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Homological and Combinatorial Properties of Monomial Ideals and Their Powers

Thesis Info

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Author

Adnan Aslam

Supervisor

Jurgen Herzog

Program

PhD

Institute

Government College University

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/215

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726375470

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In this thesis we classify all unmixed monomial ideals I of codimension 2 which are generically a complete intersection and which have the property that the sym- bolic power algebra A(I) is standard graded. We give a lower bound for the highest degree of a generator of A(I) in the case that I is a modification of the vertex cover ideal of a bipartite graph, and show that this highest degree can be any given num- ber. We furthermore give an upper bound for the highest degree of a generator of the integral closure of A(I) in the case that I is a monomial ideal which is generically a complete intersection. Minh and Trung presented criteria for the Cohen-Macaulayness of a monomial ideal in terms of its primary decomposition. We extend their criteria to characterize √ the unmixed monomial ideals for which the equality depth(S/I) = depth(S/ I) holds. As an application we characterize all the pure simplicial complexes ∆ which have rigid depth, that is, which satisfy the condition that for every unmixed mono- √ mial ideal I ⊂ S with I = I ∆ one has depth(I) = depth(I ∆ ). It is shown that a squarefree principal Borel ideal satisfies the persistence prop- erty for the associated prime ideals. For the graded maximal ideal we compute the index of stability with respect to squarefree principal Borel ideals and determine their stable set of associated prime ideals.
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آپؐ کے نقشِ پا سے مزین زمیں ، خاتم المرسلیں

آپؐ کے نقشِ پا سے مزین زمیں، خاتم لمرسلیںؐ!
اَرضِ بطحا نے پائے ہیں کیسے نگیں، خاتم لمرسلیںؐ!

آپؐ کی بات کا صدق دل سے یقیں ،اے رسولِ امیں!ؐ
آپؐ کو غیر کہتے ہیں صادق امیں ،خاتم لمرسلیںؐ!

آپؐ کو جو رکھیںجان و دل کے قریں ،رحمتِ عالمیں!ؐ
صاف کہتا ہے قرآں انہیں مومنیں ، خاتم لمرسلیںؐ!

آپؐ کا جو ہوا ، سب اُسی کا ہوا ، اے حبیب خداؐ!
آپؐ کا جو نہیں ، وہ کہیں کا نہیں ، خاتم لمرسلیںؐ!

خوش طبع ، خوش ادا ، سیرت خوش صفا ، صورتِ والضحیٰ
خوش خط و خوبرو ، دلکش و دلنشیں ، خاتم لمرسلیںؐ

آپؐ کے بعد آئے نبیؐ دُوسرا ؛ میں نہیں مانتا
سیّد الاوّلیں ، سیّد الآخریں ، خاتم لمرسلیںؐ!

تُو لکھے حرفِ مدحت، پڑھے نعت کیا ، تیری اوقات کیا
دی گئے تجھ کو عرفانؔ! لحنِ حسیں ، خاتم لمرسلیںؐ

أهمية ثقافة الحوار في الإسلام وجهود المملكة العربية السعودية في نشرها

This is the unique quality of Islam that it respects all the religions. It strictly opposes the preaching of religion based on enforcement, power, misconduct, and discrimination and promotes the culture of dialogue to create an atmosphere of harmony. In this way, it emphasis upon the trends of mutual understanding and cooperation. Allah Almighty has directed it because commonalities on dialogue the start to (صلى الله عليه وسلم) Prophet Holy enhances the interfaith harmony. This research work discusses the importance of culture of dialogue in Islam and highlights the efforts of the KSA in disseminating and promoting that culture at national, regional and international levels. It also refers to the efforts exerted by official and non-official Saudi institutions in advocating dialogue and rapprochement between sects in different societies, promoting peaceful coexistence among different religions and civilizations, and activating conferences and scientific seminars that discuss dialogue and peaceful coexistence. In this research, I used the deductive analysis methodology and concluded that the Kingdom of Saudi Arabia serves Islam by: -Opening the horizons of communication and exchange of knowledge with the other in order to provide a true picture of Islam. -Working to promote the real teachings of Islam in terms of tolerance and passion. -Cooperating in spreading security, peace, virtuous values and building a global system of ethics.

Effect of Essential Oils and Other Chemicals Against Varroa Mites in Honey Bee Apis Mellifera L.

