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Mathematical Modeling of the Effect of Mass Media for the Transmission Dynamics of Polio With Vaccination

Thesis Info

Author

Aleeza Maqsood

Department

Department of Mathematics, UET

Institute

University of Engineering and Technology

Institute Type

Public

Campus Location

UET Main Campus

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2017

Thesis Completion Status

Completed

Page

iv, 35 . : ill, table, grah ; 28cm+ CD

Subject

Mathematics

Language

English

Other

Hard Cover.; Include bibliographical references and index.

Added

2021-02-17 19:49:13

Modified

2023-01-07 20:44:54

ARI ID

1676712722015

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ادریس طوطی

ادریس طوطی

پیپلز پارٹی کا یہ بہادر نوجوان 1963ء کو دھرم پورہ لاہور میں پیدا ہوا ۔سولہ سال کی عمر میں 1979ء کو پی ایس ایف میں شامل ہوا ۔ضیاء آمریت کے دور میں گھر پر مسلسل چھاپوں اور اہل خانہ کو ہراساں کر نے پر کابل چلا گیا ۔واپسی پر گرفتار ہوا ۔1983ء میں پھانسی دی گئی ۔پھانسی کے وقت آپ کی عمر 21سال تھی ۔

 

The Circumstances Where the Quantum of Punishment Prescribed by Islam for Certain Crimes Can Be Reduced or Enhanced

The crime of theft if committed in unavoidable circumstances like extreme hunger or famine, Hadd punishment shall remain suspended. A crime of Zina if committed in a situation where the life of a woman is in danger because of hunger or thirst and she committed Zina to acquire food items or drinking water to save her life, she will be exonerated from the charges of Zina. In the light of Quranic injunctions, the punishment of a slave girl, if she committed Zina, is half as compare to independent women and the punishment for the wives of the Holy Prophet for committing the crime of fawahish or disobedience (Nushuz), is double as compare to other women. 4. Contrary to this principle, if a respectable person committed crimes under Tazir, he deserves lesser punishment or mere admonition in the light of tradition of the Holy Prophet: (Pardon the wrong done by the nobles of the society”.5. For awarding the punishment of Rajm, if the condition of Ihsan is fulfilled, he/she will be killed by stoning. According to Shiah Imamiah, Allama Rasheed Raza and others, when a person who is once married but due to divorce or separation, is living alone or miles away from his wife and not in a position to enjoy her company. If such person committed Zin┐, he or she will not be awarded the punishment of stoning.6. In the light of tradition, it is not allowed to award death punishment except the following three circumstances. Firstly, if a person, being a Mohsan, committed Zina, . Secondly, after accepting Islam, if a person converted to other religion. Thirdly, death punishment can be awarded in retaliation of murder committed

Effect of Magnetic Field on Laser Induced Breakdown Spectroscopy of Metallic Alloys

