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 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.
Abstract : The aim of this paper is to investigate Betchov-Da Rios equation by using null Cartan, pseudo null and partially null curve in Minkowski spacetime. Time derivative formulas of frame of $s$ parameter null Cartan, pseudo null and partially null curve are examined, respectively. By using the obtained derivative formulas, new results are given about the solution of Betchov-Da Rios equation. The differential geometric properties of these solutions are obtained with respect to Lorentzian causal character of $s$ parameter curve. For a solution of Betchov-Da Rios equation, it is seen that null Cartan $s$ parameter curves are space curves in three-dimensional Minkowski space. Then all points of the soliton surface are flat points of the surface for null Cartan and partially null curve. Thus, it is seen from the results obtained that there is no surface corresponding to the solution of Betchov-Da Rios equation by using the pseudo null $s$ parameter curve.
Abstract : The goal of this article is to introduce the concept of pseudo-weighted Browder spectrum when the underlying Hilbert space is not necessarily separable. To attain this goal, the notion of $\alpha$-pseudo-Browder operator has been introduced. The properties and the relation of the weighted spectrum, pseudo-weighted spectrum, weighted Browder spectrum, and pseudo-weighted Browder spectrum have been investigated by extending analogous properties of their corresponding essential pseudo-spectrum and essential pseudo-weighted spectrum. The weighted spectrum, pseudo-weighted spectrum, weighted Browder, and pseudo-weighted Browder spectrum of the sum of two bounded linear operators have been characterized in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces. This exploration ends with a characterization of the pseudo-weighted Browder spectrum of the sum of two bounded linear operators defined over the arbitrary Hilbert spaces under certain conditions.
Abstract : Let ${\mathcal A}=(A_n)_{n\geq 0}$ be an increasing sequence of rings. We say that ${\mathcal I}=(I_n)_{n\geq 0}$ is an associated sequence of ideals of ${\mathcal A}$ if $I_0=A_0$ and for each $n\geq 1$, $I_n$ is an ideal of $A_n$ contained in $I_{n+1}$. We define the polynomial ring and the power series ring as follows: ${\mathcal I}[X]=\lbrace f={\sum_{i=0}^n}a_iX^i\in {\mathcal A}[X]: n\in \mathbb{N}, a_i\in I_i\rbrace$ and ${\mathcal I}[[X]]=\lbrace f={\sum_{i=0}^{+\infty}}a_iX^i\in {\mathcal A}[[X]]: a_i\in I_i\rbrace$. In this paper we study the Noetherian and the SFT properties of these rings and their consequences.
Abstract : 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.
Abstract : It is shown that every nilpotent-invariant module can be decomposed into a direct sum of a quasi-injective module and a square-free module that are relatively injective and orthogonal. This paper is also concerned with rings satisfying every cyclic right $R$-module is nilpotent-invariant. We prove that $R\cong R_1\times R_2$, where $R_1, R_2$ are rings which satisfy $R_1$ is a semi-simple Artinian ring and $R_2$ is square-free as a right $R_2$-module and all idempotents of $R_2$ is central. The paper concludes with a structure theorem for cyclic nilpotent-invariant right $R$-modules. Such a module is shown to have isomorphic simple modules $eR$ and $fR$, where $e,f$ are orthogonal primitive idempotents such that $eRf\ne 0$.
Abstract : Zero-difference balanced (ZDB) functions can be applied to many areas like optimal constant composition codes, optimal frequency hopping sequences etc. Moreover, it has been shown that the image set of some ZDB functions is a regular partial difference set, and hence provides strongly regular graphs. Besides, perfect nonlinear functions are zero-difference balanced functions. However, the converse is not true in general. In this paper, we use the decomposition of cyclotomic polynomials into irreducible factors over $\mathbb F_p$, where $p$ is an odd prime to generalize some recent results on ZDB functions. Also we extend a result introduced by Claude et al. [3] regarding zero-difference-$p$-balanced functions over $\mathbb F_{p^n}$. Eventually, we use these results to construct some optimal constant composition codes.
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 are no amphicheiral 3-stranded pretzel knots with symmetric union presentations.
Abstract : We show that a pseudo-Anosov map constructed as a product of the large power of Dehn twists of two filling curves always has a geodesic axis on the curve graph of the surface. We also obtain estimates of the stable translation length of a pseudo-Anosov map, when two filling curves are replaced by multicurves. Three main applications of our theorem are the following: (a) determining which word realizes the minimal translation length on the curve graph within a specific class of words, (b) giving a new class of pseudo-Anosov maps optimizing the ratio of stable translation lengths on the curve graph to that on Teichm{\" u}ller space, (c) giving a partial answer of how much power is needed for Dehn twists to generate right-angled Artin subgroup of the mapping class group.
Binlin Dai, Zekun Li
Bull. Korean Math. Soc. 2023; 60(2): 307-313
https://doi.org/10.4134/BKMS.b210928
Zhengmao Chen
Bull. Korean Math. Soc. 2023; 60(4): 1085-1100
https://doi.org/10.4134/BKMS.b220531
Weike Yu
Bull. Korean Math. Soc. 2022; 59(6): 1423-1438
https://doi.org/10.4134/BKMS.b210799
Tahire Ozen
Bull. Korean Math. Soc. 2023; 60(6): 1463-1475
https://doi.org/10.4134/BKMS.b220573
Ramon Flores
Bull. Korean Math. Soc. 2023; 60(6): 1497-1522
https://doi.org/10.4134/BKMS.b220669
Dong-Soo Kim, Young Ho Kim
Bull. Korean Math. Soc. 2023; 60(4): 905-913
https://doi.org/10.4134/BKMS.b220393
Mustafa Altın, Ahmet Kazan, Dae Won Yoon
Bull. Korean Math. Soc. 2023; 60(5): 1299-1320
https://doi.org/10.4134/BKMS.b220680
Sangeet Kumar, Megha Pruthi
Bull. Korean Math. Soc. 2023; 60(4): 1003-1016
https://doi.org/10.4134/BKMS.b220452
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