We introduce Banach algebras arising from tensor norms. By these Banach algebras we make Arensregular Banach algebras such that tensor product becomes irregular, where is tensor norm. Weillustrate injective tensor product, does not preserve bounded approximate identity and it is notalgebra norm.

We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued vectors. Algebraic methods exist for computing complex-valued decompositions of symmetric tensors, but here we focus on real-valued decompositions, both unconstrained and nonnegative. We discuss when solutions exist and how to formulate the mathematical program. Numerical results sh...

For any real inner product space V , let T (V ) denote its tensor algebra. We give a theorem giving conditions under which a real-valued algebra homomorphism from certain subalgebras of T (V ) can be extended to T (V ). The main applications are characterizations of combinatorial parameters by means of ‘reflection positivity’. The proof method follows mainly that of Szegedy [4], whose theorem i...

A survey of the development of algorithms for enforcing nonnegativity constraints in scientific computation is given. Special emphasis is placed on such constraints in least squares computations in numerical linear algebra and in nonlinear optimization. Techniques involving nonnegative low-rank matrix and tensor factorizations are also emphasized. Details are provided for some important classic...

In this paper, we calculate the relativistic bulk tensor and shear tensor of the relativistic accretion ows in the Kerr metric, overall and without any approximation. We obtain the relations of all components of the relativistic bulk and shear tensor in terms of components of four-velocity and its derivatives, Christoffel symbols and metric components in the BLF. Then, these components are deri...

In this paper, we study the tensor commutativity degree of pair of finite groups. Erdos introduced the relative commutativity degree and studied its properties. Then, Mr. Niroomand introduced the tensor relative commutativity degree, calculated tensor relative degree for some groups, and studied its properties. Also, he explained its relation with relative commutativity degree. In this paper, w...

This paper presents a modified digital image watermarking method based on nonnegative matrix factorization. Firstly, host image is factorized to the product of three nonnegative matrices. Then, the centric matrix is transferred to discrete cosine transform domain. Watermark is embedded in low frequency band of this matrix and next, the reverse of the transform is computed. Finally, watermarked ...