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Refinements of Jensen-Steffensen and Related Inequalities

Thesis Info

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Author

Khalid, Sadia

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2009

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1360

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727073839

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As the title suggests, the present dissertation deals with the refinements of Jensen- Steffensen and related inequalities. We extend some classical results and give some new refinements of several well known inequalities including Jensen’s inequality, Jensen- Steffensen inequality, Hermite-Hadamard inequality, majorization-type inequality, generalized weighted Favard and Berwald inequalities. We also provide the refine- ments of some companion inequalities to the Jensen’s inequality, namely Slater’s inequality and the inequalities obtained by M. Mati ́ and J. Peˇari ́ in [44]. We c c c sharpen the lower bounds of the Jensen’s functional. Some inequalities in terms of Gˆteaux derivatives for convex functions are also provided. Finally, we present not aonly the generalizations of Hardy-Littlewood-P ́lya inequality [26, Theorem 134] but o also generalizations of some results given in [8] and [36].
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اللغة العربية

اللغة العربية

(حسب ترتيب حروف الهجاء)

 

سنة الطبع

 

إسم المطبعه

 

إسم الكتاب

 

إسم المؤلف

الرقم

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أهمية كشف ممارسات المحاسبة الإبداعية من خلال دور معايير المحاسبة الدولية والإفصاح المحاسبي

تناولت الورقة البحثية العلاقة الإيجابية بين كل من الإفصاح المحاسبي عن المعلومات الواجب توافرها ونشرها عن المنشأة، من خلال أساليب الإفصاح التي هي الطرق التي تسهل فهم وقراءة البيانات المالية، وكل أسلوب يكمل ويفسر كل غموض وارد في القوائم المالية خاصة وأن الإفصاح ضرورة مهمة تقتضيها عملية توصيل المعلومات المناسبة وبالنوعية المطلوبة في الوقت المناسب. كما ناقش الباحثون مفهوم المحاسبة الإبداعية وممارساتها، وكيفية تسكين هذه الممارسات بين الجائزة وعدم الجائزة، حيث تطرق الباحثون إلى هذه الممارسات التي تضمنتها المعايير الدولية لإعداد التقارير المالية . IFRS

Dynamics of Bacterial Assisted Phytoremediation of Soil Contaminated by Quinolone Antibiotics

Recently there has been growing concern about public health and ecosystems due to the presence of trace quantities of quinolone antibiotics in the environment. These antibiotics enter the environment through irrigation by contaminated waste water, particularly in the areas that are arid or semi-arid. Another route of these antibiotics is the application of sludge and manure containing antibiotics as soil amendments on agricultural land. Once they enter the environment they can cause ecotoxic effect. In the current study, the concentration of ciprofloxacin, enrofloxacin, and levofloxacin in waste water and sludge were relatively higher than reported in many countries. To degrade the aforementioned antibiotics in agricultural soil, eight bacterial strains were isolated and characterized. The isolated bacterial strains possess multiple antibiotic resistance and degraded ciprofloxacin by whole cell activity. No DNA transformation were observed when naked DNA of the isolated bacterial strain were exposed to indigenous soil microbes. The isolated bacterial strains survived well under aerobic conditions in soil treated with ciprofloxacin at the concentration of 5 mg kg-1, 50 mg kg-1 and 100 mg kg-1. The quinolone antibiotics did not affect germination of wheat even at 400 mg L-1 concentration but the young wheat seedlings were sensitive to the antibiotics at relatively low concentrations (5 mg L-1). The toxicity of the quinolone antibiotics ciprofloxacin (CIP), enrofloxacin (ENR), levofloxacin (LEV), and a mixture (MIX) of the same were tested in a greenhouse study with wheat for 20 days. Antioxidants, which play a vital role in detoxifying reactive oxygen species (ROS) during stress, were xxii also studied. The highest antibiotic concentrations, 100 and 300 mg L-1, significantly decreased plant growth and caused oxidative stress. The quinolone antibiotics ciprofloxacin (CIP), enrofloxacin (ENR), levofloxacin (LEV), and a mixture (MIX) in agricultural soil were readily sorbed when tested in agricultural soil. The antibiotics showed high sorption coefficient (Kd) values at low concentration and low Kd values at high concentrations, which means sorption was concentration dependent and time for sorption decreased with increasing concentrations. In both the individual and MIX treatment the order of sorption was CIP > ENR > LEV and for desorption it was LEV > ENR > CIP. In a bacterial assisted phytoremediation study, wheat was grown in greenhouse conditions in soil supplemented with CIP, ENR, and LEV at 5, 50 and 100 mg kg-1 in individual and MIX treatments. CIP, ENR and LEV accumulated in plant roots and shoots from soil and more accumulation was observed in roots. The order of accumulation in plant parts was LEV > ENR > CIP both in individual and MIX treatments. The pots having only plants enhanced the recovery of antibiotics from soil compared to those where there were only bacteria but greater degradation was observed where plants were grown in the presence of bacteria. CIP, ENR, and LEV were completely degraded in individual treatments at 5 and 50 mg kg-1 level in the presence of plants and bacteria after 30 days compared to the control. In the MIX treatment all three antibiotics were less degraded compared to individual treatments in the presence of plants and bacteria after 30 days because of the higher concentration of each antibiotic in the pots.