In this paper, a high-order oscillation-free (OF) discontinuous Galerkin (DG) scheme is presented for one-dimensional compressible multi-material flows. For describing the dynamics of fluid mixture, we couple a conservative equation related to the volume-fraction model with the Euler equations. For controlling the oscillations, some damping terms are added into the weak formulation of the system to automatically adjust the high-order terms. There are not any parameters which need to be adjusted artificially in the new damping terms, and the difficulties in solving discontinuous solutions and complexities of designing limiters can be avoided. Our scheme can be applied to the simulation of compressible multi-material flows efficiently with the essentially non-oscillatory property. Moreover, our scheme can be extended to the one with any high order as long as the order of basis functions is increased. In this paper, we only study the third-order OFDG scheme with the basis functions up to the quadratic polynomial. Some examples are tested to demonstrate the third-order accuracy and essentially non-oscillatory property of our scheme.
In this paper, considering the effect of light on phytoplankton, we develop a nonlocal reaction-diffusion-advection model to study the effects of environmental toxicants on phytoplankton in a polluted water column. We first establish the existence and uniqueness of positive solutions to the system and then, by the eigenvalue theory, we investigate the stability of the semi-trivial steady state. Finally, we establish a priori estimate of the steady state of system, and prove the existence of positive steady states under certain conditions by using fixed point index theory.
This article introduces a new generalized inverse weak, namely, m-MPD inverse and discusses its related properties. Several different representations of the weak m-MPD inverse are listed, including Hartwig-Spindelböck decomposition forms. Next, the solution of a new equation corresponding to the weak m-MPD inverse is explored. Besides, the perturbation formula for the weak m-MPD inverse is derived.
Observation-driven integer-valued autoregressive models are wide-ly used for modeling count time series exhibiting dynamic dependence,yet their performance critically depends on the way that thinning probabilities are linked to past observations.Most existing specifications rely on the logit link and may respond excessively to large counts.In this paper,we introduce a class of new observation-driven integer-valued autoregressive models using logarithmic and soft-clipping links that attenuate the influence of large obser-vations.The proposed framework allows for stochastic covariates.Estima-tion is carried out using conditional maximum likelihood and conditional least squares methods.Simulation studies and two real data applications are used to illustrate the proposed models.
In this work, a homogeneous two-phase flow model in two-dimensional space is proposed for systems without a sharp interface between phases. The model allows the two phases to coexist within the same domain with distinct pressures, while their local proportions are represented by volume fractions. Within an arbitrary Lagrangian-Eulerian (ALE) framework, a two dimensional Riemann solver is developed to construct the numerical scheme with novel formulations for numerical fluxes and nodal velocities, ensuring consistency on moving control volumes. Furthermore, a new moving-mesh strategy is designed, in which the evolution of the volume fraction is obtained directly from the geometric motion of the mesh and mass conservation, thereby avoiding solving the non-conservative convective equation with source terms. This enables the incorporation of physical drag models and finite relaxation coefficients, allowing the gradual equilibration of velocity and pressure between the two phases to be calculated. Based on the volume-fraction formulation, a discrete representation of the pressure work term is derived. Finally, a series of numerical experiments are presented to demonstrate the accuracy, stability, and physical consistency of the proposed model and numerical scheme.
The purpose of this paper is to solve equation for a class of quasilinear elliptic operators containing the p(·)-Laplacian and the mean curvature operator with mixed boundary conditions. More precisely, we are concerned with the problem that has the Dirichlet condition in one part of the boundary and the Steklov condition in another. Using a symmetric mountain pass lemma and its corollary, we show the existence of infinitely many weak solutions of the equation and the boundedness of the sequence of solutions, or convergence tozero of the sequence of solutions according to the hypotheses about the data functions.
In this article, a compact finite difference scheme for the Rosenau-RLW equation is established using the continuous reduction method, which achieves second-order accuracy in time and fourth-order accuracy in space. In addition, the conservation of both mass and energy, boundedness, and uniqueness of solutions are also established. Finally, combined with the Gronwall inequality, the convergence of this scheme is given.
