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Configurational Structure and Ideals of Bcc/Weak Bcc-Algebras

Thesis Info

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Author

Bushra, Shaban Ali Bhatti

Program

PhD

Institute

University of the Punjab

Institute Type

Public

City

Lahore

Province

Punjab

Country

Pakistan

Thesis Completing Year

2010

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/657

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725781637

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The study of algebras motivated by known logics is interesting and very useful for corresponding logics. In such kinds of algebras we can introduce a natural partial order which has many interesting properties and gives decomposition of algebras into subsets called branches. In the theory of these algebras an important role plays also ideals and congruences. This thesis is devoted to study of branches and ideals of weak BCC- algebras called in China – BZ-algebras. Such algebras are strongly con- nected with a weak BIK+ -logic. Basic properties of branches and connec- tions between various types of ideals are described by using the so-called Dudek’s map. A new type of ideals are introduced and characterized. Con- nections between ideals saving some basic properties are investigated. De- compositions of weak BCC-algebras into branches are presented and it is proved that a decomposition of a weak BCC-algebra X into branches in- duces on X a congruence θ such that the quotient algebra X/θ is isomorphic to subalgebra of X containing only initial elements of X. A decomposition of a medial weak BCC-algebra into direct product of subalgebras generated by one element is presented too. Next we propose two new decompositions which are in fact two new generalizations of weak BCC-algebras. The first decomposition is a decomposition of a basic set X into a set theoretic union of two weak BCC-algebras X1 and X2 having common distinguished ele- ment. The second decomposition is a decomposition of a basic operation defined on X into two new operations in this way that these two operations save a distinguished element of X, a partial order defined on X and some basic properties of weak BCC-algebras.
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تنقید کے اصول

موضوع4:تنقید کے اصول
تنقید کے اصول:
تنقید کے اصول اور طریقہ کار میں فرق ہے۔تنقید کے دو مروجہ طریقے ہیں:
• استخراجی طریقہ کار • استقرائی طریقہ کار
استخراجی طریقہ کار:
اس طریقہ کار میں کل سے جزویا عام سے خاص کی طرف جاتے ہیں۔مثلا تمام انسان فانی ہیں لہذابلال بھی فانی ہے۔
استقرائی طریقہ کار:
اس طریقہ کار میں جزو سے کل یا خاص سے عا م کی طرف جایا جاتا ہے۔مثلا خیبر پختونخواہ کے کوے کالے ہیں، پنجاب کے کوے کالے ہیں، بلوچستان کے کوے کالے ہیں لہذاپاکستان بھر کے کوے کالے ہیں۔
تنقید کے اصول
غیر جانبداری:
تنقید کا پہلا اصول غیر جانبداری ہے۔دوستی ،تعلق داری یا پیسے کی لالچ میں جانبداری کا مظاہرہ کرنا نہیں۔اصل نقاد غیر جانبداری کا مظاہر ہ کرتا ہے۔
محنت اور لگن سے کام:
نقاد ہمیشہ محنت سے کام کرتا ہے۔ اچھا نقاد کسی کتاب کو پڑھ کر ہی اس پر تنقید کر سکتا ہے اور رائے دے سکتا ہے۔
حقائق سے آگاہی:
نقاد کو حقیقتوں کا پتہ ہونا چاہیے مثلا انٹرنیٹ کے مسائل ہر جگہ پر ہیں۔ اس حقیقت کو مدنظر رکھ کر رائے دینی چاہیئے یعنی حقیقت پسند ہونا چاہیئے۔
مضمون پر عبور:
ایک نقاد کو اپنے مضمون پر بھرپور عبور ہونا چاہییمثلا نظم پر تنقید کرتے ہوئے نظم کی بنیادی چیزیں مثلا وزن، بحر، ردیف، قافیہ، مطلع، مقطع و?غیرہ کا پتہ ہونا چاہیئے۔ اسی طرح ناول پر تنقید کرنے کے لیے اس کے پلاٹ، موضوع، کردار نگاری،مکالمہ نگاری وغیرہ یعنی اس موضوع کی بنیادیں چیزوں سے آگاہ ہو۔
جرات اظہار:
ایک اچھے نقاد کے اندر جرات اظہارکا ہون ازحد ضروری ہے یعنی مصنف کے قد کاٹھ کو دیکھنے کی بجائے اس کے کام میں جہاں غلطی ہو اسے ببانگ دہل بیان کرسکے۔
شخصیت پرستی سے پرہیز:
نقاد کے لیے لازم ہے کہ وہ شخصیت پرستی سے...

