasi-Newton method with a full-rank update of the Jacobian approximates. A solution to the secant equation presented earlier was based on the Wolfe-Popper procedure. The secant equation was splitted into two equations by introducing an auxiliary variable. A simplified algorithm is given in this paper for the full-rank update procedure.It directly solves the secant equation with the pseudoinverse of the Jacobian approximate matrix. Numerical examples are shown for demonstration purposes. The convergence and efficiency of the suggested method are discussed and compared with the convergence and efficiency of classic linearization methods. Full article

The final goal of this paper is to organize the tools needed to study digital Quantum Communications, where classical information is entrusted to quantum states represented by density operators. A density operator is usually defined starting from a set of kets in the Hilbert space and a probability distribution. A fundamental problem in Quantum Communications is the factorization of such operators of the form $\rho =\gamma {\gamma }^{*}$, where $\gamma$ is a matrix called a density factor (DF). The environments considered are finite dimensional Hilbert space (discrete variables) and infinite dimensional Hilbert space (continuous variables). Using discrete variables, the multiplicity and the variety of DFs are investigated using the tools of matrix analysis, arriving in particular to establish the DF with minimal size. With continuous variables, the target is the closed-form factorization, which is achieved with recent results for the important class of Gaussian states. Finally, an application is carried out in Quantum Communications with noisy Gaussian states. Full article

Imaginary coquaternions cℍ can be represented by matrices of negative feedback $N^{-}$, positive feedback $P^{+}$, and reciprocal links $R^{\pm }$. An added environmental element $E^{\pm }$ endows biologic systems with the structure of cℍ module. Although cℍ representation links base patterns with the geometric structure of the pseudo-Euclidean ${\mathbb{R}}_2^4$ space, unknown physiologic aspects of relationships between base elements may add new functional features to the structure of a functional module. Another question is whether achieving and remaining in the equilibrium state provides stability for a biologic system. Considering the property of a biologic system to return deviated conditions to the equilibrium, the system of ordinary differential equations describing the behavior of a mechanical pendulum was modified and used as a basic tool to find the answers. The results obtained show that in evolving systems, the regulatory patterns are organized in a sequence $NPRN$ of base elements, allowing the system to perform a high amount of energy-consuming functions. In order to keep dissipating energy at the same level, the system bifurcates and finalizes its regulatory cycle in $R^{\pm }$ by splitting $P^{+}$ after which the next cycle may begin. Obtained flows are continuous pathways that do not interfere with equilibrium states, thus providing a homeostasis mechanism with nonequilibrium dynamics. Functional transformations reflect changes in the geometry and metric index of the coquaternion. Related coquaternion dynamics show the transformation of a hyperbolic hyperboloid into the closed surface, which is the fusion of the portions of the hyperbolic hyperboloid and two spheres. Full article

Diabetic retinopathy (DR) is a severe microvascular complication of diabetes that affects the eyes, leading to progressive damage to the retina and potential vision loss. Timely intervention and detection are crucial for preventing irreversible damage. With the advancement of technology, deep learning (DL) has emerged as a powerful tool in medical diagnostics, offering a promising solution for the early prediction of DR. This study compares four convolutional neural network architectures, DenseNet201, ResNet50, VGG19, and MobileNetV2, for predicting DR. The evaluation is based on both accuracy and training time data. MobileNetV2 outperforms other models, with a validation accuracy of 78.22%, and ResNet50 has the shortest training time (15.37 s). These findings emphasize the trade-off between model accuracy and computational efficiency, stressing MobileNetV2’s potential applicability for DR prediction due to its balance of high accuracy and a reasonable training time. Performing a 5-fold cross-validation with 100 repetitions, the ensemble of MobileNetV2 and a Graph Convolution Network exhibits a validation accuracy of 82.5%, significantly outperforming MobileNetV2 alone, which shows a 5-fold validation accuracy of 77.4%. This superior performance is further validated by the area under the receiver operating characteristic curve (ROC) metric, demonstrating the enhanced capability of the ensemble method in accurately detecting diabetic retinopathy. This suggests its competence in effectively classifying data and highlights its robustness across multiple validation scenarios. Moreover, the proposed clustering approach can find damaged locations in the retina using the developed Isolate Regions of Interest method, which achieves almost a 90% accuracy. These findings are useful for researchers and healthcare practitioners looking to investigate efficient and effective powerful models for predictive analytics to diagnose diabetic retinopathy. Full article