Douglas-Rachford splitting (DRS) and the alternating direction method of multipliers (ADMM) are two fundamental first-order methods for structured convex optimization. Although derived from different viewpoints, ADMM can be interpreted as the application of DRS to the dual problem. Based on this structural equivalence, this paper studies how algorithmic improvement strategies can be transferred between the two methods. We classify transferable strategies into three categories: exact operator-level transfer, parameter-driven transfer, and heuristic transfer. Representative examples including relaxation, metric scaling, adaptive parameter updates, and residual balancing are discussed to illustrate the different levels of transferability. This perspective provides a systematic way to understand the relationship between DRS and ADMM and clarifies how algorithmic ideas developed for one method may inform the design of variants of the other, offering a unified framework that both explains existing variants and guides the design of new ones.
This paper investigates the algebraic structure of a supersymmetric extension of the Heisenberg-Virasoro algebra. We prove that the second cohomology group with trivial coefficients is four-dimensional, thereby determining its universal central extension. We determine the derivation algebra and show that the first cohomology group is four-dimensional. Furthermore, we provide a complete classification of all biderivations by decomposing them into skew-supersymmetric and supersymmetric components. Finally, we classify all automorphisms and describe the algebraic structure of the full automorphism group.
This paper studies a multidimensional delay-claim risk model in which an insurance company operates d(d≥2)lines of business exposed to a common renewal counting process.Each catastrophic event simultaneously produces main and delayed claims across all business lines,where the delayed claims are settled after random delay periods.The surplus process incorporates a geometric Lévy price process to describe investment returns.Assuming that the main and delayed claims follow subexponential distributions and satisfy a conditional linear dependence structure,we derive asymptotic estimates for the finite-time ruin probability.The obtained results extend existing findings on delay-claim models to the multidimensional framework and contribute to a deeper understanding of ruin behavior under dependence and heavy-tailed risks.
We develop a numerical method for the Keller-Segel chemotaxis sys-tem that is designed to(ⅰ)preserve the model's fundamental structural properties(positivity/bound preservation,mass conservation,and energy dissipation),(ⅱ)efficiently and accurately resolve the near-singular dynamics associated with spike formation and finite-time blow-up.Our approach combines a linear,positivity-preserving scalar auxiliary vari-able(SAV)scheme(following the framework in[15])with a Fourier spectral spatial discretization and an moving-mesh PDE-based method.The SAV re-formulation provides a convenient platform for stable,linear time stepping while maintaining energy dissipation;the Fourier spectral discretization de-livers high accuracy in smooth regions;and the moving-mesh PDE mesh redis-tribution concentrates collocation points in regions of large gradients so that sharp,localized structures can be resolved without prohibitive cost.We show that the proposed moving mesh SAV scheme inherits positivity preservation,mass conservation,and discrete energy dissipation provided the mesh motion avoids element overlap.Two-dimensional tests demonstrate the method's abil-ity to capture fine spike profiles and estimate blow-up times with substantially reduced computational effort;the formulation extends straightforwardly to three spatial dimensions.Numerical results show that the proposed method is a practical and effective method for accurate simulation of chemotactic ag-gregation.
This paper concerns continuous subsonic-sonic potential flows in a two-dimensional,convergent nozzle,which is governed by a free bound-ary problem of a quasilinear degenerate elliptic equation.It is shown that for a given nozzle perturbed from a straight one,a given point on its wall where the curvature is zero,a given inlet which is a perturbation of an arc centered at the vertex,and a given incoming flow angle perturbed from the angle of the in-ner normal of the inlet,there exists uniquely a continuous subsonic-sonic flow whose velocity vector is along the normal direction at the sonic curve,which satisfies the slip conditions on the nozzle walls and whose sonic curve inter-sects the upper wall at the given point.Furthermore,the sonic curve of this flow is a free boundary,where the flow is singular in the sense that the speed is only C1/2 Hölder continuous and the acceleration blows up.The perturbation problem is solved in the potential plane,where the flow is governed by a free boundary problem of a degenerate elliptic equation with three free boundaries and two nonlocal boundary conditions,and the equation is degenerate at one free boundary.
We construct an algebra of rapidly decaying C0 functions on an étale(Lie)groupoid,which extends the standard algebra of compactly supported noncommutative differential forms.In particular,using the theory of bisec-tions,we prove that this algebra is closed under convolution.This construction clarifies the superconnection proof of Gorokhovsky and Lott.
