Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.Journal of Frame and Matrix Theory3041-85261120230601The "other" Kolmogorov's inequality in Riesz spaces1818228110.22034/jfmt.2023.182281ENMahin SadatDivandarDepartment of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.0009-0001-9008-7212AliAbbasniaDepartment of Health, Torbat Heydariyeh University of Medical Sciences, Torbat Heydariyeh, IranJournal Article20230919We establish a maximal probability inequality for a class of random variables in the framework of measure-free, Riesz spaces. In the ``other" Kolmogorov's inequality, we consider an upper bound for independent random variables and estimate the lower bound for the sums of random variables in Riesz spaces setting. Furthermore, we get an upper bound for the variance of the sum of random variables.https://jfmt.hsu.ac.ir/article_182281_f7d8f6bd14b6c74ff902f0177f5890e9.pdfFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.Journal of Frame and Matrix Theory3041-85261120230601A modification to $L_{p,\alpha}$ and its applicability in error estimation of triangular functions91418276810.22034/jfmt.2023.421933.1008ENOmidBaghaniHakim Sabzevari University0000-0002-5429-9373HadisAzinDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranJournal Article20231022Error estimate and rate of convergence are two important topics in the field of numerical analysis. A convenient normed space corresponding to the problem under regard can have better upper bounds. This paper introduces a weighted normed space $L_{p,\omega}$ which from the measure theory point of view, is a special case of $L^{p}$ space. This space is a modification of $L_{p,\alpha}$ space, which is introduced before in \cite{Baghani}. Next, by using $L_{p,\alpha}$-norm, we compute a two-variable upper bound of the triangular function.https://jfmt.hsu.ac.ir/article_182768_2bce70a73dede43bcfefe05965d8b169.pdfFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.Journal of Frame and Matrix Theory3041-85261120230601Iteration operator frames: duality and stability152218277010.22034/jfmt.2023.416885.1005ENElaheAgheshte MoghadamHakim university0000000250583377Journal Article20230920The purpose of the paper is to analyze frames $\{f_k\}_{k \in \mathbb{Z}}$ having the form $\{T^{k}f_{0}\}_{k \in \mathbb{Z}}$; so called iteration operator frames for some bounded linear operator $T$ and a fixed vector $f_0$. We state the duality of such frames with respect to their generators. Moreover, we characterize all duals of iteration operator frames with the same structure. We also show that the duals of two iteration operator frames are close to each other provided that the original frames are sufficiently close to each other and vise versa.https://jfmt.hsu.ac.ir/article_182770_aae4917825413d1dda735aa4e8aade91.pdfFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.Journal of Frame and Matrix Theory3041-85261120230601On c-completely regular frames233318277110.22034/jfmt.2023.416420.1003ENMostafaAbediEsfarayen University of Technology, Esfarayen, North Khorasan, Iran.0000-0003-1508-7404Ali AkbarEstajiAli Akbar Estaji,
Faculty of Mathematics and Computer Sciences,
Hakim Sabzevari University,
Sabzevar,
Iran.Journal Article20230914Motivated by definitions of countable completely regular spaces and completely below relations of frames, we define what we call a $c$-completely below relation, denoted by $\prec\!\!\prec_c$, in between two elements of a frame. We show that $a\prec\!\!\prec_c b$ for two elements $a, b$ of a frame $L$ if and only if there is $\alpha\in\mathcal{R}L$ such that $\coz\alpha\wedge a=0$ and $\coz(\alpha-{\bf1})\leq b$ where the set $\{r\in\mathbb{R} : \coz(\alpha-{\bf r})\ne 1\}$ is countable. We say a frame $L$ is a $c$-completely regular frame if $a=\bigvee \limits_{x\prec\!\!\prec_ca}x$ for any $a\in L$. It is shown that a frame $L$ is a $c$-completely regular frame if and only if it is a zero-dimensional frame. An ideal $I$ of a frame $L$ is said to be $c$-completely regular if $a\in I$ implies $a\prec\!\!\prec_c b$ for some $b\in I$. The set of all $c$-completely regular ideals of a frame $L$, denoted by ${\mathrm{c-CRegId}}(L)$, is a compact regular frame and it is a compactification for $L$ whenever $it$ is a $c$-completely regular frame. We denote this compactification by $\beta_cL$ and it is isomorphic to the frame $\beta_0L$, that is, Stone-Banaschewski compactification of $L$. Finally, we show that open and closed quotients of a $c$-completely regular frame are $c$-completely regular.https://jfmt.hsu.ac.ir/article_182771_66f9b8039752dfd37ba3b52d27ffb612.pdfFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.Journal of Frame and Matrix Theory3041-85261120230601Strongly 2-absorbing subacts over monoids with unique zero344118277210.22034/jfmt.2023.417477.1006ENGholamrezaMoghaddasiHakim Sabzevari UniversityNasrinSarvghadHakim Sabzevari UniversityJournal Article20230922In this article, we introduce (strongly) 2-absorbing ideals of monoids and generalize them to (strongly) 2-absorbing subacts of an act over monoids. Among some useful lemmas, we show that the radical ideal of a strongly 2-absorbing ideal is either a prime ideal or the intersection of two ideals which are only distinct prime ideals minimal over it. Also, we prove that for each strongly 2-absorbing ideal I of a monoid, there exists a strongly 2-absorbing S-act A such that Ann(A) = I and vice versa. Moreover, some of their basic properties are developed.https://jfmt.hsu.ac.ir/article_182772_2103049d962d7bc23a943857fe040271.pdfFaculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.Journal of Frame and Matrix Theory3041-852611202306012-Local higher derivations424718277310.22034/jfmt.2023.418086.1007ENTayebeLal ShateriHakim Sabzevari UniversityJournal Article20230926The paper is devoted to 2-local higher derivations on some algebras. It is shown that continuous 2-local higher derivations on B(H), for an infinite dimensional separable Hilbert space H are higher derivations and each 2-local inner higher derivation on F(H) (the ideal of all finite-dimensional operators from B(H)) is a higher derivation. Also, we prove that every 2-local higher derivation from a commutative ∗-subalgebra of the matrix algebra Mn over C is a higher derivation.https://jfmt.hsu.ac.ir/article_182773_588cf592326fa15fbaca7e1973a15aa3.pdf