Journal of the
Korean Mathematical Society
JKMS
ISSN(Print) 0304-9914
ISSN(Online) 2234-3008
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2022-09-01
Weakly equivariant classification of small covers over a product of simplicies
Aslı Güçlükan İlhan, Sabri Kaan Gürbüzer
Abstract : Given a dimension function $\omega$, we introduce the notion of an $\omega$-vector weighted digraph and an $\omega$-equivalence between them. Then we establish a bijection between the weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over a product of simplices $\Delta^{\omega(1)}\times\cdots \times \Delta^{\omega(m)}$ and the set of $\omega$-equivalence classes of $\omega$-vector weighted digraphs with $m$-labeled vertices, where $n$ is the sum of the dimensions of the simplicies. Using this bijection, we obtain a formula for the number of weakly $(\mathbb{Z}/2)^n$-equivariant homeomorphism classes of small covers over a product of three simplices.
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2023-05-01
Gradient type estimates for linear elliptic systems from composite materials
Youchan Kim, Pilsoo ShinAbstract : In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise H\"{o}lder continuous but locally H\"{o}lder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient H\"{o}lder continuity which was obtained by the previous results.
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2022-11-01
On limit behaviours for Feller's unfair-fair-game and its related model
Jun AnAbstract : Feller introduced an unfair-fair-game in his famous book \cite{Feller-1968}. In this game, at each trial, player will win $2^k$ yuan with probability $p_k=1/2^kk(k+1)$, $k\in \mathbb{N}$, and zero yuan with probability $p_0=1-\sum_{k=1}^{\infty}p_k$. Because the expected gain is 1, player must pay one yuan as the entrance fee for each trial. Although this game seemed ``fair", Feller \cite{Feller-1945} proved that when the total trial number $n$ is large enough, player will loss $n$ yuan with its probability approximate 1. So it's an ``unfair" game. In this paper, we study in depth its convergence in probability, almost sure convergence and convergence in distribution. Furthermore, we try to take $2^k=m$ to reduce the values of random variables and their corresponding probabilities at the same time, thus a new probability model is introduced, which is called as the related model of Feller's unfair-fair-game. We find out that this new model follows a long-tailed distribution. We obtain its weak law of large numbers, strong law of large numbers and central limit theorem. These results show that their probability limit behaviours of these two models are quite different.
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2023-07-01
Classification of solvable lie algebras whose non-trivial coadjoint orbits of simply connected lie groups are all of codimension 2
Hieu Van Ha, Vu Anh Le, Tu Thi Cam Nguyen, Hoa Duong QuangAbstract : We give a classification of real solvable Lie algebras whose non-trivial coadjoint orbits of corresponding to simply connected Lie groups are all of codimension 2. These Lie algebras belong to a well-known class, called the class of MD-algebras.
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2024-03-01
Positive solutions to discrete harmonic functions in unbounded cylinders
Fengwen Han, Lidan WangAbstract : In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in $\mathbb{Z}^d$. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.
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2023-03-01
The Harbourne-Hirschowitz condition and the anticanonical orthogonal property for surfaces
Abel Castorena, Juan Bosco Fr\'ias-MedinaAbstract : In this paper we give the first steps toward the study of the Harbourne-Hirschowitz condition and the anticanonical orthogonal property for regular surfaces. To do so, we consider the Kodaira dimension of the surfaces and study the cases based on the Enriques-Kodaira classification.
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2023-03-01
The gradient flow equation of Rabinowitz action functional in a symplectization
Urs FrauenfelderAbstract : Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.
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The Difference of Hyperharmonic Numbers via Geometric and Analytic Methods
\c{C}a\u{g}atay Altunta\c{s}
, Haydar G\"{o}ral, Do\u{g}a Can Sertba\c{s}J. Korean Math. Soc. 2022; 59(6): 1103-1137
https://doi.org/10.4134/JKMS.j210630 -
Some algebras having relations like those for the 4-dimensional Sklyanin algebras
Alexandru Chirvasitu, S. Paul Smith
J. Korean Math. Soc. 2023; 60(4): 745-777
https://doi.org/10.4134/JKMS.j220200 -
Pseudo-Riemannian Sasaki solvmanifolds
Diego Conti, Federico A. Rossi, Romeo Segnan Dalmasso
J. Korean Math. Soc. 2023; 60(1): 115-141
https://doi.org/10.4134/JKMS.j220232 -
New congruences for $\ell$-regular overpartitions
Ankita Jindal, Nabin K. Meher
J. Korean Math. Soc. 2022; 59(5): 945-962
https://doi.org/10.4134/JKMS.j220011
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Rigidity and nonexistence of Riemannian immersions in semi-Riemannian warped products via parabolicity
Railane Antonia, Henrique de Lima, Márcio Santos
J. Korean Math. Soc. 2024; 61(1): 41-63
https://doi.org/10.4134/JKMS.j220523 -
Some abelian McCoy rings
Rasul Mohammadi, Ahmad Moussavi, masoome zahiri
J. Korean Math. Soc. 2023; 60(6): 1233-1254
https://doi.org/10.4134/JKMS.j220625 -
Geometry of the moduli space of Higgs pairs on an irreducible nodal curve of arithmetic genus one
Sang-Bum Yoo
J. Korean Math. Soc. 2024; 61(1): 161-181
https://doi.org/10.4134/JKMS.j230278 -
An intrinsic proof of Numata's theorem on Landsberg spaces
Salah Gomaa Elgendi, Amr Soleiman
J. Korean Math. Soc. 2024; 61(1): 149-160
https://doi.org/10.4134/JKMS.j230263
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