Abstract : We study some K3 surfaces obtained as minimal resolutions of quotients of subgroups of special reflection groups. Some of these were already studied in a previous paper by W.~Barth and the second author. We give here an easy proof that these are K3 surfaces, give equations in weighted projective space and describe their geometry.
Abstract : Let $\mathrm{G}$ be an arbitrary, connected, simply connected and unimodular Lie group of dimension $3$. On the space $\mathfrak{M}(\mathrm{G})$ of left-invariant Lorentzian metrics on $\mathrm{G}$, there exists a natural action of the group ${\rm Aut}(\mathrm{G})$ of automorphisms of $\mathrm{G}$, so it yields an equivalence relation $\backsimeq$ on $\mathfrak{M}(\mathrm{G})$, in the following way: $h_1\backsimeq h_2 \Leftrightarrow h_2=\phi^{*}(h_1) \;\textrm{for some}\; \phi \in {\rm Aut}(\mathrm{G}).$ In this paper a procedure to compute the orbit space ${\rm Aut}(\mathrm{G})/\mathfrak{M}(\mathrm{G})$ (so called moduli space of $\mathfrak{M}(\mathrm{G})$) is given.
Abstract : For an arbitrary integer $x$, an integer of the form $T(x)\!=\!\frac{x^2+x}{2}$ is called a triangular number. Let $\alpha_1,\dots,\alpha_k$ be positive integers. A sum $\Delta_{\alpha_1,\dots,\alpha_k}(x_1,\dots,x_k)=\alpha_1 T(x_1)+\cdots+\alpha_k T(x_k)$ of triangular numbers is said to be {\it almost universal with one exception} if the Diophantine equation $\Delta_{\alpha_1,\dots,\alpha_k}(x_1,\dots,x_k)=n$ has an integer solution $(x_1,\dots,x_k)\in\mathbb{Z}^k$ for any nonnegative integer $n$ except a single one. In this article, we classify all almost universal sums of triangular numbers with one exception. Furthermore, we provide an effective criterion on almost universality with one exception of an arbitrary sum of triangular numbers, which is a generalization of ``15-theorem" of Conway, Miller, and Schneeberger.
Abstract : In this paper, we present a method of characterizing minimal polynomials on the ring ${\mathbf Z}_p$ of $p$-adic integers in terms of their coefficients for an arbitrary prime $p$. We first revisit and provide alternative proofs of the known minimality criteria given by Larin [11] for $p=2$ and Durand and Paccaut [6] for $p=3$, and then we show that for any prime $p\geq 5,$ the proposed method enables us to classify all possible minimal polynomials on ${\mathbf Z}_p$ in terms of their coefficients, provided that two prescribed prerequisites for minimality are satisfied.
Abstract : In this paper we give conditions on a matrix which guarantee that it is similar to a centrosymmetric matrix. We use this conditions to show that some $4 \times 4$ and $6 \times 6$ Toeplitz matrices are similar to centrosymmetric matrices. Furthermore, we give conditions for a matrix to be similar to a matrix which has a centrosymmetric principal submatrix, and conditions under which a matrix can be dilated to a matrix similar to a centrosymmetric matrix.
Abstract : For two dimensional lattices, a Gaussian basis achieves all two successive minima. For dimension larger than two, constructing a pairwise Gaussian basis is useful to compute short vectors of the lattice. For three dimensional lattices, Semaev showed that one can convert a pairwise Gaussian basis to a basis achieving all three successive minima by one simple reduction. A pairwise Gaussian basis can be obtained from a given basis by executing Gauss algorithm for each pair of basis vectors repeatedly until it returns a pairwise Gaussian basis. In this article, we prove a necessary and sufficient condition for a pairwise Gaussian basis to achieve the first $k$ successive minima for three dimensional lattices for each $k\in\{1,2,3\}$ by modifying Semaev's condition. Our condition directly checks whether a pairwise Gaussian basis contains the first $k$ shortest independent vectors for three dimensional lattices. LLL is the most basic lattice basis reduction algorithm and we study how to use LLL to compute a pairwise Gaussian basis. For $\delta\ge 0.9$, we prove that LLL($\delta$) with an additional simple reduction turns any basis for a three dimensional lattice into a pairwise SV-reduced basis. By using this, we convert an LLL reduced basis to a pairwise Gaussian basis in a few simple reductions. Our result suggests that the LLL algorithm is quite effective to compute a basis with all three successive minima for three dimensional lattices.
Abstract : We describe a construction which takes as an input a left order of the fundamental group of a manifold, and outputs a (singular) foliation of this manifold which is analogous to a taut foliation. We investigate this construction in detail in dimension $2$, and exhibit connections to various problems in dimension $3$.
Abstract : This paper considers a parabolic-hyperbolic-hyperbolic type chemotaxis system in $\mathbb{R}^{d}$, $d\ge3$, describing tumor-induced angiogenesis. The global existence result and temporal decay estimate for a unique mild solution are established under the assumption that some Sobolev norms of initial data are sufficiently small.
Abstract : Let $\mathfrak{a}$ be an ideal of a commutative noetherian ring $R$. We give some descriptions of the $\mathfrak{a}$-depth of $\mathfrak{a}$-relative Cohen-Macaulay modules by cohomological dimensions, and study how relative Cohen-Macaul-\\ayness behaves under flat extensions. As applications, the perseverance of relative Cohen-Macaulayness in a polynomial ring, formal power series ring and completion are given.
Abstract : In this paper, using the theory of majorization, we discuss the Schur $m$ power convexity for $L$-conjugate means of $n$ variables and the Schur convexity for weighted $L$-conjugate means of $n$ variables. As applications, we get several inequalities of general mean satisfying Schur convexity, and a few comparative inequalities about $n$ variables Gini mean are established.
Cédric Bonnafé, Alessandra Sarti
J. Korean Math. Soc. 2023; 60(4): 695-743
https://doi.org/10.4134/JKMS.j220014
Mohamed Boucetta, Abdelmounaim Chakkar
J. Korean Math. Soc. 2022; 59(4): 651-684
https://doi.org/10.4134/JKMS.j210460
Jangwon Ju
J. Korean Math. Soc. 2023; 60(5): 931-957
https://doi.org/10.4134/JKMS.j220231
Sangtae Jeong
J. Korean Math. Soc. 2023; 60(1): 1-32
https://doi.org/10.4134/JKMS.j210494
Jangwon Ju
J. Korean Math. Soc. 2023; 60(5): 931-957
https://doi.org/10.4134/JKMS.j220231
Sangtae Jeong
J. Korean Math. Soc. 2023; 60(1): 1-32
https://doi.org/10.4134/JKMS.j210494
Cédric Bonnafé, Alessandra Sarti
J. Korean Math. Soc. 2023; 60(4): 695-743
https://doi.org/10.4134/JKMS.j220014
Mohamed Boucetta, Abdelmounaim Chakkar
J. Korean Math. Soc. 2022; 59(4): 651-684
https://doi.org/10.4134/JKMS.j210460
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