This article is dedicated to the construction of neural networks for the prediction of the current–voltage characteristic (CVC). CVC is the most important characteristic of the mass transfer process in electro-membrane systems (EMS). CVC is used to evaluate and select the optimal design and effective operating modes of EMS. Each calculation of the CVC at the given values of the input parameters, using developed analytical-numerical models, takes a lot of time, so the CVC is calculated in a limited range of parameter changes. The creation of neural networks allowed for the use of prediction to obtain the CVC for a wider range of input parameter values and much faster, saving computing resources. The regularities of the behavior of CVC for various values of input parameters were revealed. During this work, several different neural network architectures were developed and tested. The best predictive results on test samples are given by the neural network consisting of convolutional and LSTM (Long Short-Term Memory) layers. Full article

The intersection of fractals, non-Euclidean geometry, spatial autocorrelation, and urban structure offers valuable theoretical and practical application insights, which echoes the overarching goal of this paper. Its research question asks about connections between graph theory adjacency matrix eigenfunctions and certain non-Euclidean grid systems; its explorations reflect accompanying synergistic influences on modern urban design. A Minkowski metric with an exponent between one and two bridges Manhattan and Euclidean spaces, supplying an effective tool in these pursuits. This model coalesces with urban fractal dimensions, shedding light on network density and human activity compression. Unlike Euclidean geometry, which assumes unique shortest paths, Manhattan geometry better represents human movements that typically follow multiple equal-length network routes instead of unfettered straight-line paths. Applying these concepts to urban spatial models, like the Burgess concentric ring conceptualization, reinforces the need for fractal analyses in urban studies. Incorporating a fractal perspective into eigenvector methods, particularly those affiliated with spatial autocorrelation, provides a deeper understanding of urban structure and dynamics, enlightening scholars about city evolution and functions. This approach enhances geometric understanding of city layouts and human behavior, offering insights into urban planning, network density, and human activity flows. Blending theoretical and applied concepts renders a clearer picture of the complex patterns shaping urban spaces. Full article

Optimizing learning rates (LRs) in deep learning (DL) has long been challenging. Previous solutions, such as learning rate scheduling (LRS) and adaptive learning rate (ALR) algorithms like RMSProp and Adam, added complexity by introducing new hyperparameters, thereby increasing the cost of model training through expensive cross-validation experiments. These methods mainly focus on local gradient patterns, which may not be effective in scenarios with multiple local optima near the global optimum. A new technique called Learning Rate Tuner with Relative Adaptation (LRT-RA) is introduced to tackle these issues. This approach dynamically adjusts LRs during training by analyzing the global loss curve, eliminating the need for costly initial LR estimation through cross-validation. This method reduces training expenses and carbon footprint and enhances training efficiency. It demonstrates promising results in preventing premature convergence, exhibiting inherent optimization behavior, and elucidating the correlation between dataset distribution and optimal LR selection. The proposed method achieves 84.96% accuracy on the CIFAR-10 dataset while reducing the power usage to 0.07 kWh, $C{O}_2$ emissions to 0.05, and both $S{O}_2$ and $N{O}_x$ emissions to 0.00003 pounds, during the whole training and testing process. Full article

Haberman linking is a widely used method for comparing groups using the two-parameter logistic item response model. However, the traditional Haberman linking approach relies on joint item parameter estimation, which prevents the application of standard M-estimation theory for linking error calculation in the presence of differential item functioning. To address this limitation, a novel pairwise Haberman linking method is introduced. Pairwise Haberman linking aligns with Haberman linking when no items are missing but eliminates the need for joint item parameters, allowing for the use of M-estimation theory in linking error computation. Theoretical derivations and simulation studies show that pairwise Haberman linking delivers reliable statistical inferences for items and persons, particularly in terms of coverage rates. Furthermore, using a bias-corrected linking error is recommended to reduce the influence of sample size on error estimates. Full article

