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Home > A Classifier for Isolated Complete Intersection Singularities of Modality ≤ 1

A Classifier for Isolated Complete Intersection Singularities of Modality ≤ 1

Thesis Info

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Author

Deeba Afzal

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2292/1/2519S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725391894

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The aim of the present thesis is to study, develop and implement certain algorithms in order to find the type of singularities for isolated complete intersection singularities w.r.t contact equivalence of modality ≤ 1 defined over an algebraically closed field K. The new investigation is that we do not compute the normal form of a given singularity because this would be space and time consuming. We present a charac- terization of the different types of singularities in terms of certain invariants and use the characterization to identify the singularities. We describe our implementation in computer algebra system Singular. Therefore, we discuss three problems in this thesis. • Problem 1 deals with the classification of hypersurface singularities with respect to contact equivalence when the characteristic of the field p > 2 by using blowing up as a new tool. • Problem 2 studies the classification of simple complete intersection singularities in terms of certain invariants when the characteristic of the field p = 0. • Problem 3 includes to find the complete list of unimodular complete intersection space curve singularities and the characterization of these singularities in terms of certain invariants when the characteristic of the field p = 0
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When we study about the life of Holy Prophet (ﷺ), his life demand from Muslims to protect the dignity and honour of their Muslim brothers. They not only protect or care the right of their Muslim brothers in their life but also protect their dignity after their death. In the light of Holy Prophet Life the circle of human rights is so vast. In this, his life teaches us the turidicul, rights, marriage, settlement different between good or evil, isonomy and the verses of martyr and the noble behaviour with Jews and Christians. There is a big role of ethics on the human personality. The ethics is the tester of good or bad person Human with the noble ethics the Muslims. To be remembered as staying up all the night and to fast. The ethics play important role in the life of Human. In the life of Prophet (ﷺ) we know about his good deeds and noble behavior with non Muslims. The success of the Holy Prophet preaching is only because of his ethics and truthness. Islam Universal Religion. It’s Teachings and pregnative system is the everlasting. In this modern period there is no way except Islam to get Rid the unsolved problems of the age. The beloved Prophet (ﷺ) “Sira Mubarak” the way of light only. There is aspect of the life without the real pregnative system. Peace and the War both are in the teaching of the Holy Prophet (ﷺ). Peace, progress contentment, satisfaction, true, unity, brotherhood in the lightment of the “Uswa Hasna”. Let’s seek the real way in our beloved Prophet (ﷺ). Key Words: Holy Prophet, Ghazwa, Akhlaq-e-Hasanah, Ehl-e-Kitab, War, Ethics.

Novel Materials for Dye Sensitized Solar Cells

Dye sensitized solar cells (DSSCs) being third generation photovoltaics are inexpensive renewable energy resource and recently been a hot topic of research. The objective of the present research work was to develop photoanode materials for low cost efficient DSSCs. This thesis presents some novel materials for the photoanode including semiconductor material with different nanostructures such as nanoparticles, nanoflowers and nanorods and new sensitizers. Synthesis method of titanium dioxide nanoflowers is reported here. Such hierarchical morphology led to the improved device performance due to greater absorption of light through scattering; a novel photoanode with one dimensional sandwich configuration of ZnO/Au/TiO2, incorporating plasmon resonance and charging effects of Au nanoparticles for enhanced efficiency in DSSCs. New metal free calixarene sensitizers with directed flow of electrons are also studied for DSSCs. Titania nanoflowers are highly desirable in light driven applications due to their large surface area and greater light absorption capabilities. Microwave synthesis of nanomaterials is an energy efficient and quick method. Microwave treatment of titania nanopowders under alkaline conditions is carried out to see the effect of treatment duration. An instant, simple, inexpensive and environment friendly method of preparing titanium dioxide nanoflowers or hierarchical nanostructures (HNSs) is thus achieved. Production of sub-micron sized HNSs without any surfactant or hydrofluoric acid is discovered. From FESEM and TEM analysis the titania nanoflowers are found to be made of few nanometers thick radially arranged nanosheets. XRD and Raman spectra reveal no phase change during the microwave treatment. The mechanism of formation of these hierarchical nanostructures involves sheet formation under strong alkaline conditions and their radial growth under the effect of microwave radiation. The hierarchical morphology provides huge surface area for maximum exposure for light driven reactions and 3 D folding morphology allows further scattering of light to get its maximum utilization. This is evident in improved DSSC performance with synthesized nanoflowers. The HNSs produced in a time as short as 5 minutes show improvement in DSSC efficiency by about 216%. vii One dimensional nanostructures of TiO2 and ZnO have also been vastly studied for application in DSSCs. As a novelty in configuration of 1D core/shell nanostructures, the effect of Au nanoparticles inclusion as a sandwiched layer is studied. The sputter coated gold nanolayers of various sizes are applied over ZnO nanorods grown by seed assisted route. 1D Au/ZnO nanoarrays are covered with a few nanometers thick spin coated TiO2 film to make TiO2/Au/ZnO sandwich nanorod arrays. The uniform morphology and dimensions of the nanorod arrays are studied by SEM. HRTEM studies depict the Au nanoparticle size and distribution within the sandwich nanorods and they are found to be embedded at the interface of ZnO/TiO2 coreshell nanorods. The UV/Vis spectra reveal the plasmon resonance effects due to Au nanoparticles, which are also improving the solar cell efficiencies. The observed enhancement in the photocurrent density is attributed to the Localized Surface Plasmon Resonance (LSPR) effects due to sputter coated Au layers. An increase in the open circuit voltage of DSSCs is also observed due to Fermi level alignment between the Au bridged ZnO and TiO2 in the photoanodes of devices. With 2nm sputter coated Au in TiO2/Au/ZnO 1D nanostructures, a relative efficiency enhancement factor of 2.05 is achieved. Further in search of new inexpensive materials for DSSCs, a new class of metal free Donor-π-bridge-Acceptor (D-π-A) dyes based on basket shaped molecules “calixarenes” is introduced for DSSCs. As in calixarenes the flow of electrons is directed along the length of the molecules by resonance and induction effects and there is no conjugation around the molecular cup. This fact can prevent the recombination of charge carriers to a great extent. p-(6-chloro-2- benzothiazolylazo)calix[4]arene (pcb calix) and p-(1,3,4-thiadiazol-2-thiol-5- ylazo)-calix[4]arene (ptt calix) are synthesized and after characterization by FTIR, UV/Vis, NMR spectroscopy and cyclic voltametry are employed in DSSCs to sensitize titania. The HOMO LUMO levels of the dyes are found consistent with the requirement of DSSCs. An efficiency of 0.3% and 0.47% is achieved with dyes pcb-calix and ptt-calix respectively. The attachment of better absorbing chromophores to calixarene can result in obtaining better efficiencies in DSSCs.