Showing papers in "Journal of The Korean Mathematical Society in 2017"
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26 citations
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TL;DR: A deterministic model for the spread of pine wilt disease with asymptomatic carrier trees in the host pine population is designed and rigorously analyzed.
Abstract: A deterministic model for the spread of pine wilt disease with asymptomatic carrier trees in the host pine population is designed and rigorously analyzed. We have taken four different classes for t ...
10 citations
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TL;DR: In this article, it was shown that every point in a von Neumann algebra or a triangular algebra is a full-centralizable point if and only if its central carrier is the unit.
Abstract: A linear mapping $\phi$ on an algebra $\mathcal{A}$ is called a centralizable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B=A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$, and $\phi$ is called a derivable mapping at $G\in\mathcal{A}$ if $\phi(AB)=\phi(A)B+A\phi(B)$ for each $A$ and $B$ in $\mathcal{A}$ with $AB=G$. A point $G$ in $\mathcal{A}$ is called a full-centralizable point (resp. full-derivable point) if every centralizable (resp. derivable) mapping at $G$ is a centralizer (resp. derivation). We prove that every point in a von Neumann algebra or a triangular algebra is a full-centralizable point. We also prove that a point in a von Neumann algebra is a full-derivable point if and only if its central carrier is the unit.
9 citations
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9 citations
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9 citations
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TL;DR: In this article, the Ricci tensor of a threedimensional almost Kenmotsu manifold satisfying ∇ξh = 0, h 6= 0, is η-parallel if and only if the manifold is locally isometric to either the Riemannian product H(−4) × R or a non-unimodular Lie group equipped with a left invariant non-Kenmotsusu almost Kenmotu structure.
Abstract: In this paper, we prove that the Ricci tensor of a threedimensional almost Kenmotsu manifold satisfying ∇ξh = 0, h 6= 0, is η-parallel if and only if the manifold is locally isometric to either the Riemannian product H(−4) × R or a non-unimodular Lie group equipped with a left invariant non-Kenmotsu almost Kenmotsu structure.
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TL;DR: In this paper, the authors reformulate Voisin's conjecture in the setting of hyperk\"ahler fourfolds, and prove this reformulated conjecture for one family of hyper k''ahler 4folds.
Abstract: Motivated by the Bloch-Beilinson conjectures, Voisin has made a conjecture concerning zero-cycles on self-products of Calabi-Yau varieties. We reformulate Voisin's conjecture in the setting of hyperk\"ahler varieties, and we prove this reformulated conjecture for one family of hyperk\"ahler fourfolds.
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TL;DR: In this paper, the spectral properties of Volterra-type integral operators with holomorphic symbol $g$ on the Fock-Sobolev spaces were studied, and it was shown that the spectrum of $V_g$ is characterized in terms of a closed disk of radius twice the coefficient of the highest degree term in a polynomial expansion of $g.
Abstract: We study some spectral properties of Volterra-type integral operators $V_g$ and $I_g$ with holomorphic symbol $g$ on the Fock--Sobolev spaces $\mathcal{F}_{\psi_m}^p$. We showed that $V_g$ is bounded on $\mathcal{F}_{\psi_m}^p$ if and only if $g$ is a complex polynomial of degree not exceeding two, while compactness of $V_g$ is described by degree of $g$ being not bigger than one. We also identified all those positive numbers $p$ for which the operator $V_g$ belongs to the Schatten $\mathcal{S}_p$ classes. Finally, we characterize the spectrum of $V_g$ in terms of a closed disk of radius twice the coefficient of the highest degree term in a polynomial expansion of $g$.
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TL;DR: In this paper, the authors constructed new smooth 4-manifolds with signature 4 which are surface bundles over surfaces with small fiber and base genera and derived improved upper bounds for the minimal genus of surfaces representing the second homology classes of a mapping class group.
Abstract: The signature of a surface bundle over a surface is known to be divisible by 4. It is also known that the signature vanishes if the fiber genus is less than or equal to 2 or the base genus is less than or equal to 1. In this article, we construct new smooth 4-manifolds with signature 4 which are surface bundles over surfaces with small fiber and base genera. From these we derive improved upper bounds for the minimal genus of surfaces representing the second homology classes of a mapping class group.
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TL;DR: In this article, a basic attractor theory on topological spaces under appropriate separation axioms is presented. But the existence results of attractors are not discussed, and the Morse decomposition of attractor decompositions is not considered.
Abstract: In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.
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TL;DR: Sior et al. as discussed by the authors formulated necessary and sufficient conditions of the existence of Spin-structure on real Bott manifolds. But they did not consider the case where k is even.
Abstract: Let $$M_{n}\\stackrel{\\mathbb R P^1}\\to M_{n-1}\\stackrel{\\mathbb R P^1}\\to\\ldots\\stackrel{\\mathbb R P^1}\\to M_{1}\\stackrel{\\mathbb R P^1}\\to M_0 = \\{ \\bullet\\} $$ be a sequence of real projective bundles such that $M_i\\to M_{i-1}$, $i=1,2,\\ldots,n$, is a projective bundle of a Whitney sum of a real line bundle $L_{i-1}$ and the trivial line bundle over $M_{i-1}$. The above sequence is called the real Bott tower and the top manifold $M_n$ is called the real Bott manifold.
