In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...

‎The object of the present paper is to introduce and study a type of non-flat semi-Riemannian manifolds‎, ‎called‎, ‎super generalized recurrent manifolds which generalizes both the notion of hyper generalized recurrent manifolds [‎A.A‎. ‎Shaikh and A‎. ‎Patra‎, On a generalized class of recurrent manifolds‎, Arch‎. ‎Math‎. ‎(Brno) 46 (2010) 71--78‎.] and weakly generalized recurrent manifolds ...

We understand a lot about fiber bundle F → E → B, when F is a vector space and the structure group is a linear group. We can compute their cohomology completely. However, if we consider other bundles, such as bundles with fiber F a manifold, where the structure group is the diffeomorphism group, we know nearly nothing at all. In this article, we discuss surface bundles, which is the first step ...

The equation that approximately traces the trajectory in the concentration phase space of chemical kinetics is derived based on the rate of entropy production. The equation coincides with the true chemical kinetics equation to first order in a variable that characterizes the degree of quasi-equilibrium for each reaction, and the equation approximates the trajectory along at least final part of ...

The fundamental manifold (FM), an extension of the fundamental plane formalism, incorporates all spheroid-dominated stellar systems from dwarf ellipticals up to the intracluster stellar populations of galaxy clusters by accounting for the continuous variation of the mass-to-light ratio within the effective radius re with scale. Here, we find that Local Group dwarf spheroidal and dwarf elliptica...

The time evolution of several interacting Ginzburg-Landau vortices according to an equation of Schrödinger type is approximated by motion on a finite-dimensional manifold. That manifold is defined as an unstable manifold of an auxiliary dynamical system, namely the gradient flow of the Ginzburg-Landau energy functional. For two vortices the relevant unstable manifold is constructed numerically ...

We use rudiments of the Seiberg-Witten gluing theory for trivial circle bundles over a Riemann surface to relate de Seiberg-Witten basic classes of two 4manifolds containing Riemann surfaces of the same genus and self-intersection zero with those of the 4-manifold resulting as a connected sum along the surface. We study examples in which this is enough to describe completely the basic classes. ...

Random projections are able to perform dimension reduction efficiently for datasets with nonlinear low-dimensional structures. One well-known example is that random matrices embed sparse vectors into a subspace nearly isometrically, known as the restricted isometric property in compressed sensing. In this paper, we explore some applications of deep neural networks. We provide expressive power f...