Search from the Journals, Articles, and Headings
Advanced Search (Beta)
Loading...
Loading...
Loading...
Loading...
Loading...
Loading...

جب سورج ڈھلنے لگتا ہے

جب سورج ڈھلنے لگتا ہے
یاد مجھے تُو کیوں آتا ہے

تُو نے پہنے ہیں دستانے
میرے دل کا خون ہوا ہے

تیرے شہر میں آ کر مجھ کو
اپنا آپ ہی بھول گیا ہے

تُو نے نہیں بنایا اپنا
تیرے شہر کو اپنایا ہے

تیری ساری باتیں سچی
کیسے کہوں میں تُو جھوٹا ہے

کوئی تری مجبوری ہو گی
میں نے اب یہ سوچ لیا ہے

اِس دل کو کیسے سمجھائوں
یہ تجھ کو اپنا سمجھا ہے

عشق کی آگ یہ کیسی بھڑکی
سب کچھ جل کر راکھ ہُوا ہے

تیرے شہر سے جانے لگا ہوں
کوئی مجھ کو روک رہا ہے

Cartoons as A Tool of Religious Instruction for School-Going Children: A Case Study of Sheikhupura City

This research elaborates on utilization of cartoons as a tool of religious instruction for children. Cartoons can be used as an instrument for children’s mental development because a child’s mind is like a plain slate, what you write leaves a long-lasting impact. Cartoons have become a favorite activity of children and they spend most of their leisure time on watching cartoons. Children’s interest in cartoons also impacts their mind according to the content and concept of cartoons. For this aim, cartoons with religious instructions were shown to children and interview of some children’s parents and teachers were done in Sheikhupura. The data collected from the observations and interviews done qualitatively for this research shows that cartoons are a very effective source of religious instruction for children. Children not only understand these instructions easily but also try to follow them.

Algebras of Block Toeplitz Matrices and Matrix Valued Truncated Toeplitz Operators and Related Problems

The present thesis entitled ”Algebras of block Toeplitz matrices and matrix valued truncated Toeplitz operators and related problems” includes a part of research work carried out by the author during the last four years at the Abdus Salam School of Mathematical sciences Government college university Lahore Pakistan and Simion Stoilow Insitute of the Mathematics of the Romania Academy Bucharest Romania. The thesis comprises five chapters and each chapter is subdivided into various sections. The maximal algebras of scalar Toeplitz matrices are known to be formed by generalized circulants. A similar simple description cannot be obtained for block Toeplitz matrices. The identification of algebras consisting of block Toeplitz matrices is a harder problem, that has received little attention up to now. We consider the case when the block entries of the matrices belong to a commutative algebra A. We introduce and investigate certain families of maximal commutative algebras of block Toeplitz matrices. After obtaining some general results, we classify all the maximal algebras for certain particular cases of A. In the last decade, a large amount of research has concentrated on a generalization of Toeplitz matrices, namely truncated Toeplitz operators. For matrix valued truncated Toeplitz operators, which are compressions of multiplication operators to model subspaces of the vector valued Hardy space H2(E) , likewise block Toeplitz matrices case the problem of characterizing the maximal algebras becomes now very hard and there seem to be no chances to treat it in a general way. However, under certain assumptions, we obtain criteria for commutation relations for matrix valued truncated Toeplitz operators. The results show an analogy to the case of Toeplitz matrices which will be the basis for the extension of Sedlock classes of truncated Toeplitz operators to matrix valued case.
Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.