There are a few ways to decide whether there exists a Spin-structure on an oriented flat manifold $M^n$. An oriented flat manifold $M^n$ has a Spin-structure if and only if there exists a homomorphism $\\epsilon\\colon\\Gamma\\to\\operatorname{Spin}(n)$ such that $\\lambda_n\\epsilon=p$, where $\\lambda_n:\\operatorname{Spin}(n)\\to\\operatorname{SO}(n)$ is the covering map. There is an equivalent condition for existence of Spin-structure. This is well known that the closed oriented differential manifold $M$ has a Spin-structure if and only if the second Stiefel-Whitney class vanishes.
Our paper is a sequel of A. G\\k{a}sior, A. Szczepa\\'nski, Flat manifolds with holonomy group $Z_2^k$ of diagonal type, Osaka J. Math. 51 (2014), 1015 - 1025. There are given non-complete conditions of the existence of Spin-structures on real Bott manifolds. In this paper, if k is even, we formulate necessary and sufficient conditions of the existence of Spin-structure on real Bott manifolds. Here is our main result
The real Bott manifold $M(A)$ has a Spin-structure if and only for all $1\\leq i
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TL;DR: In this paper, the authors studied abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces and proved the existence of unique local mild solutions and showed their regularity.
Abstract: This paper is devoted to studying abstract stochastic semilinear evolution equations with additive noise in Hilbert spaces. First, we prove the existence of unique local mild solutions and show their regularity. Second, we show the regular dependence of the solutions on initial data. Finally, some applications to stochastic partial differential equations are presented.
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TL;DR: In this paper, the authors investigate the additivity of bijective maps from a non-zero scalar to a scalar such that the sum of the two scalars is constant.
Abstract: Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^{*}$-algebras such that $\mathcal{A}$ is prime. In this paper, we investigate the additivity of maps $\Phi$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective and satisfy $$\Phi(A^{*}B+\eta BA^{*})=\Phi(A)^{*}\Phi(B)+\eta \Phi(B)\Phi(A)^{*}$$ for all $A, B\in \mathcal{A}$ where $\eta$ is a non-zero scalar such that $\eta
eq \pm1$. Moreover, if $\Phi(I)$ is a projection, then $\Phi$ is a $\ast$-isomorphism.
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TL;DR: In this paper, it was shown that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of RN(H) is extended from a homogeneous ideal of R, and if R̄H\Q was a graded-Prüfer domain for all homogeneous maximal t-ideals Q of R.
Abstract: Let R = ⊕ α∈Γ Rα be an integral domain graded by an arbitrary torsionless grading monoid Γ, R̄ be the integral closure of R, H be the set of nonzero homogeneous elements of R, C(f) be the fractional ideal of R generated by the homogeneous components of f ∈ RH , and N(H) = {f ∈ R | C(f)v = R}. Let RH be a UFD. We say that a nonzero prime ideal Q of R is an upper to zero in R if Q = fRH ∩ R for some f ∈ R and that R is a graded UMT-domain if each upper to zero in R is a maximal t-ideal. In this paper, we study several ring-theoretic properties of graded UMT-domains. Among other things, we prove that if R has a unit of nonzero degree, then R is a graded UMT-domain if and only if every prime ideal of RN(H) is extended from a homogeneous ideal of R, if and only if R̄H\Q is a graded-Prüfer domain for all homogeneous maximal t-ideals Q of R, if and only if R̄N(H) is a Prüfer domain, if and only if R is a UMT-domain.
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TL;DR: In this paper, the authors studied normal, cohyponormal, hyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces, and proved that for some weighted Hardy spaces, the normal weighted composition operator (C_{\psi,\varphi}f(z)=
Abstract: If $\psi$ is analytic on the open unit disk $\mathbb{D}$ and $\varphi$ is an analytic self-map of $\mathbb{D}$, the weighted composition operator $C_{\psi,\varphi}$ is defined by $C_{\psi,\varphi}f(z)=\psi(z)f (\varphi (z))$, when $f$ is analytic on $\mathbb{D}$. In this paper, we study normal, cohyponormal, hyponormal and normaloid weighted composition operators on the Hardy and weighted Bergman spaces. First, for some weighted Hardy spaces $H^{2}(\beta)$, we prove that if $C_{\psi,\varphi}$ is cohyponormal on $H^{2}(\beta)$, then $\psi$ never vanishes on $\mathbb{D}$ and $\varphi$ is univalent, when $\psi
ot \equiv 0$ and $\varphi$ is not a constant function. Moreover, for $\psi=K_{a}$, where $|a| < 1$, we investigate normal, cohyponormal and hyponormal weighted composition operators $C_{\psi,\varphi}$. After that, for $\varphi $ which is a hyperbolic or parabolic automorphism, we characterize all normal weighted composition operators $C_{\psi,\varphi}$, when $\psi
ot \equiv 0$ and $\psi$ is analytic on $\overline{\mathbb{D}}$.
Finally, we find all normal weighted composition operators which are bounded below.
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