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Optimal Embeddings of Generalized Homogeneous Besov Spaces and Calderón Spaces

Thesis Info

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External Link

Author

Bashir, Zia

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2008

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/210

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726813335

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We prove optimal embedding of generalized homogeneous Besov spaces into the re- arrangment invariant sapce and the optimal embedding of Calder ́on spaces into the generalized H ̈older-Zygmund spaces CH.
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علم بڑی دولت ہے

علم بڑی دولت ہے
نحمدہ ونصلی علی رسولہ الکریم امّا بعد فاعوذ بااللہ من الشیطن الرجیم
بسم اللہ الرحمن الرحیم
قُلْ ھَلْ یَسْتَوِی الَّذِیْنَ یَعْلَمُوْنَ وَالَّذِیْنَ لَا یَعْلَمُوْن۔صَدَقَ اللہ الْعَظِیْم
صاحب صدر معزز اسا تذہ کرام اور میرے ہم مکتب ساتھیو! آج مجھے جس موضوع پر تقریر کرنے کا موقع فراہم کیا گیا ہے وہ ہے:’’علم بڑی دولت ہے‘‘
صدرِذی وقار!
انسان حسن و جمال میں ایک دوسرے کے برابر ہوسکتا ہے، رنگ و روپ میں ایک دوسرے کے برابرہوسکتا ہے۔ قد کاٹھ میں ایک دوسرے کے برابر ہو سکتا ہے، گفتار ورفتار میں ایک دوسرے کی برابری کر سکتا ہے تحریرو تقریر میں یکسانیت کا امکان ہے، مال و دولت میں ہم پلہ ہوسکتا ہے، سونے چاندی کے ڈھیر کے پیما نے برابر ہو سکتے ہیں، قوت وسطوت میں برابری ہوسکتی ہے لیکن علم ایک ایسی دولت ہے جس میں جاہل اور عالم برابر نہیں ہو سکتے جس کے ترازوکا پلڑاعلم کے وزن سے بھاری ہو جاتا ہے پھر دنیا کی کوئی شے اس کا مقابلہ نہیں کر سکتی اس کے پلڑے کو اُوپر اٹھانا تو در کنار اس کی برابری کا تصور تک نہیں کر سکتا۔
معزز سامعین!
یہ صرف میں نہیں کہہ رہا کہ علم بڑی دولت ہے، بلکہ تاریخ اسلام کی نامور ہستیوں نے کہا۔ صالحین نے کہا کہ علم بڑی دولت ہے، متقین نے کہا کہ علم بڑی دولت ہے، اولیاء نے کہا کہ علم بڑی دولت ہے، ابدال نے کہا کہ علم بڑی دولت ہے، قطب نے کہا کہ علم بڑی دولت ہے، غوث نے ہزاروں کے مجمعے میں پیغامِ تو حید پہنچا کر کہا کہ علم بڑی دولت ہے،حضرت بلال ص نے اپنے آپ کوتپتی ر یت پر لٹا کر کہا کہ علم بڑی دولت ہے، خبیبص نے خود کوسولی پر چڑھا کر کہا کہ علم بڑی دولت...

A COMPARISON OF THE VISUAL PERCEPTUAL SKILLS IN TYPICAL AND CEREBRAL PALSY CHILDREN

Objective: The purpose of this study is to evaluate the difference at occupational performance skills related to visual perception among typical developing children and cerebral palsy children by using measuring test of MVPT-R. Design And Sampling Technique: Quantitative cross-sectional study, convenience sampling method. Study Setting And Participants: A total of 400 Cerebral palsy children (all types) and typical children each from different mainstream schools, rehab centers, pediatric occupational therapy departments, and special education centers located in Karachi. Interventions / Data Collection: Test of visual perception that is Motor Free visual perceptual test- Revised MVPT-R. Result: Result shows difference in perceptual ages (PA) between typical and cerebral palsy children. Perceptual age (PA) was greater than the chronological age (CA) in the typical group. Conversely, in the CP group the perceptual age (PA) was lesser than the chronological age (CA). Conclusion:  Visual perception skills play a key role in a child’s achievement at school and at home. Children require intact visual perception for the successful performance of their daily living as well as academic tasks like good eye-hand coordination, handwriting, reading, shape perception, play skills, and copying patterns, etc. This study is helpful to identify those children who have visual perception issues and sorting this problem will form the baseline for better evaluating and planning of useful visual perception activities for typical and cerebral palsy children.

