Search or add a thesis

Advanced Search (Beta)
Home > Kernel Operators in Some New Function Spaces

Kernel Operators in Some New Function Spaces

Thesis Info

Access Option

External Link

Author

Zaighum, Muhammad Asad

Supervisor

Alexander Meskhi

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/bitstream/123456789/2740/1/2905S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726566511

Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.

Similar


The thesis is devoted to the weighted criteria for integral operators with positive ker- nels in variable exponent Lebesgue and amalgam spaces. Similar results for multiple kernel operators defined with respect to a Borel measure in the classical Lebesgue spaces are also obtained. More precisely, we established necessary and sufficient conditions on a weight function v governing the boundedness/compactness of the weighted positive kernel operator Kv f (x) = v(x) x 0 k(x, y)f (y)dy from Lp(·) (R+ ) to Lq(·) (R+ ) under the local log-H ̈lder continuity condition and the decay condition at o infinity on the exponents p and q. In the case when Kv is bounded but not compact, two-sided estimates of the measure of non-compactness (essential norm) for Kv are obtained in terms of the weight v and kernel k. Criteria guaranteeing the boundedness /compactness of weighted kernel operators defined on R+ (resp. on R) in variable ex- ponent amalgam spaces are found. The kernel operators under consideration involve, x for example, the Riemann-Liouville transform Rα f (x) = 0 f (t) dt, (x−t)1−α 0 < α < 1. Necessary and sufficient conditions ensuring weighted estimates for maximal and po- tential operators in variable exponent amalgam spaces are also established under the local log-H ̈lder continuity condition on exponent of spaces. Further, we establish o criteria on measures governing the boundedness of integral operators with product positive kernels defined with respect to a Borel measure in the classical Lebesgue spaces. Finally, we point out that Fefferman-Stein type inequality for the multi- ple Riemann-Liouville transform defined with respect to a product Borel measure is derived.
Loading...
Loading...

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

Chapter 3: Sources of the Qur’ānic Thoughts of Dr. Isrār Aḥmad

Influences of ‘Allāma Muḥammad Iqbāl on Thoughts of Dr. Isrār Aḥmad

            Dr. Isrār Aḥmad(d:1431A. H/2010A. D) admits this fact that his personality is deeply influenced by Dr. ‘Allāma Muḥammad Iqbāl(d:1357A. H/1938A. D). In his book titled Da‘vat Rujū‘ ilā al-Qur’ān kā Manẓar-o-Pasmanẓar, he writes:

            “The foremost and the deepest imprint on my mind is that of late ‘Allāma Iqbāl’s Urdu Poetry as I spent my high school life (1941-1947A. D) in reading and humming of bāng-e-darā, bāl-e-Jibra’īl, zarb-e-Kalīm and verses of armughān-e-Ḥijāz. This aroused in me a national passion so I, in that era, found the only like-minded group of the Muslim League, associated myself as per my little ability with the Muslim Students Federation- a body of the Muslim League movement. [1]

            At another point in the same book, he further writes:

            “No denying the fact that like howal awwalo wal ākhiro, my thoughts and vision have the initial and final impact of late ‘Allāma Iqbāl; the former mostly being ‘passionate’ with the outcome of ‘Passion for the Community’ whereas the latter is purely ‘Conceptual’; thus, my concept has the objectivity of “Studying the Qur’ān in the background of Modern Concepts” or “Analysis and Review of the Modern Thoughts in the Light of the Qur’ān”. [2]

            The above lines explain that the vision of Dr. Isrār Aḥmad(d:1431A. H/2010A. D) had the initial impact on ‘Allāma Iqbāl’s personality. The thoughts propounded by Dr. Isrār Aḥmad all his life have the footprints leading to the poetry of Iqbāl.

Political System in Islām

Politically, ‘Allāma Iqbāl was strictly against a democratic government as he says:

 tou nay kiā dekhā nahi maghrib kā Jamhōri...

