@article {
author = {Kajla, Arun and Gupta, Ruchi},
title = {Differences of operators of generalized Szász type},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {141-154},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109811},
abstract = {We derive the approximation of differences of operators. Firstly, we study quantitative estimates for the difference of generalized Szász operators with generalized Szász-Durrmeyer, Szász-Puãltvänea operators, and generalized Szász--Kantorovich operators. Finally, we obtain the quantitative estimate in terms of the weighted modulus of smoothness for these operators.},
keywords = {Positive approximation process,Szasz operators,Pualtvanea operators},
url = {http://www.kjm-math.org/article_109811.html},
eprint = {http://www.kjm-math.org/article_109811_063527dcdf3c26b57d02e2a97cd9e179.pdf}
}
@article {
author = {Le, Anh},
title = {Admissible inertial manifolds for second order in time evolution equations},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {155-173},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109813},
abstract = {We prove the existence of admissible inertial manifolds for the second order in time evolution equations of the form $$ \ddot{x}+2\varepsilon \dot{x}+Ax=f(t,x)$$ when $A$ is positive definite and self-adjoint with a discrete spectrum and the nonlinear term $f$ satisfies the $\varphi$-Lipschitz condition, that is, $\|f(t,x)-f(t,y)\|\leqslant\varphi(t)\left \|A^{\beta}(x-y)\right \|$ for $\varphi$ belonging to one of the admissible Banach function spaces containing wide classes of function spaces like $L_{p}$-spaces, the Lorentz spaces $L_{p,q}$, and many other function spaces occurring in interpolation theory.},
keywords = {Admissible inertial manifolds,second order in time evolution equations,admissible function spaces,Lyapunov--Perron method},
url = {http://www.kjm-math.org/article_109813.html},
eprint = {http://www.kjm-math.org/article_109813_372333a09954785108dc346740036a94.pdf}
}
@article {
author = {Akray, Ismael and Mrakhan, Mediya},
title = {$n$-Absorbing $I$-ideals},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {174-179},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109814},
abstract = {Let $R$ be a commutative ring with identity, let $ I $ be a proper ideal of $ R $, and let $ n \ge 1 $ be a positive integer. In this paper, we introduce a class of ideals that is closely related to the class of $I$-prime ideals. A proper ideal $P$ of $R$ is called an {\itshape $n$-absorbing $I$-ideal} if $a_1,\ a_2,\ \dots ,\ a_{n+1} \in R$ with $a_1 a_2 \dots a_{n+1} \in P-IP$, then $a_1 a_2 \dots a_{i-1} a_{i+1} \dots a_{n+1} \in P$ for some $i\in \left\{1,\ 2,\ \dots ,\ {n+1} \right\}$. Among many results, we show that every proper ideal of a ring $R$ is an {\itshape $n$-absorbing $I$-ideal} if and only if every quotient of $ R$ is a product of $(n+1)$-fields.},
keywords = {$2$-absorbing ideal,$n$-absorbing ideal,$I$-prime ideal,Prime ideal,$n$-absorbing $I$-ideal},
url = {http://www.kjm-math.org/article_109814.html},
eprint = {http://www.kjm-math.org/article_109814_41bf620131018d2506a78fe17acb8a4a.pdf}
}
@article {
author = {Harikrishnan, Panackal and Lafuerza Guillen, Bernardo},
title = {Some classes of Probabilistic Inner product spaces and related inequalities},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {180-192},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109815},
abstract = {We give a new definition for probabilistic inner product spaces, which is sufficiently general to encompass the most important class of probabilistic inner product spaces (briefly, PIP spaces). We have established certain classes of PIP spaces and especially, illustrated that how to construct a real inner product from a Menger PIP space. Finally, we have established the analogous of Cauchy--Schwarz inequality in this general PIP spaces.},
keywords = {Probabilistic normed spaces,$t$-norm,$t$-conorm},
url = {http://www.kjm-math.org/article_109815.html},
eprint = {http://www.kjm-math.org/article_109815_64d0951ded0a74c231310779685b3daa.pdf}
}
@article {
author = {Barootkoob, Sedighe},
title = {On the Arens regularity of a module action and its extensions},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {193-198},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109816},
