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Order Properties of Product Spaces and Quotient Spaces of Ordered Topological Linear Spaces

Thesis Info

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Author

Bhatti, Muhammad Iqbal

Program

PhD

Institute

University of Engineering and Technology

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2006

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/200

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726826434

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Very few we find in literature the order properties that product spaces of ordered linear spaces and ordered normed spaces carry from their component spaces. Some authors have studied certain order properties of ordered linear spaces which are carried by their quotient spaces. A little work is done in connection with the order properties of ordered normed spaces that the quotient spaces inherit from their parent spaces. In this thesis we have studied several order properties of ordered linear spaces and ordered normed spaces that are preserved with or without conditions in the formation of products. We have also studied several order properties of quotient spaces of ordered linear spaces and ordered normed spaces by discussing inheritance of order properties of the parent space X to its quotient space X/E. This thesis consists of six chapters. Chapter 1 includes some basic definitions and results. Chapter 2 provides almost all possible results available in 108the literature regarding the topological properties that are preserved in the formation of products. Chapter 3 is about the quotient spaces and includes several results available in the literature for the quotient spaces of (i) topological spaces (ii) linear spaces (iii) topological groups and (iv) topological linear spaces. Chapter 4 and Chapter 5 include the research work. Six research papers have been published from the work contained in these chapters; out of which four are published in the journals approved by the Higher Education Commission (HEC). Two more research papers are being submitted in some journals of international repute. Chapter six also includes the research work and presents only results from a past publication.
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امیر احمد صدیقی

آہ جناب امیر احمد صدیقی
یہ خبر بھی بڑے افسوس کے ساتھ سنی جائے گی کہ ۲۳؍ مارچ کو مشہور ادبی ماہ نامہ ’’نیادور‘‘ لکھنو کے سابق مدیر جناب امیر احمد صدیقی نشاط گنج میں اپنی رہایش گاہ پر وفات پاگئے، ان کا آبائی وطن لکھنو کے مضافات میں اجریاوں تھا، وہیں تدفین ہوئی، ان کی عمر ۸۲ سال تھی۔
وہ ۱۹۴۸؁ء میں محکمہ اطلاعات و رابطہ عامہ اترپردیش سے اس وقت منسلک ہوئے تھے جب جناب علی جواد زیدی، صباح الدین عمر، فرحت اﷲ انصاری اور خورشید احمد صاحب اس سے وابستہ تھے، اب اس دور کی تنہا یہی یاد گار رہ گئے تھے، آخر وہ بھی چل بسے۔
مرحوم مختلف وقتوں میں محکمہ اطلاعات میں افسر اطلاعات، فیچر رایٹر، جوائنٹ اڈیٹر، اڈیٹر نیا دور اور اسسٹنٹ ڈائرکٹر اردو رہے اور اپنے رفقائے کار میں تنہا ان ہی کو ملازمت میں ڈھائی سال کی توسیع ملی تھی:
نیا دور ہی کے وسیلے سے ان سے میرے تعلقات کی ابتدا ہوئی، میں نے جب اس میں مضامین لکھنا شروع کیا تو اس وقت یہ اس کے جوائنٹ اور خورشید احمد صاحب چیف اڈیٹر تھے، مضامین کی وصولی کی رسید اکثر ان ہی کی جانب سے آتی تھی اور جب یہ اڈیٹر ہوئے تو برابر خط و کتابت رہتی اور فرمایش کرکے مضامین طلب کرتے تھے، امیر احمد صاحب کے دور ادارت کا اصلی امتیاز نیا دور کے خاص نمبر ہیں جو بڑی تعداد میں نکلے اور بہت مقبول ہوئے، کئی خاص نمبروں میں ان ہی کے اصرار کی وجہ سے میں نے مضامین لکھے۔
کسی تقریب یا اردو اکیڈمی کے سمیناروں میں جاتا اور وہ موجود ہوتے تو بڑے تپاک سے ملتے، اپنے گھر بھی مدعو کرتے، ان کو معلوم ہوجاتا کہ میں آیا ہوں تو میری قیام گاہ کا پتہ لگا کر فون کرتے اور...