Effects on Surface, Structural and Mechanical Properties of Brass by Laser and Ion Beam Irradiation

Modifications to the surface, structural and mechanical properties of brass have been investigated by using three different kinds of radiation sources. The first radiation source was laser, second one was laser induced plasma ions and the third one was Pelletron accelerator. Brass targets were exposed to various laser pulses ranging from 1200 to 3000 of excimer laser (248 nm, 20 ns, 120mJ and 30 Hz) at constant fluence of 6.4 J/cm2 in oxygen atmosphere (100 Torr). In order to explore the ion induced modification in properties of brass, ions were generated by two different ion sources. The laser induced plasma was employed as a first ion source for the generation of Ni, Si and C ions. Excimer laser (248 nm, 20 ns, 120mJ and 30 Hz) was used for the generation of Ni, Si and C plasma. In order to estimate ion flux and energies, Thomson parabola technique was employed. By using this technique, magnetic field of strength 80 mT was applied on the plasma plume to give appropriate trajectory to generated ions. These ions were detected by solid state nuclear track detector (CR39). In response to stepwise increase in number of laser pulses from 3000 to 12000, the Ni ion flux varies from 60 × 1013 to 84 × 1016 5 ions/cm2 with constant energy of 138 KeV. Similarly Si ion flux varies from 45 × 1012 to 75 × 1015 ions/cm2 with constant energy of 289 KeV. The flux of C ions flux changes from 32 × 1011 to 72 × 1014 ions/cm2 with constant energy of 678 KeV. The second source of ion generation is Pelletron accelerator. Brass targets were bombarded by Ni and C ions of energy 2MeV for various ions flux ranging from 56×1012 to 26×1013 ions/cm2. Scanning Electron Microscope (SEM) and X-Ray Diffractometer (XRD) were used to analyze the surface morphology and crystallographic structure of irradiated brass respectively. Universal Testing Machine (UTM) and Vickers Hardness Tester (VHT) were employed to explore Yield Stress (YS), Ultimate Tensile Strength (UTS) and mirohardness of ion irradiated brass targets. SEM analysis reveals the formation of micro/nano sized cavities, bumps, cones and wave-like ridges with non-uniform shape and density distribution after laser irradiations. Whereas, ion irradiation causes the formation and growth of nano/micro sized cavities, pores, pits, voids and cracks for lower and moderate ion flux (in all cases). At maximum ion flux the granular morphology (in case of brass irradiated by laser induced Ni and Si ions) and dendritic morphology (in the case of brass irradiated by laser induced plasma and Pelletron accelerator C ions) are observed. XRD analysis reveals that no new phases are identified in case of laser irradiated brass. However new phases of CuZnNi (200), CuSi (311) and ZnC (0012) are identified in the brass substrate after laser induced Ni, Si and C ions irradiation respectively. Whereas, no new phases are formed in case of Ni and C ion irradiation obtained by Pelletron accelerator. The variation in peak intensity, crystallite size, dislocation line density and induced stresses along with angular shifting is observed in all cases of laser and ion irradiations. Significant variations in mechanical properties of brass are observed after laser and ion irradiations. The changes in mechanical properties of an irradiated brass are well correlated with surface and crystallographical modifications and are attributed to generation, augmentation, recombination and annihilation of the ion induced defects. The laser and ion induced surface, structural and mechanical modifications of brass are significantly influenced by nature, energy and flux of radiations.