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 : 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 study the rationality and symmetry of the Gromov-Witten invariants of the projective line twisted by certain line bundles.
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 $\nu$.
Abstract : Given a dimension function $\omega$, we introduce the notion of an $\omega$-vector weighted digraph and an $\omega$-equivalence between them. Then we establish a bijection between the weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over a product of simplices $\Delta^{\omega(1)}\times\cdots \times \Delta^{\omega(m)}$ and the set of $\omega$-equivalence classes of $\omega$-vector weighted digraphs with $m$-labeled vertices, where $n$ is the sum of the dimensions of the simplicies. Using this bijection, we obtain a formula for the number of weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over a product of three simplices.
Abstract : Our aim is to study the properties of Fischer-Marsden conjecture and Ricci-Bourguignon solitons within the framework of generalized Sasakian-space-forms with $\beta$-Kenmotsu structure. It is proven that a $(2n+1)$-dimensional generalized Sasakian-space-form with $\beta$-Kenmotsu structure satisfying the Fischer-Marsden equation is a conformal gradient soliton. Also, it is shown that a generalized Sasakian-space-form with $\beta$-Kenmotsu structure admitting a gradient Ricci-Bourguignon soliton is either $\Psi \backslash T^{k} \times M^{2n+1-k}$ or gradient $\eta$-Yamabe soliton.
Abstract : Let $R$ be a commutative ring with identity. The structure theorem says that $R$ is a PIR (resp., UFR, general ZPI-ring, $\pi$-ring) if and only if $R$ is a finite direct product of PIDs (resp., UFDs, Dedekind domains, $\pi$-domains) and special primary rings. All of these four types of integral domains are Krull domains, so motivated by the structure theorem, we study the prime factorization of ideals in a ring that is a finite direct product of Krull domains and special primary rings. Such a ring will be called a general Krull ring. It is known that Krull domains can be characterized by the star operations $v$ or $t$ as follows: An integral domain $R$ is a Krull domain if and only if every nonzero proper principal ideal of $R$ can be written as a finite $v$- or $t$-product of prime ideals. However, this is not true for general Krull rings. In this paper, we introduce a new star operation $u$ on $R$, so that $R$ is a general Krull ring if and only if every proper principal ideal of $R$ can be written as a finite $u$-product of prime ideals. We also study several ring-theoretic properties of general Krull rings including Kaplansky-type theorem, Mori-Nagata theorem, Nagata rings, and Noetherian property.
Abstract : We construct generalized Cauchy-Riemann equations of the first order for a pair of two $\mathbb{R}$-valued functions to deform a minimal graph in ${\mathbb{R}}^{3}$ to the one parameter family of the two dimensional minimal graphs in ${\mathbb{R}}^{4}$. We construct the two parameter family of minimal graphs in ${\mathbb{R}}^{4}$, which include catenoids, helicoids, planes in ${\mathbb{R}}^{3}$, and complex logarithmic graphs in ${\mathbb{C}}^{2}$. We present higher codimensional generalizations of Scherk's periodic minimal surfaces.
Abstract : Let $\mathbb F_q$ be a finite field with $q$ elements. A function $f: \mathbb F_q^d\times \mathbb F_q^d \to \mathbb F_q$ is called a Mattila--Sj\"{o}lin type function of index $\gamma \in \mathbb R$ if $\gamma$ is the smallest real number such that whenever $|E|\geq Cq^{\gamma}$ for a sufficiently large constant $C$, the set $f(E,E):=\{f(x,y): x, y\in E\}$ is equal to $\mathbb F_q$. In this article, we construct an example of a Mattila--Sj\"{o}lin type function $f$ and provide its index, generalizing the result of Cheong, Koh, Pham and Shen [1].
Abstract : In this paper we study a pointwise version of Walters topological stability in the class of homeomorphisms on a compact metric space. We also show that if a sequence of homeomorphisms on a compact metric space is uniformly expansive with the uniform shadowing property, then the limit is expansive with the shadowing property and so topologically stable. Furthermore, we give examples to illustrate our results.
Zhongkui Liu, Pengju Ma, Xiaoyan Yang
J. Korean Math. Soc. 2023; 60(3): 683-694
https://doi.org/10.4134/JKMS.j220479
Chun-Ru Fu , Huan-Nan Shi, Dong-Sheng Wang
J. Korean Math. Soc. 2023; 60(3): 503-520
https://doi.org/10.4134/JKMS.j220039
Souad Ben Seghier
J. Korean Math. Soc. 2023; 60(1): 33-69
https://doi.org/10.4134/JKMS.j210764
Eun-Kyung Cho, Su-Ah Kwon, Suil O
J. Korean Math. Soc. 2022; 59(4): 757-774
https://doi.org/10.4134/JKMS.j210605
Sebastian Petit, Hendrik Van Maldeghem
J. Korean Math. Soc. 2023; 60(4): 907-929
https://doi.org/10.4134/JKMS.j220528
Chun-Ru Fu , Huan-Nan Shi, Dong-Sheng Wang
J. Korean Math. Soc. 2023; 60(3): 503-520
https://doi.org/10.4134/JKMS.j220039
Soyoon Bak, Philsu Kim, Sangbeom Park
J. Korean Math. Soc. 2022; 59(5): 891-909
https://doi.org/10.4134/JKMS.j210701
Hailou Yao, Qianqian Yuan
J. Korean Math. Soc. 2023; 60(6): 1337-1364
https://doi.org/10.4134/JKMS.j230208
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