Let $R$ be a ring‎, ‎and let $n‎, ‎d$ be non-negative integers‎. ‎A right $R$-module $M$ is called $(n‎, ‎d)$-projective if $Ext^{d+1}_R(M‎, ‎A)=0$ for every $n$-copresented right $R$-module $A$‎. ‎$R$ is called right $n$-cocoherent if every $n$-copresented right $R$-module is $(n+1)$-coprese-nted‎, ‎it is called a right co-$(n,d)$-ring if every right $R$-module is $(n‎, ‎d)$-projective‎. ‎$R$...

let $r$ be a commutative ring with identity and $m$ be a unitary$r$-module. the primary-like spectrum $spec_l(m)$ is thecollection of all primary-like submodules $q$ such that $m/q$ is aprimeful $r$-module. here, $m$ is defined to be rsp if $rad(q)$ isa prime submodule for all $qin spec_l(m)$. this class containsthe family of multiplication modules properly. the purpose of thispaper is to intro...

In this paper, we establish some new critical fixed point theorems for the sum $AB+C$ in a Banach algebra relative to the weak topology, where $frac{I-C}{A}$ allows to be noninvertible. In addition, a special class of Banach algebras will be considered.

 We study the notion of bounded approximate Connes-amenability for‎ ‎dual Banach algebras and characterize this type of algebras in terms‎ ‎of approximate diagonals‎. ‎We show that bounded approximate‎ ‎Connes-amenability of dual Banach algebras forces them to be unital‎. ‎For a separable dual Banach algebra‎, ‎we prove that bounded‎ ‎approximate Connes-amenability implies sequential approximat...

Controlled frames have been introduced to improve the numerical efficiency of iterative algorithms for inverting the frame operator on abstract Hilbert spaces. Fusion frames and g-frames generalize frames. Hilbert C*-modules form a wide category between Hilbert spaces and Banach spaces. Hilbert C*-modules are generalizations of Hilbert spaces by allowing the inner product to take values in a C*...

various methods for parametric interpolation of nurbs curves have been proposed in the past. however, the errors caused by the approximate nature of the nurbs interpolator were rarely taken into account. this paper proposes an integrated look-ahead algorithm for parametric interpolation along nurbs curves. the algorithm interpolates the sharp corners on the curve with the pythagorean-hodograph ...

in this paper, we  study the arens regularity properties of module actions. we investigate some properties of topological centers of module actions ${z}^ell_{b^{**}}(a^{**})$ and  ${z}^ell_{a^{**}}(b^{**})$ with some conclusions in group algebras.

breast cancer is the second largest cause of cancer deaths among women. at the same time, it is also among the most curable cancer types if it can be diagnosed early. this paper presents a novel hybrid intelligent method for recognition of breast cancer tumors. the proposed method includes three main modules: the feature extraction module, the classifier module and the optimization module. in t...

Let $A$ be a Banach algebra, $\Omega(A)$ be the character space of $A$ and $\alpha\in\Omega(A)$. In this paper, we examine the characteristics of $\alpha$-projective (injective) $A$-modules and demonstrate that these character-based $A$-modules also satisfy well-known classical homological properties on Banach $A$-modules.

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...