Association of Serum Ferritin with Risk of Anemia in Non-Diabetic Adolescents with Family History of Type 2 Diabetes Mellitus

Background: Controversy occurs in the relationship between serum ferritin levels, insulin resistance and risk of developing anemia in adolescents with family history of diabetes. Aims & Objectives: This study was designed to find out the association between serum ferritin levels with risk of developing anemia in non-diabetic adolescents with family history of type 2 diabetes mellitus (T2DM). Materials & Methods: A descriptive cross-sectional was conducted in a local medical institute of Lahore. Study included 50 non-diabetic, non-obese male / female adolescent with family history of type 2 diabetes mellitus and 50 healthy male/female non-obese adolescents without family history of T2DM considered as controls. Level of serum ferritin and serum insulin was estimated by Enzyme Linked Immunosorbent Assay. Blood glucose was estimated by auto-analyzer. Insulin resistance was calculated by HOMA-IR index and beta cell function was assessed by HOMA- beta index. Results: Levels of fasting blood sugar, insulin resistance were found to be increased with decreased level of serum ferritin and decrease beta cell function in both male as well as female cases as compared to controls. Negative correlation was found between serum ferritin and insulin resistance while a positive correlation was found between serum ferritin and beta cell function. Conclusions: Low level of serum ferritin is associated with reduced beta cell function and increased insulin resistance. This may increase the risk of developing iron deficiency anemia that can affect both immune system as well as increase susceptibility to infections.

Pharmacognostic Evaluation of Ehretia Serrata Roxb. and Ehertia Obtusifolia Hocht. A. Dc. Family Boraginaceae

