1. Sufficient conditions for uniqueness In the quantisation of constrained systems it can happen that one obtains a representation of an algebra of quantum operators on a vector space without a preferred inner product. Since an inner product is necessary for the probabilistic interpretation of quantum theory, some way needs to be found of introducing an appropriate inner product on this vector ...

has been introduced by several authors like Ahmed and Hamouly [1], Kohli and Kumar [5], Biswas [4], etc. Also the notion of fuzzy norm on a linear space was introduced by Katsaras [9]. Later on many other mathematicians like Felbin [3], Cheng and Mordeso [10], Bag and Samanta [6], etc, have given different definitions of fuzzy normed spaces. In recent past lots of work have been done in the top...

Let m,n > 1 be integers and Pn,m be the point set of the projective (n − 1)-space (defined by [2]) over the ring Zmof integers modulo m. Let An,m = (auv) be the matrix with rows and columns being labeled by Pn,m, where auv = 1 if the inner product 〈u, v〉 = 0 and auv = 0 otherwise. Let Bn,m = An,mA t n,m. The eigenvalues of Bn,m have been studied by [1, 2, 3], where their applications in the stu...

this article concerned on the study of signature submanifolds for curves under lie group actions se(2), sa(2) and for surfaces under se(3). signature submanifold is a regular submanifold which its coordinate components are dierential invariants of an associated manifold under lie group action, and therefore signature submanifold is a key for solving equivalence problems.

The natural join and the inner union operations combine relations in a database. Tropashko and Spight realized that these two operations are the meet and join operations in a class of lattices, known by now as the relational lattices. They proposed then lattice theory as an algebraic approach, alternative to the relational algebra, to the theory of databases. Litak et al. proposed an axiomatiza...