commutative properties of four-dimensional generalized symmetric pseudo-riemannian manifolds were considered. specially, in this paper, we studied skew-tsankov and jacobi-tsankov conditions in 4-dimensional pseudo-riemannian generalized symmetric manifolds.

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

The aim of this paper is to characterize $3$-dimensional $N(k)$-paracontact metric manifolds satisfying certain curvature conditions. We prove that a $3$-dimensional $N(k)$-paracontact metric manifold $M$ admits a Ricci soliton whose potential vector field is the Reeb vector field $xi$ if and only if the manifold is a paraSasaki-Einstein manifold. Several consequences of this result are discuss...

We study the semi-classical limits of the first eigenfunction of a positive second order operator on a compact Riemannian manifold when the diffusion constant ǫ goes to zero. We assume that the first order term is given by a vector field b, whose recurrent components are either hyperbolic points or cycles or two dimensional torii. The limits of the normalized eigenfunctions concentrate on the r...

An m-dimensional locally conformal Khler manifold (l.c.K-manifold) is characterized as a Hermitian manifold admitting a global closed 1-form a%(called the Lee form) whose structure (F%,g%) satisfies VF -8g + 8g F + aF, where ? denotes the covariant differentiation with respect to the Hermitian metric gl, 8 -Fl a, Fl F gel and the indices 9, ,l run over the range 1,2, m. For l.c.K-manifolds, I.V...

The polynomial invariants qd for a large class of smooth 4-manifolds are shown to satisfy universal relations. The relations reflect the possible genera of embedded surfaces in the 4-manifold and lead to a structure theorem for the polynomials. As an application, one can read off a lower bound for the genera of embedded surfaces from the asymptotics of qd for large d. The relations are proved u...

We create an artificial neural network which is a version of echo state machines, ESNs. ESNs are recurrent neural networks but unlike most recurrent networks, they come with an efficient training method. We adapt this method using ideas from the neuroscale algorithm so that the network is optimal for projecting multivariate time series data onto a low dimensional manifold so that the structure ...

This paper is a continuation of research in the direction energy function (a smooth Lyapunov whose set critical points coincides with chain recurrent system) construction for discrete dynamical systems. The authors established existence an any A-diffeomorphism three-dimensional closed orientable manifold non-wandering consists chaotic one-dimensional canonically embedded surface attractor and r...

The authors discuss mainly that the Riemannian manifold Mn admitting a unit preserving circle field ? in present paper. A sufficient and necessary condition is given an Einstein by imposing some conditions on W2 curvature tensor. Further, this paper obtains algebra representation of tensors W2-recurrent R???? = 1/d2 [d?d?R?? d?d?R?? + d?d?R??].

The one dimension computational model of a sequential injection engine, which runs on compressed natural gas (CNG) with spark ignition, is developed for this study, to simulate the performance of gas flow pressure profile, under various speed conditions. The computational model is used to simulate and study of the steady state and transient processes of the intake manifold. The sequential injec...