In this survey, we provide an in-depth investigation of exponential Runge-Kutta methods for the numerical integration of initial-value problems. These methods offer a valuable synthesis between classical Runge-Kutta methods, introduced more than a century ago, and exponential integrators, which date back to the 1960s. This manuscript presents both a historical analysis of the development of these methods up to the present day and several examples aimed at making the topic accessible to a broad audience.
Image-based rock typing(IBRT)is an effective way to understand the pore scale heterogeneity of the reservoir samples.IBRT is aimed at seg-menting a rock sample's image into different regions where each region rep-resents a homogeneous porous medium,also known as rock type.Currently,the phase-field rock typing method has attracted more attention due to its im-pressive performance in classifying the heterogeneous rock images with highly irregular pore structures.In this paper,a modified specific surface CV(SSCV)model is proposed to realize the IBRT.In the SSCV model,the specific surface of a pixel is calculated within a given size neighborhood to distinguish different rock types,and the iterative convolution-thresholding method(ICTM)is ap-plied as the classifier.Compared to the LHFCV method,an existing phase-field rock typing method,the proposed SSCV is capable of processing the images with more than two rock types and can be solved by ICTM which has higher computational efficiency.The proposed SSCV method has demonstrated re-markable performance in the segmentation of various images of both synthetic and natural rock samples.
In this note,we consider the following degenerate parabolic equa-tion studied in[F.Chiarenza and R.Serapioni,Degenerate parabolic equations and Harnack inequality,Ann.Mat.Pura Appl.137(1984)]i.e.,{∂u/∂t-∂/∂xi(aij(x,t)∂u/∂xj)=-divf in Ω×(0,T),u=0 on ∂Ω×(0,T),u(x,0)=u0(x)in Ω,where f=(f1,…,fn)and Ω is a bounded domain in Rn with Lipschitz bound-ary,n≥ 2 and T＞0.In this paper,we apply Moser iteration argument to build up the explicit relationship among the coefficients ai,j(x,t),f and the maxi-mum norm of the solution.Meanwhile,we also find that the weighed Lebesgue space L2l/(l-1)to which f belongs is essentially sharp in order to establish local boundedness of the solution.Here the definition of l is found in Lemma 2.3.Our results cover the well-known results.
In this paper,we investigate the dynamical stability of transonic shock solutions for the full compressible Euler system in a two dimensional nozzle with a symmetric divergent part.Building upon the existence and uni-queness results for steady symmetric transonic shock solutions to the non-isentropic Euler system established in[Z.P.Xin and H.C.Yin,The transonic shock in a nozzle,2-D and 3-D complete Euler systems,J.Differential Equations 245(2008)],we prove the dynamical stability of the transonic shock solutions under small perturbations.More precisely,if the initial unsteady transonic flow is located in the symmetric divergent part of the nozzle and the flow is a sym-metric small perturbation of the steady transonic flow,we use the characteristic method to establish the dynamical stability.
In this note,we establish a new version of Schur-Horn type theorem for symplectic matrices.Meanwhile,we establish a necessary and sufficient condition for the equality to hold in the above result.
$SD{D_k}$ matrices are a subclass of the nonsingular $H$-matrices. The infinity norm of the inverse for $SD{D_k}$ matrices has been given. In the paper, we utilize this result in the context of the linear complementarity problem, and the error bounds of the linear complementarity problem for $SD{D_k}$ matrices are obtained. By the relationship between the $SDD$ matrices and the $SD{D_k}$ matrices, we further obtain the error bounds of the linear complementarity problem for $SDD$ matrices. In addition, it is proved that the bounds presented in this paper are sharper than the well-known bounds under some conditions. Finally, numerical examples are provided to demonstrate the effectiveness of our results.
Let $R$ be an associative ring with identity. In this paper, we consider generalizations of Gorenstein FP-injective $R$-modules and FP-injective complexes, give the definitions and characterizations of strongly Gorenstein FP-injective $R$-modules and strongly FP-injective complexes, which are induced by strongly FP-injective modules. Then we investigate the strongly FP-injective dimension of complexes.
