Viscoelastic materials have non-negative relaxation spectra. This property implies that viscoelastic response functions satisfy certain necessary and sufficient conditions. It is shown that these conditions can be expressed in terms of each viscoelastic response function ranging over a cone. The elements of each cone are completely characterized by an integral representation. The 1:1 correspond...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

We have evaluated the NMR shielding tensors for A:T,G:C,A:U in Watson-crick, and U-quartet. We have computed NMR shielding tensors at B31YP level by using 6-31G(d) basis set. We have compute anisotropy and asymmetry in A:T,G:C,A:U and U-quartet. The NMR shielding tensors were calculated using the GIAO method. The natural bonding orbital analysis (NBO) were performed. NBO calculation have been ...

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean PCA procedure, we show how PCA can be generalized to manifolds in an intrinsic way that does not resort to linearization of the data space. The underlying pr...

Anti-circulant tensors have applications in exponential data fitting. They are special Hankel tensors. In this paper, we extend the definition of anti-circulant tensors to generalized anticirculant tensors by introducing a circulant index r such that the entries of the generating vector of a Hankel tensor are circulant with module r. In the special case when r=n, where n is the dimension of the...

We present a first-order aggregation model on the space of complex matrices which can be derived from Lohe tensor tensors with same rank and size. call such matrix-valued as generalized matrix model. For proposed two cubic coupling terms, we study several structural properties conservation laws, solution splitting property. In particular, for case only one coupling, reformulate reduced into dia...

When data are organized in matrices or arrays of higher dimensions (tensors), classical regression methods first transform these into vectors, therefore ignoring the underlying structure and increasing dimensionality problem. This flattening operation typically leads to overfitting when only few training is available. In this paper, we present a mixture-of-experts model that exploits tensorial ...

In this paper we generalize the max plus algebra system of real matrices to the class of real tensors and derive its fundamental properties. Also we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverses of tensors is characterized.

We investigate higher rank Killing-Yano tensors showing that third rank Killing-Yano tensors are not always trivial objects being possible to construct irreducible Killing tensors from them. We give as an example the Kimura IIC metric were from two rank Killing-Yano tensors we obtain a reducible Killing tensor and from third rank Killing-Yano tensors we obtain three Killing tensors, one reducib...