Abstract : We study some factorization properties of the idealization $\idealztn{R}{M}$ of a module $M$ in a commutative ring $R$ which is not necessarily a domain. We show that $\idealztn{R}{M}$ is ACCP if and only if $R$ is ACCP and $M$ satisfies ACC on its cyclic submodules. We give an example to show that the BF property is not necessarily preserved in idealization, and give some conditions under which $\idealztn{R}{M}$ is a BFR. We also characterize the idealization rings which are UFRs.
Abstract : The notions of principally injective rings and modules are recalled. Some results are generalized from the case of principally injective rings to the case of principally injective modules. Moreover, it is proved that the results are valid to other extended injectivity conditions defined over modules. The influence of such injectivity conditions are studied for the trace and reject of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.
Abstract : For the classes of analytic functions $f$ defined on the unit disk satisfying $$\frac{z {f}'(z)}{f(z) - f(-z)} \prec \varphi(z) \quad \text{and} \quad \frac{(2 z {f}'(z))'}{(f(z) - f(-z))'} \prec \varphi(z) , $$ denoted by $\mathcal{S}^*_s(\varphi)$ and $\mathcal{C}_s(\varphi)$ respectively, the sharp bound of the $n^{th}$ Taylor coefficients are known for $n=2,$ $3$ and $4$. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.
Abstract : The objective of this manuscript is to study some central identities with generalized derivations and anti-automorphisms in prime rings. Using the tools of the theory of functional identities, several known results have been generalized as well as improved.
Abstract : In this paper, we establish the curvature estimates for a class of curvature equations with general right hand sides depending on the gradient. We show an existence result by using the continuity method based on a priori estimates. We also derive interior curvature bounds for solutions of a class of curvature equations subject to affine Dirichlet data.
Abstract : In this paper, we introduce a class of Moran measures generated by quasi periodic sequences, and consider power decay of the Fourier transforms of this kind of measures.
Abstract : Let $K$, $H$, $K_{II}$ and $H_{II}$ be the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature of a timelike tubular surface $T_\gamma(\alpha)$ with the radius $\gamma$ along a timelike curve $\alpha(s)$ in Minkowski 3-space $E_{1}^3$. We prove that $T_\gamma(\alpha)$ must be a $(K,H)$-Weingarten surface and a $(K,H)$-linear Weingarten surface. We also show that $T_{\gamma}(\alpha)$ is $(X,Y)$-Weingarten type if and only if its central curve is a circle or a helix, where $(X,Y)\in \{(K,K_{II}), (K,H_{II}),$ $(H,K_{II}), (H,H_{II}), (K_{II},H_{II}) \}$. Furthermore, we prove that there exist no timelike tubular surfaces of $(X,Y)$-linear Weingarten type, $(X,Y,Z)$-linear Weingarten type and $(K,H,K_{II},H_{II})$-linear Weingarten type along a timelike curve in $E_{1}^3$, where $(X,Y,Z)\in \{(K,H,K_{II}),(K,H,H_{II})$, $(K,K_{II},H_{II}),(H,K_{II},H_{II}) \}.
Abstract : In this paper, we characterize amphicheiral 2-bridge knots with symmetric union presentations and show that there exist infinitely many amphicheiral 2-bridge knots with symmetric union presentations with two twist regions. We also show that there do not exist amphicheiral 3-stranded pretzel knots with symmetric union presentations.
Abstract : Using a Reilly type integral formula due to Li and Xia (J. Geom. Anal., 2017, 27: 2539-2556), we prove several geometric inequalities for affine connections on Riemannian manifolds. We obtain some general De Lellis-Topping type inequalities associated with affine connections. These not only permit to derive quickly many well-known De Lellis-Topping type inequalities, but also supply a new De Lellis-Topping type inequality when the $1$-Bakry-\'{E}emery Ricci tcurvature is bounded from below by a negative function. On the other hand, we also achieve some Lichnerowicz type estimate for the first (nonzero) eigenvalue of the affine Laplacian with the Robin boundary condition on Riemannian manifolds.
Abstract : For a knot in the 3-sphere, the Upsilon invariant is a piecewise linear function defined on the interval [0,2]. It is known that this invariant of an L-space knot is the Legendre-Fenchel transform (or, convex conjugate) of a certain gap function derived from the Alexander polynomial. To recover an information lost in the Upsilon invariant, Kim and Livingston introduced the secondary Upsilon invariant. In this note, we prove that the secondary Upsilon invariant of an L-space knot is a concave conjugate of a restricted gap function. Also, a similar argument gives an alternative proof of the above fact that the Upsilon invariant of an L-space knot is a convex conjugate of a gap function.