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Accountability is essential for proper working of government and its institutes. If it the head and other members of government are not hold accountable then they can cross their limits and rights of people may not be preserved. Authoritative persons may take advantage of their position. Western political thinkers are of mix opinion, some of them think it necessary to be held accountable but a few deny this. Islam strictly prohibit the miss use of authority so accountability is its essential part. Since the reign of Holy Prophet (PBUH) as the head of first Islamic state, special focus has been put on accountability. People were appoint for this purpose. Caliphates put themselves in front of their masses to ask whatever their want to ask. They are only be obeyed until they order according to the Islamic law.

Optical Characterization of Semiconductor Nanostructures

Self assembled semiconductor nanostructures, such as Quantum wells, nanowires and Quantum Dots, offer a variety of novel properties different from the bulk material. The new properties of low dimensional structures make them a potential candidate in optoelectronic industry. Efforts are now being made to reveal the underlying physics and phenomena of quasi one-dimensional and zero dimensional structures. The work presented herein deals with optical characterization of III-V semiconductor nanowires and III-N-V based emitters i.e., quantum wells and quantum dots, in long wavelength range. Spintronic is an emerging field where dilute magnetic semiconductors are used to achieve magnetic properties. Nanowires with magnetic impurity is considered to be a step towards one-dimensional spintronic devices. Au is the most commonly used catalyst for the VLS growth of NWs. But it also introduces the deep acceptor levels. One way to avoid deep acceptor levels and induce a magnetic impurity is the use of Mn as catalyst. In this thesis, gold (Au) and manganese (Mn) catalyzed self-assembled GaAs and InAs nanowires (NWs) were characterized. The samples were fabricated by molecular beam epitaxial (MBE) technique, on various substrates, at various temperature (540 to 620) oC. Scanning electron microscope (SEM) images revealed high density one-dimensional nanostructures with diameters in the range of 20 to 200 nm and lengths of few microns. Mn was found to diffuse into the stem of wires. HRTEM images show the presence of defects (stacking faults) in nanowires. Raman spectroscopy was used for optical characterization of nanowires and thus to determine the quality of these wires. Defects (stacking faults) were analyzed as the violation of Raman selection rules, which resulted in the asymmetrical broadening and the downshift of the LO and TO modes. We also observed some peaks at the low energy side of the TO peak of the GaAs and InAs NWs, irrespective of the catalyst used for the growth of NWs due to the oxide layer that surrounds the NWs. Surface optical phonons (SO) were found to be activated in both GaAs and InAs NWs. Phonon confinement model (PCM) was used to fit the LO phonon peaks, which also takes into account the contribution for asymmetry in the line shape caused by the presence of SO phonons and structural defects. This allowed to determine the correlation lengths in these wires, the average distance between defects and the defect density in these nanowires. Influence of these defects on SO phonon was also investigated. A good agreement between the experimental results and calculated for SO phonon mode by using the model presented by Ruppin and Englman was obtained. Statistical analysis ofthe data showed a distribution pattern of correlation length related to the growth conditions. Both Au and Mn catalyzed nanowires were found to exhibit similar quality, which indicates that Mn can replace Au catalyst resulting in magnetic impurity in the nanowires and giving us the opportunity to avoid the Au activated deep acceptor levels. To obtain the optical communication wavelength of 1.31 and 1.55 μm on GaAs substrates, InGaAs(N)/GaAs quantum wells and InAs(N)/GaAs(N) quantum dot structures were studied using photoluminescence spectroscopy. The samples were grown by MBE with a proper design of the samples by using stepped barriers to improve carrier trapping efficiency. Comparison of the luminescence from InAsN/GaAs and InAsN/GaAsN quantum dots was made with InGaNAs/GaAs quantum wells, grown under the same experimental conditions. Quantum dot emitters were found to exhibit higher thermal stability. The use of GaAsN barriers as opposed to GaAs barriers provided for narrower and more intense quantum-dot luminescence. Efficient room temperature emission of 1.41 μm (0.88 eV) has been obtained.