The stock market index future price forecasting is one of the imperative financial time series problems. Accurately estimated future closing prices can play important role in making trading decisions and investment plannings. This work proposes a new multi-output ensemble framework that integrates the hybrid systems generated through importance score based feature weighted learning models through a continuous multi-colony ant colony optimization technique (MACO-LD) for multi-day ahead index future price forecasting. Importance scores are obtained through four different importance score generation strategies (F-test, Relief, Random Forest, and Grey correlation). Multi-output variants of three baseline learning algorithms are brought in to address multi-day ahead forecasting. This study uses three learning algorithms namely multi-output least square support vector regression (MO-LSSVR), multi-output proximal support vector regression (MO-PSVR) and multi-output $\epsilon$-twin support vector regression (MO-$\epsilon$-TSVR) as the baseline methods for the feature weighted hybrid models. For the purpose of forecasting the future price of an index, a comprehensive collection of technical indicators has been taken into consideration as the input features. The proposed study is tested over eight index futures to explore the forecasting performance of individual hybrid predictors obtained after incorporating importance scores over baseline methods. Finally, multi-colony ant colony optimization algorithm is employed to construct the ensemble results from the feature weighted hybrid models along with baseline algorithms. The experimental results for all the eight index futures established that the proposed ensemble of importance score based feature weighted models exhibits superior performance in index future price forecasting compared to the baseline methods and that of importance score based hybrid methods. Full article

We present the derivation of generic equations describing the long gravity waves in incompressible fluid with a decaying effect. We show that in this theory, the only restriction to the surface deviation is connected to the stability condition for the waves. Derivation of these generic equations is based on Euler equations for inviscid incompressible fluid and the definition of dynamic pressure which leads to a correct dispersion equation for gravity waves. These derived generic equations for the velocity of fluid and the surface deviation describe the propagation of long gravity waves in incompressible fluid with finite amplitude. We also find the necessary and sufficient conditions for generic equations with dissipation of energy or a decaying effect. The developed approach can significantly improve the accuracy of theory for long gravity waves in incompressible fluid. We also find the quasi-periodic and solitary wave solutions for generic equations with a decaying effect. Full article

The information paradox suggests that the black hole loses information when it emits radiation. In this way, the spectrum of radiation corresponds to a mixed (non-pure) quantum state even if the internal state generating the black hole is expected to be pure in essence. In this paper we propose an argument solving this paradox by developing an understanding of the process by which spontaneous symmetry breaks when a black hole selects one of the many possible ground states and emits radiation as a consequence of it. Here, the particle operator number is the order parameter. This mechanism explains the connection between the density matrix, corresponding to the pure state describing the black hole state, and the density matrix describing the spectrum of radiation (mixed quantum state). From this perspective, we can recover black hole information from the superposition principle, applied to the different possible order parameters (particle number operators). Full article

According to the latest data from CryptoSlam, as of November 2024, NFT sales have approached USD 7.43 billion, with trading profits exceeding USD 33.303 million. In the buyer–seller market, the potential demand for NFT transactions continues to grow, leading to rapid development in the NFT market and giving rise to various issues, such as price manipulation, counterfeit products, hacking of investment platforms, identity verification errors, data leaks, and wallet security failures, all of which have caused significant financial losses for investors. Currently, the NFT investment market faces challenges such as legal uncertainty, information security, and high price volatility due to speculation. This study conducted expert interviews and adopted a two-stage research methodology to analyze the most common risk factors when selecting NFT investments. It employed the Decision-Making Trial and Evaluation Laboratory (DEMATEL) and the Analytic Network Process (ANP) to explore risk factors such as legal issues, security concerns, speculation, and price volatility, aiming to understand how these factors influence investors in choosing the most suitable NFT investment platform. The survey was conducted between February and June 2023, targeting professionals and scholars with over 10 years of experience in the financial market or financial research, with a total of 13 participants. The empirical results revealed that speculation had the greatest impact compared to legal issues, security concerns, and NFT price volatility. Speculation and price volatility directly influenced other risk factors, potentially increasing the risks faced by NFT investment platforms. In contrast, legal and security issues had less influence on other factors and were more affected by them, indicating a relatively lower likelihood of occurrence. Thus, investors must be cautious of short-term speculation, particularly when dealing with rare NFTs. The best approach is to set an exit price to minimize potential losses if the investment does not proceed as planned. Full article