Abstract : Quantization for probability distributions concerns the best approximation of a $d$-dimensional probability distribution $P$ by a discrete probability with a given number $n$ of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on $mathbb R$. For such a probability measure $P$, an induction formula to determine the optimal sets of $n$-means and the $n$th quantization error for every natural number $n$ is given. In addition, using the induction formula we give some results and observations about the optimal sets of $n$-means for all $ngeq 2$.
Abstract : Let $\mathcal{M}$ be a stable Serre subcategory of the category of $R$-modules. We introduce the concept of $\mathcal{M}$-minimax $R$-modules and investigate the local-global principle for generalized local cohomology modules that concerns to the $\mathcal{M}$-minimaxness. We also provide the $\mathcal{M}$-finiteness dimension $f^{\mathcal{M}}_I(M,N)$ of $M,N$ relative to $I$ which is an extension the finiteness dimension $f_I(N)$ of a finitely generated $R$-module $N$ relative to $I$.
Abstract : In the present study, we consider some curvature properties of generalized $B$-curvature tensor on Kenmotsu manifold. Here first we describe certain vanishing properties of generalized $B$ curvature tensor on Kenmostu manifold. Later we formulate generalized $B$ pseudo-symmetric condition on Kenmotsu manifold. Moreover, we also characterize generalized $B$ $\phi$-recurrent Kenmotsu manifold.
Abstract : In this note, we apply a maximum principle related to vo-lu-me growth of a complete noncompact Riemannian manifold, which was recently obtained by Al'{i}as, Caminha and do Nascimento in~cite{Alias-Caminha-Nascimento}, to es-ta-blish new uniqueness and nonexistence results concerning maximal spacelike hypersurfaces immersed in a generalized Robertson-Walker (GRW) spacetime obeying the timelike convergence condition. A study of entire solutions for the maximal hypersurface equation in GRW spacetimes is also made and, in particular, a new Calabi-Bernstein type result is presented.
Abstract : In this paper a generalization of convergent sequences in connection with generalized topologies and filters is given. Additionally, properties such as uniqueness, behavior related to continuous functions are established and notions relative to product spaces.
Abstract : In this paper, we establish Liouville type theorems for the fractional powers of multidimensional Bessel operators extending the results given in \cite{GMQ18}. In order to do this, we consider the distributional point of view of fractional Bessel operators studied in \cite{Mo18}.
Abstract : Let $\mathfrak{A}$ and $\mathfrak{B}$ be unital prime $*$-algebras such that $\mathfrak{A}$ contains a nontrivial projection. In the present paper, we show that if a bijective map $\Theta:\mathfrak{A}\to\mathfrak{B}$ satisfies $\Theta(_*[X\diamond Y, Z])={}_*[\Theta(X)\diamond \Theta(Y), \Theta(Z)]$ for all $X, Y, Z\in\mathfrak{A}$, then $\Theta$ or $-\Theta$ is a $*$-ring isomorphism. As an application, we shall characterize such maps in factor von Neumann algebras.
Abstract : In this article, we show that the family of all $\mathcal{I}^\mathcal{K}$-open subsets in a topological space forms a topology if $\mathcal{K}$ is a maximal ideal. We introduce the notion of $\mathcal{I}^\mathcal{K}$-covering map and investigate some basic properties. The notion of quotient map is studied in the context of $\mathcal{I}^\mathcal{K}$-convergence and the relationship between $\mathcal{I}^\mathcal{K}$-continuity and $\mathcal{I}^\mathcal{K}$-quotient map is established. We show that for a maximal ideal $\mathcal{K}$, the properties of continuity and preserving $\mathcal{I}^\mathcal{K}$-convergence of a function defined on $X$ coincide if and only if $X$ is an $\mathcal{I}^\mathcal{K}$-sequential space.
Abstract : In this paper, h-quasi-hemi-slant submersions and almost h-quasi-hemi-slant submersions from almost quaternionic Hermitian manifolds onto Riemannian manifolds are introduced. Fundamental results on h-quasi-hemi-slant submersions: the integrability of distributions, geometry of foliations and the conditions for such submersions to be totally geodesic are investigated. Moreover, some non-trivial examples of the h-quasi-hemi-slant submersion are constructed.
Abstract : In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth \begin{equation*} \begin{cases} -\Delta_\lambda u -\mu v =|v|^{p-1}v &\;\text{ in } \Omega,\\ -\Delta_\lambda v -\mu u=|u|^{q-1}u &\;\text{ in } \Omega,\\ u = v = 0 &\;\text{ on } \partial\Omega, \end{cases} \end{equation*} where $p, q>1$ and $\Omega$ is a smooth bounded domain in $\mathbb{R}^N$, $N\ge 3$. Here $\Delta_\lambda$ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.
Baha' Abughazaleh, Omar AbedRabbu Abughneim
Commun. Korean Math. Soc. 2022; 37(4): 969-975
https://doi.org/10.4134/CKMS.c210348
Sugi Guritman
Commun. Korean Math. Soc. 2023; 38(2): 341-354
https://doi.org/10.4134/CKMS.c220110
Dumitru Baleanu, Banupriya Kandasamy, Ramkumar Kasinathan, Ravikumar Kasinathan, Varshini Sandrasekaran
Commun. Korean Math. Soc. 2023; 38(3): 967-982
https://doi.org/10.4134/CKMS.c220231
Mahmoud Benkhalifa
Commun. Korean Math. Soc. 2023; 38(2): 643-648
https://doi.org/10.4134/CKMS.c220179
Ahmad Alinejad, Morteza Essmaili, Hatam Vahdati
Commun. Korean Math. Soc. 2023; 38(4): 1101-1110
https://doi.org/10.4134/CKMS.c220364
Anass Assarrar, Najib Mahdou
Commun. Korean Math. Soc. 2023; 38(4): 1001-1017
https://doi.org/10.4134/CKMS.c230004
M. Alimohammady, A. Rezvani, C. Tunc
Commun. Korean Math. Soc. 2023; 38(4): 1045-1061
https://doi.org/10.4134/CKMS.c220308
Rezvan Varmazyar
Commun. Korean Math. Soc. 2023; 38(4): 993-999
https://doi.org/10.4134/CKMS.c220338
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