abstract = {It is known that if the second dual $A^{**}$ of a Banach algebra $A$ is Arens regular, then $A$ is Arens regular itself. However, the converse is not true, in general. Young gave an example of an Arens regular Banach algebra whose second dual is not Arens regular. Later Pym has polished Young's example for presenting more applicable examples. In this paper, we mimic the methods of Young and Pym to present examples of some Arens regular bilinear maps and module actions whose some extensions are not Arens regular. Finally, some relationships between the topological centers of certain Banach module actions are investigated.},
keywords = {Bilinear map,Banach algebra,module action,Arens regular},
url = {http://www.kjm-math.org/article_109816.html},
eprint = {http://www.kjm-math.org/article_109816_130168186224906cc95a0197cf770c0e.pdf}
}
@article {
author = {Alikhani, Saeid and Soltani, Samaneh},
title = {Distinguishing number (index) and domination number of a graph},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {199-205},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109817},
abstract = {The distinguishing number (index) of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling (edge labeling) with $d$ labels that is preserved only by the trivial automorphism. A set $S$ of vertices in $G$ is a dominating set of $G$ if every vertex of $V(G)\setminus S$ is adjacent to some vertex in $S$. The minimum cardinality of a dominating set of $G$ is the domination number of $G$. In this paper, we obtain some upper bounds for the distinguishing number and the distinguishing index of a graph based on its domination number.},
keywords = {distinguishing number,Distinguishing index,Domination number},
url = {http://www.kjm-math.org/article_109817.html},
eprint = {http://www.kjm-math.org/article_109817_a3bf156522e2b7558c7dc5148bbbdf86.pdf}
}
@article {
author = {Rostami, Amin and Mirzavaziri, Madjid and Rahbarnia, Freydoon},
title = {Strong rainbow coloring of unicyclic graphs},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {206-216},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109818},
abstract = {A path in an edge-colored graph is called a \textit{rainbow path}, if no two edges of the path are colored the same. An edge-colored graph $G$, is \textit{rainbow-connected} if any two vertices are connected by a rainbow path. A rainbow-connected graph is called strongly rainbow connected if for every two distinct vertices $u$ and $v$ of $V(G)$, there exists a rainbow path $P$ from $u$ to $v$ that in the length of $P$ is equal to $d(u,v)$. The notations {\rm rc}$(G)$ and {\rm src}$(G)$ are the smallest number of colors that are needed in order to make $G$ rainbow connected and strongly rainbow connected, respectively. In this paper, we find the exact value of {\rm rc}$(G)$, where $G$ is a unicyclic graph. Moreover, we determine the upper and lower bounds for {\rm src}$(G)$, where $G$ is a unicyclic graph, and we show that these bounds are sharp.},
keywords = {Rainbow connection number,strong rainbow connection number,unicyclic graph},
url = {http://www.kjm-math.org/article_109818.html},
eprint = {http://www.kjm-math.org/article_109818_301fa61eefbf5cce342037ce7790283b.pdf}
}
@article {
author = {Makheloufi, Hocine and Bahlil, Mounir and Benaissa, Abbes},
title = {Stability result of the Bresse system with delay and boundary feedback},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {217-235},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109819},
abstract = {Our interest in this paper is to analyze the asymptotic behavior of a Bresse system together with three boundary controls, with delay terms in the first, second, and third equations. By using the semigroup method, we prove the global well-posedness of solutions. Assuming the weights of the delay are small, we establish the exponential decay of energy to the system by using an appropriate Lyapunov functional.},
keywords = {Bresse system,delay,global solutions,Stability,damping,exponential decay},
url = {http://www.kjm-math.org/article_109819.html},
eprint = {http://www.kjm-math.org/article_109819_a6fe24f2fbf18095d111f0f18897fdc8.pdf}
}
@article {
author = {Naimi, Mehdi and Benharrat, Mohammed},
title = {Anderson's theorem for some class of operators},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {236-242},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109820},
