Photonic crystal fiber interferometers (PCFIs) are widely used for sensing applications. This work presented solid core-PCFs based on Mach-Zehnder modal interferometer for sensing refractive index. The general structure of sensor was 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). A high sensitive optical spectrum analyzer (OSA) was used to monitor and record the transmitted wavelength. This work studied a Mach-Zahnder interferometer refractive index sensor based on splicing point tapered SMF-PCF-SMF. Relation between refractive index sensitivity and taper waist diameter were studied through simulation and experiments. The experimental and simulation results show that sensitivity would be increased with a decrease of taper waist diameter. The response of the PCFI is observed for a range of refractive index values from (1.33 to 1.38). When the length of PCF was (4)cm with different taper waist diameter (125,107,90,60)μm, the maximum refractive index sensitivity of (20 pm / RIU) was achieved. When taper waist diameter became (60)μm, the rate of increase in sensitivity was 12.4% compared with the taper waist diameter (125)μm.
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Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assumes the variable takes on real values over the interval [0,∞]. One of the new studies in statistics is when the variables take on discrete values. The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and β where 0 < q < 1 and b > 0. Weibull models for modelling discrete random variables assume only non-negative integer values. Such models are useful for modelling for example; the number of cycles to failure when components are subjected to cyclical loading. Discrete Weibull models can be obta
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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.
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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.
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Throughout this work we introduce the notion of Annihilator-closed submodules, and we give some basic properties of this concept. We also introduce a generalization for the Extending modules, namely Annihilator-extending modules. Some fundamental properties are presented as well as we discuss the relation between this concept and some other related concepts.
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Abstract
Research title: The legal ruling of advice.
This research deals with the topic of advice, as the research included the following:
Preamble: I explained in it the meaning of advice in the Qur’an and Sunnah, and that what is meant by it is a good performance of the duty, then explaining its importance, importing it, and the difference between advice and what is similar to it, from enjoining good, denial, reproach and reprimand, backbiting and the will.
The first topic: It dealt with the ruling on advice, whether it is recommended or disliked, or forbidden, because what is meant by it is to give advice to others may be an obligation in kind, or it may be desirable or dislike
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