Photonic crystal fiber interferometers are widely used for sensing applications. In this work, solid core-Photonic crystal fiber based on Mach-Zehnder modal interferometer for sensing refractive index was presented. The general structure of sensor applied by splicing short lengths of PCF in both sides with conventional single mode fiber (SMF-28). To apply modal interferometer theory; collapsing technique based on fusion splicing used to excite higher order modes (LP01 and LP11). Laser diode (1550 nm) has been used as a pump light source. Where a high sensitive optical spectrum analyzer (OSA) was used to monitor and record the transmitted. The experimental work shows that the interference spectrum of Photonic crystal fiber interferometer exhibits good sensitivity to refractive index variations. The response of the PCFI is observed for a range of refractive index values from (1.33 to 1.38), the position of the interference peaks is found to be shifted to longer wavelength with refractive index increasing. A different length of PCFs (2, 3, 4) cm were used, and the maximum refractive index sensitivity of (7.5 pm / RIU) is achieved with a PCF length of 4 cm. This refractive index sensor has distinguished properties as that it small size, high sensitivity, fast response time, design flexibility, and immunity to electromagnetic interference.
The soft sets were known since 1999, and because of their wide applications and their great flexibility to solve the problems, we used these concepts to define new types of soft limit points, that we called soft turning points.Finally, we used these points to define new types of soft separation axioms and we study their properties.
Let R be a commutative ring with identity and M be a unitary R- module. We shall say that M is a primary multiplication module if every primary submodule of M is a multiplication submodule of M. Some of the properties of this concept will be investigated. The main results of this paper are, for modules M and N, we have M N and HomR (M, N) are primary multiplications R-modules under certain assumptions.
The main goal of this paper is to introduce and study a new concept named d*-supplemented which can be considered as a generalization of W- supplemented modules and d-hollow module. Also, we introduce a d*-supplement submodule. Many relationships of d*-supplemented modules are studied. Especially, we give characterizations of d*-supplemented modules and relationship between this kind of modules and other kind modules for example every d-hollow (d-local) module is d*-supplemented and by an example we show that the converse is not true.
Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.
The purpose of this paper is to give some results theorems , propositions and corollaries concerning new algebraic systems flower , garden and farm with accustomed algebraic systems groupoid , group and ring.
A new class of generalized open sets in a topological space, called G-open sets, is introduced and studied. This class contains all semi-open, preopen, b-open and semi-preopen sets. It is proved that the topology generated by G-open sets contains the topology generated by preopen,b-open and semi-preopen sets respectively.