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Home > O N the B Oundedness and M Easure of N on - Compactness for M Aximal and P Otential O Perators

O N the B Oundedness and M Easure of N on - Compactness for M Aximal and P Otential O Perators

Thesis Info

Access Option

External Link

Author

Muhammad Asif

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/123456789/605

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726789433

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The essential norm of maximal and potential operators defined on homogeneous groups is estimated in terms of weights. The same problem is discussed for par- tial sums of Fourier series, Poisson integrals and Sobolev embeddings. In some cases we conclude that there is no a weight pair (v, w) for which the given operator is compact from L pw to L qv . It is proved that the measure of non-compactness of a bounded linear operator from a Banach space into a weighted Lebesgue space with variable parameter is equal to the distance between this operator and the class of finite rank operators. The p(x) essential norm of the Hilbert transform acting from L w p(x) to L v is estimated from below. As a corollary we have that there is no a weight pair (v, w) and a function p from the class of log-H ̈older continuity such that the Hilbert transform is compact p(x) from L w p(x) to L v . Necessary and sufficient conditions on a weight pair (v, w) governing the bound- edness of generalized fractional maximal functions and potentials on the half-space q(x) from L pw (R n ) to L v (R n+1 + ) are derived. As a corollary, we have criteria for the trace inequality for these operators in variable exponent Lebesgue spaces.
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ڈاکٹر سید محمود

ڈاکٹر سید محمود
افسوس ہے کہ ملک و ملت کی وہ شمع جو ایک عرصہ سے جھلملا رہی تھی، ہمیشہ کے لیے خاموش ہوگئی اور ڈاکٹر سید محمود صاحب نے ۲۸؍ ستمبر کی صبح کو اس جہاں فانی کو الوداع کہا، ڈاکٹر صاحب جیسی جامع اوصاف شخصیتیں کم پیدا ہوتی ہیں، ان میں مذہب و سیاست، علم و فن اور تہذیب و شرافت کا نہایت متناسب اجتماع تھا، شرافت اور وضعداری کا تو مجسم پیکر تھے، آخر کے چند برسوں کو چھوڑ کر جب وہ بالکل معذور ہوگئے تھے، ان کی پوری زندگی ملک و وطن اور قوم وملت کی خدمت میں گزری، وہ ابتدا سے کانگریسی اور پنڈت جواہر لال نہرو کے پرانے رفیق تھے، ان دونوں کے تعلقات اتنے عزیزانہ تھے کہ ڈاکٹر صاحب پنڈت جی کے گھر کے ایک فرد سمجھے جاتے تھے، جنگ آزادی میں ان کے دوش بدوش حصہ لیا، اور ان کے ساتھ قید و بند کی مصیبتیں جھیلیں، آزادی کے بعد صوبہ بہار کے راجیہ سبھا کے ممبر تھے، پھر مرکزی حکومت میں وزیر مملکت برائے امور خارجہ ہوئے، چند سال پہلے تک راجیہ سبھا کے ممبر تھے پھر اپنی معذوریوں کی وجہ سے اس سے بھی الگ ہوگئے تھے ان کا آخری کارنامہ مجلس مشاورت کا قیام ہے، اس کو انھوں نے ہندو مسلم اتحاد، ان دونوں کے درمیان غلط فہمیوں کے ازالہ اور ملک و ملت کی مشترک خدمت کے لیے قائم کیا تھا، اور ابتدا میں بڑی سرگرمی سے اس کے کاموں میں حصہ لیا، اور ضعف پیری کے باوجود ملک کے مختلف حصوں کا دورہ کیا جس کا ملک کی فضا پر بہت اچھا اثر پڑا، لیکن پھر مجلس مشاورت کی پالیسی میں بعض ارکان سے اختلاف کی بنا پر اس سے الگ ہوگئے، وہ چند دنوں سے شیعہ سنی اتحاد کی کوشش میں تھے۔
وہ...

Cultural Heritage Management: Preserving and Promoting Cultural Treasures

This article delves into the profound and transcendent concept of cosmic beauty as it relates to the natural world. Through an exploration of awe-inspiring landscapes, celestial phenomena, and the intricate web of life on Earth, we examine the capacity of nature to evoke deep aesthetic experiences. This multidisciplinary inquiry draws from philosophy, science, and the arts to unravel the profound connection between human consciousness and the cosmic beauty inherent in the universe.

Determination of Residues of Pesticide in Meat and Their Effects on Enzymes and Proteins

The present work is concerned with the determination of pesticide residues in meat samples and effects of pesticides on enzymes levels and protein. Different samples of meat were collected from (chicken, cow and goat). Later organs (fat, heart, kidney, liver and muscle) were isolated. The experiment was done under two conditions such as fresh and other one kept in 10˚C. Meat samples were collected randomly from butcher`s shops. All samples were taken to lab and the collected samples were separately kept in plastic bags. For this standard method described in materials and method was adopted. The pesticide residues, estimation of biochemical contents, enzymes activities and protein content were investigated in 90 samples of meat, additionally, 15 samples meat of each (chicken, beef and mutton) were also collected and considered as control or normal subject for enzymes activity and biochemical content. In all chicken samples, the activity of GOT contents showed significant increase, whereas GPT content significantly decreased than those of detected in control or normal subject. However, ALP and protein were higher in maximum number of samples. In all beef samples GOT and GPT content showed increase in all samples while ALP decreased in all sample but protein increased in all samples. In all mutton samples GPT and GOT content showed significant decrease whereas ALP and protein showed significant increase than those of detected in control or normal subject. Most probable reason of this variation in biochemical contents and enzymes activity may be presence of pesticides residues, socioeconomic factor, metabolic factor and environmental factor. The standard chromatogram of permethrin was prepared on HPLC and retention time (RT) was noted. Chromatograms of cypermethrin, deltamethrin, diazinon, DDE, DDT, malathion and monocrotophos were taken from previous study which was run under the same condition. Total 90 samples were run on HPLC for pesticide residues analysis. The residues amount was noted from the chromatograms. The two set of chicken samples which comprise 30 in numbers were taken from two different locations. The first set of chicken samples contained fifteen different organs (fat, heart, kidney liver and muscle) and also had two conditions of fresh and stored 10˚C. Five samples of fresh ones were run on HPLC for pesticides residues and four were found positive for pesticide. Ten samples stored at 10˚C for 3 days and run on HPLC for pesticides analysis and all were positive for residues analysis. In all the samples, the residues of cypermethrin, DDE, DDT and malathion were detected in noticeable amount. The second set of chicken samples stored were run on HPLC for pesticide residues analysis. Out of 15 samples, 3 samples were found positive for residues of deltamethrin and malathion. Two set of beef samples (30) were run on HPLC for pesticide residues analysis and 19 were positive for pesticides residues. After analysis it was found that cypermethrin was found in 8 samples, DDT in 3 samples, DDE in 8 samples, diazinon in 5 samples, deltamethrin in 13 and malathion only in 2 samples were detected. While mutton samples also 30 in number and were run on HPLC for pesticide residues analysis and 8were positive for pesticides residues. Cypermethrin was found in 2 samples, deltamethrin in 10 samples, diazinon in 7 samples and monocrotophos in 2 samples.