Abstract : Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we introduce and study the notions of $u$-$S$-pure $u$-$S$-exact sequences and uniformly $S$-absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then we characterize uniformly $S$-von Neumann regular rings and uniformly $S$-Noetherian rings using uniformly $S$-absolutely pure modules.
Abstract : In this paper, we consider the existence of time periodic solutions for the compressible magneto-micropolar fluids in the whole space $\mathbb{R}^3$. In particular, we first solve the problem in a sequence of bounded domains by the topological degree theory. Then we obtain the existence of time periodic solutions in $\mathbb{R}^3$ by a limiting process.
Abstract : We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.
Abstract : In this paper, we introduce the concepts of (quasi-)weakly almost periodic point and minimal center of attraction for $\mathbb{Z}^d_+$-actions, explore the connections of levels of the topological structure the orbits of (quasi-)weakly almost periodic points and discuss the relations between (quasi-)weakly almost periodic point and minimal center of attraction. Especially, we investigate the chaotic dynamics near or inside the minimal center of attraction of a point in the cases of $S$-generic setting and non $S$-generic setting, respectively. Actually, we show that weakly almost periodic points and quasi-weakly almost periodic points have distinct topological structures of the orbits and we prove that if the minimal center of attraction of a point is non $S$-generic, then there exist certain Li-Yorke chaotic properties inside the involved minimal center of attraction and sensitivity near the involved minimal center of attraction; if the minimal center of attraction of a point is $S$-generic, then there exist stronger Li-Yorke chaotic (Auslander-Yorke chaotic) dynamics and sensitivity ($\aleph_0$-sensitivity) in the involved minimal center of attraction.
Abstract : We study the rationality and symmetry of the Gromov-Witten invariants of the projective line twisted by certain line bundles.
Abstract : As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction $C(\tau)$. We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.
Abstract : In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.
Abstract : In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual $L^2$ and discrete $H^1$ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.
Abstract : This paper studies the eigenvalues of the $G(\cdot)$-Laplacian \linebreak Dirichlet problem $$\left \{ \begin{aligned} \displaystyle -\text{div}\left(\frac{g(x,|\nabla u|)}{|\nabla u|}\nabla u\right) & = \displaystyle \lambda \left(\frac{g(x,|u|)}{|u|}u\right) & &\text{in} \; \Omega,\\ u & = 0 & &\text{on} \; \partial\Omega, \end{aligned} \right.$$ where $\Omega$ is a bounded domain in $\mathbb R^N$ and $g$ is the density of a generalized $\Phi$-function $G(\cdot)$. Using the Lusternik-Schnirelmann principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues.
Abstract : We compute explicitly traces of one-dimensional diffusion processes. The obtained trace forms can be regarded as Dirichlet forms on graphs. Then we discuss conditions ensuring the trace forms to be conservative. Finally, the obtained results are applied to the Bessel process of order $\nu$.
Jaewook Ahn, Myeonghyeon Kim
J. Korean Math. Soc. 2023; 60(3): 619-634
https://doi.org/10.4134/JKMS.j220424
Hyungryul Baik, Sebastian Hensel, Chenxi Wu
J. Korean Math. Soc. 2022; 59(4): 699-715
https://doi.org/10.4134/JKMS.j210535
Noureddine Ghiloufi , Safa Snoun
J. Korean Math. Soc. 2022; 59(3): 449-468
https://doi.org/10.4134/JKMS.j200373
Zhongkui Liu, Pengju Ma, Xiaoyan Yang
J. Korean Math. Soc. 2023; 60(3): 683-694
https://doi.org/10.4134/JKMS.j220479
Shuchao Li, Wanting Sun, Wei Wei
J. Korean Math. Soc. 2023; 60(5): 959-986
https://doi.org/10.4134/JKMS.j220341
Sebastian Petit, Hendrik Van Maldeghem
J. Korean Math. Soc. 2023; 60(4): 907-929
https://doi.org/10.4134/JKMS.j220528
Jongsu Kim
J. Korean Math. Soc. 2022; 59(3): 649-650
https://doi.org/10.4134/JKMS.j210761
Eui Chul Kim
J. Korean Math. Soc. 2023; 60(5): 999-1021
https://doi.org/10.4134/JKMS.j220480
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