Abstract : Let $Y$ be the quintic del Pezzo $4$-fold defined by the linear section of $\textrm{Gr}(2,5)$ by $\mathbb{P}^7$. In this paper, we describe the locus of double lines in the Hilbert scheme of coincs in $Y$. As a corollary, we obtain the desigularized model of the moduli space of stable maps of degree $2$ in $Y$. We also compute the intersection Poincar\'e polynomial of the stable map space.
Abstract : In this paper we study a nudging continuous data assimilation algorithm for the three-dimensional Leray-$\alpha$ model, where measurement errors are represented by stochastic noise. First, we show that the stochastic data assimilation equations are well-posed. Then we provide explicit conditions on the observation density (resolution) and the relaxation (nudging) parameter which guarantee explicit asymptotic bounds, as the time tends to infinity, on the error between the approximate solution and the actual solution which is corresponding to these measurements, in terms of the variance of the noise in the measurements.
Abstract : In this paper we consider a sequence of polynomials defined by some recurrence relation. They include, for instance, Poupard polynomials and Kreweras polynomials whose coefficients have some combinatorial interpretation and have been investigated before. Extending a recent result of Chapoton and Han we show that each polynomial of this sequence is a self-reciprocal polynomial with positive coefficients whose all roots are unimodular. Moreover, we prove that their arguments are uniformly distributed in the interval $[0,2\pi)$.
Abstract : 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.
Abstract : In this article, we find bases for the spaces of modular forms $M_{2}(\Gamma _{0}(88),\big( \frac{d}{\cdot }\big) )$ for $d=1,8,44\text{ and }88$. We then derive formulas for the number of representations of a positive integer by the diagonal quaternary quadratic forms with coefficients $1,2,11$ and $ 22 $.
Abstract : In this note, we show that a strongly $\phi$-ring $R$ is a $\phi$-$\rm PvMR$ if and only if any $\phi$-torsion-free $R$-module is $\phi$-$w$-flat, if and only if any $\rm GV$-torsion-free divisible $R$-module is nonnil-absolutely $w$-pure, if and only if any $\rm GV$-torsion-free $h$-divisible $R$-module is nonnil-absolutely $w$-pure, if and only if any finitely generated nonnil ideal of $R$ is $w$-projective.
Abstract : Erratum/Addendum to the paper ``Biisometric operators and biorthogonal sequences" [Bull. Korean Math. Soc. {\bf 56} (2019), No. 3, pp. 585--596].
Abstract : Let $u$ be a function on a connected finite graph $G=(V, E)$. We consider the mean field equation \begin{equation}\label{5} -\Delta u=\rho\bigg{(}\frac{he^u}{\int_V he^ud\mu}-\frac{1}{|V|}\bigg{)}, \end{equation} where $\Delta$ is $\mu$-Laplacian on the graph, $\rho\in \mathbb{R}\backslash\{0\}$, $h: V\ra\mathbb{R^+}$ is a function satisfying $\min_{x\in V}h(x)>0$. Following Sun and Wang \cite{S-w}, we use the method of Brouwer degree to prove the existence of solutions to the mean field equation $(\ref{5})$. Firstly, we prove the compactness result and conclude that every solution to the equation $(\ref{5})$ is uniformly bounded. Then the Brouwer degree can be well defined. Secondly, we calculate the Brouwer degree for the equation $(\ref{5})$, say \begin{equation*}d_{\rho,h}=\left\{\begin{array}{lll} -1,\quad \rho>0,\\ \ 1,\quad \ \rho
Abstract : The main purpose of this paper is to study the hybrid mean value problem involving generalized Dedekind sums, generalized Hardy sums and Kloosterman sums. Some exact computational formulas are given by using the properties of Gauss sums and the mean value theorem of the Dirichlet L-function. A result of W. Peng and T. P. Zhang [12] is extended. The new results avoid the restriction that $q$ is a prime.
Abstract : {Let $K$ be an algebraically closed field of characteristic 0 and let $f$ be a non-fibered planar quadratic polynomial map of topological degree 2 defined over $K$. We assume further that the meromorphic extension of $f$ on the projective plane has the unique indeterminacy point.} We define \emph{the critical pod of $f$} where $f$ sends a critical point to another critical point. By observing the behavior of $f$ at the critical pod, we can determine a good conjugate of $f$ which shows its statue in GIT sense.
Jun Ho Lee
Bull. Korean Math. Soc. 2023; 60(2): 315-323
https://doi.org/10.4134/BKMS.b220094
Daiqing Zhang
Bull. Korean Math. Soc. 2023; 60(1): 47-73
https://doi.org/10.4134/BKMS.b210850
Art\= uras Dubickas
Bull. Korean Math. Soc. 2022; 59(5): 1269-1277
https://doi.org/10.4134/BKMS.b210728
Ahmad Abbasi, Mona Gholamnia~Taleshani
Bull. Korean Math. Soc. 2022; 59(3): 685-695
https://doi.org/10.4134/BKMS.b210416
Gaoshun Gou, Yueping Jiang, Ioannis D. Platis
Bull. Korean Math. Soc. 2023; 60(1): 225-235
https://doi.org/10.4134/BKMS.b220059
Zhicheng Wang
Bull. Korean Math. Soc. 2023; 60(1): 23-32
https://doi.org/10.4134/BKMS.b210703
Bayram Ali Ersoy, Ünsal Tekir, Eda Yıldız
Bull. Korean Math. Soc. 2024; 61(1): 83-92
https://doi.org/10.4134/BKMS.b230023
Namjip Koo, Hyunhee Lee, Nyamdavaa Tsegmid
Bull. Korean Math. Soc. 2024; 61(1): 195-205
https://doi.org/10.4134/BKMS.b230071
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