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Analog of M-Grobner basis in convergent power series ring

Thesis Info

Author

Shaheen, Imran

Program

MS

Institute

Institute of Business Administration

Institute Type

Private

City

Karachi

Province

Sindh

Country

Pakistan

Thesis Completing Year

2018

Page

25

Subject

Mathematics

Language

English

Other

CallNo: 512.4

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676720937653

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In this dissertation we have developed the theory of M-Sagbi bases in Convergent power series ring and created a criterion through which we can check whether a set of power series is a M-Sagbi basis or not. Moreover, we have constructed an algorithm to compute Sagbi basis through M-Sagbi basis
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حرفے چند

ارضِ اقبال آفاقیت کے آئینے میں‘‘ڈاکٹر نصیر احمداسد کے مختلف تحقیقی و تنقیدی نوعیت کے مضامین پر مشتمل کتاب ہے۔بیشتر مضامین مختلف تحقیقی و تنقیدی رسائل کی زینت بن چکے ہیں۔ اُنھوں نے جن جن شخصیات پر قلم اٹھایا ہے،ان کے بارے میں معلومات کا ایک ذخیرہ جمع کر دیا ہے۔جہاں جہاں ضرورت محسوس کی ہے اپنی ناقدانہ رائے کا اظہار بھی بڑی خوب صورتی سے کیا ہے۔
    مَیں نے ڈاکٹر نصیر احمد  اسدکے مزاج میں ایک خاص بات محسوس کی ہے کہ وہ اپنے کام سے نہایت مخلص ہیں اور اپنی دُھن میں علمی خدمات میں ہمہ وقت مصروف  نظر آتے ہیں۔ان کے اسلوب کی سادگی اور روانی بات کو بوجھل نہیں ہونے دیتی۔ ان مضامین کے مطالعہ سے قاری نہ صرف مختلف شخصیات سے متعارف ہوتا ہے بلکہ ان کی علمی خدمات سے بھی ایک حد تک مستفید ہوتا ہے۔
    ’’مولوی فیروز الدین ڈسکوی‘‘ اور’’مولوی ابراہیم میر سیالکوٹی‘‘ والے مضامین میں مذکورہ شخصیات سے متعلق عمدہ معلومات جمع کی گئی ہیں۔ان شخصیات کے تعارف کے ساتھ ساتھ ان کی علمی خدمات پر بھی روشنی ڈالی گئی ہے۔اسی طرح ’’سیالکوٹ میں اردو شاعری کا ارتقا‘‘ اور’’ریاض حسین چودھری ایک نعت گو شاعر‘‘ میں ناقدانہ انداز نظر سے کام لیا گیا ہے۔دیگر مضامین بھی اپنی نوعیت کے خوب صورت مضامین ہیں۔الغرض مذکورہ کتاب ان کی تحقیقی و تنقیدی بصیرت کی آئینہ دار ہے۔
ڈاکٹر محمد افضل صفی
صدر شعبہ اردو گورنمنٹ گریجوایٹ کالج ،کروڑ لعل عیسن، ضلع لیہ

دال و مدلول کا باہمی ربط و تعلق: عصری رجحانات، قرآن و سنت پر اس کے اثرات

The issue of signification in language is as old as man. Structuralism has changed the relation of signifier and signified. According to the modern approach language is not more than a name of cultural codes, in this way, importance has been given to the signifying system rather than meaning. In Islamic intellectual history, a group of Muslim scholars had an opinion of natural relation between word and its meaning. One of them was Abbas b. Sulaiman a Mutazali scholar. But ahl al-Sunnah wa al-Jamat scholars’ have different approach. In short, if we have a belief that a society gives meaning to a word then the approach to Shariah and the Quranic injunctions will be interpreted in the light of societal demands. We will have to admit the authority of time, space and society over meaning of the Quran and Sunnah which is against the teachings of Islam

Associative and Surface Active Properties of Block Copolymers and Their Interactions With Surfactants

