A two step method has been devised for the statistical inference of deformation changes. In the first step of this method and based on Procrustes analysis of deformation tensors, the significance of the change in a time or space series of deformation tensors is statistically analyzed. In the second step significant change(s) in deformations are localized. In other words, they are assigned to ce...

In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the qu...

The dual symmetry between electric and magnetic fields is an important intrinsic property of Maxwell equations in free space. This symmetry underlies the conservation of optical helicity and, as we show here, is closely related to the separation of spin and orbital degrees of freedom of light (the helicity flux coincides with the spin angular momentum). However, in the standard field-theory for...

Accurate numerical calculations of electronic structure are often dominated in cost by tensor contractions. These tensors are typically symmetric under interchange of modes, enabling reduced-size representations as well as a reduced computation cost. Direct evaluation algorithms for such contractions use matrix and vector unfoldings of the tensors, computing and accumulating products of input e...

Abstract. The aim of this work is to develop a systematic manner to close overdetermined systems arising from conformal Killing tensors (CKT). The research performs this action for 1-tensor and 2-tensors. This research makes it possible to develop a new general method for any rank of CKT. This method can also be applied to other types of Killing equations, as well as to overdetermined systems c...

Tensors are effective representations for complex and time-varying networks. The factorization of a tensor provides a high-quality low-rank compact basis for each dimension of the tensor, which facilitates the interpretation of important structures of the represented data. Many existing tensor factorization (TF) methods assume there is one tensor that needs to be decomposed to low-rank factors....