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BKMS
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2024-03-31
Some factorization properties of idealization in commutative rings with zero divisors
Sina Eftekhari, Sayyed Heidar Jafari, Mahdi Reza KhorsandiAbstract : We study some factorization properties of the idealization $R$(+)$M$ of a module $M$ in a commutative ring $R$ which is not necessarily a domain. We show that $R$(+)$M$ 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 $R$(+)$M$ is a BFR. We also characterize the idealization rings which are UFRs.
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2024-03-31
On the generalized principally injective modules
Fatemeh Gholami, Zohreh Habibi, Alireza NajafizadehAbstract : Some results are generalized from principally injective rings to principally injective modules. Moreover, it is proved that the results are valid to some other extended injectivity conditions which may be defined over modules. The influence of such injectivity conditions are studied for both the trace and the reject submodules of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.
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2024-03-31
Sharp bounds of fifth coefficient and Hermitian-Toeplitz determinants for Sakaguchi classes
SURYA GIRI, S. SIVAPRASAD KUMARAbstract : For the classes of analytic functions $f$ defined on the unit disk satisfying $$\frac{2 z {f}'(z)}{f(z) - f(-z)} \prec \varphi(z) \quad \text{and} \quad \frac{(2 z {f}'(z))'}{(f(z) - f(-z))'} \prec \varphi(z) , $$ 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.
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2024-03-31
Certain differential identities in prime rings with anti-automorphisms
Abbas Hussain Shikeh, Mohammad Aslam SiddeequeAbstract : The objective of this paper is to study some central identities involving 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.
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2024-03-31
Curvature estimates for a class of fully nonlinear elliptic equations with general right hand sides
Jundong ZhouAbstract : 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.
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2024-03-31
Fourier decay of Moran measure with quasi periodic sequence
Zong Sheng LiuAbstract : 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.
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2024-03-31
Timelike tubular surfaces of Weingarten types and linear Weingarten types in Minkowski 3-space
He Chenghong, Sun He-JunAbstract : 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 $(X,Y,Z)\in\{(K,H,K_{II})$, $(K,H,H_{II})$, $(K,K_{II},H_{II})$, $(H$, $K_{II},H_{II})\}$.
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2024-03-31
The amphicheiral 2-bridge knots with symmetric union presentations
Toshifumi TanakaAbstract : 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 are no amphicheiral 3-stranded pretzel knots with symmetric union presentations.
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2024-03-31
Geometric inequalities for affine connections on Riemannian manifolds
Huiting Chang, Fanqi ZengAbstract : Using a Reilly type integral formula due to Li and Xia \cite{LiXia2017}, 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}mery Ricci curvature 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.
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2024-03-31
Bj\"{o}rling problem for zero mean curvature surfaces in the three-dimensional light cone
Joseph Cho, So Young Kim, Dami Lee, Wonjoo Lee, Seong-Deog YangAbstract : We solve the Bj\"{o}rling problem for zero mean curvature surfaces in the three-dimensional light cone. As an application, we construct and classify all rotational zero mean curvature surfaces.
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2024-03-31
The secondary Upsilon function of L--space knots is a concave conjugate
Masakazu TeragaitoAbstract : 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.
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2024-03-31
Large time convergence for a chemotaxis model with degenerate local sensing and consumption
Philippe LAURENCOTAbstract : Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is $C^1$-smooth on $[0,\infty)$, vanishes at zero, and is positive on $(0,\infty)$. A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.
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2024-03-31
Wavelet characterizations of variable Hardy-Lorentz spaces
Yao HeAbstract : 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.
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2024-03-31
Using rotationally symmetric planes to establish topological finiteness of manifolds
Eric ChoiAbstract : Let $(M, p)$ denote a noncompact manifold $M$ together with arbitrary basepoint $p$. In \cite{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 $\mathbb{R}^n$.
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2024-03-31
Resolution of quotient singularities via $G$-constellations
Seung-Jo JungAbstract : For a finite subgroup $G$ of $GL_n(\mathbb C)$, 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 $X:=\mathbb C^3/G$.
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2024-03-31
The boundedness of bilinear pseudodifferential operators in Triebel-Lizorkin and Besov spaces with variable exponents
Yin Liu, Lushun WangAbstract : 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.
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2024-03-31
Quasilinear Schr\"{o}dinger equations for the Heisenberg ferromagnetic spin chain
Yongkuan Cheng, Yaotian ShenAbstract : In this paper, we consider a model problem arising from a classical planar Heisenberg ferromagnetic spin chain \begin{equation*} -\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}, \end{equation*} where $2\leq p<2^*, N\geq 3$. By the Ekeland variational principle, the cut off technique, the change of variables and the $L^{\infty}$ estimate, we study the existence of positive solutions. Here, we construct the $L^{\infty}$ estimate of the solution in an entirely different way. Particularly, all the constants in the expression of this estimate are so well known.
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2024-03-31
Six dimensional almost complex torus manifolds with Euler number six
Donghoon Jang, Jiyun ParkAbstract : 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 $M$.
March, 2024 | Volume 61, No. 2
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