The emerged demand for high-performance systems promotes the development of two-dimensional (2D) graphene-based photodetectors. However, these photodetectors are usually fabricated by an expensive photolithography and complicated transferred process. Here, a semi-transparent reduced graphene oxide (rGO) photodetector on polyethylene terephthalate (PET) substrate with ultra-low power operation s...

let $r$ be a commutative ring with identity and $m$ be an$r$-module. let $fspec(m)$ denotes the collection of all prime fuzzysubmodules of $m$. in this regards some basic properties of zariskitopology on $fspec(m)$ are investigated. in particular, we provesome equivalent conditions for irreducible subsets of thistopological space and it is shown under certain conditions$fspec(m)$ is a $t_0-$spa...

During this search all rings are commutative and modules unitary. In we introduced the concept of Restrict Nearly semi-prime Sub-modules as generalization give some basic properties, examples charactarizations concepts stablished sufficient conditions on to be

Some length-preserving operations on strings only permute the symbol positions in strings; such an operation X gives rise to a family {Xn}n≥2 of similar permutations. We investigate the structure and the order of the cyclic group generated by Xn. We call an integer n X-prime if Xn consists of a single cycle of length n (n ≥ 2). Then we show some properties of these X-primes, particularly, how X...

One-state deterministic top-down tree transducers (or, tree homomorphisms) cannot handle “prime copying,” i.e., their class of output (string) languages is not closed under the operation L --) {$(w%~‘“’ 1 w E L, f(n) > 11, where f is any integer function whose range contains numbers with arbitrarily large prime factors (such as a polynomial). The exact amount of nonclosure under these copying o...

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Several ways of interleaving, as studied in theoretical computer science, and some subjects from mathematics can be modeled by length-preserving operations on strings, that only permute the symbol positions in strings. Each such operation X gives rise to a family {Xn}n≥2 of similar permutations. We call an integer n X-prime if Xn consists of a single cycle of length n (n ≥ 2). For some instance...