Abstract : In this paper, let $q\in(0,1]$. We establish the boundedness of intrinsic $g$-functions from the Hardy-Lorentz spaces with variable exponent ${H}^{p(\cdot),q}(\mathbb R^{n})$ into Lorentz spaces with variable exponent ${L}^{p(\cdot),q}(\mathbb R^{n})$. Then, for any $q\in(0,1],$ via some estimates on a discrete Littlewood-Paley $g$-function and a Peetre-type maximal function, we obtain several equivalent characterizations of ${H}^{p(\cdot),q}(\mathbb R^{n})$ in terms of wavelets.
Abstract : Let (M, p) denote a noncompact manifold M together with arbitrary basepoint p. In KonTan-II, Kondo-Tanaka show that (M, p) can be compared with a rotationally symmetric plane M_m in such a way that if $M_m$ satisfies certain conditions, then M is proved to be topologically finite. We substitute Kondo-Tanaka's condition of finite total curvature of M_m with a weaker condition and show that the same conclusion can be drawn. We also use our results to show that when M_m satisfies certain conditions, then M is homeomorphic to R^n.
Abstract : For a finite subgroup $G$ of $\mathrm{GL}_n({\mathbb C})$, the moduli space ${\mathcal M}_{\theta}$ of $\theta$-stable $G$-constellations is rarely smooth. This note shows that for a group $G$ of type $\frac{1}{r}(1,a,b)$ with $r=abc+a+b$, there is a generic stability parameter $\theta\in \Theta$ such that the birational component $Y_{\theta}$ of $\theta$-stable $G$-constellations provides a resolution of the quotient singularity $X:={\mathbb C}^3/G$.
Abstract : In this paper, using the Fourier transform, inverse Fourier transform and Littlewood-Paley decomposition technique, we prove the boundedness of bilinear pseudodifferential operators with symbols in the bilinear H\"{o}rmander class BS_{1,1}^m in variable Triebel-Lizorkin spaces and variable Besov spaces.
Abstract : In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain -\Delta u+V(x)u-\frac{u}{\sqrt{1-u^2}}\Delta \sqrt{1-u^2}=\lambda |u|^{p-2}u,\ x\in\mathbb{R}^{N}, Where 2≤p
Abstract : An almost complex torus manifold is a $2n$-dimensional compact connected almost complex manifold equipped with an effective action of a real $n$-dimensional torus $T^n \simeq (S^1)^n$ that has fixed points. For an almost complex torus manifold, there is a labeled directed graph which contains information on weights at the fixed points and isotropy spheres. Let $M$ be a 6-dimensional almost complex torus manifold with Euler number 6. We show that two types of graphs occur for $M$, and for each type of graph we construct such a manifold $M$, proving the existence. Using the graphs, we determine the Chern numbers and the Hirzebruch $\chi_y$-genus of $M$.
Abstract : Using the Nevanlinna value distribution theory of algebroid functions, this paper investigates the growth of two types of complex algebraic differential equation with admissible algebroid solutions and obtains two results, which extends the growth of complex algebraic differential equation with meromorphic solutions obtained by Gao [Acta Math. Sci., 2002,22B(4),149-156].
Abstract : In this paper, we formally introduce the notion of general parametric digamma function Ψ(−s; A, a) and we find the Laurent expansion of Ψ(−s; A, a) at the integers and poles. Considering the contour integrations involving Ψ(−s; A, a), we present some new identities for infinite series involving Dirichlet type parametric harmonic numbers by using the method of residue computation. Then applying these formulas obtained, we establish some explicit relations of parametric linear Euler sums and some special functions (e.g trigonometric functions, digamma functions, Hurwitz zeta functions etc.). Moreover, some illustrative special cases as well as immediate consequences of the main results are also considered.
Duranta Chutia, Rajib Haloi
Bull. Korean Math. Soc. 2022; 59(3): 757-780
https://doi.org/10.4134/BKMS.b210469
Jiankui Li, Shan Li, Kaijia Luo
Bull. Korean Math. Soc. 2022; 59(2): 277-283
https://doi.org/10.4134/BKMS.b200772
Dongli Liu, Jian Tan, Jiman Zhao
Bull. Korean Math. Soc. 2022; 59(3): 547-566
https://doi.org/10.4134/BKMS.b201019
Mohamed Chhiti, Soibri Moindze
Bull. Korean Math. Soc. 2022; 59(2): 397-405
https://doi.org/10.4134/BKMS.b210293
Sunben Chiu, Pingzhi Yuan, Tao Zhou
Bull. Korean Math. Soc. 2023; 60(4): 863-872
https://doi.org/10.4134/BKMS.b220166
Imsoon Jeong, Gyu Jong Kim, Changhwa Woo
Bull. Korean Math. Soc. 2023; 60(4): 849-861
https://doi.org/10.4134/BKMS.b220152
Arezoo Soufi Karbaski, Karim Samei
Bull. Korean Math. Soc. 2022; 59(2): 265-276
https://doi.org/10.4134/BKMS.b200214
Rosihan M. Ali, Sushil Kumar, Vaithiyanathan Ravichandran
Bull. Korean Math. Soc. 2023; 60(2): 281-291
https://doi.org/10.4134/BKMS.b210368
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