AIMS Mathematics最新文献

Traditional numerical methods, such as computational fluid dynamics (CFD), demand large computational resources and memory for modeling fluid dynamic systems. Hence, deep learning (DL) and, specifically Convolutional Neural Networks (CNN) autoencoders have resulted in accurate tools to obtain approximations of the streamwise and vertical velocities and pressure fields, when stationary flows are considered. The novelty of this paper consists of predicting the future instants from an initial one with a CNN autoencoder architecture when an unsteady flow is considered. Two neural models are proposed: The former predicts the future instants on the basis of an initial sample and the latter approximates the initial sample. The inputs of the CNNs take the signed distance function (SDF) and the flow region channel (FRC), and, for the representation of the temporal evolution, the previous CFD sample is added. To increment the amount of training data of the second neural model, a data augmentation technique based on the similarity principle for fluid dynamics is implemented. As a result, low absolute error rates are obtained in the prediction of the first samples near the shapes surfaces. Even in the most advanced time instants, the prediction of the vortices zone is quite reliable. 62.12 and 9000 speed-up ratios are achieved by the predictions of the first and second neural models, respectively, compared to the computational cost regarded by the CFD simulations.

In this paper, we consider a higher-order numerical scheme for two-dimensional nonlinear fractional Hadamard integral equations with uniform accuracy. First, the high-order numerical scheme is constructed by using piecewise biquadratic logarithmic interpolations to approximate an integral function based on the idea of the modified block-by-block method. Secondly, for $ 0 < gamma, lambda < 1 $, the convergence of the high order numerical scheme has the optimal convergence order of $ O(Delta_{s}^{4-gamma}+Delta_{t}^{4-lambda }) $. Finally, two numerical examples are used for experimental testing to support the theoretical findings.

In this paper, we apply piecewise derivatives with both singular and non-singular kernels to investigate a malaria model. The singular kernel is the Caputo derivative, while the non-singular kernel is the Atangana-Baleanu operator in Caputo's sense (ABC). The existence, uniqueness, and numerical algorithm of the proposed model are presented using piecewise derivatives with both kernels. The stability is also presented for the proposed model using Ulam-Hyers stability. The numerical simulations are performed considering different fractional orders and compared the results with the real data to evaluate the efficiency of the proposed approach.

Dengue presents over 390 million cases worldwide yearly. Releasing Wolbachia-infected male mosquitoes to suppress wild mosquitoes via cytoplasmic incompatibility has proven to be a promising method for combating the disease. As cytoplasmic incompatibility causes early developmental arrest of the embryo during the larval stage, we introduce the Ricker-type survival probability to assess the resulting effects. For periodic and impulsive release strategies, our model switches between two ordinary differential equations. Owing to a Poincaré map and rigorous dynamical analyses, we give thresholds $ T^*, c^* $ and $ c^{**} (>c^*) $ for the release period $ T $ and the release amount $ c $. Then, we assume $ c > c^* $ and prove that our model admits a globally asymptotically stable periodic solution, provided $ T > T^* $, and it admits at most two periodic solutions when $ T < T^* $. Moreover, for the latter case, we assert that the origin is globally asymptotically stable if $ cge c^{**} $, and there exist two positive numbers such that whenever there is a periodic solution, it must initiate in an interval composed of the aforementioned two numbers, once $ c^* < c < c^{**} $. We also offer numerical examples to support the results. Finally, a brief discussion is given to evoke deeper insights into the Ricker-type model and to present our next research directions.

In this paper, we propose an algorithm for computing mod $ ell $ Galois representations associated to modular forms of weight $ k $ when $ ell < k-1 $. We also present the corresponding results for the projective Galois representations. Moreover, we apply our algorithms to explicitly compute the mod $ ell $ projective Galois representations associated to $ Delta_{k} $ for $ k = 16, 20, 22, 26 $ and all the unexceptional primes $ ell $, with $ ell < k-1 $. As an application, for $ k = 16, 20, 22, 26 $, we obtain the new bounds $ B_k $ of $ n $ such that $ a_n(Delta_k)ne0 $ for all $ n < B_k $.

Taking into account the delayed fear induced by predators on the birth rate of prey, the counter-predation sensitiveness of prey, and the direct consumption by predators with stage structure and interference impacts, we proposed a prey-predator model with fear, Crowley-Martin functional response, stage structure and time delays. By use of the functional differential equation theory and Sotomayor's bifurcation theorem, we established some criteria of the local asymptotical stability and bifurcations of the system equilibrium points. Numerically, we validated the theoretical findings and explored the effects of fear, counter-predation sensitivity, direct predation rate and the transversion rate of the immature predator. We found that the functional response as well as the stage structure of predators affected the system stability. The fear and anti-predation sensitivity have positive and negative impacts to the system stability. Low fear level and high anti-predation sensitivity are beneficial to the system stability and the survival of prey. Meanwhile, low anti-predation sensitivity can make the system jump from one equilibrium point to another or make it oscillate between stability and instability frequently, leading to such phenomena as the bubble, or bistability. The fear and mature delays can make the system change from unstable to stable and cause chaos if they are too large. Finally, some ecological suggestions were given to overcome the negative effect induced by fear on the system stability.

Time series of counts are observed widely in actuarial science, finance, epidemiology and biology. These time series may exhibit over-, equi- and under-dispersion. The Poisson distribution is commonly used in count time series models, but it is restricted by the equality of mean and variance. Other distributions such as the generalized Poisson, double Poisson, hyper-Poisson, and COM-Poisson distributions have been proposed to replace the Poisson distribution to model the different levels of dispersion in time series of counts. These models have certain limitations such as complex expressions for the mean and variance which complicate the formulation as GARCH models. In this study, we propose an alternative hyper-Poisson (AHP) distribution, with simple forms of conditional mean and variance, for an integer-valued GARCH (INGARCH) model for time series of counts that also exhibit the different levels of dispersion. We demonstrate that the AHP-INGARCH model is comparable to some existing INGARCH models. Additionally, the model can cover a wider range of dispersion. The maximum likelihood estimation can be used to estimate the parameters of the proposed model. Applications to three real-life data sets related to polio, internet protocol and daily COVID-19 new deaths underscore the usefulness of the proposed model in studying both over-dispersed and under-dispersed time series of counts.

We introduce the concept of an effective neutrosophic soft set, which aims to capture the influence on three independent membership functions representing degrees of truth (T), indeterminacy (I) and falsity (F). We go further by presenting a generalization of the effective neutrosophic soft set, which includes the incorporation of a degree to signify the potential for an approximate value-set. This enhancement contributes to improved efficiency and realism in the concept. Notably, this innovative approach leverages the strengths of both the generalized neutrosophic set and the effective neutrosophic soft set. The subsequent sections delve into fundamental operations on the generalized effective neutrosophic soft set, providing clarity through illustrative examples and propositions. Furthermore, we demonstrate the practical application of the generalized effective neutrosophic soft set in addressing decision-making problems and medical diagnoses.

In this paper, we study the Schur complement problem of $ S $-SOB matrices, and prove that the Schur complement of $ S $-Sparse Ostrowski-Brauer ($ S $-SOB) matrices is still in the same class under certain conditions. Based on the Schur complement of $ S $-SOB matrices, some upper bound for the infinite norm of $ S $-SOB matrices is obtained. Numerical examples are given to certify the validity of the obtained results. By using the infinity norm bound, an error bound is given for the linear complementarity problems of $ S $-SOB matrices.