The current investigation is carried out to detect the pharmacognostic, physicochemical and pharmacological evaluation of leaf, stem bark and root of Ehretia serrata Roxb. andEhretia obtusifolia Hochst. Ex A. DC which belongs to the family Boraginaceae. The morphological study showed that E. serrata is a small size deciduous tree, less than 10 m tall, locally named as puran and punna in Urdu.Its Leaf is simple with oblong shape (5-16 cm long and 2.8-6.5 cm wide), serrulated margins and glabrous surface. E. serrata contains drupe globose type fruit with yellowish green-light color when unripe and black when ripe. Stem bark is irregular with up to 2.5 cm wide, dark brown outer color and whitish golden inner surface color. E. obtusifolia is a deciduous small shrub or small tree up to 6 m tall; straggling or with several branches from the base. The Leaf is oblong-elliptic or oboviate with obtuse apex, entire margins and reticulate venation. Microscopic study of E. serrata showed the presence of conical trichomes and anomocytic type of stomata on both surfaces where as anisocytic type of stomata was observed only on the lower epidermis with stomatal index 36.7μ. Upper surface showed 30.4 μ stomatal index. Other parameter includes palisade ratio (6.4+0.894 per mm2), vein Islet number (19.4+1.79 per mm2), stomata number (21.8+1.78 per mm2) and vein termination number (10.6+1.987 per mm2). A Similar microscopic anatomical study was carried out of leaf of E. obtusifolia and we observed two types of trichomes i.e simple conical trichomes and capitate glandular trichome on both surfaces. Stomatal cluster was observed only on the lower epidermis with three types of stomata i.e anomocytic, anisocytic and hemiparacytic. Other observed parameters were palisade ratio (6.2 + 0.81 per mm2), vein islets number (18.6 + 1.14 per mm2), vein termination number (8.2 + 0.828 mm2), stomatal number (21.8 + 1.78 per mm2) and stomatal index (35.7 + 6.12 μ). Stem bark anatomy of both experimented plants showed clear layers of cork, cork cambium, phloem elements, medullary rays and tracheids, etc. Fruit anatomy of both plants showed a clear distinction between three layers of pericarps and seeds.Powder drug microscopy of leaf, stem bark and fruits of E. serrata and E. obtusifolia was carried out and observed stomata, epidermal cells, fibers, tracheids and vessels, etc. Results of qualitative preliminary phytochemical screenings of examining parts of E. serrata and E. obtusifolia are given, presenting the presence of phenol compounds, starch, protein, reducing sugar, steroids, terpenoids, fats, aldehydes, anthraquinones, glycosides, amino acids, saponins, alkaloids, tannins, phlobatannin. Similarly, results of a fluorescence study of leaf, stem bark and fruit of E. serrata and E. obtusifolia are also given. Results of elemental analysis showed the presence of some essential elements in all examined parts of these two plants. The most abundant elements found in all three parts of E. serrata and E. obtusifolia were Mg, Na, and Fe and which may contribute to analgesic and anti-inflammatory effects of these plants. Proximate analysis of both plants showed carbohydrate, proteins, fibers, fats and moisture in fairly large amounts. The methanolic extracts of E. serrata and E. obtusifolia leaf, stem bark and fruit were non-toxic against Swiss albino mice. Methanolic extract of leaf of E. serrata showed the highest (P<0.01) cytotoxic activity (83.3%) with the LD50 values 15.29 µg/mL at dose level 1000 µg/mL and in E. obtusifolia the fruit methanolic extract showed highest (P<0.01)(80.0%) cytotoxic activity at 1000 µg/mL with an LD50 value of 16.07 µg/mL. All experimented parts of both plants showed non-significant (P>0.05) Phytotoxic activity at all dose levels of 10, 100 and 1000 µg/mL. The anti-oxidant effect of all parts (leaf, stem bark and fruit) of both plants was dose dependent. High (94.1%) DPPH inhibition was shownby stem bark extract of E. serrata at dose level 1000 µg/mL after 60 min and fruit extract of E. obtusifolia (85.01%) at level 1000 µg/mL after 30 minutes. Based on IC50 (µg/mL) stem bark of E. obtusifolia and leaf of E.serrata showed significant values as compared to ascorbate. Both plant methanolic extract was not that much more effective against bacterial strains inhibition. The prominent antibacterial zone (7 mm) was observed in the leaf methanolic extract of E.serrata as compared to reference drug (31.5 mm) at dose level 1000 µg/mL. Similarly, different parts of E. obtusifolia tested against various bacteria which showed no significant results and the most prominent (7 mm) anti-bacterial zone was observed at dose level 1000 µg/mL of leaf extract compared to reference drug (30.2 mm). Toxicological studies showed that both plants are safe for human use. Analgesic effect was found dose dependent and time dependent and all parts of both investigated parts (P<0.05) showed significant results. The highly significant analgesic effect was shown by all experimented parts (P<0.01) at all dose level 100 mg/kg, 200 mg/kg and 300 mg/kg over 60 minutes in E. Serrata except stem bark. Stem bark of E. obtusifolia showed highly significant (P<0.01) at all dose after 60 minutes. Anti-inflammatory effect of all three investigated parts of E. serrata and E. obtusifolia were observed and it is noticed that all parts of E. serrata showed high significancy (P<0.01) at all dose i.e 100 mg/kg, 200 mg/kg and 300 mg/kg after 2 and 3 hours. Similar results were shown by E.obtusifolia. Antispasmodic effects of methanolic extract of leaf stem bark and fruit of E. serrata and E. obtusifolia was tested in swiss albino mice. Stem bark methanolic extract showed highly significant (P<0.01) results at dose of 200 mg/kg and 300 mg/kg. E. obtusifolia causes better relaxation of the smooth muscles at very low concentrations. Leaf extract at dose of 200 mg/kg and 300 mg/kg, fruit at level of 300 mg/kg and stem bark at all dose showed highly significant (P<0.01) results thus providing a scientific proof for its ethnopharmacological use as an antispasmodic drug. The present study has revealed the enormous and different medicinal properties of E. serrata and E. obtusifolia both can be exploited for therapeutic preparations on a commercial scale.