Experiment of essential oils and other chemicals on infested colonies of honey bee apiary the present study was conducted and three experiments laid out under completely Randomized design (CRD) 2 ways factorial during 2014 and 2015 at The University of Agriculture, Peshawar Pakistan. In these experiments there were taxonomic studies of varroa mites on Apis mellifera in different region of Khyber Pakhtunkhwa byusing De Guzman and Fernandez and C0ineau, 2007 key for identificati0n of the mite samples i.e. length and width (b0dy size), locati0n of seta, shape, size (i.e. bristle hair, stiff) on d0rsal shield, chaet0taxy and structure 0f the sterna, ana1, metap0dal, and epigyna1 shie1ds, periterme, morpho1ogy of setae 0n the 1egs and pa1ps it arrangement and number were 0bserved. M0re than 1000 specimen of mites were c0llected from different regi0n of Khyber Pakhtunkhwa (i.e. Peshawar, Mardan, K0hat and Chitra1). The present study resu1ted that the specimens were Varr0a destruct0r, however, no specimen of Varr0a jacobs0ni were rec0rded during Chaet0taxy and morphologica1 studied. During 2014 by using different essentia1 0ils and 0ther chemica1s i.e. euca1yptus 0il, basi10il, geranium 0il, spearmint 0il, r0semary 0il, f0rmic acid 65%, fluva1inate strips, icing sugar dusting and contro1 were used t0 find 0ut the efficacy of these 0ils and chemica1s. The experiment was divided in different parameters i.e. adu1t w0rker and brood of h0ney bees in m0nth of March- April and in September. Efficacy of r0semary 0il pr0ved best and significant results where the percent reducti0n of varr0a mites in m0nth of March –April during year 2014 the percent reducti0n on adu1t w0rker and brood 0f h0ney bees were 96.45% and 96.25% similar trend were 0bserved in f0rmic acid 65% where the mite reducti0n on adult w0rker and broods were 95.10%and 93.58%, fluva1inate strip 87.46% and 90.08%, icing sugar dusting 86.62% and 88.85%, spearmint 0il 84.62% and 87.86%, eucalyptus oil 83.63% and 72.57%, geranium 0il 81.05% and 76.10%, and basi1 0il 78.53% and 74.59% respectively. In m0nth of September during 2014 the reducti0n of varroa mites ofinfested co1onies of h0ney bee once again rosemary oil gave best results on adult workers and brood with the mean on third treatment was 96.32% and 93.33% followed by f0rmic acid 65% with mean 0f 96.26% and 82.99%, icing sugar dusting 91.06% and 81.73%, fluvalinate strip 86.96% and 78.28%, spearmint 0il 86.42% and 72.17%, basil oil 81.84% and 73.06%, geranium 0il 79.62% and 67.65% and euca1yptus 0il 76.49% and 71.62% respectively. Application of different essentia1 0ils and chemicals on infested colonies of honey bee i.e. adult worker and broodduring year 2015, in month of March and Aprilagain rosemary oil gave better results on both adult worker and brood of honey bees with mean reduction of 95.93% and 94.67%, similar trend was observed in formic acid 65% with the mean of 95.12% and 93.04%, fluvalinate strips 93.91% and 92.13%, icing sugar dusting 91.09% and 89.09%, spearmint oil 88.84% and 84.83%, basil oil 86.80% and 84.24%, geranium oil 85.06% and 81.52% and eucalyptus oil 82.47% and 81.89% vi respectively. In month of September during year 2015 rosemary oil on adult worker and brood the maximum percent reduction were observed with the mean on third treatment was 91.37% and 89.97%, whereas similar results were followed by formic acid 65% where mean were 89.93% and 93.96%, icing sugar dusting 82.77% and 86.60%, spearmint oil 82.73% and 92.52%, fluvalinate strip 79.57% and 85.75%, basil oil 72.68% and 82.74%, geranium oil 72.21% and 82.07% and eucalyptus oil 70.01% and 82.31% respectively. In both year 2014 and 2015during month of March- April and September interaction of oil, year and treatment, rosemary oil proved best amongst all essential oils and chemical and significantly different from control followed by formic acid 65%, fluvalinate strips, icing sugar dusting, spearmint oil, basil oil, geranium oil and eucalyptus oil. When year 2014 and 2015 were compared during both season March –April and September year 2015 proved best and gave maximum percent reduction of varroa mites on infested colonies of honey bees. By using GC-Mass to find out the residues in honey during year 2014 and 2015 eucalyptol in eucalyptus oil was (0.006 µg/g and 0.00 µg/g ), bernol in basil was (0.025 µg/g and 0.00 µg/g), geranol in geranium 0il (0.13 µg/g and 0.13 µg/g), menth0l in spearmint oil (0.23 µg/g and 0.028 µg/g), linalool in rosemary oilwas (1.04 µg/g and 0.01 µg/g), in formicacid 65% the level was 81 and fluvalinate strip the level was below 50ppb which is accepted by the Environmental protection agency EPA, European Agency for Evaluation of Medical product (EMEA), Swiss food legislation, as well as European Union council Regulation (EEC). In conclusion, taxonomic studied showed that specimens from Pakistan indicated Varroa destructor not V. jacobsoni. Similarly Rosemary essential 0il was found the effective against Varroa destructor in honey bee (Apis mellifera) and significantly different as compare with formic acid (65%), fluva1inate strips, and icing sugar dusting, spearmint oil against Varroa mite populations in honey bee colonies in a context of essential oils. Further by there is no residues were found in h0ney. All the above outcomes provided essential information needed for decision making regarding the use of essentia1 0ils and other chemicals for the integrated management of Varroa destructor.