PENERAPAN TEORI KONSTRUKTIVIS DALAM PEMBELAJARAN

Constructivism is the basis for thinking of a contextual approach, namely that knowledge is built not a set of facts, concepts, or rules that are ready to be remembered. Students must construct that knowledge and give meaning through real experience. Students need to be accustomed to solving problems, finding something useful for themselves, and struggling with ideas. The teacher will not be able to give all knowledge to students. Students must construct knowledge in their own minds. Knowledge is not static, but is constantly evolving and changing as students construct new experiences that force them to base themselves and modify previous knowledge. Learning must be packaged into the process of constructing knowledge rather than receiving knowledge. In the learning process, students build their own knowledge through active involvement in the learning and teaching process. Students become the center of activities, not teachers. Critical thinking is an attempt by someone to check the truth of information using the availability of evidence, logic, and awareness of bias. Critical thinking skills are the cognitive processes of students in analyzing systematically and specifically the problems faced, distinguishing these problems carefully and thoroughly, as well as identifying and reviewing information to plan problem solving strategies.

Characterization and Evaluation of Anti-Campylobacter Potential of Indigenous Lactobacilli in Poultry

IN VITRO CHARACTERIZATION OF PROBIOTIC PROPERTIES AND ANTICAMPYLOBACTER ACTIVITY OF LACTOBACILLI ISOLATED FROM POULTRY The aim of the present study was to isolate, characterize and develop indigenous probiotic lactobacilli targeting mitigation of Campylobacter jejuni. Lactobacilli (n=150) were isolated from poultry (62), fermented foods (78) and human faeces (10).All isolates were preliminarily screened for their anticampylobacter activity by well diffusion assay. Sixteen pre-selected isolates had activity against Campylobacter jejuni (n=4). Cell free supernatants (CFSs) of eight isolates (PL22, PL53, PL88, PL120, PL135, PL141, PL145 and PL149) retained activity after pH adjustment (6.5), while CFS of seven isolates (PL22, PL53, PL120, PL135, PL141, PL145 and PL149) retained activity after boiling at 80°C for 10 minutes. Selected isolates were further characterized for their tolerance to low pH and bile salts, antibiotic susceptibility, auto-aggregation and co-aggregation properties. All selected isolates had significant tolerance to low pH (>50% survival at pH 3), bile salts (0.3%), autoaggregation and coaggregation properties. Selected isolates were safe and had no acquired resistance to penicillin, tetracycline, ampicillin and erythromycin. PL53, PL120 and PL149 showed significantly higher reduction (> 3 log reduction) of Campylobacter jejuni ATCC 33291 in broth culture. It is concluded that Lactobacillus gallinarum PL 53, Lactobacillus casei PL 120 and Lactobacillus gallinarum PL 149 had probiotic potential and anti-campylobacter properties.Keywords: probiotics, Lactobacillus, Campylobacter, pH tolerance, antimicrobial activity EFFECT OF NEWLY CHARACTERIZED PROBIOTIC LACTOBACILLI ON WEIGHT GAIN, IMMUNOMODULATION AND GUT MICROBIOTA OF CAMPYLOBACTER JEJUNI CHALLENGED BROILER CHICKEN The aim of the present study was to determine the competitive exclusion of Campylobacter jejuni inpoultry gut by three potential probiotic lactobacilli strains. A total of 135 birds of one day age were randomly divided into nine groups. The groups of prevention model received respective strains from day 1-35 and treatment model received lactobacilli from day 15-35 (after challenging with C. jejuni). These groups were given lactobacilli (~108 CFUs) while challenged with C. jejuni on day 14 by oral gavage (106 CFUs/bird). There were three control groups including A, B and I. Negative control (A) did not receive any treatment, C. jejuni was given to group B and group I was given Enrofloxacin formulation. Cloacal swabs were collected from birds of each group before and after challenge while the ceca were collected from birds after slaughtering (on day 35) for enumeration of aerobic bacteria, coliform, C. jejuni, lactobacilli and Bifidobacterium on selective agar plates. Effect of lactobacilli on weight gain and New Castle Disease vaccine (NDV) titer were also evaluated. Probiotic strain Lactobacillus gallinarum PL 53 considerably decreased log10 values of aerobic plate count (3.19±0.66), coliform count (2.83±0.22) and C. jejuni (3.98±0.77) in poultry. The probiotics also enhanced Lactobacillus and Bifidobacterium spp. counts (~2-3 log increase). Treatment group C had maximum weight gain (1994±188.32g) and geometric mean titer (274.4) on day 28. The results of in-vivo experiments concluded that probiotic administration may be effective for targeted mitigation of C. jejuni in broiler birds.