The dissertation deals with the investigation of magnetic field effect on plasma parameters and surface structuring of two metallic alloys (Cu & Mg) after laser irradiation. The plasma parameters are evaluated by using Laser Induced Breakdown Spectroscopy (LIBS) technique, whereas, micro/nano structuring of metallic alloys is explored by Scanning Electron Microscopy (SEM) analysis. This dissertation consists of following two parts. In part (A) the effect of magnetic field on ns-LIBS analysis and surface modifications of both metallic alloys has been investigated. Part (A) is further divided into sections. In section I, the effect of laser irradiance on metallic alloys plasma is exposed in the presence and absence of Transverse Magnetic Field (TMF) while keeping the pressure of environmental gases constant i.e. 5 Torr. For this purpose both metallic alloys were exposed to Nd: YAG laser (1064 nm, 10 ns) pulsed energies ranging from 25 mJ to 200 mJ. Cu-alloy is exposed at various ns laser irradiances ranging from 1.9 GW/cm2 to 5 GW/cm2, whereas, for Mg alloy irradiances are ranging from 0.3 GW/cm2 to 2.6 GW/cm2 under Argon (Ar), Neon (Ne), and Helium (He). Section II of this part deals with the investigation of different pressures of environmental gases with & without magnetic field by keeping irradiance constant. For this purpose time integrated Laser Produced Plasma (LPP) parameters of metallic alloys evaluated under Ar, Ne and He environments at different pressures ranging from 1 Torr to 100 Torr at constant irradiance of 4.4 GW/cm2 (Cu-alloy) and 2 GW/cm2 (Mg-alloy) and at constant time delay of 1.25 µs have been explored. The values of excitation temperature (Texc) and electron number density (ne) of LPP of metallic alloys are higher in the presence of 1.1 Tesla magnetic field as compared to field free case. Both Cu & Mg alloys show similar trends for used range of ns laser irradiances in the presence of Ar, Ne & He. It is also found that trends of both excitation temperature and electron number density are increasing with increasing laser irradiances from 1.9 GW/cm2 to 4.4 GW/cm2 for Cu-alloy & from 0.3 GW/cm2 to 2 GW/cm2 for Mg-alloy. For the highest used irradiance for both metallic alloys the decrease in both parameters is observed. In the case of pressure variation an increase in both plasma parameters is observed by increasing pressure from 1 Torr to 5 Torr at fixed irradiance of 4.4 GW/cm2 & 2 GW/cm2 for Cu-alloy and Mg-alloy respectively. A decrease in LPP parameters by increasing pressure from 5 Torr to 100 Torr for both metallic alloys is observed. The magnetic confinement validity is confirmed by analytically evaluating thermal beta (βt), directional beta (βd), confinement radius (Rb) and diffusion time (td) for LPP of both Cu and Mg-alloys. Surface modifications of laser ablated Cu & Mg alloys is performed by Scanning Electron Microscope (SEM) analysis. The formation of less distinct surface structures are observed on Cu-alloy in the presence of TMF as compared to field free case. Whereas, for Mg-alloy distinct and well-defined structuring is observed with TMF as compared to absence of field. In order to investigate the effect of femtosecond laser irradiation effects on plasma parameters and surface modifications, part (B) is performed. In part (B), the effect of magnetic field on fs-LIBS analysis and surface modifications of both metallic alloys has been investigated. Femto second pulses of Ti: Sapphire laser system (800 nm, 35 fs, 1 KHz) are employed as source of irradiation. Part (B) is further divided into sections. Section I, deals with measurements performed at various irradiances ranging from 0.011 PW/cm2 to 0.117 PW/cm2 for Cu-alloy and irradiances ranging from 0.0052 PW/cm2 to 0.0526 PW/cm2 for Mg alloy under fixed 15 torr pressure of Ar and Ne with & without TMF. This section also deals with exploring the effect of different pressures of Ar ranging from 1 Torr to 35 Torr with & without TMF at fixed irradiance of 0.082 PW/cm2 & 0.043 PW/cm2 for Cu-alloy and Mg-alloy respectively. For fs-LIBS analysis the same trends of Texc and ne are observed as have been observed for ns-LIBS for both metallic alloys for irradiance variation as well as pressure variation. In order to confirm the validity of magnetic confinement for fs- LIBS analysis. The values of βt, βd, Rb and td are also evaluated.To correlate the LPP parameters of metallic alloys with surface modifications Field Emission Scanning Electron Microscope (FE-SEM) analysis is performed. It reveals the formation of Laser Induced Periodic Surface Structures (LIPSSs). These LIPSSs are of two kinds LSFL (Low-spatial-frequency LIPSSs) and HSFL (High-spatial-frequency LIPSSs) along agglomers and nano rims which are not formed in case of ns-laser ablation. For both metallic alloys distinct and well-defined surface structuring is observed in the presence of the field as compared to absence of field.The comparison is made between ns-LIBS and fs-LIBS analyses. It is observed that both LPP parameters i.e. Texc and ne for both metallic alloys are higher for ns-LIBS as compared to fs-LIBS. It is also revealed that ns laser irradiation is responsible for micro scale surface structuring, whereas, in case of fs laser ablation nano scale well defined LIPSSs are formed. When comparison is made between Cu-alloy and Mg-alloy, it is observed that higher excitation temperature is associated with Mg-alloy plasma whereas, electron number density for Cu-alloy plasma is greater for both ns and fs laser. It is also revealed that both excitation temperature and electron number density play a substantial part for the growth of surface structures on both metallic alloys. It is concluded that by applying external magnetic field during laser irradiation, controlled material surface structuring is possible for applications such as formation of gratings and field emitters where spatial uniformity is critically important.