abstract = {Anderson's theorem states that if the numerical range of an $n\times n$ matrix is contained in the closed unit disk and intersects with the unit circle at more than $n$ points, then the numerical range coincides with the closed unit disk. In an infinite-dimensional setting, an analogue of this result for a compact operator was established by Gau and Wu and for operator being the sum of a normal and compact operator by Birbonshi et al. We consider here three classes of operators: Operators being the sum of compact and operator with numerical radius strictly less than 1, operators with essentially numerical range coinciding with the convex hull of its essential spectrum, and quasicompact operators. },
keywords = {Numerical Range,essentially numerical range,essentially normal operator,hyponormal operator,quasicompact operator},
url = {http://www.kjm-math.org/article_109820.html},
eprint = {http://www.kjm-math.org/article_109820_543970f9d472b56b147308cd0dc9ecaf.pdf}
}
@article {
author = {Aqalmoun, Mohamed and Ouarrachi, Mounir},
title = {Radically principal rings},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {243-249},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109821},
abstract = {Let $A$ be a commutative ring. An ideal $I$ of $A$ is radically principal if there exists a principal ideal $J$ of $A$ such that $\sqrt{I}=\sqrt{J}$. The ring $A$ is radically principal if every ideal of $A$ is radically principal. In this article, we study radically principal rings. We prove an analogue of the Cohen theorem, precisely, a ring is radically principal if and only if every prime ideal is radically principal. Also we characterize a zero-dimensional radically principal ring. Finally we give a characterization of polynomial ring to be radically principal.},
keywords = {radical,radically principal,polynomial ring},
url = {http://www.kjm-math.org/article_109821.html},
eprint = {http://www.kjm-math.org/article_109821_13bebfe55715bbb4a8fec12a006e6f52.pdf}
}
@article {
author = {Talabeigi, Amin},
title = {Embedding topological spaces in a type of generalized topological spaces},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {250-256},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109822},
abstract = {A stack on a nonempty set $X$ is a collection of nonempty subsets of $X$ that is closed under the operation of superset. Let $(X, \tau)$ be an arbitrary topological space with a stack $\mathcal{S}$, and let $X^*=X \cup \{p\}$ for $p \notin X$. In the present paper, using the stack $\mathcal{S}$ and the topological closure operator associated to the space $(X, \tau)$, we define an envelope operator on $X^*$ to construct a generalized topology $\mu_\mathcal{S}$ on $X^*$. We then show that the space $(X^*, \mu_\mathcal{S})$ is the generalized extension of the space $(X, \tau)$. We also provide conditions under which $(X^*, \mu_\mathcal{S})$ becomes a generalized Hausdorff space.},
keywords = {Generalized topology,generalized extension,one-point generalized extension,strong generalized topology,Stack},
url = {http://www.kjm-math.org/article_109822.html},
eprint = {http://www.kjm-math.org/article_109822_48153543d90491ae26ff4e6f0859818e.pdf}
}
@article {
author = {Acar, Ecem and Karahan, Done and Kirci Serenbay, Sevilay},
title = {Approximation for the Bernstein operator of max-product kind in symmetric range},
journal = {Khayyam Journal of Mathematics},
volume = {6},
number = {2},
pages = {257-273},
year = {2020},
publisher = {Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)},
issn = {2423-4788},
eissn = {2423-4788},
doi = {10.22034/kjm.2020.109823},
abstract = {In the approximation theory, polynomials are particularly positive linear operators. Nonlinear positive operators by means of maximum and product were introduced by B. Bede. In this paper, the max-product of Bernstein operators for symmetric ranges are introduced and some upper estimates of approximation error for some subclasses of functions are obtained. Also, we investigate the shape-preserving properties.},
keywords = {Max-product,degree of approximation,symmetric range,shape-preserving properties},
url = {http://www.kjm-math.org/article_109823.html},
eprint = {http://www.kjm-math.org/article_109823_a7fe73d3f8242f905b067eb48196f51c.pdf}
}