The associative, micellar and surface active properties of various EmBn, EmBnEm and of some tip-modified, oxyethylene-oxybutylene block copolymers in aqueous media under varying solution conditions and their interactions with conventional surfactants are reported in this thesis. The tipped block copolymers (Me2N(CH2)2OEmBn denoted as DEmBn and I-Me3N+(CH2)2OEmBn denoted as TEmBn) have dimethylamino and trimethylammonium groups at the end of their hydrophilic blocks respectively. For all copolymers, E represents an oxyethylene (-[CH2CH2O]-) unit and B an oxybutylene (-[CH(C2H5)CH2O]-) unit while the subscripts denote the number average block length. This work is mainly divided in two parts; the first part is related to the associative/micellar, thermodynamic and surface active/adsorptive properties of various E/B block copolymers in aqueous and salt added solutions at various temperatures. While in the second part, the interactions of these polymers with conventional surfactants (anionic, cationic and non-ionic) have been reported. The first part of this study is based on applying some fundamental techniques like surface tensiometry, viscometry, densimetry along with some advance techniques such as laser light scattering (DLS and SLS), mT-jump stopped flow technique and quartz crystal microbalance with dissipation (QCM-D). Surface tension measurements were used to estimate various fundamental parameters such as, surface excess concentrations (Γm), area per molecule (as1) at air/water interface, critical micelle concentration (CMC) and various thermodynamic parameters like; standard Gibbs free energy change (DG0), standard enthalpy change (DH0) and standard entropy change (DS0) for both adsorption at air/water interface and micellization at several temperatures. Density and viscosity measurements were implied to investigate the effect of various internal as well as external parameters on the micellar/associative properties for the aqueous solution of E/B block copolymers. To calculate the intrinsic viscosities [h] and inter-micellar interaction parameter (KH), viscosity measurements were made. Partial specific volume (n mic) and density of the micelle (ρmic) were obtained from the density measurements at various temperatures. Besides that the hydration value (Wh) of micelle plus shape factor (υ) of aggregates were evaluated by combining the results of density and viscosity. Viscosities and densities data also support the temperature dependent micellization/aggregation and change in the shape of aggregates with temperature. Dynamic light scattering was used to investigate the hydrodynamic radius of micelle (rh), hydrodynamic volume (Vh) and hydrodynamic expansion factor (dh). Likewise static laser light scattering technique was used to determine apparent micellar molar mass (Mw), association number (Nw), thermodynamic volume (Vt), thermodynamic radius (rt) and thermodynamic expansion factor (dt). The effect of E/B- blocks length, variation in the hydrophilic end group, addition of NaCl and changing the solution temperature on various parameters deduced from light scattering (DLS and SLS) are also discussed in detail. The kinetics of micellar aggregation was also studied by using mT-jump stopped-flow technique in the temperature range 20 to 50oC. Most of the temperature jump stopped-flow kinetics results show that mainly three relaxation processes are involved in our micellar dynamic system. The first one (τ1) involves the growth of small micelle and increase in aggregation number within short time upon jumping to higher temperature. The second relaxation process (τ2) is associated with micelle formation/breakup and rearrangement, resulting in micelle with larger aggregation numbers and hence lower number density of micelles. The final process (τ3) is related to further rearrangement of the micelle size, shape etc and also to the clustering of micelle. Similarly, the adsorption of poly(ethylene oxide)-b-poly(butylene oxide) diblock copolymers at the solid-liquid interface was studied using a quartz crystal microbalance with dissipation monitoring (QCM-D). The effect of modifying the end- group of the hydrophilic block was investigated by comparing the behavior of TEmBn and DEmBn respectively. For EmBn block copolymer, the effect of E/B block ratio and nature of the substrate (gold-coated and silica-coated surfaces) was also investigated. In the second part, we have discussed the interactions of some EmBn and tip-modified TEmBn and DEmBn block copolymers with conventional surfactants (anionic, cationic and nonionic surfactants). In this work we have tried to highlight the type and strength of such interactions by using the some of the experimental techniques such as surface tensiometry, conductometry, LLS and quartz crystal microbalence. Surface tension and conductivity measurements of the copolymer-surfactant mixture were used to estimate the critical aggregation concentration (CAC) and the polymer saturation point (PSP). DLS has been used to estimate the size and types of the mixed aggregates present in the mixed system. We have studied the effect of polymers block length, end group, nature of surfactants, and also the impact of adding NaCl. To know the influence of the nature and size head group of surfactant we have used anionic (SDS), cationic (CTAB) and non-ionic (TX-100) surfactants for our system. DLS results show that there are different types of mixed species depending upon the amount of surfactant added to the copolymers solution. Quartz crystal microbalance with dissipation monitoring (QCM-D) has also been used to study the adsorption and interaction behaviour of block copolymers- surfactants complexes at the solid-liquid interface. Changes in adsorption/desorption phenomenon and conformational behaviour of block copolymers in presence of SDS and CTAB are discussed in detail. The changes in frequency and dissipation responses indicate that different copolymer-surfactant mixed structures depend on the amount of added surfactants to the mixed system.