AIMS Mathematics最新文献

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.

In this paper we are concerned with the Lane-Emden-Fowler equation

begin{document}$ begin{equation*} left{begin{array}{rll}-Delta u & = u^{frac{n+2}{n-2}- varepsilon}& {rm{in}}; Omega, u&>0& {rm{in}}; Omega, u& = 0& {rm{on}}; partial Omega, end{array} right. end{equation*} $end{document}

where $ Omega subset mathbb{R}^n $ ($ n geq 3 $) is a nonconvex polygonal domain and $ varepsilon > 0 $. We study the asymptotic behavior of minimal energy solutions as $ varepsilon > 0 $ goes to zero. A main part is to show that the solution is uniformly bounded near the boundary with respect to $ varepsilon > 0 $. The moving plane method is difficult to apply for the nonconvex polygonal domain. To get around this difficulty, we derive a contradiction after assuming that the solution blows up near the boundary by using the Pohozaev identity and the Green's function.

In this paper, we investigate a min matrix and obtain its $ LU $-decomposition, determinant, permanent, inverse, and norm properties. In addition, we obtain a recurrence relation provided by the characteristic polynomial of this matrix. Finally, we present an example to illustrate the results obtained.

This paper is concerned with a population model with prey refuge and a Holling type Ⅲ functional response in the presence of self-diffusion and cross-diffusion, and its Turing pattern formation problem of Hopf bifurcating periodic solutions was studied. First, we discussed the stability of periodic solutions for the ordinary differential equation model, and derived the first derivative formula of periodic functions for the perturbed model. Second, applying the Floquet theory, we gave the conditions of Turing patterns occurring at Hopf bifurcating periodic solutions. Additionally, we determined the range of cross-diffusion coefficients for the diffusive population model to form Turing patterns at the stable periodic solutions. Finally, our research was summarized and the relevant conclusions were simulated numerically.

Let $ H $ be a graph with edge set $ E_H $. The Sombor index and the reduced Sombor index of a graph $ H $ are defined as $ SO(H) = sumlimits_{uvin E_H}sqrt{d_{H}(u)^{2}+d_{H}(v)^{2}} $ and $ SO_{red}(H) = sumlimits_{uvin E_H}sqrt{(d_{H}(u)-1)^{2}+(d_{H}(v)-1)^{2}} $, respectively. Where $ d_{H}(u) $ and $ d_{H}(v) $ are the degrees of the vertices $ u $ and $ v $ in $ H $, respectively. A cactus is a connected graph in which any two cycles have at most one common vertex. Let $ mathcal{C}(n, k) $ be the class of cacti of order $ n $ with $ k $ cycles. In this paper, the lower bound for the Sombor index of the cacti in $ mathcal{C}(n, k) $ is obtained and the corresponding extremal cacti are characterized when $ ngeq 4k-2 $ and $ kgeq 2 $. Moreover, the lower bound of the reduced Sombor index of cacti is obtained by similar approach.

In this article, the global well-posedness of weak solutions for 2D non-autonomous g-Navier-Stokes equations on some bounded domains were investigated by the Faedo-Galerkin method. Then the existence of pullback attractors for 2D g-Navier-Stokes equations with nonlinear damping and time delay was obtained using the method of pullback condition (PC).

Correctly determining a company's market worth during an entire year or a certain period presents a difficulty to decision-makers. In the case of the merger of companies, the need performs heavier when both the companies' owners are attracted to establishing a fair price at the optimal time to merge. The effectiveness of representing, connecting and manipulating both uncertainty and periodicity information becomes highly required. Hence, study and nhance some properties and conditions of the algebraic structure of complex hesitant fuzzy graphs. Therefore, the degree of composition between two complex hesitant fuzzy graphs is proposed. Also, the formal definitions of union, joint and complement are presented to be covered in the realm of complex hesitant fuzzy graphs. A real-life application is illustrated to show the relation between vertices and edges in the form of complex hesitant fuzzy graphs.

We introduce a generalized concept of arbitrage, excess profit relative to the benchmark asset under $ alpha $-confidence level, $ alpha $-REP, in a single-period market model with proportional transaction costs. We obtain a fundamental theorem of asset pricing with respect to the absence of $ alpha $-REP. Moreover, we discuss the relationships between classical arbitrage, strong statistical arbitrage and $ alpha $-REP.